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, or Abiosus, a physician and mathematician, born at Bagnuolo, in the kingdom of Naples, flourished towards

, or Abiosus, a physician and mathematician, born at Bagnuolo, in the kingdom of Naples, flourished towards the end of the fifteenth and beginning of the sixteenth century. Some of his works were much esteemed. His “Dialogus in Astrologiae defensionem, item Vaticinium a diluvio usque ad Christi annos 17,” Venice, 1474, 4to, was put into the Index Expurgatovius, and is extremely rare.

, a mathematician and physician, was born at Nuremberg, in 1702. He was at first

, a mathematician and physician, was born at Nuremberg, in 1702. He was at first intended for his father’s business, that of a bookseller, but appears to have gone through a regular course of study at Altdorf. In 1735, he published his “Commercium literarinm ad Astronomiae incrementum inter hujus scientiæ amatores communi consilio institutum,” Nuremberg, 8vo; which procured him the honour, of being admitted a member of the royal academy of Prussia. In 1743 he was invited to Altdorf to teach mathematics, and three years after was made professor of logic. He died in 1779. He published also a monthly work on. Celestial Phenomena, in German.

y were held. The family of Afflito has produced other celebrated men, as 1. John Afflito, an eminent mathematician, particularly skilled in the art of fortification, and employed

Afflitto’s works are: 1. “Commentarius in Constitutiones Siciliae et Neapolis,” Francfort, 1603, fol. 2. “Commentarius-buper tres libros Feudorum,” Venice, 1534, fol.; Lyons, 1548, and 1560 4 Francfort, 1598, 1608, 1629. 3. “Decisiones Neapolitans antiquse et novae,” Venice, 1564, 1600, and 1635, fol.; and Francfort, 1616, and 1635, fol. 4. “Lecturæ super consuetudinibus Neapolitani Siciliaeque regni,” Leyden, 1535, fol.; reprinted under different titles, and with the additions of other writers on the subject. 5. “De Jure Protomiseos cum Baldo et Marantha, Tr. Tr. xviii.” Francfort, 1571, and 1588; reprinted at Spires, 1603, 8vo. 6. “Enumeratio u fisci,” Basle, 1550, fol. 7. “Lecturse super 7 Codicis Justiniani,” 1560. 8. “De consiliariis principum et officialibus eligendis, ad justitiam regendam,” Naples; a very scarce work. The frequent editions of these voluminous works sufficiently prove the high estimation in which they were held. The family of Afflito has produced other celebrated men, as 1. John Afflito, an eminent mathematician, particularly skilled in the art of fortification, and employed as an engineer by John of Austria in some of his wars. He published, in Spanish, a treatise on the subject, 2 vols. 4to, and a volume of “Theological and Philosophical Miscellanies.” He died at Naples, 1673. 2. Gaetan-Andre D‘Afflitto, advocate-general, who published law-pleadings and decisions at Naples, 1655. And lastly, Cæsar D’Afflitto, who left a work on the feudal laws.

quam Mercuric: a very good soldier, and a very good scholar, an admirable linguist, philosopher, and mathematician.”

Alasco was twice married: his first wife died in 1552, and the second survived him; he appears to have had children by both. It was probably a descendant of his, Albertus Alasco, who was most magnificently entertained by the university of Oxford in 1583, by special command of queen Elizabeth. “Such an entertainment it was,” says Wood, “that the like before or since was never made for one of his degree, costing the university, with the colleges, about c350. And, indeed, considering the worthiness of the person for whom it was chiefly made, could not be less. He was one tarn Marti quam Mercuric: a very good soldier, and a very good scholar, an admirable linguist, philosopher, and mathematician.

, a mathematician and poet, of the thirteenth century, was a gentleman of Provence,

, a mathematician and poet, of the thirteenth century, was a gentleman of Provence, and born in the environs of Gap, from which circumstance he was surnamed Gapencois. He resided a long time at Sisteron, where he died. Others writers say, that he was of Tarascon, of the family of Malespine; bnt perhaps he only lived in the latter of these towns. He was equally devoted to polite literature and to the fair sex, and composed several poems in honour of his platonic mistress, the marchioness of Malespine, who was the most accomplished lady of Provence in that age. He wrote also some treatises on mathematical subjects. It is said that he died of grief, and that he delivered his poems to a friend, in order to be presented to his favourite marchioness; but this friend sold them tp Faber d‘Uzes, a lyric poet, who published them as his own. When the fraud was discovered, d’Uzes was seized, and underwent the punishment of whipping for his plagiarism, agreeably to the law established by the emperors against that crime, but which, unfortunately for authors, has been repealed in all countries.

erstood the Latin, Greek, and Hebrew languages extremely well; was an excellent orator, philosopher, mathematician, and, according to William of Malmesbury, the best English divine

Charlemagne often solicited him to return to court, but he excused himself, and remained at Tours until his death, May 19, 804. He was buried in the church of St. Martin, where a Latin epitaph of twenty-four verses, of his own, composition, was inscribed upon his tomb. This epitaph is preserved by father Labbe, in his Thesaurus Epitaphiorum, printed at Paris 1686. He understood the Latin, Greek, and Hebrew languages extremely well; was an excellent orator, philosopher, mathematician, and, according to William of Malmesbury, the best English divine alter Bede and Adhelme. How greatly France was indebted to him for her flourishing state of learning in that and the following ages, we learn from a German poet, cited by Camden in his Britannia:

Zanotti, his first masters, Fabri of Bologna, Metastasio, Frugoni, Bettinelli, Frisi the celebrated mathematician and physician, Mazzuchelli, Paradisi, &c.; the Prussians, Frederic

Algarottihad also studied the fine arts, and produced many excellent specimens of painting and engraving. In particular he designed and engraved several plates of heads in groupes, one of which, containing thirteen in the antique style, is dated Feb. 15, 1744. He travelled likewise over Italy, with a painter and draftsman in his suite; and what he has published on the arts discovers extensive knowledge and taste. Frederick II. who had become acquainted with his talents when prince-royal, no sooner mounted the throne, than he invited him to Berlin. Algarotti was then in London, and, complying with his majesty’s wish, remained at Berlin many years. Frederick conferred on him the title of count of the kingdom of Prussia, with reversion to his brother and descendants. He made him also his chamberlain, and knight of the order of Merit, bestowing on him at the same time many valuable presents, and other marks of his esteem; and after Algarotti left Berlin, the king corresponded with him for twenty-five years. The king of Poland, Augustus III. also had him for some time at his court, and gave him the title of privy-­counselloir of war. Nor was he held in less esteem by the sovereigns of Italy, particularly pope Benedict XIV. the duke of Savoy, and the duke of Parma. The excellence of his character, the purity of his morals, his elegant manners, and the eclat which surrounds a rich amateur of the arts, contributed to his celebrity perhaps as much as the superiority of his talents, and his acknowledged taste. Wherever he travelled he was respected equally by the rich, and the learned, by men of letters, by artists, and by men of the world. The climate of Germany having sensibly injured his health, he returned first to Venice, and afterwards to Bologna, where he had determined to reside, but his disorder, a consumption of the lungs, gained ground rapidly, and put an end to his life, at Pisa, March 3, 1764. He is said to have met death with composure, or, as his biographer terms it, with philosophical resignation. In his latter days he passed his mornings with Maurino (the artist who used to accompany him in his travels), engaged in the study of painting, architecture, and the fine arts. After dinner he had his works read to him, then printing at Leghorn, and revised and corrected the sheets: in the evening he had a musical party. The epitaph he wrote for himself is taken from Horace’s non omnis moriar, and contains only the few words, “Hicjacet Fr. Algarottus non omnis” The king of Prussia was at the expense of a magnificent monument in the Campo Santo of Pisa; on which, in addition to the inscription which Algarotti wrote, he ordered the following, “Algarotto Ovidii emulo, Newtoni discipulo, Fredericus rex,” and Algarotti’s heirs added only “Fredericus Magnus.” The works of Algarotti were published at Leghorn, 1765, 4 vols. 8vo; at Berlin, 1772, 8 vols. 8vo; and at Venice, 17 vols. 8vo, 1791--1794. This last, the most complete and correct edition, is ornamented with vignettes, the greater part of which were taken from the author’s designs. These volumes contain 1. Memoirs of his life and writings, and his poetry. 2. An analysis of the Newtonian system. 3. Pieces on architecture, painting, the opera, essays on vario is languages, on history, philology, on Des Cartes, Horace, &c. 4 and 5. Essays on the military art, and on the writers on that subject. 6. His travels in Russia, preceded by an Essay on the metals of that empire: the congress of Cytherea, the life of Pallavicini, the Italian poet; and a humorous piece against the abuse of learning. 7. Thoughts on different subjects of philosophy and philology. 8. Letters on painting and architecture. 9 and 10. Letters on the sciences. 11 to 16. His correspondence, not before published, with the literati of Italy, England, and France. 17. An unfinished critical essay on the triumvirate of Crassus, Pompey, and Gassar. Among his correspondents we find the names of the Italians, Manfredi and Zanotti, his first masters, Fabri of Bologna, Metastasio, Frugoni, Bettinelli, Frisi the celebrated mathematician and physician, Mazzuchelli, Paradisi, &c.; the Prussians, Frederic II. several princes of the same family, and Form ey, &c.; the English, lords Chesterfield and Hervey, Mr. Hollis, lady Montague, &c.; jand the French, Voltaire, Maupercuis, du Chastellet, mad. du Boccage,; &c. His Essays on painting, on the opera, his Letters to lord Hervey and the marquis Maffei, and his Letters, military and political, have been translated and published in English. His biographers have generally handed down his character without a blemish; aiui Fabroni, on whom ive mostly rely, is equally lavish in his praises. Wiule we take his personal merits from these authorities, we have evident proof from his works that he was an universal scholar, and wrote with facility and originality on every subject he took in hand. They present a greater variety of reading and thought than almost any scholar of the eighteenth century; but they are not without redundancy, and sometimes affectation. His fame is said to be fixed on a more solid basis in his own country, than in those where he has been viewed only througn the medium of translations.

, an eminent mathematician of the sixteenth century, was born at Uttoxeter in Staffordshire,

, an eminent mathematician of the sixteenth century, was born at Uttoxeter in Staffordshire, Dec. 21, 1542, and was a descendant, through six generations, of Henry Allen, or Alan, lord of the manor of Buckenhall in that county. He was admitted scholar of Trinity college, Oxford, June 4, 1561, became fellow in 1565, and in 1567, took his master’s degree. From a strong inclination to a retired life, and a dislike to entering into holy orders, to which, according to the statutes, he ftmst have been called, he quitted the college, resigned his fellowship, and went to Gloucester-hall (now Worcester college), in 1570. Here he studied very closely, and acquired a high reputation for his knowledge in antiquity, philosophy, and mathematics. Having received an invitation from Henry earl of Northumberland, a great friend and patron of the mathematicians, he spent some time at the earl’s house, where he became acquainted with those celebrated mathematicians Thomas Harriot, John Dee, Walter Warner, and Nathanael Torporley. Robert earl of Leicester had a particular esteem for Mr. Allen, and would have conferred a bishopric upon him, but his love of solitude and retirement made him decline the offer. He was also highly respected by other celebrated contemporaries, sir Thomas Bodley, sir Henry Savile, Mr. Camden, sir Robert Cotton, sir Henry Spelman, Mr. Selden, &c. His great skill in the mathematics made the ignorant and vulgar look upon him as a magician or conjuror: and the author of a book, intituled “Leicester’s Commonwealth,” has absurdly accused him of using the art of figuring, to bring about the earl of Leicester’s schemes, and endeavouring, by the black art, to effect a match betwixt him and queen Elizabeth. It is more certain the earl placed such confidence in Allen, that nothing material in the state was transacted without his knowledge, and he had constant information, by letter from Allen, of what passed in the university. Allen was very curious and indefatigable in collecting scattered manuscripts relating to history, antiquity, astronomy, philosophy, and mathematics, which collections have been quoted by several learned authors, &c. There is a catalogue of them, bearing date 1622, among Anthony Wood’s papers in the Ashmolean museum. He published in Latin the second and third books of Ptolemy, “concerning the Judgment of the Stars,” or, as it is commonly called, of the quadripartite construction, with an exposition. He wrote also notes on many of Lilly’s books, and some on John Bale’s work, “De scriptoribus Maj. Britanniae.” Having lived to a great age, he died at Gloucester-hall, Sept. 30, 1632, and was buried with a solemnity suited to the greatness of his character. He bequeathed a valuable portrait of himself, which has since been engraven, to the president of Trinity college and his successors. Mr. Burton, the author of his funeral oration, calls him not only the Coryphaeus, but the very soul and sun of all the mathematicians of his time. Mr. Selden mentions him as “omni eruditionis genere summoque judicio ornatissimus, cele-” berrimae academies Oxoniensis dec us insignissimum; a person of the most extensive learning and consummate judgment, the brightest ornament of the university of Oxford.“Camden says, he was” Plurimis optimisque artibus Ornatissimus; skilled in most of the best arts and sciences.“Mr. Wood has transcribed part of his character from a manuscript in the library of Trinity college, in these words:” He studied polite literature with great application; he was strictly tenacious of academic discipline, always highly esteemed both by foreigners and those of the university, and by all of the highest stations in the church of England and the university of Oxford. He was a sagacious observer, and an agreeable companion.

, an Italian scholar and mathematician, was a native of Ferrara, and lived in the fifteenth century.

, an Italian scholar and mathematician, was a native of Ferrara, and lived in the fifteenth century. The three works on which his fame rests are, 1. “Observations on Petrarch,” which are inserted in the edition of that poet, Venice, 1539, 8vo. 2. “Le Richesse della Lingua Volgare,” Venice, 1545, fol. in which he has collected, alphabetically, the most elegant words and phrases used by Boccaccio. 3. “Della Fabbrica del Mondo,” Venice, 1526, 1556, 1557, 1558, 1562, consisting of ten books, in which are enumerated all the words used by the earliest Italian writers, but with no very happy arrangement. Alunno was likewise distinguished for a talent perhaps more curious than useful, that of being able to write an exceeding small hand. We are told, that when at Bologna he presented Charles V. with the belief and the first chapter of the gospel of St. John, in the size of a denier, or farthing; and Aretine adds, that the emperor employed a whole day in decyphering this wonderful manuscript.

, an eminent mathematician, was born at Aberdeen towards the end of the sixteenth century.

, an eminent mathematician, was born at Aberdeen towards the end of the sixteenth century. Where he was educated, or under what masters, we have not learned: probably he studied the belles lettres and philosophy in the university of his native city, and, as was the practice in that age of all who could afford it, went afterwards abroad for the cultivation of other branches of science. But wherever he studied, his progress must have been rapid; for early in the seventeenth century, we find him professor of mathematics in the university of Paris, where he published several ingenious works, and among others, “Supplementum Apollonii Redivivi, &c.” Paris, 1612, 4to; “Afliotoyus, pro Zetetico Apolloniani problematis a se jam priclem edilo in supplemento Apollenii Redivivi, &c.” Paris, 1615, 4to; “Francisci Vietae de Equationum recognitione et emendatione tractatus duo,” with a dedication, preface, and appendix by himself, Paris, 1615, 4to; “Vieta’s Angulares Sectiones:” to which he added demonstrations of his own.

, an Italian mathematician, was educated under Bonaventure Cavalieri, the most eminent

, an Italian mathematician, was educated under Bonaventure Cavalieri, the most eminent Italian scholar in that science in the seventeenth century. He was at first a Jesuit, but that order being suppressed in 1668, he applied closely to the study of mathematics, and taught at Padua with great success, publishing various works, and carrying on a controversy on the opinions of Copernicus with Riccioli and others. Moreri, from a manuscript account of the learned men of Italy, written by father Poisson, gives a numerous list of his publications, some of which were in Latin, and some in Italian. We have only seen his “Miscellaneum hyperbolicum et parabolicum,” Venice, 1659, 4to, and “Delia gravita dell' Aria e Fluidi, Dialogi V.” Padua, 1671—2, 4to. His controversy on Copernicus was begun in “Considerazioni sopra la forza d'alcune cagioni fisiche matematiche addote dal Pad. Riccioli, &c.” Venice, 1667, 4to, and continued in a second, third, and fourth part, 1669—9, 4to.

o. He took the title of Nepos to distinguish himself from another George Anselme, his grandfather, a mathematician and astronomer, who died about 1440, leaving in manuscript “Dialogues

, a Latin poet of the sixteenth century, was born at Parma, of a very ancient family, and was afterwards eminent as a physician, and a man of general literature. The volume which contains his poetry, and is very scarce, is entitled “Georgii Anselmi Nepotis Epigrammaton libri septem: Sosthyrides: Palladis Peplus: Eglogæ quatuor,” Venice., 1528, 8vo. He took the title of Nepos to distinguish himself from another George Anselme, his grandfather, a mathematician and astronomer, who died about 1440, leaving in manuscript “Dialogues on Harmony,” and “Astrological institutions.” Our author wrote, besides his poems, some illustrations of Plautus, under the title of “Epiphyllides,” which are inserted in Sessa’s edition of Plautus, Venice, 1518; and had before appeared in the Parma edition of 1509, fol. He wrote also the life of Cavicco or Cayicio, prefixed to his romance of “Libro de Peregrine,” Venice, 1526, 8vo, and 1547. He died in 1528.

oscorus and Alexander, physicians, Metrodorus, a grammarian, and our Anthemius, who was an excellent mathematician, and availed himself of that science in the works which he erected.

, an eminent architect of the sixth century, was born at Tralles in Lydia. His father had five sons, Olympius, a lawyer, Dioscorus and Alexander, physicians, Metrodorus, a grammarian, and our Anthemius, who was an excellent mathematician, and availed himself of that science in the works which he erected. It appears likewise that he was acquainted with the more modern secrets of philosophy and chemistry, as historians inform us that he could imitate thunder and lightning, and even the shock of an earthquake, In consequence of a trifling dispute with Zeuo, his neighbour, respecting the walls or windows of their contiguous houses, in which Zeno appeared to have the advantage, Anthemius played him a trick, which is thus described: he arranged several vessels or cauldrons of water, each of them covered by the wide bottom of a leathern tube which rose to a narrow top, and was artificially conveyed among the joists and rafters of the adjacent building. A fire was kindled beneath the cauldron, and the steam of the boiling water ascended through the tubes: the house was shaken by the efforts of the imprisoned air, and the trembling inhabitants wondered that the city was unconscious of an earthquake which they felt. At another time the friends of Zeno, as they sat at table, were dazzled by the intolerable light which flashed in their eyes from the reflecting mirrors of Anthemius; they were astonished by the noise which he produced from a collision of certain minute and sonorous particles: and Zeno declared to the senate, that a mere mortal must yield to the power of an antagonist who shook the earth with the trident of Neptune, and imitated the thunder and lightning of Jove himself. But the genius of Anthemius appeared to most advantage in the erection of the new church of St. Sophia at Constantinople. This he undertook by order of the emperor Justinian, and was assisted by ten thousand workmen, whose payment, we are told, doubtless as a hint to modern surveyors, was made in fine silver, and never delayed beyond the evening. It was completed in five years, eleven months, and ten days. Gibbon has given a splendid description of this edifice, now the principal Turkish mosque, which continues to excite the fond admiration of the Greeks, and the more rational curiosity of European travellers. Anthemius died about the year 534. He is said to have written on the subject of machinery, and Dupuy, secretary to the French academy of inscriptions, published a fragment of his in 1777, on mechanics and dioptrics, in which Anthemius endeavours to explain the burning mirrors employed by Archimedes in destroying the Roman ships.

, called in German Brenkwitz, a celebrated astronomer and mathematician, was born at Leisnig or Leipsic in Misnia, 1495, and made professor

, called in German Brenkwitz, a celebrated astronomer and mathematician, was born at Leisnig or Leipsic in Misnia, 1495, and made professor of mathematics at Ingolstadt in 1524, where he died in 1552, aged fifty-seven. He wrote treatises upon many of the mathematical sciences, and greatly improved them, especially astronomy and astrology, which in that age were much the same thing: also geometry, geography, arithmetic. He particularly enriched astronomy with many instruments, and observations of eclipses, comets, &c. His principal work was the “Astronomicum Caesareum,” published in folio at Ingolstadt in 1540, and which contains a number of interesting observations, with the descriptions and divisions of instruments. In this work he predicts eclipses, and constructs the figures of them in piano. In the second part of the work, or the “Meteoroscopium Planum,” he gives the description of the most accurate astronomical quadrant, and its uses. To it are added observations of five different comets, viz. in the years 1531, 1532, 1533, 1538, and 1539: where he first shows that the tails of a comet are always projected in a direction from the sun.

Constantinople, from whence they were brought into Italy; and here they were foundry that excellent mathematician John Muller, otherwise called Regiomontanus, who brought them

There have been various editions of the existing writings of Archimedes. The whole of these works, together with the commentary of Eutocius, were found in their original Greek language, on the taking of Constantinople, from whence they were brought into Italy; and here they were foundry that excellent mathematician John Muller, otherwise called Regiomontanus, who brought them into Germany; where they were, with that commentary, published long after, viz. in 1544, at Basil, most beautifully printed in folio, Gr. & Lat. by Hervagius, under the care of Thomas Gechauff Venatorius. A Latin translation was published at Paris, 1557, by Pascalius Hamellius. Another edition of the whole, in Greek and Latin, was published at Paris, 1615, fol. by David Rivaltus, illustrated with new demonstrations and commentaries; a life of the author is prefixed: and at the end of the volume is added some account, by way of restoration, of the author’s other works, which have been lost. In 1675, Dr. Isaac Barrow published a neat edition of the works, in Latin, at London, 4to; illustrated, and succinctly demonstrated in a new method. But the most complete of any, is the magnificent edition, in folio, printed at the Clarendon press, in Oxford, in 1792. This edition was prepared ready for the press by the learned Joseph Torelli, of Verona, who was discouraged by the prospect of the expence that was likely to attend the publication. He had finished it some time before his death; and, while he was demurring in regard to the mode of publishing it, he was induced by the advice and recommendation of the late earl Stanhope, whose zeal in the cause of science reflects distinguished honour on his name and memory, to commence a treaty with the curators of the Clarendon press at Oxford. Torelli, unwilling to give up the charge of superintending the publication, still hesitated, and died before the transaction was completed. The treaty was again renewed by Alberto Albertini, the executor of the learned editor’s will, who entrusted the work to the university of Oxford. Ah th papers which Torelli had prepared with a view to. this edition, Alhertini presented to the university, and transmitted, at the original cost, all the engravings of figures that were necessary for the completion of it. John Strange, esq. the British resident at Venice, was very active in conducting and terminating the business. The arrangement of the papers, the correction of the press, and the whole superintewdance of the edition, were committed by the university to Mr. (now Dr.) Abraham Robertson, of Christ church, a gentleman in every respect qualified for the trust reposed in him. The Latin translation of this edition is a new one. Torelli also wrote a preface, a commentary on some of the pieces, and notes on the whole. An account of the life and writings of Torelli is prefixed by Clement Sibiliati; of this a sketch will be given in its proper place. At the end a large appendix is added, in two parts: the first being a commentary on Archimedes’s paper upon “Bodies that flow on fluids,” by Dr. Robertson; and the latter is a large collection of various readings in the ms works of Archimedes, found in the library of the last king of France, and of another at Florence, as collated with the Basil edition above mentioned.

, of Tarentum, a celebrated mathematician, cosmographer, and Pythagorean philosopher, flourished about

, of Tarentum, a celebrated mathematician, cosmographer, and Pythagorean philosopher, flourished about 400 years before Christ, and was the master of Plato, Eudoxus, and Philolaus. He gave a method of finding two mean proportionals between two given lines; and thence the duplication of the cube, by means of the conic sections. His skill in mechanics was such, that he was said to be the inventor of the crane and the screw: and he made a wooden pigeon that could fly about, when it was once set off, but it could not rise again of itself, after it rested. He wrote several works, though few are now extant. It is said'he invented the ten categories. He acquired great reputation both in his legislative and military capacity, having commanded an army seven times without ever being defeated. He was at last shipwrecked, and drowned in the Adriatic sea. His philosophy as well as his moral character was more pure than that of many of the ancient philosophers. The sum of his moral doctrine was, that virtue is to be pursued for its own sake in every condition of life; that all excess is inconsistent with virtue; that the mind is more injured by prosperity than by adversity, and that there is no pestilence so destructive to human happiness as pleasure. Brucker thinks that Aristotle was indebted to Archytas for many of his moral ideas, particularly for the notion which runs through his ethical pieces, that virtue consists in avoiding extremes. With respect to his personal character, it is said of him that he never chastised a servant, or punished an inferior, in wrath. To one of his dependants who had offended him, he said, “It is well for you that I am angry; otherwise, I know not what you might expect.” We have only a metaphysic work by Archytas, “On the nature of the Universe,” published in Greek by Camerarius, Leipsic, 1564, 8vo; Venice, 1571, 4to. Gr. and Lat. and sundry fragments on “Wisdom,” and “Of the good and happy man,” preserved by Stobseus, and edited from him by Gale.

, an Italian mathematician, was born at Tagliacozzo in the kingdom of Naples, in 1570;

, an Italian mathematician, was born at Tagliacozzo in the kingdom of Naples, in 1570; Being involved in his own country in some difficulties, occasioned by his attachment to astrological reveries, ha thought proper to retire to Venice, where the senate, perceiving the extent of his merit, appointed him professor of mathematics in the university of Padua; at the same time conferring on him the title of chevalier of St. Mark in 1636. He died in 1653. His writings are, 1. “De diebus criticis,1652, 4to. 2. “Ephemerides,” from 1620, 4 vols. 4to, and 3. Observations on the Comet of 1653, in Latin, printed the same year. His Ephemerides were reprinted at Padua and Lyons, and continued to the year 1700.

at friendship with him to the day of his death. He was likewise very intimate with Mr. Oughtred, the mathematician, and with Dr. Wharton, a physician of great racter and experience.

, an eminent philosopher, chemist, and antiquary, of the seventeenth century, and founder of the noble museum at Oxford, which still bears his name, was the only son of Mr. Simon Ashmole, of the city of Litchfield, in Staffordshire, sadler, by Anne, the daughter of Mr. Anthony Boyer, of Coventry, in Warwickshire, woollen-draper. He was born May 23, 1617, and during his early r education in grammar, was taught music, in which he made such proficiency as to become a chorister in the cathedral at Litchfield. When he had attained the age of sixteen he was taken into the family of James Paget, esq. a baron of the exchequer, who had married his mother’s sister, and as his father died in 1634, leaving little provision for him, he continued for some years in the Paget family, during which time he made considerable progress in the law, and spent his leisure hours in perfecting himself in music and other polite accomplishments. In March 1638, he married Eleanor, daughter of Mr. Peter Manwaring, of Smallwood, in the county Palatine of Chester, and in Michaelmas term the same year, became a solicitor in Chancery. On February 11, 1641, he was sworn an attorney of the court of common pleas, and on December 5th, in the same year, his wife died suddenly, of whom he has left us a very natural and affectionate memorial. The rebellion coming on, he retired from London, being always a zealous and steady loyalist, and on May 9, 1645, became one of the gentlemen of the ordnance in the garrison at Oxford, whence he removed to Worcester, where he was commissioner, receiver, and register of the excise, and soon after captain in the lord Ashley’s regiment, and comptroller of the ordnance. In the midst of all this business he entered himself of Brazen-Nose college, in Oxford, and applied himself vigorously to the sciences, but especially natural philosophy, mathematics, and astronomy; and his intimate acquaintance with Mr. (afterwards sir George) Wharton, seduced him into the absurd mysteries of astrology, which was in those days in great credit. In the month of July, 1646, he lost his mother, who had always been a kind parent to him, and for whom he had a very pious regard. On October 16th, the same year, be was elected a brother of the ancient and honourable society of Free and Accepted Masons, which he looked upon as a high honour, and has therefore given us a particular account of the lodge established at Warrington in Lancashire and in some of his manuscripts, there are very valuable collections relating to the history of the free masons. The king’s affairs being now grown desperate, Mr. Ashmole withdrew himself, after the surrender of the garrison of Worcester, into Cheshire, where he continued till the end of October, and then came up to London, where he became acquainted with Mr. (afterwards sir Jonas) Moore, William Lilly, and John Booker, esteemed the greatest astrologers in 'the world, by whom he was caressed, instructed, and received into their fraternity, which then made a very considerable figure, as appeared by the great resort of persons of distinction to their annual feast, of which Mr. Ashmole was afterwards elected steward. Jn 1647 he retired to Englefield, in Berkshire, where he pursued his studies very closely, and having so fair an opportunity, and the advantage of some very able masters, he cultivated the science of botany. Here, as appears from his own remarks, he enjoyed in privacy the sweetest moments of his life, the sensation of which perhaps was quickened, by his just idea of the melancholy state of the times. It was in this retreat that he became acquainted with Mary, sole daughter of sir William Forster, of Aldermarston, in the county of Berks, bart. who was first married to sir Edward Stafford, then to one Mr. Hamlyn, and lastly to sir Thomas Mainwaring, knt recorder of Reading, and one of the masters in chancery and an attachment took place but Mr. Humphrey Stafford, her second son, had such a dislike to the measure, that when Mr. Ashmole happened to be very ill, he broke into his chamber, and if not prevented, would have murdered him. In the latter end of 1648, lady Mainwaring conveyed to him her estate at Bradfield, which was soon after sequestered on account of Mr. Ashmole’s loyalty but the interest he had with William Lilly, and some others of that party, enabled him to get that sequestration taken off. On the sixteenth of November, 1649, he married lady Mainwaring, and settled in London, where his house became the receptacle of the most learned and ingenious persons that flourished at that time. It was by their conversation, that Mr. Ashmole, who hud been more fortunate in worldly affairs than most scholars are, and who had been always a curious collector of manuscripts, was induced to publish a treatise written by Dr. Arthur Dee, relating to the Philosopher’s stone, together with another tract on the same subject, by an unknown author. These accordingly appeared in the year following but Mr. Ashmole was so cautious, or rather modest, as to publish them by a fictitious name. He at the same time addressed himself to a work of greater consequence, a complete collection of the works of such English chemists, as had till then remained in ms. which cost him a great deal of labour, and for the embellishment of which he spared no expence, causing the cuts that were necessary, to be engraved at his own house in Black-Friars, by Mr. Vaughan, who was then the most eminent artist in that department in England. He imbibed this affection for chemistry from his intimate acquaintance with Mr. William Backhouse, of Swallowfield in the county of Berks, who was reputed an adept, and whom, from his free communication of chemical secrets, Mr. Ashmole was wont to call father, agreeably to the custom which had long prevailed among the lovers of that art, improperly, however, called chemistry for it really was the old superstition of alchemy. He likewise employed a part of his time in acquiring the art of engraving seuls, casting in sand, and the mystery of a working goldsmith. But all this time, his great work of publishing the ancient English writers in chemistry went on and finding that a competent knowlege of the Hebrew was absolutely necessary for understanding and explaining such authors as had written on the Hermetic science, he had recourse to rabbi Solomon Frank, by whom he was taught the rudiments of Hebrew, which he found very useful to him in his studies. At length, towards the close of the year 1652, his “Theatrum Chymicum Britannicum” appeared, which gained him great reputation in the learned world, as it shewed him to be a man of a most studious disposition, indefatigable application, and of wonderful accuracy in his compositions. It served also to extend his acquaintance considerably, and among others the celebrated Mr. Seiden took notice of him in the year 1653, encouraged his studies, and lived in great friendship with him to the day of his death. He was likewise very intimate with Mr. Oughtred, the mathematician, and with Dr. Wharton, a physician of great racter and experience. His marriage with lady -Main-waring, however, involved him in abundance of law-suits with other people, and at last produced a dispute between themselves, which came to a hearing on October 8, 1657, in the court of chancery, where serjeant Maynard having observed, that in eight hundred sheets of depositions taken on the part of the lady, there was not so much as a bad word proved against Mr. Ashrnole, her bill was dismissed, and she delivered back to her husband. He had now for some time addicted himself to the study of antiquity and records, which recommended him to the intimate acquaintance of Mr. (afterwards sir William) Dugdale, whom about this time he attended in his survey of the Fens, and was very useful to him in 'that excellent undertaking. Mr. Ashmole himself soon after took the pains to trace the Roman road, which in Antoninus’s Itinerary is called Bennevanna, from Weeden to Litchfield, of which he gave Mr. Dugdale an account, in a letter addressed to him upon that subject. It is very probable, that after his studies had thus taken a new turn, he lost somewhat of his relish for chemistry, since he discontinued the Theatrum Chemicum, which, according to his first design, was to have consisted of several volumes yet he still retained such a remembrance of it, as induced him to part civilly with the sons of art, by publishing a treatise in prose on the philosopher’s stone, to which he prefixed an admirable preface, in which he wishes to apologize for taking leave of these fooleries. In the spring of the year 1658, our author began to collect materials for his history of the order of the garter, which he afterwards lived to finish, and thereby rendered both the order and himself immortal, the just reward of the prodigious pains he took in searching records in the Tower, and elsewhere, comparing them witU each other, and obtaining such lights as were requisite to render so perplexed a subject clear, and to reduce all the circumstances of such a vast body of history into their proper order. In September following he made a journey to Oxford, where he was extremely well received, and where he undertook to make a full and distinct description of the coins given to the public library by archbishop Laud, which was of great use to him in the works which he afterwards composed. He had lodged and boarded sometimes at a house in South Lambeth, kept by Mr. John Tradescant, whose father and himself hud been physic-gardeners there for many years, and had collected avast number of curiosities, which, after mature deliberation, Mr. Tradescant and his wife determined to bestow on Mr. Ashmole, and accordingly sealed and delivered a deed of gift for that purpose, on December 16, 1659. On the restoration of king Charles II. Mr. Ashmole was Dearly introduced into the presence and favour of his majesty, and on June 18, 1660, which was the second time he had the honour of discoursing with the king, he graciously bestowed upon him the place of Windsor herald. A few days after, he was appointed by the king to make a description of his medals, and had them delivered into his hands, and king Henry VHIth’s closet assigned for his use, being also allowed his diet at court. On August 21st, in the same year, he presented the three books which he had published, to his majesty, who, as he both loved and understood chemistry, received them very graciously. On September 3, he had a warrant signed for the office of commissioner of the excise, in consequence of a letter written by his majesty’s express command, to the earl of Southampton, then lord high-treasurer, by Mr. Se^ cretary Morris. About this time, a commission was granted to him as incidental to the care of the king’s medals, to examine the famous, or rather infamous, Hugh Peters, about the contents of the royal library which had fallen into his hands, and which was very carefully and punctually executed, but to very little purpose. On November 2d, he was called to the bar in Middle-Temple hall, and January 15, 1661, he was admitted a fellow of the Royal Society. On February 9th following, the king signed a warrant for constituting him secretary of Surinam in the West Indies. In the beginning of the year 1662, he was appointed one of the commissioners for recovering the king’s goods, and about the same time he sent a set of services and anthems to the cathedral church of Litchfield, in memory of his having been once a chorister there, and he gave afterwards twenty pounds towards repairing the cathedral. On June 27, 1664, the White Office was opened, of which he was appointed a commissioner. On Feb. 17, 1665, sir Edward By she sealed his deputation for visiting Berkshire, which visitation he began on the llth of March following, and on June 9, 1668, he was appointed by the lords commissioners of the treasury, accomptant-general, and country accomptant in the excise. His second wife, lady Main waring, dying, April 1, in the same year, he soon after married Mrs. Elizabeth Dugdale, daughter to his good friend sir William Dugdale, kht. garter king at arms, in Lincoln’s-inn chapel, on Novembers. The university of Oxford, in consideration of the many favours they had received from Mr. Ashmole, created him doctor of physic by diploma, July 19, 1669, which was presented to him on the 3d of November following, by Dr. Yates, principal of Brazen-Nose college, in the name of the university. He was now courted and esteemed by the greatest people in the kingdom, both in point of title and merit, who frequently did him the honour to visit him at his chambers in the Temple, and whenever he went his summer progress, he had the same respect paid him in the country, especially at his 'native town of Litchfield, to which when he came, he was splendidly entertained by the corporation. On May 8, 1672, he presented his laborious work on the most noble order of the garter, to his most gracious master king Charles II. who not only received it with great civility and kindness, but soon after granted to our author, as a mark of his approbation of the work, and of his personal esteem for him, a privy seal for 400 pounds out of the custom of paper. This was his greatest undertaking, and had he published nothing else, would have preserved his memory, as it certainly is in its kind one of the most valuable books in our language. On January 29, 1675, he resigned his office of Windsor herald, which by his procurement, was bestowed on his brother Dugdale, It was with great reluctancy that the earl marshal parted with him, and it was not long after, that he bestowed on him the character of being the best officer in his office. On the death of sir Edward Walker, garter king at arms, Feb_ 20, 1677, the king and the duke of Norfolk, as earl marshal, contested the right of disposing of his place, on which Mr. Ashmole was consulted, who declared in favour of the king, but with so much prudence and discretion as not to give any umbrage to the earl marshal. He afterwards himself refused this high office, which was conferred on his father-in-law sir -William Dugdale, for whom he employed his utmost interest. About the close of 1677, a proposal was made to Mr. Ashmole to become a candidate for the city of Litchfield, but finding himself poorly supported by the very persons who would have encouraged him to stand, he withdrew his pretensions. On the 26th of January, 1679, about ten in the morning, a fire began in the Middle Temple, in the next chambers to Mr. Aslimole’s,- by which he lost a library he had been collecting thirty-three years; but his Mss. escaped, by their being at his house in South Lambeth. He likewise lost a collection of 9000 coins, ancient and modern but his more valuable collection of gold medals were likewise preserved by being at Lambeth his vast repository of seals, charters, and other antiquities and curiosities, perished also in the flames. In 1683, the university of Oxford having finished a noble repository near the theatre, Mr. Ashmole sent thither that great collection of rarities which he had received from the Tradescants before-mentioned, together with such additions as he had made to them; and to this valuable benefaction he afterwards added that of his Mss. and library, which still remain a monument of his generous love to learning in general, and to the university of Oxford in particular. In the beginning of the year 1685, he was invited by the magistrates, and by the dean of Litchfield, to represent that corporation in parliament but upon king James’s intimating to him, by the lord Dartmouth, that he would take it kindly if he would resign his interest to Mr. Levvson, he instantly complied.

, F. R. S. an eminent mathematician, was born in 1746, and admitted of Westminster school in 1759,

, F. R. S. an eminent mathematician, was born in 1746, and admitted of Westminster school in 1759, from whence he was elected to Trinity college, Cambridge, in 1765, where he took his bachelor’s degree in 1769 and his master’s in 1772. He was for some time a tutor, and for many years a fellow of that college, and read to the whole university lectures upon several branches of experimental philosophy, part of which he published under the title of “An Analysis of a course of Lectures on the principles of Natural Philosophy, read in the university of Cambridge, by G. A. &c.1784, 8vo. These lectures were much attended and justly admired“. The right hon. Wm. Pitt having been one of his auditors, was induced to form a more intimate acquaintance with him; and discovering that his talents might be eminently useful in the public service, bestowed upon him, in 1784, the place of patent searcher of the customs, London, that he might be enabled to devote a larger portion of his time to financial calculations, in which Mr. Pitt employed him, not more to his own satisfaction than to the advantage of the revenue. He continued in this employment under that eminent statesman, until his declining health rendered him incapable of intense application. In 1784, he also published” A treatise on the rectilinear Motion and Rotation of Bodies, with a description of original Experiments relative to the subject," 8vo. He contributed several papers to the Philosophical Transactions, and was honoured, on one occasion, with the Copleian medal. He died at his house in Westminster, July 1807, and was interred in St. Margaret’s church, justly esteemed by a numerous list of friends, and by the friends of science.

, an able astronomer and mathematician, was born at Saorgio, near Nice, in Provence, in 1714. At the

, an able astronomer and mathematician, was born at Saorgio, near Nice, in Provence, in 1714. At the age of sixteeeri he entered the order of St. Dominic, and made rapid progress in his studies, not only in sacred literature, but in mathematics, and the languages. In his thirty-fifth year he was appointed second librarian of the Casanata, and ten years aftenvards first librarian, which office he held until his death. His studies were extended to mathematics, astronomy, antiquities, natural history, criticism, and bibliography but astronomy was his favourite pursuit, on which he published many pieces. He was appointed by the late pope Pius VI. to make mineralogical observations on the new mines of Tolfa. He died July 3, 1794. His published works are, 1. “Mercurius in sole visus, observatio habita Romae, &c.” Rome, 1753, 4to. 2. “Phenomena ccelestia observata,” Rome, 1754, 8vo. 3. “Otia astronomica,” Rome, 1755, 4to. 4. “Novissimus Mercurii transitus,” Rome, 1756, 8vo. 5. “Passaggio di Venere, &c.” 4to, without place or date, but most probably 1761. 6. “Transitus Veneris, &c.1762. This appears to be cither the same work as the preceding, or a Latin translation. 7. “Investigatio Parallaxis Solaris, &c.” Rome,. 1765, 8vo, published under the anagrammatical name of Dadeus Ruffus. 8. “De Solis Parallaxi commentarius,” Rome, 1766, 8vo. 9. “Dimostrazione della theoria, &c.” of the Comet of the year 1769, published in a literary journal at Rome, 1770. 10. “Letere typografiche,” under the name of the abbe Nicolas Ugolini de Foligno, addressed to Xavier Laire, author of the historical essay on the Roman typography of the 15th century, Mentz, 1778, 8vo, a satirical attack on father Laire. 11. “Catalogus historico-criticus Romanarum editionum saeculi 15.” Rome, 1783, 4to. 12. “Catalogus librorum typis impressorum bibliothecae Casanatensis, praestantioribus notis et observationibus illustratus,” 4 vols. fol. 1762, 1768, 1775, 1788. 13. “Specimen historico-criticum editionum Italicarum ssGCuli 15,” Rome, 1794, 4to. In some of the foreign journals, are other essays by him on astronomical subjects.

, a learned printer at Louvain, of the sixteenth century, was also an able mathematician, and wrote, 1. “De compositione et usu Decretorii Pianetardm,”

, a learned printer at Louvain, of the sixteenth century, was also an able mathematician, and wrote, 1. “De compositione et usu Decretorii Pianetardm,1530, 4 to. 2. “De compositione et usu Quadrantis,1534, 4to. He published also, but without his name, “Tabulae perpetuae Longitudinum ac Latitudinum Planetarum, ad Meridianum Lovanierisem,” edited by Gilbertus Masius, 1528, 4to.

, an Arabian mathematician, is usually classed among the authors of the tenth century.

, an Arabian mathematician, is usually classed among the authors of the tenth century. He is said to have written some treatises on geometry, and among others, one entitled “De superficierum divisionibus,” which Dr. Dee of London, and Frederic Commandini of Urbino, translated into Latin. The latter published his translation at Pesaro in 1570, with another on the same subject of his own composition. Some, however, are of opinion that the original treatise was by Euclid, to whom Proclus ascribes one on that subject, and that Bagdedin was only the translator of it into the Arabic language.

of M. Voltaire. He is a pretty good master of the Latin, understands some Greek, is reckoned no bad mathematician for his years, and knows a great deal of natural history, both

Mr. Baker was a constant and useful attendant at the meetings of the royal and antiquary societies, and in both was frequently chosen one of the council. He was peculiarly attentive to all the new improvements which were made in natural science, and very solicitous for the prosecution of them. Several of his communications are printed in the Philosophical Transactions and, besides the papers written by himself, he was the means, by his extensive correspondence, of conveying to the society the intelligence and observations of other inquisitive and philosophical men. His correspondence was not confined to his own country. To him we are obliged for a true history of the coccus polonicus, transmitted by Dr. Wolfe. It is to Mr. Baker’s communications that we owe the larger alpine strawberry, of late so much cultivated and approved of in England. The seeds of it were sent in a letter from professor Bruns of Turin to our philosopher, who gave them to several of his friends^ by whose care they furnished an abundant increase. The seeds likewise of the true rhubarb, or rheum palmatum, now to be met with in almost every garden in this country, were first transmitted to Mr. Baker by Dr. Mounsey, physician to the empress of Russia. These, like the former, were distributed to his various acquaintance, and some of the seeds vegetated very kindly. It is apprehended that all the plants of the rhubarb now in Great Britain were propagated from this source. Two or three of Mr. Baker’s papers, which relate to antiquities, may be found in the Philosophical Transactions. The society for the encouragement of arts, manufactures, and commerce, is under singular obligations to our worthy naturalist. As he was one of the earliest members of it, so he contributed in no small degree to its rise and establishment. At its first institution, he officiated for some time gratis, as secretary. He was many years chairman ^of the committee of accounts and he took an active part in the general deliberations of the society. In his attendance he was almost unfailing, and there were few questions of any moment upon which he did not deliver his opinion. Though, fronl the lowness of his voice, his manner of speaking was not powerful, it was clear, sensible, and convincing; what he said, being usually much to the purpose, and always proceeding from the best intentions, had often the good effect of contributing to bring the society to rational determinations, when many of the members seemed to have lost themselves in the intricacies of debate. He drew up a short account of the original of this society, and of the concern he himself had in forming it; which was read before the society of antiquaries, and would be a pleasing present to the public. Mr*. Baker was a poetical writer in the early part of his life. His “Invocation of Health” got abroad without his knowledge; but was reprinted by himself in his “Original Poems, serious and humourous,” Part the first, 8vo, 1725. The second part came out iri 1726. He was the author, likewise, of “The Universe^ a poem, intended to restrain the pride of man,” which has been several times reprinted. His account of the water polype, which was originally published in the Philosophical Transactions, was afterwards enlarged into a separate treatise, and hath gone through several editions. In 1728 he began, and for five years conducted the “Universal Spectator,” a periodical paper, under the assumed name of Henry Stonecastle a selection of these papers was afterwards printed in 4 vols. 12mo. In 1737 he published “Medulla Poetarum Romanorum,” 2 vols. 8vo, a selection from the Roman poets, with translations. But his principal publications are, “The Microscope made easy,” and “Employment for the Microscope.” The first of these, which was originally published in 1742, or 1743, has gone through six editions. The second edition of the other, which, to say the least of it, is equally pleasing and instructive, appearedin 1764. These treatises, and especially the latter, contain the most curious and important of the observations and experiments which Mr. Baker either laid before the royal society, or published separately. It has been said of Mr. Baker, “that he was a philosopher in little things.” If it was intended by this language to lessen his reputation, there is no propriety in the stricture. He was an intelligent, upright and benevolent man, much respected by those who knew him best. His friends were the friends of science and virtue and it will always be remembered by his contemporaries, that no one was more ready than himself to assist those with whom he was conversant in their various researches and endeavours for the advancement of knowledge and the benefit of society. His eldest son, David Erskine Baker, was a young man of genius and learning, and, like his father, a philosopher, an antiquary, and a poet. Being very partial to mathematical and geometrical studies, the duke of Montague, then master of the ordnance, placed him in the drawing-room in the Tower, to qualify him for the royal engineers. In a letter to Dr. Doddridge, dated 1747, his father speaks of him in these terms: “He has been somewhat forwarder than boys usually are, from a constant conversation with men. At twelve years old he had translated the whole twenty-four books of Telemachus from the French before he was fifteen, he translated from the Italian, and published, a treatise on physic, of Dr. Cocchi, of Florence, concerning the diet and doctrines of Pythagoras and last year, before he was seventeen, he likewise published a treatise of sir Isaac Newton’s Metaphysics, compared with those of Dr. Leibnitz, from the French of M. Voltaire. He is a pretty good master of the Latin, understands some Greek, is reckoned no bad mathematician for his years, and knows a great deal of natural history, both from reading and observation, so that, by the grace of God, I hope he will become a virtuous and useful man.” In another letter he mentions a singular commission given to his son, that of making drawings of all the machines, designs, and operations employed in the grand fire- works to be exhibited on occasion of the peace of 1748. It is to be regretted, however, that his father’s expectations were disappointed by a reverse of conduct in this son, occasioned by his turn for dramatic performances, and his marrying the daughter of a Mr. Clendon, a clerical empiric, who had, like himself, a similar turn. In consequence of this unhappy taste, he repeatedly engaged with the lowest strolling companies, in spite of every effort of his father to reclaim him. The public was, however, indebted to him for “The Companion to the Playhouse,1764, 2 vols. 12mo; a work which, though imperfect, had considerable merit, and shewed that he possessed a very extensive knowledge of our dramatic authors and which has since (under the title of “Biographia Dramatica”) been considerably improved, first in 1782, by the late Mr. Isaac Reed, 2 vols. 8vo, and more recently, in 1812, enlarged and improved by Mr. Stephen Jones, so as to form 4 vols. 8vo. He died Feb. 16, 1767. Mr. Baker’s other son, Henry, followed the profession of a lawyer, and occasionally appeared as a poet and miscellaneous writer. In 1756 he published te Essays Pastoral and Elegiac,“2 vols. 8vo, and left ready for the press an arranged collection of all the statutes relating to bankruptcy, with cases, precedents, &c. entitled” The Clerk to the Commission," a work which is supposed to have been published under another title in 1768.

, an eminent mathematician in the seventeenth century, the son of James Baker of Ikon in

, an eminent mathematician in the seventeenth century, the son of James Baker of Ikon in Somersetshire, steward to the family of the Strangways of Dorsetshire, was born at Ikon about the year 1625, and entered in Magdalen-hall, Oxon, in the beginning of the year 1640. In April 1645, he was elected scholar of Wadham college and did some little servicb to king Charles I. within the garrison of Oxford. He was admitted bachelor of arts, April 10, 1647, but left the university without completing that degree by determination. Afterwards he became vicar of Bishop’s-Nymmet in Devonshire, where he lived many years in studious retirement, applying chiefly to the study of the mathematics, in which he made very great progress. But in his obscure neighbourhood, he was neither known, nor sufficiently valued for his skill in that useful branch of knowledge, till he published his famous book. A little before his death, the members of the royal society sent him some mathematical queries to which he returned so satisfactory an answer, that they gave him a medal with an inscription full of honour and respect. He died at Bishop’s-Nymmet aforementioned, on the 5th of June 1690, and was buried in his own church. His book was entitled “The Geometrical Key, or the Gate of Equations unlocked, or a new Discovery of the construction of all Equations, howsoever affected, not exceeding the fourth degree, viz. of Linears, Quadratics, Cubics, Biquadratics, and the rinding of all their roots, as well false as true, without the use of Mesolahe, Trisection of Angles, without Reduction, Depression, or any other previous Preparations of Equations, by a Circle, and any (and that one only) Farabole, &c.” London, 1684, 4to, in Latin and English. In the Philosophical Transactions, it is observed, that the author, in order to free us of the trouble of preparing the equation by taking away the second term, shews us how to construct all affected equations, not exceeding the fourth power, by the intersection of a circle and parabola, without omission or change of any terms. And a circle and a parabola being the most simple, it follows, that the way which our author has chosen is the best. In the book (to render it intelligible even to those who have read no conies), the author shews, how a parabola arises from the section of a cone, then bow to describe it in piano, and from that construction demonstrates, that the squares of the ordinates are one to another, as the correspondent sagitta or intercepted diameters then he shews, that if a line be inscribed in a parabola perpendicular to any diameter, a rectangle made of the segments of the inscript, will be equal to a rectangle rr.ade of the intercepted diameter and parameter of the axis. From this last propriety our author deduces the universality of his central rule for the solution of ai! 2 biquadratic and cubic equations, however affected or varied in terms or signs. After the synthesis the author shews the analysis or method, by which he found this rule which, in the opinion of Dr. R. Plot (who was then secretary to the royal society) is so good, that nothing can be expected more easy, simple, or universal.

, son of the above, an eminent mathematician and divine, in the sixteenth century, was born in Pembrokeshire.

, son of the above, an eminent mathematician and divine, in the sixteenth century, was born in Pembrokeshire. In 1560 he was entered commoner of Baliol college in Oxford; and in 1564, having taken a degree in arts, he left the university, and went to sea; but in what capacity is uncertain however, he thence acquired considerable knowledge in the art of navigation, as his writings afterwards shewed. About the year 1573, he entered into orders, and became prebendary of Winchester, and rector of Easton, near that city. In 1588 he was made prebendary of Lichneld, which he exchanged for the office of treasurer of that church. He afterwards was appointed chaplain to prince Henry, eldest son of king James the first and in 1614, archdeacon of Salisbury. Barlowe was remarkable, especially for having been the first writer on the nature and properties pf the loadstone, twenty years before Gilbert published his book on that subject. He was the first who made the inclinatory instrument transparent, and to be used with a glass on both sides. It was he also who suspended it in a compass-box, where, with two ounces weight, it was made fit for use at sea. He also found out the difference between iron and steel, and their tempers for magnetical uses. He likewise discovered the proper way of touching magnetical needles and of piecing and cementing of loadstones and also why a loadstone, being double-capped, must take up so great a weight.

rles II. was the son of Isaac Barrow of Spiney Abbey irt Cambridgeshire, and uncle of the celebrated mathematician, who will form the subject of the next article. He was born

, bishop of St.Asaph in the reign of Charles II. was the son of Isaac Barrow of Spiney Abbey irt Cambridgeshire, and uncle of the celebrated mathematician, who will form the subject of the next article. He was born in 1613, admitted July 1639 of Peterhouse, Cambridge, next year chosen scholar, and in 1631, librarian. In Dec. 1641, he was presented to the vicarage of Hin ton, by his college, of which he was a fellow, and resided there until ejected by the presbyterians in 1643. He then removed to Oxford, where his learning and abilities were well known, and where he was appointed one of the chaplains of New College, by the interest of his friend, Dr. Pink, then warden. Here he continued until the surrender of Oxford to the parliamentary army, when he was obliged to shift from place to place, and suffer with his brethren, who refused to submit to the usurping powers. At the restoration, however, he was not only replaced in his fellowship at Peterhouse, but chosen a fellow of Eton college, which he held in commendam with the bishopric of Mann. In 1660, being then D. D. he was presented by Dr. Wren, bishop of Ely, to the rectory of Downham, in the Isle of Ely; and, in 1662, resigned his fellowship of Peterhouse. In July 1663, he was consecrated bishop of Mann, in king Henry Vllth’s chapel, Westminster, on which occasion his nephew, the mathematician, preached the consecration sermon. In April 1664, he was appointed governor likewise of the Isle of Mann, by his patron, Charles earl of Derby; and executed his office with the greatest prudence and honour during all the time in which he held the diocese, and for some months after his translation to the see of St. Asaph. He was ever of a liberal, active mind; and rendered himself peculiarly conspicuous as a man of public spirit, by forming and executing good designs for the encouragement of piety and literature. The state of the diocese of Mann at this time was deplorable, as to religion. The clergy were poor, illiterate, and careless, the people grossly ignorant and dissolute. Bishop Barrow, however, introduced a very happy change in all respects, by the establishment of schools, and improving the livings of the clergy. He collected with great care and pains from pious persons about eleven hundred pounds, with which he purchased of the earl of Derby all the impropriations in the island, and settled them upon the clergy in due proportion, He obliged them all likewise to teach schools in their respective parishes, and allowed thirty pounds per annum for a free-school, and fifty pounds per annum for academical learning. He procured also from king Charles II. one hundred pounds a year (which, Mr. Wood says, had like to have been lost) to be settled upon his clergy, and gave one hundred and thirty-five pounds of his own money for a lease upon lands of twenty pounds a year, towards the maintenance of three poor scholars in the college of Dublin, that in time there might be a more learned body of clergy in the island. He gave likewise ten pounds towards the building a bridge, over a dangerous water; and did several other acts of charity and beneficence. Afterwards returning to England for the sake of his health, and lodging in a house belonging to the countess of Derby in Lancashire, called Cross-hall, he received news of his majesty having conferred on him the bishopric of St. Asaph, to which he was translated March 21, 1669, but he was permitted to hold the see of Sodor and Mann in commendam, until Oct. 167 1, in order to indemnify him for the expences of his translation. His removal, however, from Mann, was felt as a very great loss, both by the clergy at large, and the inhabitants. His venerable, although not immediate, successor, Dr. Wilson, says of him, that “his name and his good deeds will be remembered as long as any sense of piety remains among them.” His removal to St. Asaph gave him a fresh opportunity to become useful and popular. After being established here, he repaired several parts of the cathedral church, especially the north and south ailes, and new covered them with lead, and wainscotted the east part of the choir. He laid out a considerable sum of money in repairing the episcopal palace, and a mill belonging to it. In ] 678 he built an alms-house for eight poor widows, and endowed it with twelve pounds per annum for ever. The same year, he procured an act of parliament for appropriating the rectories of Llanrhaiader and Mochnant in Denbighshire and "Montgomeryshire, and of Skeiviog in the county of Flint, for repairs of the cathedral church of St. Asaph, and the better maintenance of the choir therein, and also for the uniting several rectories that were sinecures, and the vicarages of the same parishes, within the said diocese. He designed likewise to build a free-school, and endow it, but was prevented by death; but in 1687, Bishop Lloyd, who succeeded him in the see of St. Asaph, recovered of his executors two hundred pounds, towards a free-school at St. Asaph.

, an eminent mathematician and divine of the seventeenth century, was descended from an

, an eminent mathematician and divine of the seventeenth century, was descended from an ancient family of that name in Suffolk. His father was Mr. Thomas Barrow, a reputable citizen of London and linen-draper to king Charles I.; and his mother, Anne, daughter of William Buggin of North-Cray in Kent, esq. whose tender care he did not long experience, she dying when he was about four years old. He was born at London in October 1630, and was placed first in the Charterhouse school for two or three years, where his behaviour afforded but little hopes of success in the profession of a scholar, for which his father designed him, being quarrelsome, riotous, and negligent. But when removed to Felstead school in Essex, his disposition took a more happy turn, and he quickly made so great a progress in learning, that his master appointed him a kind of tutor to the lord viscount Fairfax of Emely in Ireland, who was then his scholar. During his stay at Felstead, he was admitted, December the 15.th 1643, being fourteen years of age, a pensioner of Peter-house in Cambridge, under his uncle Mr. Isaac Barrow, then fellow of that college. But when he was qualified for the university, he was entered a pensioner in Trinity-college, the 5th of February 1645; his uncle having been ejected, together with Seth Ward, Peter Gunning, and John Barwick, who had written against the covenant. His father having suffered greatly in his estate by his attachment to the royal cause, our young student was obliged at first for his chief support to the generosity of the learned Dr. Hammond, to whose memory he paid his thanks, in an excellent epitaph on the doctor. In 1647, he was chosen a scholar of the house; and, though he always continued a staunch royalist, and never would take the covenant, yet, by his great merit and prudent behaviour he preserved the esteem and goodwill of his superiors. Of this we have an instance in Dr. Hill, master of the college, who had been put in by the parliament in the room of Dr. Comber, ejected for adhering to the king. One day, laying his hand upon our young sflident’s head, he said, “Thou art a good lad, ‘tis pity thou art a cavalier;’ 7 and when, in an oration on the Gunpowder-treason, Mr. Barrow had so celebrated the former times, as to reflect much on the present, some fellows were provoked to move for his expulsion but the master silenced them with this,” Barrow is a better man than any of us.“Afterwards when the engagement was imposed, he subscribed it; but, upon second thoughts, repenting of what he had done, he applied himself to the commissioners, declared his dissatisfaction, and prevailed to have his name razed out of the list. He applied himself with great diligence to the study of all parts of literature, especially natural philosophy; and though he was yet but a young scholar, his judgment was too great to rest satisfied with the shallow and superficial philosophy, then taught and received in the schools. He applied himself therefore to the reading and considering the writings of the lord Verulam, M. Des Cartes, Galileo, &c. who seemed to offer something more solid and substantial. In 1648, Mr. Barrow took the degree of bachelor of arts. The year following, he was elected fellow of his college, merely out of regard to his merit; for he had no friend to recommend him, as being of the opposite party. And now, finding the times not favourable to men of his opinions in matters of church and state, he turned his thoughts to the profession of physic, and made a considerable progress in anatomy, botany, and chemistry: but afterwards, upon deliberation with himself, and with the advice of his uncle, he applied himself to the study of divinity, to which he was further obliged by his oath on his admission to his fellowship. By reading Scaliger on Eusebius, he perceived the dependance of chronology on astronomy; which put him upon reading Ptolemy’s Almagest: and finding that book and all astronomy to depend on geometry, he made himself master of Euclid’s Elements, and from thence proceeded to the other ancient mathematicians. He made a short essay towards acquiring the Arabic language, but soon deserted it. With these severer speculations, the largeness of his mind had room for the amusements of poetry, to which he was always strongly addicted. This is sufficiently evident from the many performances he has left us in that art. Mr. Hill, his biographer, tells us, he was particularly pleased with that branch of it, which consists in description, but greatly disliked the hyperboles of some modern poets. As for our plays, he was an enemy to them, as a principal cause of the debauchery of the times; the other causes he thought to be, the French education, and the ill example of great persons. For satires, he wrote none his wit, as Mr. Hill expresses it, was” pure and peaceable."

nd learning; a perfect master of the Latin and Greek languages; and also an eloquent orator, an able mathematician and philosopher, and a sound divine. The foundation of his great

, more commonly known by the name of Basingstochius, or de Basingstoke, was born at Basingstoke, a town in the north part of Hampshire, and thence took his surname. He was a person highly eminent for virtue and learning; a perfect master of the Latin and Greek languages; and also an eloquent orator, an able mathematician and philosopher, and a sound divine. The foundation of his great learning he laid in the university of Oxford, and, for his farther improvement, went to Paris, where he resided some years. He afterwards travelled to Athens, where he made many curious observations, and perfected himself in his studies, particularly in the knowledge of the Greek tongue. At his return to England, he brought over with him several curious Greek manuscripts, and introduced the use of the Greek numeral figures in to this kingdom. He became also a very great promoter and encourager of the study of that language, which was much neglected in these western parts of the world: and to facilitate it, he translated from Greek into Latin a grammar, which he entitled “The Donatus of the Greeks.” Our author’s merit and learning recommended him to the esteem of all lovers of literature: particularly to the favour of Robert Grosteste, bishop of Lincoln, by whom he was preferred to the archdeaconry of Leicester, as he had been some time before to that of London. He died in 1252. The rest of his works are, 1. A Latin translation of a Harmony of the Gospels. 2. A volume of sermons. 3. “Particulue sententiarum per distinctiones,” or a Commentary upon part of Lombard’s Sentences, &c. It was he also that informed Robert, bishop of Lincoln, that he had seen at Athens a book called “The Testament of the XII Patriarchs.” Upon which the bishop sent for it, and translated it into Latin, and it was printed among the “Orthodoxographa,” Basilero, 1555, fol. and afterwards translated into English, and often reprinted, 12mo.

, an eminent mathematician, is supposed by Pits to have flourished about 1420. He studied

, an eminent mathematician, is supposed by Pits to have flourished about 1420. He studied at Oxford, where he applied himself to natural philosophy in general, but chiefly to the mathematics, in which he made a very great proficiency, as is evident by his writings in that science, which introduced him to the acquaintance and intimacy of the greatest men of his time. It is not known when he died. He wrote, 1. “De Sphcerae concavae fabrica et usu;” which Bale saw in the library of Dr. Robert Recorde, a learned physician. 2. tf De Sphsera solida.“3.” De operatione Astrolabii.“4.” Conclusiones Sophise."

, otherwise Behaim, Bœhm, or Behenira, an eminent geographer and mathematician of the fifteenth century, was born at Nuremberg, an imperial

, otherwise Behaim, Bœhm, or Behenira, an eminent geographer and mathematician of the fifteenth century, was born at Nuremberg, an imperial city in the circle of Franconia, of a noble family, not yet extinct. He had the best education which the darkness of that age permitted, and his early studies were principally directed to geography, astronomy, and navigation. As he advanced in life, he often thought of the existence of the antipodes, and of a western continent, of which he was ambitious to make the discovery.

vensburgh in Suabia, in 1665, and was taught the first rudiments of his art by his father, who was a mathematician, and practised painting only for his amusement, and explained

, an artist, was born at Ravensburgh in Suabia, in 1665, and was taught the first rudiments of his art by his father, who was a mathematician, and practised painting only for his amusement, and explained the principles of it to his son. By an assiduous practice for some years, Beisch proved a good artist, and was employed at the court of Munich, to paint the battles which the elector Maximilian Emanuel had fought in Hungary. While the elector was absent on some of his expeditions, Beisch embraced that opportunity to visit Italy, and took the most effectual methods for his improvement, by studying and copying those celebrated spots which have always claimed general admiration. He had three different manners: his first, before his journey to Italy, was true, but too dark; his second had more clearness and more truth; and his last, still more clear, was likewise weaker than all. The scenes of his landscapes, however, are agreeably chosen, and very picturesque: his touch is light, tender, and full of spirit; and his style of composition frequently resembled that of Gaspar Poussin, or Salvator Rosa. Solimene, a superior artist, did not disdain to copy some of Beisch' s landscapes. This artist died in 1748, aged eighty-three.

, an eminent Italian mathematician, was born at Udina, Nov. 16, 1704, and from his infancy afforded

, an eminent Italian mathematician, was born at Udina, Nov. 16, 1704, and from his infancy afforded the promise of being an ornament to his family and country. At Padua, where he was first educated, his proficiency was extraordinary, and at the age of nineteen he excited considerable attention by an elegant Latin oration he delivered in honour of cardinal Barbadici. He afterwards entered the society of the Jesuits at Udina, and having completed his noviciate, went to Bologna, and studied mathematics and theology at Parma, where he was appointed professor of mathematics and had the direction of the observatory, and became eminent as an observer of the phenomena of nature, and a profound antiquary. When the society of the Jesuits was suppressed, Belgrade went to Bologna, and was appointed rector of the college of St. Lucia, where, and in other parts of Italy, he occasionally resided until his death in 1789. The extent and variety of his knowledge will be best understood by a list of his works. 1. “Gratulatio Cardinali J. F. Barbadico, &c.” already noticed, Padua, 1723. 2. “Ad disciplinam Mechanicam, Nauticam, et Geographicam Acroasis critica et historica,” Parma, 1741. 3. “Ad disciplinam Hydrostaticam Acroasis historica et critica,” ibid. 1742. 4. “De altitudine Atmospherae aestimanda critica disquisitio,” ib. 1743. 5. “De Phialis vitreis ex minimi silicis casa dissilientibusAcroasis,” Padua, 1743. 6. “De Gravitatis legibus Acroasis Physico-mathematica,” Parma, 1744. 7. “Devita B. Torelli Puppiensis commentarius,” Padua, 1745. 8. “De corporis elasticis disquisit. physico-mathem.'' Parma, 1747. 9.” Observatio Soils defectus et Lunae,“Parma, 1748. 10.” I fenomeni Elettrici con i corollari da lor dedotti,“Parma, 1749. 11.” Ad Marchionem Scipionem Maphejum epistolae quatuor,“Venice, 1749. 12.” Delia Reflessionc de Gorpi dall' Acqua,“&c. Parma, 1753. 13.” Observatio defectus Lunae habita die 30 Julii in novo observatorio, 1757.“14.” Dell‘ azione del caso nelle invenzioni, e dell’ influsso degli Astri ne' corpi terrestri, dissertationi due,“Padua, 1757. 15.” Observatio defectus Lunae,“Parma, 1761. 16.” De utriusque Analyseos usu in re physica,“vol.11, ibid. 1761. 17.” Delle senzazioni del calore, e del freddo, dissertazione,“ibid. 1764. 18.” II Trono di Nettuno illustrate,“Cesene, 1766. 19.” Theoria Cochleae. Archimedis,“Parma, 1767. 20.” Dissertazione sopra i Torrenti,“ibid. 1768. 21.” Delia Rapid ita delle idee dissertazione,“Modena, 1770. 22.” Delia proporzione tra i talenti dell' Uomo, e i loro usi, dissertazione,“Padua, 1773. 23.” De Telluris viriditate, dissertatio,“Udina, 1777. 24.” Delia Esistenza di Dio da' Teoremi Geometrici dimostrata, dissert.“Udina, 1777. 25.” Dall‘ Esistenza d’una sola specie d‘esseri ragionevoli e liberi si arguisce l’Esistenza di Dio, dissertazione,“ibid. 1782. 26.” Del Sole bisoguevole d‘alimento, e dell’ Oceano abile a procacciarglielo, dissert. Fisico-matematica,“Ferrara, 1783. 27.” Dell' Architettura Egiziana, dissert." Parma, 1786. He left also several manuscript works, and published some pieces in the literary journals, being a correspondent of the academy of sciences at Paris, and a member of the institute of Bologna.

poke of it to the prince de Dombes, who was master of the ordnance. The prince was astonished that a mathematician, who served under him, and on whom he had conferred favours,

, a member of the academies of sciences of Paris and Berlin, was born in Catalonia in 1697. Being left an orphan at the age of five years, he was educated by an engineer, a friend of his father’s family, and very early discovered a genius for mathematics. In the course of time he was appointed royal professor of the schools of artillery of la Fere, and superintended the education of some scholars who proved worthy of him. His success in this situation procured him also the place of provincial commissary of artillery, but here' his zeal cost him both places. Having discovered by some experiments that a smaller quantity of powder was sufficient to load a cannon than commonly employed: that, for example, eight pounds of powder would produce the same effect as twelve, which was the usual quantity, he thought to pay court to the cardinal de Fleury, then prime minister, by communicating to him in private a scheme by which government might make so important a saving. The cardinal, who was partial to all schemes of economy, listened with pleasure to this of Belidor, and spoke of it to the prince de Dombes, who was master of the ordnance. The prince was astonished that a mathematician, who served under him, and on whom he had conferred favours, should not have communicated this to him, and irritated by what he considered as a mark of disrespect, dismissed him from the posts he held, and obliged him to leave la Fere. t De Valliere, lieutenant-general of artillery, took upon him on this occasion to justify the prince’s conduct, in a printed memorial, and endeavoured at the same time to refute Belidor’s opinion and experiments, with what success we are not told. Belidor, however, originally born without fortune, was now stripped of the little he had acquired by his talents, and might probably have remained in poverty, had not the prince of Conti, who knew his merit, taken him with him to Italy, and bestowed on him the cross of St. Lewis, an honour which procured him some notice at court. The marshal Bellisle engaged him in his service, and when war-minister, appointed him to the office of inspector of artillery, and gave him apartments in the arsenal at Paris, where he died in 1761. During his laborious and checquered life, he found leisure to write, 1. “Sommaire d‘un cours d’architecture rnilitaire, civil et hydraulique,1720, 12 mo. 2. “Nouveau cours de Mathematique, a T usage de I'Artilierie et du Genie,” 4 to, Paris, 1725, a work previously examined by a committee of the academy of sciences, and approved and recommended by them. 3. “La Science des ingenieurs,”. 1729, 4to. 4. “Le Bombardier Francoise,1731, 4to. 5. “Architecture Hydraulique,1735 1737, 4 vols. 4to. 6. “Dictionnaire portatif de l'ingenieur,1738, 8vo. S. “Traite des Fortifications,” 2 vols. 4to. 9. “La science des Ingenieurs dans la concluite des travaux des Fortifications,1749, 4to. His biographer says that the most of these works are useful, but that Belidor was not a mathematician of the first order.

, an Italian Jesuit, physician, and mathematician of considerable eminence, was born at Leghorn, Feb. 8, 1716.

, an Italian Jesuit, physician, and mathematician of considerable eminence, was born at Leghorn, Feb. 8, 1716. He began his noviciate among the Jesuits at the age of sixteen, but did not take the four vows, according to the statutes of that order, until eighteen years afterwards. He had already published a funeral oration on Louis Ancajani, bishop of Spoleto, 1743, and a species of oratorio, to be set to music, entitled “Cristo presentato al tempio,” but it was neither as an orator or poet that he was destined to shine. He became professor of philosophy at Fermo, and when father Boscovich was obliged to leave Rome to complete the chorographical chart of the papal state, which he published some years afterwards, Benvenuti succeeded him in the mathematical chair of the Roman college, and also resumed his lectures on philosophy in the same college. His first scientific work was an Italian translation of Clairaut’s Geometry, Rome, 1751, 8vo and he afterwards published two works, which gained him much reputation: 1. “Synopsis Physics generalis,” a thesis maintained by one of his disciples, the marquis de Castagnaga, on Benvenuti’s principles, which were those of sir Isaac Newton, Rome, 1754, 4to. 2. “De Lumine dissertatio physica,” another thesis maintained by the marquis, ibid. 1754, 4to. By both these he contributed to establish the Newtonian system in room of those fallacious principles which had so long obtained in that college; but it must not be concealed that a considerable part of this second work on light, belongs to father Boscovich, as Benvenuti was taken ill before he had completed it, and after it was sent to press. After the expulsion of the Jesuits, there appeared at Rome an attack upon them, entitled “Riflessioni sur Gesuitismo,1772, to which Benvenuti replied in a pamphlet, entitled “Irrefiessioni sur Gesuitismo” but this answer gave so much offence, that he was obliged to leave Rome and retire into Poland, where he was kindly received by the king, and became a favourite at his court. He died at Warsaw, in September, 1789.

, a French mathematician and astronomer, was born at Lyons, March 5, 1703, entered among

, a French mathematician and astronomer, was born at Lyons, March 5, 1703, entered among the Jesuits, and became professor of humanity at Vienne and at Avignon, and of mathematics and philosophy at Aix. In 1740 he was invited to Lyons and appointed professor of mathematics, director of the observatory, and keeper of the medals and the same year he became astronomer to the academy, the memoirs of which are enriched by a great many of his observations, particularly that on the passage of Mercury on the Sun, May 6, 1753, during which he saw and demonstrated the luminous ring round that planet, which had escaped the notice of all the astronomers for ten years before. In all his results, he entirely agreed with Lalande, who had made the same observations at Paris, and with the celebrated Cassini. All his observations, indeed, are creditable to his talents, and accord with those of the most eminent astronomers. Among his other papers, inserted in the memoirs of the academy, we find several on vegetation, on the evaporation of liquids, and the ascent of vapours, on light, a physical theory on the rotation of the earth and the inclination of its axis, &c. In meteorology, he published observations on the tubes of thermometers, with an improvement in the construction of them, which was the subject of three memoirs read in the academy of Lyons in 1747. He has also endeavoured to account for metals reduced to calcination weighing heavier than in their former state, and maintains, against Boyle, that fire is incapable of giving this additional weight, and likewise refutes the opinion of those who attribute it to air, or to substances in the air which the action of fire unites to the metal in fusion. This memoir was honoured with the prize by the academy of Bourdeaux in 1747, and contained many opinions which it would have been difficult to contradict before the experiments of Priestley, Lavoisier, and Morveau. In 1748, he received the same honour, from that academy, for a paper in which he maintained the connexion between magnetism and electricity, assigning the same cause to both. In 1760, he received a third prize from the same academy, for a dissertation on the influences of the moon on vegetation and animal oeconomy. Beraud was also a corresponding member of the academy of sciences in Paris, and several of his papers are contained in their memoirs, and in those of the academy of Lyons. He wrote several learned dissertations on subjects of antiquity. On the dissolution of the society of Jesuits, he left his country for some time, as he could not conscientiously take the oaths prescribed, and on his return, notwithstanding many pressing offers to be restored to the academy, he preferred a private life, never having recovered the shock which the abolition of his order had occasioned. In this retirement he died June 26, 1777. His learning and virtues were universally admired he was of a communicative disposition, and equal and candid temper, both in his writings and private life. Montucla, Lalande, and Bossu, were his pupils and father Lefevre of the Oratory, his successor in the observatory of Lyons, pronounced his eloge in that academy, which was printed at Lyons, 1780, 12mo. The Dict. Hist, ascribed to Beraud, a small volume, “La Physique des corps animus,” 12mo.

le, and the religion itself an imposture.” The bishop, therefore, addressed to him, as to an infidel mathematician, a discourse called the “Analyst” with-a view to show that mysteries

About this time he engaged in a controversy with the mathematicians, which made a good deal of noise in the literary world and the occasion of it is said to have been, this: Mr. Addison had, many years before this, given him an account of their common friend Dr. Garth’s behaviour in his last illness, which was equally un pi easing to both these advocates of revealed religion. For, when Addison. went to see the doctor, and began to discourse with him seriously about another world, “Surely, Addison,” replied he, “I have good reason not to believe those trifles, since my friend Dr. Halley, who has dealt so much in demonstration, has assured me, that the doctrines of Christianity are incomprehensible, and the religion itself an imposture.” The bishop, therefore, addressed to him, as to an infidel mathematician, a discourse called the “Analyst” with-a view to show that mysteries in faith were unjustly objected to by mathematicians, who admitted much greater mysteries, and even falsehoods in science, of which he endeavoured to prove, that the doctrine of fluxions furnished a clear example. This attack gave occasion to a smart controversy upon the subject of fluxions the principal answers to the “Analyst” were written by a person under the name of Philalethes Cantabrigiensis, generally supposed to be Dr. Jurin, who published a piece entitled “Geometry no friend to Infidelity,1734. To this the bishop replied in “A Defence of Freethinking in Mathematics,1735; which drew a second answer the same year from Philalethes, styled “The minute Mathematician, or the Freethinker no just thinker” and here the controversy ended, and whatever fault, mathematicians may find in this hostile attempt of our bishop, it must be acknowledged they have reaped no inconsiderable advantage from it, inasmuch as it gave rise to the Treatise of Fluxions by Maclaurin, in which the whole doctrine is delivered with more precision and fulness than ever was done before, or probably than ever would have been done, if no attack had been made upon it.

, the brother of the preceding, and a celebrated mathematician, was born at Basil the 7th of August 1667. His father intended

, the brother of the preceding, and a celebrated mathematician, was born at Basil the 7th of August 1667. His father intended him for trade; but his own inclination was at first for the belles-lettres, which however, like his brother, he left for mathematics. He laboured with his brother to discover the method used by Leibnitz, in his essays on the Differential Calculus, and gave the first principles of the Integral Calculus. Our author, with messieurs Huygens and Leibnitz, was the first who gave the solution of the problem proposed by James Bernoulli, concerning the catenary, or curve formed by a chain suspended by its two extremities.

o laugh at him), “am Isaac Newton.” Another time having to dinner with him the celebrated Koenig the mathematician, who boasted, with some degree of self-complacency, of a difficult

Our author was extremely respected at Basil; and to bow to Daniel Bernoulli, when they met him in the streets, was one of the first lessons which every father gave every child. He was a man of great simplicity and modesty of manners. He used to tell two little adventures, which he said had given him more pleasure than all the other honours he had received. Travelling with a learned stranger, who, being pleased with his conversation, asked his name “I am Daniel Bernoulli,” answered he with great modesty “And I,” said the stranger (who thought he meant to laugh at him), “am Isaac Newton.” Another time having to dinner with him the celebrated Koenig the mathematician, who boasted, with some degree of self-complacency, of a difficult problem he had resolved with much trouble, Bernoulli went on doing the honours of his table, and when they went to drink coffee he presented Koenig with a solution of the problem more elegant than his own. After a long, useful, and honourable life, Daniel Bernoulli died the 17th of March 1782, in the eighty-third year of his age.

al Lemoine, where he made great proficiency in the learned languages, and became an able theologian, mathematician, philosopher, and historian. In 1550 he was at Agen as preceptor

, was born at St. Denis near Paris, and was educated at the college of the cardinal Lemoine, where he made great proficiency in the learned languages, and became an able theologian, mathematician, philosopher, and historian. In 1550 he was at Agen as preceptor to Hector Fregosa, afterwards bishop of that city, and here he was converted to the Protestant religion along with Scaliger and other learned men. When he arrived at Paris in 1558, he was chosen preceptor to Theodore Agrippa d' Aubigne“but the persecution arising, he was arrested at Constance and condemned to be burnt, a fate from which he was preserved by the kindness of an officer who favoured his escape. He then went to Orleans, Rochelle, and Sancerre, and distinguished himself by his courage during the siege of this latter place by the marshal de Lachatre. In 1574 we find him at Geneva, officiating as minister and professor of philosophy. His death is supposed to have taken place in 1576. He wrote a curious book entitled” Chronicon, sacrse Scripture auctoritate constitutnm,“Geneva, 1575, fol. In this he maintains that all chronological authorities must be sought in the holy scriptures Vossius and Scaliger speak highly of his talents. Draudius, in his” Bibliotheca Classica,“mentions another work in which he was concerned,” G. Mercatoris et Matthei Beroaldi chronologia, ab initio mundi ex eclipsis et observationibus astronomicis demonstrata," Basil, 1577, Cologne, 1568, fol. We have some doubts whether this is not the same as the work mentioned above.

, a celebrated French mathematician, member of the academies of sciences and the marine, and examiner

, a celebrated French mathematician, member of the academies of sciences and the marine, and examiner of the guards of the marine and of the scholars of artillery, was born at Nemours the 31st of March 1730. In the course of his studies he met with some books of geometry, which gave him a taste for that science; and the Eloges of Fontenelle, which shewed him the honours attendant on talents and the love of the sciences. His father in vain opposed the strong attachment of young Bezout to the mathematical sciences. April 8, 1758, he was named adjoint-mechanician in the French academy of sciences, having before that sent them two ingenious memoirs on the integral calculus, and given other proofs of his proficiency in the sciences. In 1763, he was named to the new office of examiner to the marine, and appointed to compose a course of mathematics for their use; and in 1768, on the death of M. Camus, he succeeded as examiner of the artillery scholars.

, an excellent mathematician, and lord-mayor of London in the reign of queen Elizabeth, was

, an excellent mathematician, and lord-mayor of London in the reign of queen Elizabeth, was son to Roger Biilingsley of Canterbury. He spent near three years in his studies at the university of Oxford, during which time he contracted an acquaintance with an eminent mathematician, whose name was Whitehead, and who had been an Augustin friar at Oxford, but Biilingsley being removed from the university, and bound apprentice to an haberdasher in London, he afterwards raised himself so considerable a fortune by trade, that he was successively chosen sheriff, alderman, one of the commissioners of the customs for the port of London, and at last lord mayor of that city in 1597, and received the honour of knighthood. He made a great progress in the mathematics, by the assistance of his friend Mr. Whitehead, who being left destitute upon the dissolution of the monasteries in the reign of king Henry VIII. was received by Mr. Biilingsley into his family, and maintained by him in his old age in his house at London and when he died, he gave our author all the mathematical observations, which he had made and collected, with his notes upon Euclid’s Elements, which he had drawn up and digested with prodigious pains. He was one of the original society of antiquaries. Sir Henry Billingsley died very much advanced in years, Nov. 22, 1606, and was interred in the church of St. Catherine Coleman, London. He translated the Elements of Euclid into English, to which he added a great number of explanations, examples, scholia, annotations, and inventions, collected from the best mathematicians both of the former times, and those in which he lived, published under the title of “The Elements of Geometry of the most antient philosopher Euclid of Megara, faithfully translated into the English tongue. Whereunto are added certain scholia, annotations,” &c. London, 1570, fol. Dr. John Dee prefixed to this work a long preface, full of variety of learning relating to the mathematics.

, an Italian mathematician, was born at Sienna about the end of the fifteenth century,

, an Italian mathematician, was born at Sienna about the end of the fifteenth century, and died about the middle of the sixteenth. After having served in the wars under the dukes of Parma and Ferrara, and the republic of Venice, he employed himself in studying the art of fusing and casting metal for cannon, and improving the quality of gunpowder. He was the first of his nation who wrote upon these subjects. The work in which he laid down his experience and practice, was entitled “Pirotecnia, nella quale si tratta non sole della diversita delle minere, ma anco di quanto si ricerca alia pratica di esse, e che s’appartienne all‘arte della fusione o getto de’ metalli,” Venice, 1540, 4to, often reprinted and translated.

, a Greek mathematician, whose country is unknown, wrote a treatise on warlike machines,

, a Greek mathematician, whose country is unknown, wrote a treatise on warlike machines, which he dedicated to Attains, king of Pergamus, about the year 239 B.C. It is printed in Gr. and Lat. in the “Mathematici Veteres,” Paris, 1693, fol.

, an eminent mathematician, who flourished in the 16th and 17th centuries, was the son

, an eminent mathematician, who flourished in the 16th and 17th centuries, was the son of John Blagrave, of Bulmarsh, esq. and was born at Reading, but in what year is not known. He acquired the rudiments of his education at Reading, whence he removed to St. John’s college, Oxford, but soon quitted the university, and retired to Southcote Lodge at Reading, where he devoted his time to study and contemplation. His genius seemed to be turned most to mathematics; and that he might study this science without interruption, he devoted himself to a retired life. He employed himself chiefly in compiling such works as might render speculative mathematics accurate, and the practical parts easy. He accordingly finished some learned and useful works, in all which he proposed to render those sciences more universally understood. He endeavoured to shew the usefulness of such studies, that they were not mere amusements for scholars and speculative persons, but of general advantage, and absolutely indispensable in many of the necessaries and conveniences of life with this view he published the four following works: 1. “A Mathematical Jewel, shewing the making and most excellent use of an instrument so called: the use of which jewel is so abundant, that it leadeth the direct path-way through the whole art of astronomy, cosmography, geography,” &c. 1582, folio. 2. “Of the making and use of the Familiar Staff, so called for that it may be made useful and familiarly to walk with, as for that it performeth the geometrical mensuration of all altitudes,1590, 4to. 3. “Astrolabium uranicum generale a necessary and pleasant solace and recreation for navigators in their long journeying containing the use of an instrument, or astrolabe,” &c. 1596, 4to. 4. “The art of Dialling, in two parts.1609, 4to.

on; and might, possibly, as Mr. Coates conjectures, be an unpublished work of Mr. John Blagrave, the mathematician, by whose will he inherited an estate in Swallowfield, yet we

, probably a relation of the preceding, was born in the parish of St. Giles, Reading, in 1610, and was a great enthusiast in astrological studies. He published “An introduction to Astrology,1682, 8vo, to which is prefixed an engraving of him mentioned by Granger. He was the author of a large supplement to Culpepper’s Herbal; to which is added “An account of all the Drugs that were sold in the druggists and apothecaries shops, with their dangers and connexions.” To this book is subjoined “A new tract of Chirurgery,” 8vo. He was also author of “The Astrological practise of Physick, discovering the true method of curing all kinds of diseases, by such herbs and plants as grow in our nation,” 8vo. In the Biographia Britannica, is an account of a manuscript which had been seen by Dr. Campbell, the author of that article, and had been bought at the sale of the library of an eminent physician near Covent-garden. In the first leaf it was said to be written by Mr. J. Blagrave, and was dedicated to Mr. B. (Backhouse) of Swallowfield. It appeared, from some mention of the royal society, and its members, to have been written in 1669, or 1670. The title was, “A remonstrance in favour of Ancient Learning against the proud pretensions of the moderns, more especially in respect to the doctrine of the Stars.” From the distribution of the several heads, and the extracts from them, it seems to be the work of an ingenious writer; one far superior to Joseph Blagrave in style and composition; and might, possibly, as Mr. Coates conjectures, be an unpublished work of Mr. John Blagrave, the mathematician, by whose will he inherited an estate in Swallowfield, yet we know not how to reconcile this with the dates respecting the royal society, which certainly did not exist in the mathematician’s time. This Joseph Blagrave died in 1679.

, a celebrated French mathematician and military engineer, was born at Ribemond in Picardy, in 1617.

, a celebrated French mathematician and military engineer, was born at Ribemond in Picardy, in 1617. While he was yet but young, he was chosen regius professor of mathematics and architecture at Paris. Not long after, he was appointed governor to Lewis-Henry de Lomenix, count de Brienne, whom he accompanied in his travels from 1652 to 1655, of which he published an account. He enjoyed many honourable employments, both in the navy and army; and was entrusted with the management of several negociations with foreign princes. He arrived at the dignity of marshal de camp, and counsellor of state, and had the honour to be appointed mathematical preceptor to the Dauphin. He was a member of the royal academy of sciences, director of the academy of architecture, and lecturer to the royal college in all which he supported his character with dignity and applause. Blondel was no less versed in the knowledge of the belles lettres than in the mathematical sciences, as appears by the comparison he published between Pindar and Horace, 1675, 12mo, and afterwards reprinted in Rapin’s miscellaneous works. He died at Paris, the 22d of February, 1686, in the sixty-ninth year of his age. His chief mathematical works were 1. “Cours d' Architecture,” Paris, 1675, folio. 2. “Resolution des quatre principaux problemes d' Architecture,” Paris, 1676, fol. 3. “Histoire du Calendrier Romain,” Paris, 1682, 4to. 4. “Cours de Mathematiques,” Paris, 1683, 4to. 5. “L'Art de jetter des Bombes,” La Haye, 1685, 4to. Besides a “New method of fortifying places,” and other works. Blondel had also many ingenious pieces inserted in the memoirs of the French academy of sciences, particularly in the year 1666.

he manner reported, it formed an exact counterpart of what he records to have happened to Euclid the mathematician. Euclid had demonstrated, as a mathematical problem, that all

, a satirical wit, was born at Loretto in 1556, the son of an architect of a Roman family, about the beginning of the seventeenth century. The method he took to indulge his turn for satire, or rather plot of his publications, was the idea that Apollo, holding his courts Oh Parnassus, heard the complaints of the wholeworld, and gave judgment as the case required. He was received into the academies of Italy, where he gained great applause by his political discourses, and his elegant criticisms. The cardinals Borghese and Cajetan having declared themselves his patrons, he published his “News from Parnassus/' and” Apollo’s Secretary,“a continuation which being well received, he proceeded further, and printed his” Pietra di Paragone“wherein he attacks the court of Spain, setting forth their designs against the liberty of Italy, and inveighing particularly against themfor the tyranny they exercised in the kingdom of Naples. The Spaniards complained of him in form, and were determined at any rate to be revenged. Boccalini was frightened, and retired to Venice. Some time after he was murdered in a surprising manner. He lodged with one of his friends, who having got up early one morning, left Boccalini in bed; when a minute after four armed men entered his chamber, and gave him so many blows with bags full of sand that they left him for dead so that his friend, upon his return, found him unable to utter one word. Great search was made at Venice for the authors of this murder and though they were never discovered, yet it was universally believed that they were set to work. by the court of Spain. This story, however, has been called in question by Mazzuchelli, and seems indeed highly improbable at least it can by no means stand upon its present foundation. His attacking the court of Spain in his” Pietra di Paragone,“is said to have been the cause of his murder but another cause, if he really was murdered, must be sought, for he died, by whatever means, Nov. 10, 1613, and the” Pietra“was not published until two years after that event. It appears likewise from one of his letters, that he had kept the manuscript a profound secret, communicating it only to one confidential frienc!, to whom the above letter was written. Besides, the register of the parish in which he died, mentions that on Nov. 10, 1613, the signor Trajan Boccalini died at the age of fiftyseven, of a cholic accompanied with a fever. Apostolo Zeno, vrho mentions this circumstance in his notes on Fontanini’s” Italian Library,“adds, that in a speech publicly delivered at Venice in 1<320, in defence of Trissino, whom. Boccalini had attacked, ample mention rs made of him, who had then been dead seven years, and in terms of severe censure; but not a word was said of his assassination, which could not have then been a secret, nor could there be any reason for concealing it. If indeed he suffered in the manner reported, it formed an exact counterpart of what he records to have happened to Euclid the mathematician. Euclid had demonstrated, as a mathematical problem, that all the lines both of princes’” and private men’s thoughts meet in one centre namely, to pick money out of other men’s pockets and put it into their own and for this he was attacked by some of his hearers who beat him with sand-bags and perhaps, as a foundation for the story, some of Boccalini’s readers may have said that he ought to have been punished in the same manner. Boccal'mi’s works are: 1. “Itagguagli di Parnaso, centuria prima,” Venice, 1612, 4to. “Centuria secxinda,” ibid. 1613, 4to, neither published long enough before his death to have excited much general odium. These two parts were afterwards frequently reprinted in one volume. There is unquestionably in this work, much to make it popular, and mnch to excite hostility. His notions on government, liberty, &c. were too free for his age and country and his treatment of literary characters is frequently captious and unjust, yet the work upon the whole is amusing, and original in its plan. A third part was published by Jerome Briani, of Modena, at Venice, 165O, 8vo, and die whole was translated and published in English, tinder the inspection of Hughes the poet, 1705, lol. 2. “Pietra del Paragone politico,” Cosmopoli (Amsterdam), 1615, 4to, and often, reprinted in various sizes; that of Amsterdam, 1653, 24mo, is reckoned the best. It has been translated into Latin, French, and English, first in 1626, 4to, and afterwards in Hughes’s edition and into German. This “political touchstone” bears hard on the Spanish monarchy, and may be considered as a supplement to his “News from Parnassus.” 3. “Commentari sopra Cornelio Tacito,” Geneva, 1669, 4to, Cosmopoli (Amsterdam), 1677, 4to, and afterwards in a collection published under the title “La Bilancia politica di tutte le opere di Trajano Boccalini,” &c. with notes and observations by the chevalier Louis du May, at Castellana, 167S, 3 vols. 4to. The first two volumes of this scarce work contain the Tacitus, on which the annotator, not content with being very free in his religious opinions, takes some extraordinary liberties with the text, and therefore they were soon inserted in the Index Expurgatorius. They contain, however, many curious facts which tend to illustrate the political affairs of the time. The third volume is filled with political and historical letters, collected hy Gregorio Leti but although these are signed with Boccalini’s name, they are supposed to have been written by his son, and by the editor Leti, a man not very scrupulous in impositions of this kind. 6. “La Segretaria d'Apollo,” Amst. 1653, 24mo, a sort of continuation of the “Ragguagli,” very much in Boccalini’s manner, but most probably we owe it to the success of his acknowledged works.

, a celebrated French mathematician and natural philosopher, was born at Dax, in the department

, a celebrated French mathematician and natural philosopher, was born at Dax, in the department of the Landes, May 4, 1733. His mother was Maria Theresa de Lacroix, and his father John Anthony Borda, whose ancestors had acquired considerable distinction in the French army. He began his studies in the college of the Barnabites at Dax, where he gave early indications of his future genius. He was a considerable time after put under the charge of the Jesuits of La Fleche, and by his ardour for study and superior talents, frequently carried off the prizes which were held out as the reward of youthful genius. This induced the Jesuits to endeavour to press him into their order, but his attachment to geometry was too powerful to be weakened by their persuasions. He encountered afterwards a more formidable opposition from his father, who was hostile to the prosecution of what he called unprofitable studies, and endeavoured to please him by proposing to enter into the engineer service of the army, where the objects of his profession would necessarily require a knowledge of geometry and physics. His father, however, having eleven children, and being obliged to support two of his sons who were already in the army, was anxious that Charles should look forward to some situation in the magistracy, which might be obtained without much expence and trouble. To these views Borda reluctantly submitted; but after having thus lost some of the most precious years of his youth, a friar, who was a particular friend of his father, obtained, by earnest solicitation, that he should be allowed to devote himself to his favourite science; and, every restraint being now removed, he was in 1753, when only twenty years of age, introduced to D'Alembert, who advised him to remain in the capital, and look forward to a situation in the academy. Borda accordingly entered the light horse, and continuing his mathematical studies, he became professor to his comrades.

, a celebrated philosopher and mathematician, was born at Naples the 28th of January, 1608. He was professor

, a celebrated philosopher and mathematician, was born at Naples the 28th of January, 1608. He was professor of philosophy and mathematics in some of the most celebrated universities of Italy, particularly at Florence and Pisa, where he became highly in favour with the princes of the house of Medici. But having been concerned in the revolt of Messina, he was obliged to retire to Rome, where he spent the remainder of his life under the protection of Christina queen of Sweden, who honoured him with her friendship, and by her liberality towards him softened the rigour of his hard fortune. He continued two years in the convent of the regular clergy of St. Pantaleon, called the Pious Schools, where he instructed the youth in mathematical studies. And thi’s study he prosecuted with great diligence for many years afterward, as appears by his correspondence with several ingenious mathematicians of his time, and the frequent mention that has been made of him by others, who have endeavoured to do justice to his memory. He wrote a letter to Mr. John Collins, in which he discovers his great desire and endeavours to promote the improvement of those sciences: he also speaks of his correspondence with, and great affection for, Mr. Henry Oldenburgh, secretary of the royal society; of Dr. Wallis; of the then late learned Mr. Boyle, and lamented the loss sustained by his death to the commonwealth of learning. Mr. Baxter, in his “Enquiry into the Nature of the Human Soul 3” makes frequent use of our author’s book “De Motu Animalium,” and tells us, that he was the first who discovered that the force exerted within the body prodigiously exceeds the weight to be moved without, or that nature employs an immense power to move a small weight. But he acknowledges that Dr. James Keil had shewn that Borelli was mistaken in his calculation of the force of the muscle of the heart; but that he nevertheless ranks him with the most authentic writers, and says he is seldom mistaken: and, having remarked that it is so far from being true, that great things are brought about by small powers, on the contrary, a stupendous power is manifest in the most ordinary operations of nature, he observes that the ingenious Borelli first remarked this in animal motion; and that Dr. Stephen Hales, by a course of experiments in his “Vegetable Statics,” had shewn the same in the force of the ascending sap in vegetables. After a course of unceasing labours, Borelli died at Pantaleon of a pleurisy, the 31st of December 1679, at 72 years of age, leaving the following works: 1. “Delle cagioni dellefebri maligni,1649, 12mo. 2. “Euclides restitutus,” &c. Pisa, 1658, 4to. 3. “Apollonii Pergaei conicorum, libri v. vi. & vii. paraphraste Abalphato Aspahanensi nunc primum editi,” &c. Floren. 1661, fol. 4. “Theoriæ Medicorum Planetarum ex causis physicis deductae,” Flor. 1666, 4to. 5. “De Vi Percussionis,” Bologna, 1667, 4to. This piece was reprinted, with his famous treatise “De Motu Animalium,” and that “De Motionibus Naturalibus,” in 1686. 6. “Osservazione intorno alia virtu ineguali degli occhi.” This piece was inserted in the Journal of Rome for the year 1669. 7. “De motionibus naturalibus e gravitate pemlentibus,” Regio Julio, 1670, 4to. 8. “Meteorologia Ætnea,” &c. Regio Julio, 1670, 4to. 9. “Osservazione dell' ecclissi lunare, fatta in Roma,1675. Inserted in the Journal of Rome, 1675, p. 34. 10. “Elementaconica Apollonii Pergoei et Archimedis opera nova et breviori methodo demonstrata,” Rome, 1679, 12mo, at the end of the 3d edition, of his Euclides restitutus. 11. “De Motu Animaiium: pars prima, et pars altera,” Romae, 1681, 4to. This was reprinted at Leyden, revised and corrected; to which was added John Bernouilli’s mathematical meditations concerning the motion of the muscles. “12. At Leyden, 1686, in 4to, a more correct and accurate edition, revised by J. Broen, M. D. of Leyden, of his two pieces” De vi percussionis, et de motionibus de gravitate pendentibus,“&c. 13.” De renum usu judicium:“this had been published with Bellini’s book” De structura renum," at Strasburgh, 1664, 8vo.

fatiguing, and often perilous operation, he was assisted by the English Jesuit, Mayer, an excellent mathematician, and was amply provided with the requisite instruments and attendants.

Benedict XIV. who was a great encourager of learning, and a beneficent patron of learned men, gave Boscovich many proofs of the esteem he had for him; and both he and his enlightened minister, cardinal Valenti, consulted Boscovich on various important objects of public economy, the clearing of harbours, and the constructing of roads and canals. On one occasion, he was joined in a commission with other mathematicians and architects, invited from different parts of Italy, to inspect the cupola of St. Peter’s, in which a crack had been discovered. They were divided in opinion; but the sentiments of Boscovich, and of the marquis Poleni, prevailed. In stating, however, the result of the consultation, which was to apply a circle of iron round the building, Poleni forgot to refer the idea to its real author, and this omission grievously offended Boscovich, who was tenacious of fame, and somewhat irritable“in temper. About the same time other incidents had concurred to mortify his pride; and he became at last disgusted with his situation, and only looked for a convenient opportunity of quitting Rome. While in this temper of mind, an application was made by the court of Portugal to the general of the Jesuits, for ten mathematicians of the society to go out to Brazil, for the purpose of surveying that settlement, and ascertaining the boundaries which divide it from the Spanish dominions in America. Wishing to combine with that object the mensuration of a degree of latitude, Boscovich offered to embark in the expedition, and his proposition was readily accepted. But cardinal Valenti, unwilling to lose his services, commanded him, in the name of the pope, to dismiss the project, and persuaded him to undertake the same service at home in the Papal territory. In this fatiguing, and often perilous operation, he was assisted by the English Jesuit, Mayer, an excellent mathematician, and was amply provided with the requisite instruments and attendants. They began the work about the close of the year 1750, in the neighbourhood of Rome, and extended the meridian line northwards, across the chain of the Appennines as far as Rimini. Two whole years were spent in completing the various measurements, which were performed with the most scrupulous accuracy. The whole is elaborately described by Boscovich in a quarto volume, full of illustration and minute details’, and with several opuscules, or detached essays, which display great ingenuity, conjoined with the finest geometric taste. We may instance, in particular, the discourse on the rectification of instruments, the elegant synthetical investigation of the figure of the earth, deduce^ both from the law of attraction, and from the actual measurement of degrees, and the nice remarks concerning the curve and the conditions of permanent stability. This last tract gave occasion, however, to some strictures from D'Alembert, to which Boscovich replied, in a note annexed to the French edition of his works. The arduous service which Boscovich had now performed was but poorly rewarded. From the pope he received only a hundred sequins, or about forty-five pounds sterling, a gold box, and” abundance of praise." He now resumed the charge of the mathematical school, and besides discharged faithfully the public duties of religion, which are enjoined by his order. A trifling circumstance will mark the warmth of his temper, and his love of precedence. He had recourse to the authority of cardinal Valenti, to obtain admission into the oratory of Caravita, from which his absence excluded him, and which yet afforded only the bent-fit of a free, but frugal supper. In presiding at that social repast, the philosopher relaxed from the severity of his studies, and shone by his varied, his lively, and fluent conversation.

, a celebrated French mathematician, was born at Croisic, in Lower Bretagne, the 10th of February

, a celebrated French mathematician, was born at Croisic, in Lower Bretagne, the 10th of February 1698. He was the son of John Bouguer, professor royal of hydrography, a tolerable good mathematician, and author of “A complete Treatise on Navigation.” Young Bouguer was accustomed to learn mathematics from his father, from the time he was able to speak, and thus became a very early proficient in those sciences. He was sent soon after to the Jesuits’ college at Vannes, where he had the honour to instruct his regent in the mathematics, at eleven years of age. Two years after this he had a public contest with a professor of mathematics, upon a proposition which the latter had advanced erroneously; and he triumphed over him; upon which the professor, unable to bear the disgrace, left the country. Two years after this, when young Bouguer had not yet finished his studies, he lost his father, whom he was appointed to succeed in his office of hydrographer, after a public examination of his qualifications, being then only fifteen years of age; an occupation which he discharged with great respect and dignity at that early age.

mother’s brother, a man of singular capacity and genius, and eminent as a divine, a physician, and a mathematician. In the two former capacities he went to the East-Indies in

It appears that thus early in life he had many friends; and it is probable that by some of them he might have risen to eminence in the church, had not his natural inclination led him to pursue other studies, in which he afterwards shone so conspicuously. He received his first rudiments of the mathematics from his uncle Dr. James Pound, who resided at his living of Wanstead in Essex, where our astronomer was some time curate: this gentleman was his mother’s brother, a man of singular capacity and genius, and eminent as a divine, a physician, and a mathematician. In the two former capacities he went to the East-Indies in the company’s service; and was one of those who had the good fortune to escape from the massacre of the factory, on the island of Pulo Condore, in Cochin China. An account of this shocking scene remains amongst Dr. Bradley’s papers, written by Dr. Pound, together with a journal kept by him on board the Rose sloop, until, after many difficulties* and distresses, they arrived at Batavia the 18th of April 1705. The public suffered much in this catastrophe, by the loss of Dr. Pound’s papers, and other valuable curiosities collected by him, which all perished in the conflagration; as he had no time to save any thing but his own life. With this relation, to whom he was dear even more than by the ties of blood, he spent all his vacations from other duties: it was whilst with him at Wanstead, that he first began the observations with the sector, which led to his future important discoveries.

polished them, while he was chancellor of the diocese of London. As Bradwardine was a very excellent mathematician, he endeavoured to treat theological subjects with a mathematical

, archbishop of Canterbury, is supposed to have been born at Hortfield, in Cheshire, about the middle of the reign of king Edward I. in the fourteenth century. He was of Merton colle'ge, Oxford, and was one of the proctors of that university in 1325. He excelled in mathematical knowledge, and was in general distinguished for his accurate and solid investigations in divinity, which procured him the title of the “profound Doctor.” He was confessor to Edward III. and attended that monarch in his French wars, often preaching before the army. Sir Henry Savile informs us that some writers of that time attributed the signal victories of Edward, rather to the virtues and holy character of his chaplain, than to> the bravery or prudence of the monarch or of any other person. He made it his business to calm and mitigate the fierceness of his master’s temper when he saw him eitherimmoderately fired with warlike rage, or improperly flushed with the advantages of victory. He also often addressed the army, and with so much meekness and persuasive discretion, as to restrain them from those insolent excesses which are too frequently the attendants of military success. When the see of Canterbury became vacant, the monks of that city chose him archbishop, but Edward, who was fond of his company, refused to part with him. Another vacancy happen ing soon after, the monks again elected him^ and Edward yielded to their desires. The modesty and innocence of his manners, and his unquestionable piety and integrity, seem to have been the principal causes of his advancement. He was, however, by no means adapted to 'a court, where his personal manners and character became an object of derision, the best proof history can afford us of their excellence. Even when he was consecrated at Avignon, cardinal Hugh, a nephew of the pope, ridiculed the prelate by introducing into the hall a person in a peasant’s habit, ridiog on an ass, petitioning the pope to make him archbishop of Canterbury, but the jest was so ill relished that the pope and cardinals resented the indignity, and frowned on the insolent contriver. Bradwardine was consecrated in 1349; but not many weeks after his consecration, and only seven days after his return into England, he died at Lambeth. His principal work “De Causa Dei,” against the Pelagian heresy, was edited from the ms. in Merton college library by sir Henry Savile, 1618, fol. with a biographical preface, in which he informs us that Bradwardine devoted his principal application to theology and mathematics; and that particularly in the latter he distanced, perhaps, the most skilful of his contemporaries. These mathematical works are, 1. “Astronomical tables,” in ms. in the possession of Sir Henry. 2. “Geometria Speculativa, cum Arithmetica specuiativa,” Paris, 1495, 1504, fol. The arithmetic had been prAited separately ia 1502, and other editions of both appeared in 1512 and 1530. 3. “De proportionibus,” Paris, 1495, Venice, 1505, fol. 4. “De quadratura circuli,” Paris, 1495, fol. Sir Henry Savile informs us that the treatise against Pelagius was first delivered in lectures at Oxford, and the author, at the request of the students of Merton college, arranged, enlarged, and polished them, while he was chancellor of the diocese of London. As Bradwardine was a very excellent mathematician, he endeavoured to treat theological subjects with a mathematical accuracy, and was the first divine, as far as I know, says sir Henry, who pursued that method. Hence this book against Pelagianism is one regular, connected series of reasoning, from principles or conclusions which have been demonstrated before; and if, in the several lemmas and propositions, a mathematical accuracy is not on all occasions completely preserved, the reader must remember to ascribe the defect to the nature of the subject, rather than to the author.

onsiderable number of letters of the landgrave William, his father, and of Christopher Rothmann, the mathematician of that prince, to Tycho, and of Tycho to them. 6. “The mechanical

Gassendus, in his “Equitis Dani Tychonis Brahe Astronomorum Coryphaei vita,” gives the following list of his principal writings: 1. “An account of the new star which appeared Nov. 12th, 1572, in Cassiopeia,” Copenhagen, 1573, 4to. 2. “An oration concerning the mathematical sciences, pronounced in the university of Copenhagen, in 1574,” published by Conrad Aslac, of Bergen, in Norway. 3. “A treatise on the comet of the year 1577, immediately after it disappeared.” Upon revising it nine years afterwards, he added a tenth chapter, printed at Uraniburgh, 1589. 4. “Another treatise on the new phenomena of the heavens;” in the first part of which he treats of the restitution, as he calls it, of the sun, and of the fixed stars; and in the second part, of a new star which had then made its appearance. 5. “A collection of' astronomical epistles,” Uraniburgh, 1596, 4to; Nuremberg, 1602, and Francfort, 1610. It was dedicated to Maurice, landgrave of Hesse, because it contains a considerable number of letters of the landgrave William, his father, and of Christopher Rothmann, the mathematician of that prince, to Tycho, and of Tycho to them. 6. “The mechanical principles of Astronomy restored,” Wandesburg, 1598, folio. 7. “An answer to the letter of a certain Scotchman concerning the comet in the year 1577.” 8. “On the composition of an elixir for the plague; addressed to the emperor Rodolphus.” 9. “An elegy upon his exile,” Rostock, 1614, 4to. 10. “The Rodolphine tables,” revised and published by Kepler, according to Tycho’s desire. 11. “An accurate enumeration of the fixed stars, addressed to the emperor Rodolphus.” 12. “A complete catalogue of 1000 of the fixed stars, which Kepler has inserted in the Rodolphine tables.” 13. “Historia caelestis or a history of the heavens, in two parts” the first containing the observations he had made at Uraniburgh, in 16 books; the latter containing the observations made at Wandesburg, Wittenberg, Prague, &c. in four books. 14. “An epistle to Caster Pucer,” printed at Copenhagen, 1668.

, an eminent mathematician of the seventeenth century, son of Thomas Brancker, some time

, an eminent mathematician of the seventeenth century, son of Thomas Brancker, some time bachelor of artsj,in Exeter college, Oxford, was born in Devonshire in 1636, and was admitted batler (and not butler, as some late biographical compilations blunderingly assert), of the said college, Nov. 8, 1652, in the seventeenth year of his age. In 1655, June 15, he took the degree of bachelor of arts, and was elected probationary fellow the 30th of the same month. In 1658, April 22, he took the degree of master of arts, and became a preacher; but after the restoration, refusing to conform to the ceremonies of the church of England, he quitted his fellowship in 1662, and retired to Chester: but not long after, he became reconciled to the service of the church, took orders from a bishop, and was made a minister of Whitegate. He had, however, for some time, enjoyed great opportunity and leisure for pursuing the bent of his genius in the mathematical sciences; and his skill both in the mathematics and chemistry procured him the favour of lord Brereton, who gave him the rectory of Tilston. He was afterward chosen master of the well-endowed school at Macclesfield, in that county, where he spent the remaining years of his life, which was terminated by a short illness in 1676, at 40 years of age; and he was interred in the church at Macclesfield.

, a learned mathematician and antiquary, was the son of Robert Brerewood, a reputable

, a learned mathematician and antiquary, was the son of Robert Brerewood, a reputable tradesman, who was three times mayor of Chester. Our author was born in that city in 1565, where he was educated in grammar learning at the free school; and was afterwards admitted, in 1581, of Brazen-nose college, Oxford, where he soon acquired the character of a hard student; as he has shewn by the commentaries he wrote upon Aristotle’s Ethics, when no more than twenty-one years of age. In 1596 he was chosen the first professor of astronomy in Gresham college, being one of the two who, at the desire of the electors, were recommended to them by the university of Oxford. He loved retirement, and wholly devoted himself to the pursuit of knowledge. And though he never published any thing himself, yet he was very communicative, and ready to impart what he knew to others, either in conversation or in writing. His retired situation at Gresham college being agreeable, it did not appear that he had any other views, but continued there the remainder of his life, which was terminated by a fever the 4th of November 1613, at forty-eight years of age, in the midst of his pursuits, and before he had taken proper care to collect and digest his learned labours; which, however, were not lost; being reduced to order, and published after his death, in the following order: 1. “De ponderibus et pretiis veterum nummorum, eorumque cum recentioribus collatione,1614, 4to. This was published by his nephew, Robert Brerewood of Chester, who was commoner of Brazen-nose college in 1605, aged seventeen; and who succeeded our author in his estate and fortunes. It was afterwards reprinted in the eighth volume of the Critici Sacri, and in the apparatus before the first volume of the polyglot bible. 2. “Enquiries touching the diversity of Languages and Religion, through the chief parts of the world,1614, 4to, published also by Robert Brerewood, who has written a large and learned preface to it. 3. “Elementa Logicae in gratiam studiosae juventutis in acad. Oxon.1614, 8vo. 4. “Tractatus quidam logici de praedicabilibus et proedicamentis,1628, 8vo. 5. “Treatise of the Sabbath,1630, 4to. “6.” A second treatise of the Sabbath,“1632, 4to. 7,” Tractatus duo, quorum primus est de meteoris, secundus de oculo,“1631. 8.” Commentarii in Ethica Aristotelis,“1640,. 4to. Mr. Wood tells us, that the original manuscript of this, written with his own hand, is in the smallest and neatest character that his eyes ever beheld; and that it was finished by him Oct. 27, 1586. 9.” The patriarchal government of the ancient Church," 1641, 4to.

, of Nimeguen, where he was born in 1494, and therefore sometimes called NoviOMAGUS, was an eminent mathematician of the sixteenth century, and rector of the school of Daventer,

, of Nimeguen, where he was born in 1494, and therefore sometimes called NoviOMAGUS, was an eminent mathematician of the sixteenth century, and rector of the school of Daventer, and afterwards professor of mathematics at Rostock. He died at Cologne in 1570. Saxius says that he was first of Rostock, then of Cologne, and lastly of Daventer, which appears to be probable from the dates of his writings. He wrote, 1. “Scholia in Dialecticam Georgii Trapezuntii,” Cologne and Leyden, 1537, 8vo. 2. “Arithmetica,” ibid, and Paris, 1539. 3. “De Astrolabii compositione,” Cologne, 1533, 8vo. 4. “Urbis Pictaviensis (Poitiers) tumultus, ej usque Restitutio,” an elegiac poem, Pictav. 1562, 4to. 5. “Ven. Bedae de sex mundi setatibus,” with scholia, and a continuation to the 26th of Charles V. Cologne, 1537. He also translated from the Greek, Ptolomy’s Geography.

At this time he also collected materials, and made the necessary observations (being a very good mathematician and astronomer) for a new map of Jamaica, which he published

At this time he also collected materials, and made the necessary observations (being a very good mathematician and astronomer) for a new map of Jamaica, which he published in London, in August 1755, engraved by Dr. Bayly, on two sheets, by which the doctor cleared four hundred guineas. Soon after this (March 1756) he published his “Civil and Natural History of Jamaica,” in folio, ornamented with forty-nine engravings of natural history, a whole sheet map of the island, and another of the harbour of Port-Royal, Kingston-town, &c. Of this work there were but two hundred and fifty copies printed by subscription, at the very low price of one guinea, but a few were sold at two pounds two shillings in sheets by the printer. Most unfortunately all the copper-plates, as well as the original drawings, were consumed by the great fire in Cornhill, November 7, 1765. This alone prevented in his life-time a second edition of that work, for which he made considerable preparations, by many additional plants, and a few corrections in his several voyages to these islands, for he was six different times in the West Indies; in one of those trips he lived above twelve months in the island of Antigua: however, these observations will we trust not be lost to the public, as he sent before his death to sir Joseph Banks, P. R. S. “A catalogue of the plants growing in the Sugar Islands, &c. classed and described according to the Linnaean system,” in 4to, containing about eighty pages. In Exshaw’s Gentleman’s and London Magazine for June 1774, he published “A catalogue of the birds of Ireland,” and in Exshaw’s August Magazine following, “A catalogue of its fish.” In 1788 he prepared for the press a very curious and useful catalogue of the plants of the north-west counties of Ireland, classed with great care and accuracy according to the Linnsean system, containing above seven hundred plants, mostly observed by himself, having trusted very few to the descriptions of others. This little tract, written in Latin with the English and Irish names, might be of considerable use in assisting to compile a “Flora Hibernica,” a work every botanist will allow to be much wanting.

of Mons. Des Cartes, he would undertake to shew how the world was made; a task too great, even for a mathematician.”

But, notwithstanding these encomiums on Burnet, it cannot be Affirmed that his Theory is built upon principles of mathematics and sound philosophy; on the contrary, men of science were displeased at him for presuming to erect a theory, which he would have received as true, with* out proceeding on that foundation. Flamstead is reported to have told him, somewhat peevishly, that “there went more to the making of a world, than a fine-turned period,” and that “he was able to overthrow the Theory in one sheet of paper.” Others attacked it in form. Mr. Erasmus Warren, rector of Worlington, in Suffolk, published two pieces against it soon after its appearance in English, and Dr. Burnet answered them; which pieces, with their answers, have been printed at the end of the later editions of the Theory. Mr. John Keill, Savilian professor of geometry in Oxford, published also an Examination of it in 1698, to which Dr. Burnet replied; and then Mr. Keill defended himself. Burnet’s reply to Keill is subjoined to the later editions of his Theory; and KeilPs Examination and Defence, together with his “Remarks and Defence upon Whiston’s Theory,” were reprinted together in 1734, 8vo. It is universally allowed that Keill has solidly confuted the Theory; and it is to be lamented that he did it in the rough way of controversy; yet there are many passages in his confutation, which shew, that he at the same time entertained the highest opinion of the Author. “I acknowledge him (says he) to be an ingenious writer; and if he had taken a right method, and had made a considerable progress in those sciences that are introductory to the study of nature, I doubt not but he would have made a very acute philosopher. It was his unhappiness to begin at first with the Cartesian philosophy; and not having a sufficient stock of geometrical and mechanical principles to examine it rightly, he too easily believed it, and thought that there was but little skill required 'in those sciences to become a philosopher; and therefore, in imitation of Mons. Des Cartes, he would undertake to shew how the world was made; a task too great, even for a mathematician.

e preached and wrote, and this involved him in a controversy, particularly with Edward Brerewood the mathematician. (See Brerewood.) The observation of the Sabbath was at this

, a puritan divine of considerable eminence in the beginning of the seventeenth century, was the son of Richard Byfield, minister of Stratford-uponAvon, and was born in Warwickshire about the year 1579. He became a servitor of Exeter college, Oxford, in Lent term 1596, and remained at the university upwards of four years, but left it without taking a degree. He was admitted, however, into holy orders, and was soon after invited to be pastor of St. Peter’s church, Chester, which he gladly accepted, and continued there for several years, “much followed and admired,” says Wood, “by the precise party, who esteemed his preaching profitable, and his life pious.” He was a strict observer of Sunday, on which subject he preached and wrote, and this involved him in a controversy, particularly with Edward Brerewood the mathematician. (See Brerewood.) The observation of the Sabbath was at this time a subject of much controversy, and many pamphlets were written on both sides, with the warmth natural at a period of increasing religious dissension. From Chester Mr. Byfield removed, in 1615, to the vicarage of Isleworth, where he died in 1622, leaving behind him an excellent character for learning, success in his ministry, and a pious and peaceable disposition. He was the author of many popular works, which are enumerated by Wood. Of these, his “Commentary on the First Epistle of St. Peter,” 1637, fol. and “on Colossians,” 1628, fol. are held in the highest estimation, and confirm the character which Wood, somewhat reluctantly, gives of him. Dr. Gouge, of Blackfriars, who drew up an account of his death, informs us that on his body being opened, a stone was taken out of his bladder that weighed thirty-three ounces; and was in length and breadth about thirteen inches, and solid, like a flint. A print of him was published by Richardson, in 1790, with an account of this very remarkable case. The noted Adonrram Byfield, a zealous adherent to the commonwealth revolution, was his son; and Richard Byfield, another ejected non-conformist, was his half brother; but neither had his meek, loyal, and submissive spirit. Adoniram is one of the few persons who have been, by name, stigmatized by Butler in his “Hudibras.” He was the father of Dr. Byfield, the noted Sal volatile doctor, who in his epitaph is said to be “Diu volatilis tandem Jfcms.

, a French mathematician, was born on the 25th of October 1744, at Versailles, where

, a French mathematician, was born on the 25th of October 1744, at Versailles, where he received a good education, and acquired an early taste for the mathematics. In 1768 he came to Paris, where he had an opportunity of being more thoroughly instructed. In 1774 he formed some distinguished pupils for the school of engineers, where the examinations were strict, and admission difficult to be obtained. In 1779 he gained the prize proposed by the society of arts at Geneva, for escapements. In 1783 he completed his edition of “Gardiner’s Tables of Logarithms,” which were exceedingly convenient, of great utility, and very correct; and which possessed advantages above all the others. In 1788 he was appointed professor of hydrography at Vann.es, afterwards at Dunkirk; and in 1792 he returned to Paris, and was for a few years professor des ingenieurs geographes at the depot of war. This place having been suppressed, he continued to teach in Paris, where he was always considered as one of the best mathematical masters lo whom pupils could apply. In 1795 he published the new stereotype edition of the “Tables of Logarithms,” considerably enlarged with logarithmic tables of the sines, according to the new decimal division of the circle. These are the first which ever appeared. Towards the end of 3797 he presented to the National Institute the plan of a new telegraph and a telegraphic language, accompanied with a dictionary of 12,000 French words adapted to it by A combination worthy of so able a mathematician. These labours had injured his health, and he had been a long time asthmatic, but, notwithstanding his condition, he published that year an excellent memoir on finding the longitude at sea, under the modest title of “A Supplement to the Trigonometry and Navigation of Bezout.” He died on the 14th of November, 1798, leaving behind him a daughter, born at Vannes in 1793. According to a tradition in the family, he was descended from Descartes.

, a celebrated French mathematician, examiner of the royal schools of Artillery and engineers, secretary

, a celebrated French mathematician, examiner of the royal schools of Artillery and engineers, secretary and professor of the royal academy of architecture, honorary member of that of the marine, and fellow of the royal society of London, was, born at Cressy en Brie, Aqgust 25, 1699. His early ingenuity in mechanics and his own intreaties induced his. parents to send him to study at a college in Paris, at ten, years of age; where in the space of two years his progress was so great, that he was able to give lessons in mathematics, and thus to defray his own expences at the college without any farther charge to his parents. By the assist^ ance of the celebrated Varignon, young Camus soon ran through the course of the higher mathematics, and acquired a name among the learned. He made himself more particularly known to the academy of sciences in 1727 by his me* moir upon the subject of the prize which they had proposed for that year, viz. “To determine the most advantageous way of masting ships;” in consequence of which he was named that year adjoint mechanician to the academy; and in 1730 he was appointed professor of architecture. In less than three years after, he was honoured with the secretaryship of the same; and the 18th of April 1733, he obtained the degree of associate in the academy, where he distinguished himself by his memoirs upon living forces, or bodies in motion acted upon by forces, on the figure of the teeth of wheels and pinions, on pump work, and severa^ other ingenious memoirs.

31, 1713; and was placed, when young, under the care of a Mr. Davis, of the same place, a very able mathematician, with whom, before he attained the age of nine years, he had

, an ingenious natural philosopher, was born at Stroud, in Gloucestershire, July 31, 1713; and was placed, when young, under the care of a Mr. Davis, of the same place, a very able mathematician, with whom, before he attained the age of nine years, he had gone through both vulgar and decimal arithmetic. He then proceeded to the mathematics, and particularly to algebra and astronomy, wherein he made a considerable progress, when his father took him from school, and put him to learn his own business, that of a broad-cloth weaver, but this circumstance did not damp his zeal for the acquisition of knowledge. All his leisure time was devoted to the assiduous^cultivation of astronomical science; and, by the help of the Caroline tables, annexed to Wing’s astronomy, he computed eclipses of the moon and other phsenomena. His acquaintance with that science he applied, likewise, to the constructing of several kinds of dials. But the studies of our young philosopher being frequently pursued to very late hours, his father, fearing that they would injure his health, forbade him the use of a cmidle in his chamber, any longer than for the purpose of going to bed, and would himself often see that his injunction was obeye<l. The son’s thirst of knowledge was, however, so great, that it made him attempt to evade the prohibition, and to find means of secreting his light till the family had retired to rest; when he rose to prosecute undisturbed his favourite pursuits. It was during this prohibition, and at these hours, that he computed, and cut upon stone, with no better an instrument than a common knife, the lines of a large upright sun-dial; on which, besides the hour of the day, were shewn the rising of the sun, -his place in the ecliptic, and some other particulars. When this was finished, and made known to his father, he permitted it to be placed against the front of his house, where it excited the admiration of several gentlemen in the neighbourhood, and introduced young Mr. Canton to their acquaintance, which was followed by the offer of the use of their libraries. In the library of one of these gentlemen, he found Martin’s Philosophical Grammar, which was the first bodk that gave him a taste for natural philosophy. In the possession of another gentleman, a few miles from Stroud, he first saw a pair of globes; an object that afforded him uncommon pleasure, from the great ease with which he could solve those problems he had hitherto been accustomed to compute. The dial was beautified a few years ago, at the expence of the gentlemen at Stroud; several of whom had been his school-fellows, and who continued still to regard it as a very distinguished performance. Among other persons with whom he became acquainted in early life, was the late reverend and ingenious Dr. Henry Miles of Tooting, a learned member of the royal society, and of approved eminence in natural knowledge. This gentleman, perceiving that Mr. Canton possessed abilities too promising to be confined within ^the narrow limits of a country town, prevailed on his father to permit him to come to London. Accordingly he arrived at the metropolis March 4, 1737, and resided with Dr. Miles, at Tooting (who, it may here be noticed, bequeathed to him all his philosophical instruments), till the 6th of May following; when he articled himself, for the term of five years, as a clerk to Mr. Samuel Watkins, master of the academy in Spitalsquare. In this situation, his ingenuity, diligence, and good conduct were so conspicuous, that, on the expiration of his clerkship, in the month of May 1742, he was taken into partnership with Mr. Watkins for three years; which gentleman he afterwards succeeded in Spital-square, and there continued during his whole life. On December 25, 1744, he married Penelope, the eldest daughter of Mr. Thomas Colbrooke, and niece to James Colbrooke, esq. banker in London.

, an Italian physician, mathematician, and philosopher, was born at Pa via, Sept. 24, 1501. It appears

, an Italian physician, mathematician, and philosopher, was born at Pa via, Sept. 24, 1501. It appears that his father and mother were not married, and the latter, a woman of violent passions, endeavoured to destroy him by procuring abortion. He was, however, safely born, and his father who was a lawyer by profession, at Milan, and a man well skilled in what were then called secret arts, instructed him very early in the mysteries of numbers, and the precepts of astrology, He taught him also the elements of geometry, and was desirous to have engaged him in the study of jurisprudence. But his own inclination being rather to medicine and mathematics, at the age of twenty he went to the university of Pavia, where, two years after, he explained Euclid. He then went to Padua, and, in 1524, was admitted to the degree of master of arts, and in the following year to that of doctor in medicine. In 1529, he returned to Milan, where although he obtained little fame as a physician, he was appointed professor of mathematics, for which he was better qualified; and in 1539, he became one of the medical college in Milan. Here he attempted to reform the medical practice by publishing his two first works, “De malo recentiorurn medicorum medendi usu,” Venice, 1536; and “Contradicentium Medicorum libri duo,” Lyons, 1548; but he was too supercilious and peevish to profit by the kindness of his friends, who made repeated efforts to obtain an advantageous establishment for him; and he had, in 1531, formed a matrimonial connection of which he bitterly complained as the cause of all his subsequent misfortunes.

, was elected fellow of Exeter college, to which he removed, and became distinguished as a logician, mathematician, and philosopher.- He took his degree of B. A. in 1610, of M.

, an English clergyman o great learning and parts, was born in the parsonage-house of North- Lew (not Northlegh, as Wood says), near Hatherlegh, in Devonshire, Feb. 7, 1588. His father, John Carpenter, a native of Cornwall, was at that time rector of this place, and author of some sermons enumerated by Wood. His son, after a private education, was entered of Edmund hall, Oxford; and in 1607, by the casting vote of the vice-chancellor, was elected fellow of Exeter college, to which he removed, and became distinguished as a logician, mathematician, and philosopher.- He took his degree of B. A. in 1610, of M. A. in 1613, and of B. D. in 1620, and soon after completing his master’s degree, entered into holy orders, and had the reputation of a very popular divine. About 1626 he became acquainted with

niverse, as he pretended, did not appear to be so to the abbe Saint Pierre. Though the friend of the mathematician, he attacked him, and Castel answered. The papers on both sides

, a geometrician and philosopher, born at Montpellier in 1688, entered himself of the Jesuits in 1703, and was noticed by Fontenelle and by Tournemine for the specimens he gave of his early proficiency, and as he was then in the country, they invited him to the capital, where he arrived towards the end of 1720, and supported the character which his first essays promised. The first work he published was his treatise of “Universal Gravity,1724, 2 vols. 12mo. All depended, according to him, on two principles, the gravity of bodies, and the action of minds; the former giving them a continual tendency to rest, the other renewing their motion. This doctrine, the key to the system of the universe, as he pretended, did not appear to be so to the abbe Saint Pierre. Though the friend of the mathematician, he attacked him, and Castel answered. The papers on both sides shewed much reflection, though in a singular channel. The second work of Castel was his plan of an “Abridged system of Mathematics,” Paris, 1727, 4to, which was soon followed by an “Universal system of Mathematics,1728, 4to, a work applauded both in England and France. The royal so'ciety of London admitted him of their body.

, an Italian mathematician, the particular friend of Galileo, was born of an ancient and

, an Italian mathematician, the particular friend of Galileo, was born of an ancient and noble family at Brescia, in the year 1577. In 1595, he entered into a monastery of the order of St. Benedict in his native city, but afterwards studied at Padua and at Florence, where he became a disciple of Galileo, and assisted him in his astronomical observations, and afterwards maintained a regular correspondence with him. Galileo, not only had the highest esteem for his talents, but reposed the utmost confidence in his friendship. Under his name the apology of Galileo against the censures of Ludovico delle Colombe and Vincent di Grazia appeared, though it was principally written by Galileo himself. From 1615 to 1625, he occupied the mathematical chair at Pisa. In 1625, Castelli was invited to Rome by pope Urban VIII. and made mathematical professor in the college della Sapienza. The subject of his particular attention, and in the investigation of which he chiefly excelled, was the motion of water, on which subject as connected with the health of the cities of Venice, &c. he was frequently consulted, and suggested many important improvements. In 1628, he published on the mensuration of running waters, “Delia misura dell' acque correnti,” Rome, 4to, and “Dimostrazioni geometriche clella misura dell acque correnti,” ibid. 4to. These have been inserted in the collection of the author’s works on similar topics, printed at Florence, with other treatises, on the laguna of Venice, on the improvement of the Pontine, Bolognese, Ferrarese, and Romagnese marshes, &c. in 1766. Guglielrnini, though in other things he impugns Castelli, allows him the honour of having first applied geometry to the motion of water; and Montucla calls him “The Creator of a new part of Hydraulics.” His defence of Galileo, “Riposta alle opposizioni del Sig. Ludovico delle Colombe, &c.” was published at Florence, 1615, 4 to. He deeply lamented the death of this great man, and it is supposed to have hastened his own in 1644. Duke Leopold ordered his bust to be placed beside that of Galileo.

, an eminent Italian mathematician, was born at Milan in 1593, and entered at an early age into

, an eminent Italian mathematician, was born at Milan in 1593, and entered at an early age into the order of Jesuates or Hieronymites. In the course of his studies he manifested such talents, that his superiors, after he had taken orders, thought proper to send him to the university of Pisa, a circumstance to which, though at first against his will, he owed the celebrity which he afterwards acquired. Here, with the advice of Benedict Castelli, the disciple and friend of Galileo, he applied to the study of geometry, in order to relieve the pains of the gout to which he was subject; and in this science he made such progress, and acquired such an accurate acquaintance with the ancient geometers, that Castelli and Galileo concurred in predicting the eminence at which he afterwards arrived. Soon after this period he invented his method of indivisibles. In 1629 he communicated to some ingenious persons and to the magistrates of Bologna, his treatise of indivisibles, and another on the conic sections; and obtained the honour of succeeding Maginus as professor in the university, in 1629. His celebrated work on indivisibles, entitled, “Geometria Indivisibilibus continuorum nova quadam ratione prornota,” and published at Bologna in 1635, 4to? and again in 1653, is a curious original work, in which the author conceives the geometrical figures as resolved into their very small elements, or as made up of an infinite number of infinitely small parts, and on account of which he passes in Italy for the inventor of the infinitesimal calculus. He also published a treatise of conic sections, under the title of “La Spechio Ustorio overo Trattato delle Settioni Coniche,” or “De Speculo Ustorio, &c.” Bologn. 1632, 4to; a system of trigonometry under the title of “Directorium generale Uranometricum,1632, 4to, including an account of logarithms, together with tables of the logarithms of common numbers and trigonometrical tables of natural sines, and logarithmic sines, tangents, fluents, and versed sines; of which a new and enlarged edition was published at Bologna in 1643, 4to, entitled “Trigonometria Plana. ac Sphaerica, Linearis ac Logarithmica, &c.” a “Compendium Regularum de Triangulis; and a” Centuria Problematum Astronomicorum.“He was also the author of a treatise of astrology, entitled” Rota Planetaria,“and published under the appellation of Sylvius Philomantius; and this publication was the more surprising, as he was an enemy of judicial astrology. The last of his works was entitled” Fxercitationes Geometricae sex," Bonon. 1647, 4to, and contains exercises on the method of indivisibles; answers to the objections ofGuldinus; the use of indivisibles in cossic powers, or algebra, and in considerations about gravity: with a miscellaneous collection of problems. Towards the close of this year, 1647, he died a martyr to the gout, which had deprived him of the use of his fingers.

eight years of age when he was styled a philosopher, and Chappe at that age might have been called a mathematician. An irresistible impulse, and singular disposition, as if innate,

, an eminent French astronomer, was born at Mauriac, a town in Upper Auvergne, on the 23d of May, 1728, of John Chappe, lord of the barony of Auteroche, and Magdalen de la Farge, daughter of Peter de la Farge, lord of larPierre. From his birth he enjoyed the valuable advantage of not being under the necessity of struggling, like many men of genius, with adversity and penury. The distinguished rank which his parents held in their province, added to their wealth and opulence, enabled them to bestow upon their son an excellent education, the foundation of which was laid at Mauriac, where he began his studies. Having made considerable progress here, he went afterwards to finish them at the college de Louis le Grand. M. Chappe, from his earliest infancy, shewed a surprising turn for drawing and the mathematics. Descartes was scarcely eight years of age when he was styled a philosopher, and Chappe at that age might have been called a mathematician. An irresistible impulse, and singular disposition, as if innate, led him to draw plans and make calculations; but these pursuits, quite forojgn to the studies in which he was then engaged, occupied no part of that time which was allotted for them. He applied to the former only at those moments which the regulations. of the college suffered him to call his own.

, a peer of France, but more remarkable as an astronomer and mathematician, -was born at Paris Dec. 30, 1714. He soon discovered a singular

, a peer of France, but more remarkable as an astronomer and mathematician, -was born at Paris Dec. 30, 1714. He soon discovered a singular taste and genius for the sciences; and in the tumults of armies and camps, he cultivated mathematics, astronomy, mechanics, &c. He was named honorary academician the 27th of February 1743, and few members were more punctual in attending the meetings of that body, where he often brought different constructions and corrections of instruments of astronomy, of dioptrics, and achromatic telescopes. These researches were followed with a new parallactic machine, more solid and convenient than those that were in use; as also with many reflections on the manner of applying the micrometer to those telescopes, and of measuring exactly the value of the parts of that instrument. The duke of Chaulnes proposed many other works of the same kind, which were interrupted by his death Sept. 23, 1769.

to the prince. He now devoted himself wholly to the study of divinity, though he was a considerable mathematician, and skilled particularly in astronomy. After he had continued

, an eminent Lutheran divine, and one of the reformers in Germany, was born at Britzen, a town in the marquisate of Brandenburg, in 1522. His father was a poor wool-comber, who found it difficult to give him much education, but his son’s industry supplied the want in a great measure. After having learned the rudiments of literature in a school near home, he went to Magdeburg, where he made some progress in arts and languages. Then he removed to Francfort upon the Oder, to cultivate philosophy under his relation George Sabinus; and to Wittenburg, where he studied under Philip Melancthon. Afterwards he became a school-master in Prussia; and, in 1552, was made librarian to the prince. He now devoted himself wholly to the study of divinity, though he was a considerable mathematician, and skilled particularly in astronomy. After he had continued in the court of Prussia three years, he returned to the university of Wittemberg, and lived in friendship with Melancthon, who employed him in reading the com-mon-places. From thence he removed to Brunswick, where he spent the last thirty years of his life as pastor, and commenced D. D. at Rostock. He died April 8, 1586. His principal works are, 1. “Harmonia Evangeliorum,” Francfort, 1583 and 1622, Geneva, 1623, 4to. 2. “Examen Concilii Tridentini.” 3. “A treatise against the Jesuits,” wherein he explained to the Germans the doctrines and policy of those crafty devisers, &c. His “Examination of the Council of Trent” has always been reckoned a very masterly performance, and was translated and published in English, 1582, 4to.

, an excellent Greek and Latin scholar and mathematician, was born in 1610 at Slow in the Wold, in Gloucestershire, and

, an excellent Greek and Latin scholar and mathematician, was born in 1610 at Slow in the Wold, in Gloucestershire, and became one of the clerks of Magdalen college, Oxford; and in 1632, one of the petty canons or chaplains of Christ church. Being ejected from this by the parliamentary visitors in 1648, he came to London in great necessity, and took lodgings in the house of Thomas Est, a musician and music printer, in Aldersgate street. There being a large room in this house, Chilmead made use of it for a weekly music meeting, from the profits of which he derived a slender subsistence, and probably improved it by being employed as translator. He died in 1653, having for some years received relief from Edward Bysshe, esq. garter king at arms, and sir Henry Hoibrook, the translator of Procopius. He was interred in the church of St. Botolph without Aldersgate. Among his works, our musical historians notice his tract “De musica antiqua Graeca,” printed in 1672, at the end of the Oxford edition of Aratus: he also wrote annotations on three odes of Dionysius, in the same volume, with the ancient Greek musical characters, which Chilmead rendered in the notes of Guide’s scale. His other works are, 1 “Versio Latina et Annotationes in Joan. Malalae Chronographiam,” Oxf. 1691, 8vo. 2. A translation, from the French of Ferrand, of “A Treatise on Love, or Erotic Melancholy,1640, 8vo. 3. Gaffarel’s “Unheard-of Curiosities.” 4. Campanella’s “Discourse touching the Spanish monarchy,” which not selling, Prynne prefixed an epistle and a new title, “Thomas Campanella’s advice to the king of Spain, for obtaining the universal monarchy of the world,” Lond. 1659, 4to. 5. Hues’ “Treatise of the Globes,” ibid. 1639 and 1659; and 6. Modena’s “History of the Rites, Customs, &c. of the Jews,” ibid. 1650. He also compiled the “Catalogus Mss. Grsecorum in Bibl. Bodl.” 1636, a manuscript for the use of the Bodleian, and the most complete of its time.

, a celebrated French mathematician and academician, was born at Paris, May 13, 1713, and died May

, a celebrated French mathematician and academician, was born at Paris, May 13, 1713, and died May 17, 1765. His father, a teacher of the mathematics at Paris, who was his sole instructor, taught him even the letters of the alphabet on the figures of Euclid’s Elements, by which he was able to read and write at four years of age, and by a similar stratagem calculations were rendered familiar to him. At nine years of age he put into his hands Guisnee’s “Application of Algebra to Geometry” at ten he studied l'Hopital’s “Conic Sections;” and between twelve and thirteen, he read a memoir to the academy of sciences, concerning four new geometrical curves of his own invention. About the same time he laid the first foundation of his work upon curves that have a double curvature, which he finished in 1729, at sixteen years of age. He was named adjoint-mechanician to the academy in 1731, at the age of eighteen, associate in 1733, and pensioner in 1738. During his connection with the academy, he sent a great multitude of learned and ingenious communications to their Memoirs, from 1727, almost every year, to 1762, and wrote several other works, which he published separately, as, 1. “On Curves of a Double Curvature,” in 1730, 4to. 2. “Elements of Geometry,1741, 8vo. 3. “Theory of the Figure of the Earth,1743, 8vo. 4. “Elements of Algebra,1746, 8vo. 5. “Tables of the Moon,1754, 8vo.

, a German Jesuit, was born at Bamberg, in Germany, in 1537. He became a very studious mathematician, and elaborate writer, his works making five large folio volumes;

, a German Jesuit, was born at Bamberg, in Germany, in 1537. He became a very studious mathematician, and elaborate writer, his works making five large folio volumes; and containing a complete body or course of the mathematics. They are mostly elementary, and commentaries on Euclid and others; having very little of invention of his own. His talents and writings have been variously spoken of, and it must be acknowledged that he exhibits more of industry than genius. He was sent for to Rome, to assist, with other learned men, in the reformation of the calendar, by pope Gregory; which he afterwards undertook a defence of, against Scaliger, Vieta, and others, who attacked it. He died at Rome, the 6th of February, 1612, after more than fifty years close application to the mathematical sciences.

, an eminent accomptant and mathematician, was the son of a nonconformist divine, and horn at Wood Eaton

, an eminent accomptant and mathematician, was the son of a nonconformist divine, and horn at Wood Eaton near Oxford in March 1624. At sixteen years of age he was put apprentice to a bookseller in Oxford; but soon left that trade, and was employed as clerk under Mr. John Mar, one of the clerks of the kitchen to prince Charles, afterwards Charles II. This Mar was eminent for his mathematical knowledge, and constructed those excellent dials with which the gardens of Charles I. were adorned: and under him Collins made no small progress in the mathematics. The intestine troubles increasing, he left that employment and went to sea, where he spent the greatest part of seven years in an English merchantman, which became a man of war in the Venetian service against the Turks. Here having leisure, he applied himself to merchants accompts, and some parts of the mathematics, for which he had a natural turn; and on coming home, he took to the profession of an accomptant, and composed several useful treatises upon practical subjects. In 1652 he published a work in folio, entitled “An Introduction to Merchants’ Accompts,” which was reprinted in 1665, “with an additional part, entitled” Supplements to accomptantship and arithmetic.“A part of this work, relating to interest, was reprinted in 1685, in a small 8vo volume In 1658 he published in 4to, a treatise called” The Sector on a Quadrant; containing the description and use of four several quadrants, each accommodated for the making of sun-dials, &c. with an appendix concerning reflected dialling, from a glass placed at any inclination.“In 1659, 4to, he published his” Geometrical dialling;“and also the same year, his” Mariner’s plain Scale new plained.“In the Philosophical Transactions of the Royal Society, of which he was now become a member, he fully explained and demonstrated the- rule given by the Jesuit De Billy, for” finding the number of the Julian period for any year assigned, the cycles of the sun and moon, with the Roman indiction for the years being given.“To this he has added some very neatly-contrived rules for the ready finding on what day of the week any day of the month falls for ever; and other useful and necessary kalendar rules. In the same Transactions he has a curious dissertation concerning the resolution of equations in numbers. In No. 69 for March 1671, he has given a most elegant construction of that chorographical problem, namely:” The distances of three objects in the same plane, and the angles made at a fourth place in that plane, by observing each object, being given; to find the distances of those objects from the place of observation?“In 1680 he published a small treatise in 4to, entitled” A Plea for the bringing in of Irish cattle, and keeping out the fish caught by foreigners; together with an address to the members of parliament of the counties of Cornwall and Devon, about the advancement of tin, fishery, and divers manufactures.“In 1682 he published in 4to,” A discourse of Salt and Fishery;“and in the Philosophical Transactions, No. 159, for May 1684, is published a letter of his to Dr. JohnWallis, oh some defects in algebra. Besides these productions of his own, he was the chief promoter of many other valuable publications in his time. It is to him that the world is indebted for the publication of Barrow’s” Optical and geometrical lectures;“his abridgment of” Archimedes’s works,“and of” Apollonius’s Conies“Branker’s translation of” Rhonius’s Algebra, with Pell’s additions“” Kersey’s Algebra“Wallis’s History of Algebra” “Strode of Combinations” and many other excellent works, which were procured by his unwearied solicitations.

, a celebrated mathematician and linguist, who was born at Urbino in Italy, in 1509, and

, a celebrated mathematician and linguist, who was born at Urbino in Italy, in 1509, and died in 1575, was famous for his learning and knowledge in- the sciences. To a great depth and just taste in the mathematics, he joined a critical skill in the Greek language; a happy conjunction which made him very well qualified for translating and expounding the writings of the Greek mathematicians. And, accordingly, with a most laudable zeal and industry, he translated and published several of their works for the first time. On which account, Francis Moria, duke of Urbino, who was very conversant in those sciences, proved a very affectionate patron to him. He is greatly applauded by Bianchini, and other writers and he justly deserved their encomiums. Of his own works Commandine published the following: 1. “Commentarius in Planisphserium Ptolomosi,1558, 4to. 2. “De Centre Gravitatis Solidorum,” Bonon. 1565, 4to. 3. “Horologiorum Descriptio,” Rom. 1562, 4to. He translated and illustrated with notes the following works, most of them beautifully printed, in 4to, by the celebrated printer Aldus: 1. “Archimedis Circuli Dimensio de Lineis Spiralibus Quadratura Parabolae de Conoidibus et Sphseroidibus de Arenas Numero,1558. 2. “Ptolomaei Planisphaerium et Planisphaerium Jordani,1558. 3. “Ptolomuei Analemma,1562. 4. “Archimedis de iis qua? vehuntur in aqua,1565. 5. “Apollonii Perggei Conicorum libri quatuor, una cum Pappi Alexandrini Lemmatibns, et Commentariis Eutocii AscalonitaV' &c. 1566. 6.” Machometes Bagdadinus de Superficierum Divisionibus,“1570. 7.” Elementa Euclidis,“1572. 8.” Aristarchus de magnitudinibus et distantiis Solis et Luna:,“1572. 9.” Heronis Alexandrini Spiritualium liber,“1583. 10.” Pappi Alexandrini Collectiones Mathematics.'," 1588.

, a Jesuit of Bourdeaux, was sent to China, as a missionary and mathematician in 1685, and published a book in considerable reputation before

, a Jesuit of Bourdeaux, was sent to China, as a missionary and mathematician in 1685, and published a book in considerable reputation before that of Du Halde appeared, entitled “Memoires sur la Chine/* 2 vols. 12mo, to which was added a history of the emperor’s edict in favour of Christianity. His” Memoirs" were censured by the faculty of divinity at Paris, because of his uncommon prejudices in favour of the Chinese, whom he equalled to the Jews, and maintained that they had worshipped the true God during two thousand years, and sacrificed to him in the most ample temple of the universe, while the rest of mankind were in a state of corruption. The parliament for the same reason ordered the work to be burnt, by a decree passed in 1762. Le Comte died in 1729.

, an eminent French philosopher and mathematician, was born at Ribemont in Pirardy, three leagues from Saint-Quintin

, an eminent French philosopher and mathematician, was born at Ribemont in Pirardy, three leagues from Saint-Quintin and De la Fere, September 17, 1743, of a very ancient family. At the age of fifteen he was sent to study philosophy at the college of Navarre, under Giraud de Keroudon, who has since distinguished himself by several scientific works, and was an able teacher of mathematics. During the first year of his residence there, young Condorcet exhibited but little relish for the metaphysical questions relative to the nature of ideas, of sensations, and of memory, but in the course of the following year, mathematics and natural philosophy decided his future vocation; and although he had more than one hundred and twenty fellow-students, he acquired a greater portion of fame than any of them. At Easter he supported a public thesis, at which Clairaut, D'Alembert, and Fontaine, the first geometricians of France, assisted; and his conduct on this occasion obtained their approbation. After his course of philosophy was finished, he returned to his family, but still continued to cultjrate geometry; and his attachment to it carried him back to Paris in 1762, where he lived with his old professor, in order to have more frequent opportunities of indulging his ruling passion. He at the same time attended the chemical lectures of Macquer and Beaume, and soon distinguished himself among the geometricians.

ed Condorcet another opportunity of displaying his own talents by appreciating those of the departed mathematician. The lives of Turgot and Voltaire, and the eulogy pronounced

He was received into the French academy on the 8th of March, 1769, and in the course of the same year he published a memoir on the nature of infinite series, on the extent of solutions afforded by this mode, and on a new method of approximation for the differential equations of all the orders. In the volumes of 1770, and the following years, he presented the fruits of his researches on the equations with partial and finite differences; and in 1772 he published “L‘Essai d’une methode pour distinguer les Equations differentielles possibles en termes finis de celies qui ne le sont pas,” an essay on a method to distinguish possible differential equations in finite terms, from those which are not so. The mode of calculation here presented, although an admirable instrument, is still very far distant from that degree of perfection to which it may be brought. In the midst of these studies, he published an anonymous pamphlet, entitled “A Letter to a Theologian,” in which he replied with keen satire to the attacks madfc by the author of “The Three Centuries of Literature,” against the philosophic sect. “But (subjoins the prudent La Lande) he pushed the matter somewhat too far, for, even, supposing his system demonstrated, it would be advantageous to confine those truths within the circle of the iniliated, because they are dangerous, in respect to the greater part of mankind, who are unable to replace, by means of principles, that which they are bereaved of in the shape of fear, consolation, and hope.” Condorcet was now in fact leagued with the atheists; and La Lande, who wished well to the same sect, here censures not his principles, but only regrets his rashness. In 1773 he was appointed secretary to the academy of sciences, when he composed eulogies upon several deceased members who had been neglected by Fontenelle; and in 1782 he was received into the French academy, on which occasion he delivered a discourse concerning the influence of philosophy. In the following year he succeeded D'Alembert as secretary to that academy, and pronounced an able eulogy to the memory of his deceased friend, whose literary and scientific merits are set forth with great ability. The death of Euler afforded Condorcet another opportunity of displaying his own talents by appreciating those of the departed mathematician. The lives of Turgot and Voltaire, and the eulogy pronounced upon the death of the celebrated Franklin, were decided testimonies to the abilities of Condorcet as a biographical writer. Turgot had occupied much of his time and attention with moral and political sciences, and was particularly anxious that the certainty of which different species of knowledge are susceptible, might be demonstrated by the assistance of calculation, hoping that the human species would necessarily make a progress towards happiness and perfection, in the same manner as it had done towards the attainment of truth. To second these views of Turgot, Condorcet undertook a work replete with geometrical knowledge. He examined the probability of an assembly’s rendering a true decision, and he explained the limits to which our knowledge of future events, regulated by the laws of nature, considered as the most certain and uniform, might extend. If we do not possess a real, yet he thought, we ha\ 7 e at least a mean probability, that the law indicated by events, is the same constant law, and that it will be perpetually observed. He considered a forty-five thousandth part as the value of the risk, in the case when the consideration of a new law comes in question and it appears from his calculation, that an assembly consisting of 6 1 votes, in which it is required that there should be a plurality of nine, will fulfil this condition, provided there is a probability of each vote being equal to four-fifths, that is, that each member voting shall be deceived only once in five times. He applied these calculations to the creation of tribunals, to the forms of elections, and to the decisions of numerous assemblies; inconveniences attendant on which were exhibited by him. This work, says his eulogist, furnished a grand, and at the same time, an agreeable proof of the utility of analysis in important matters to which it had never before been applied, and to which we may venture to assert it never will be applied while human reason is allowed any share in human transactions. There are many of these paradoxes in geometry, which, we are told, it is impossible to resolve without being possessed of metaphysical attainments, and a degree of sagacity not always possessed by the greatest geometricians; but where such attainments and sagacity are to be found, even Condorcet himself has not exemplified. In his “Euler’s Letters,” published in 1787-89, he started the idea of a dictionary, in which objects are to be discovered by their qualities or properties, instead of being searched for under their respective names; he also intimated a scheme for constructing tables by which ten milHards of objects might be classed together, by means of only ten different modifications.

, was a mathematician and philosopher of Samos, who flourished about the 130th olympiad,

, was a mathematician and philosopher of Samos, who flourished about the 130th olympiad, being a contemporary and friend of Archimedes, to whom Conon communicated his writings, and sent him some problems, which Archimedes received with approbation, saying they ought to be published while Conon was living, for he comprehended them with ease, and could give a proper demonstration of them. At another time he laments the loss of Conon, thus admiring his genius: “How many theorems in geometry,” says he, “which at first seemed impossible, would in time have been brought to perfection! Alas 1 Conon, though he invented many, with which he enriched geometry, had not time to perfect them, but left many in the dark, being prevented by death.'' He had an uncommon skill in mathematics, joined to an extraordinary patience and application. This is farther confirmed by a letter sent to Archimedes by a friend of Conon’s.” Having heard of Conon’s death, with whose friendship I was honoured, and with whom you kept an intimate correspondence; as he was thoroughly versed in geometry, I greatly lament the loss of a sincere friend, and a person of surprising knowledge in mathematics. I then determined to send to you, as I had before done to him, a theorem in geometry, hitherto observed by no one."

aints the scenes that fall under his eye, in glowing and various colours. He has less perhaps of the mathematician and navigator in his composition than captain Cook, and more

We cannot close this article without giving a short sketch of the characters of the different writers by whom the last voyage was given to the world. Among these we ought to reckon the rev. Dr. Douglas, the editor, who, in a grave and dignified style, suitable to the sublimity of a journey or voyage round the globe, has arranged the matter; chastised, no doubt, in some instances, the language of our circumnavigators; and pointed out to the curious and philosophic eye, the benefits that have resulted, and may yet result, from the late discoveries in the great Pacific ocean; and the attempt, though unsuccessful, to explore a northern passage from thence into the Atlantic. Although this gentleman has levelled down the more striking peculiarities of the different writers of these voyages into some appearance of equality, yet a critic can discern in each his proper features. Captain Cook, accurate, minute, and severe, surveys every object with a mathematical eye, ever intent to fix or to discover some truth in astronomy, geography, and navigation. His observations on men and manners, -.and the produce of countries, are not very subtle or refined, but always sensible and judicious. He speculates in order to establish facts, but does not inquire into facts for the airy purposes of speculation. Captain King has perhaps a greater versatility of genius than captain Cook, as well as a more lively fancy, and a greater variety and extent of knowledge. Agreeably to this character of him, he paints the scenes that fall under his eye, in glowing and various colours. He has less perhaps of the mathematician and navigator in his composition than captain Cook, and more of the author. He himself seems conscious that this is his forte, and wields the pen with alacrity, with ease and satisfaction. The gleanings that were left to his industry by captain Cook, he seems too eager to pick up, to dwell upon, and to amplify. Mr. Anderson is superior to both these writers in variety of knowledge, and subtlety and sublimity of genius. He is versant in languages ancient and modern, in mathematics, in natural history, in natural philosophy, in civil history, in the metaphysics of both morality and theology; yet, as a counterbalance to these brilliant qualities and endowments, he launches forth too much into theory, and is, in some instances, too little constrained by the limits of fact and nature in his speculations. He has found the doctrines of the immortality and the immateriality of the soul among nations, who, in all probability, have not terms to express these, and very few to signify abstracted ideas of any kind. A quick imagination and a subtle intellect can see any thing in any subject, and extend the ideas most familiar to themselves over the boundless variety of the universe.

, a monk of the Ecoles-Pies, and a mathematician and antiquary, was born at Fanano in 1702, and died in 1765,

, a monk of the Ecoles-Pies, and a mathematician and antiquary, was born at Fanano in 1702, and died in 1765, at Pisa, where the grand duke had given him a chair in philosophy. This science occupied his first studies, and his success soon appeared from the “Philosophical and Mathematical Institutions,1723 and 1724, 6 vols. 8vo. For the doctrines of Aristotle, which then were generally adopted in a part of Italy, he substituted a species of philosophy at once more useful and more true. Encouraged by the favourable reception his work had met with, he published in 1735 a new “Course of Geometrical Elements,” written with precision and perspicuity. On being appointed professor at Pisa, he revised and retouched his two performances. The former appeared, with considerable corrections, at Bologna in 1742; and the second, augmented with f< Elements of Practical Geometry,“was published at Venice in 1748, 2 vols. 8vo. He was well versed in hydrostatics and history. After having sedulously applied for several years to the classical authors, and particularly those of Greece, he proposed to write the” Fasti of the Archons of Athens,“the first volume of which appeared in 1734, in 4to, and the fourth and last, ten years after. Being called in 1746 to the chair of moral philosophy and metaphysics, he composed a” Course of Metaphysics,“which appeared afterwards at Venice in 1758. His learned friends Muratori, Gorio, Maffei, Quirini, Passionei, now persuaded him to abandon philosophy; and, at their solicitations, he returned to criticism and erudition. In 1747 he published four dissertations in 4to, on the sacred games of Greece, in which he gave an exact list of the athletic victors. Two years afterwards he brought out, in folio, an excellent work on the abbreviations used in Greek inscriptions, under this title,” De notis Graecorum.“This accurate and sagacious performance was followed by several dissertations relative to objects of learning. But the high esteem in which he was held by his acquaintance on account of his virtues and industry, was an interruption to his labours, he being appointed general of his order in 1754; yet the leisure left him by the arduous duties of his station he devoted to his former studies, and when the term of his generalship expired, he hastened back to Pisa, to resume the functions of professor. He now published several new dissertations, and especially an excellent work, one of the best of his performances, entitled” De praefectis urbis.“At length he confined the whole of hi:; application on the” History of the University of Pisa," of which he had been appointed historiographer, and was about to produce the first volume when a stroke of apoplexy carried him off, in spite of all the resources of the medical art, in December 1765.

, a celebrated mathematician, philosopher, and astronomer, was born July 10, 1682, at Burbach

, a celebrated mathematician, philosopher, and astronomer, was born July 10, 1682, at Burbach in Leicestershire, where his father Robert was rector. He was first placed at Leicester school; where, at only twelve years of age, he discovered a strong inclination to the mathematics. This being observed by his uncle, the rev. Mr. John Smith, he gave him all imaginable encouragement; and prevailed with his father to send him for some time to his house in Lincolnshire, that he might assist him in those studies. Here he laid the foundation of that deep and extensive knowledge, for which he was afterwards so deservedly famous. He removed from thence to London, and was sent to St. Paul’s school; where also he made a great progress in classical learning; yet found so much leisure as to keep a constant correspondence with his uncle, not only in mathematics, but also in metaphysics, philosophy, and divinity. This fact is said to have been often mentioned by professor Saunderson. His next remove was to Cambridge; where, April 6, 1699, he was admitted of Trinity college; and at Michaelmas 1705, after taking his first degree in arts, chosen fellow of it. He was at the same time tutor to Anthony earl of Harold, and the lord Henry de Grey, sons of the then marquis (afterwards duke of) Kent, to which noble family Mr. Cotes was related.

The early death of Mr. Cotes is always spoken of with regret by every mathematician and every philosopher; since, if his life had been continued,

The early death of Mr. Cotes is always spoken of with regret by every mathematician and every philosopher; since, if his life had been continued, he would undoubtedly have proved one of the greatest men which this country has produced.

, a learned mathematician, was a native of Scotland, in the seventeenth century, and well

, a learned mathematician, was a native of Scotland, in the seventeenth century, and well known for many papers recorded in the Philosophical Transactions, and in the Acta Eruditorum. He had a controversy with Bernouilli, in which Leibnitz took the part of Craig. He made his name, however, famous chiefly by a pamphlet of 36 pages, 4to, entitled “Theologise Christianae prinfcipia mathematica,” printed at London in 1699, and reprinted at Leipsic in 1755, with a preface upon the life and works of Craig. The author calculates the force and diminution of the probability of things. He establishes, as his fundamental proposition, that whatever we believe upon the testimony of men, inspired or uninspired, is nothing more thau probable. He then proceeds to suppose, that this probability diminishes in proportion as the distance of time from this testimony increases: and, by means of algebraical calculations, he finds at length, that the probability of the Christian religion will last only 1454 years from the date of his book; but will be nothing afterwards, unless Jesus Christ should prevent the annihilation of it by his second coming, as he prevented the annihilation of the Jewish religion by his first coming. Some in Germany and France have seriously refuted these learned reveries. The time of his death is not known.

, an eminent mathematician, was born at Geneva, in 1704, and became a pupil of John Bernouilli,

, an eminent mathematician, was born at Geneva, in 1704, and became a pupil of John Bernouilli, and a professor of mathematics at the age of nineteen. He was known all over Europe, and was of the academies of London, Berlin, Montpellier, Lyons, and Bologna. He died in 1752, worn out with study, at the baths of Languedoc, whither he had repaired for the recovery of his health. He made a most important and interesting collection of the works of James and John Bernouilli, which was published 1743, under his inspection, in 6 vols. 4to, and he had before bestowed no less pains on an edition of Christopher Wolf’s “Elementa universae matheseos,” Genev. 1732 1741, 5 vols. 4to. The only work he published of his own was an excellent “Introduction to the Theory of Curve lines,1750, 4to. L'Avocat says he was an universal genius, a living Encyclopedia, and a man of pious and exemplary conduct. His family appears to have been numerous and literary. There wap another Gabriel Cramer, probably his father, who was born at Geneva, 1641, rose to be senior of the faculty of medicine, died in 1724, and left a son, John Isaac, who took the degree of doctor in 1696, succeeded to his practice, and published an “Epitome of Anatomy,” and a “Dissertation on Diseases of the Liver,” left by his father. Also, “Thesaurus secretorum curiosorum, in quo curiosa, ad omnes corporis humani, turn internes turn externos, morbos curandos, &c. continentur,1709, 4to, He again was succeeded by his son, John Andrew Cra­Mer, who rendered himself famed by his skill in mineralogy and chemistry; and published at Leyden, in 1739, 2 vols. 8vo, “Elementa Artis Docirnasticae.” It was reprinted in 1744, and again translated into French, in 1755. He wrote also a treatise on the management of forests and timber, and gave public lectures on Assaying, both in Holland and England. He died Dec. 6, 1777. Tn his person he was excessiyely slovenly, in his temper irritable, and when disputes occurred, not very delicate in his language.

epresentation of his own play. Among the rest, he acted the divine, the philosopher, the lawyer, the mathematician, the physician, and the soldier, with such inimitable grace,

The next account we have of Crichton, and which appears to have been transmitted, through sir Thomas Urquharr, to later biographers, is of an extraordinary instance of bodily courage and skill. It is said, that at Mantua there was at this time a gladiator, who had foiled, in his travels, the most famous fencers in Europe, and had lately killed three persons who had entered the lists with him. The duke of Mantua was much grieved at having granted this man his protection, as he found it to be attended with such fatal consequences. Crichton, being informed of his highness’s concern, offered his service, not only to drive the murderer from Mantua, but from Italy, and to fight him for fifteen hundred pistoles. Though the duke was unwilling to expose such an accomplished gentleman to so great a hazard, yet, relying upon the report he had heard of his warlike achievements, he agreed to the proposal; and, the time and place being appointed, the whole court attended to behold the performance. At the beginning of the combat, Crichton stood only on his defence; while the Italian made his attack with such eagerness and fury, that, having over-acted himself, he began to grow weary. Our young Scotchman now seized the opportunity of attacking his antagonist in return; which he did with so much dexterity and vigour, that he ran him through the body in three different places, of which wounds he immediately died. The acclamations of the spectators were loud and extraordinary upon this occasion; and it was acknowledged by all of them, that they had never seen art grace nature, or nature second the precepts of art, in so lively a manner as they had beheld these two things accomplished on that day. To crown the glory of the action, Crichton bestowed the prize of his victory upon the widows of the three persons who had lost their lives in fighting with the gladiator. It is asserted, that, in consequence of this, and his other wonderful performances, the duke of Mantua made choice of him for preceptor to his son Vincentio di Gonzaga, who is represented as being of a riotous temper and a dissolute life. The appointment was highly pleasing to the court. Crichton, to testify his gratitude to his friends and benefactors, and to contribute to their diversion, framed, we are told, a comedy, wherein he exposed and ridiculed all the weaknesses and failures of the several employments in which men are engaged. This composition was regarded as one of the most ingenious satires that was ever made upon mankind. But the most astonishing part of the story is, that Crichton sustained fifteen characters in the representation of his own play. Among the rest, he acted the divine, the philosopher, the lawyer, the mathematician, the physician, and the soldier, with such inimitable grace, that every time he appeared upon the stage he seemed to be a different person . From being the principal actor in a comedy, Crichton soon became the subject of a dreadful tragedy. One night, during the time of carnival, as he was walking along the streets of Mantua, and playing upon his guitar, he was attacked by half a dozen people in masks. The assailants found that they had no ordinary person to deal with; for they were not able to maintain their ground against him. In the issue, the leader of the company, being disarmed, pulled off his mask, and begged his life, telling him that he was the prince his pupil. Crichton immediately fell on his knees, and expressed his concern for his mistake; alleging, that what he had done was only in his own defence, and that if Gonzaga had any design upon his life he might always be master of it. Then, taking his own sword by the point, he presented it to the prince, who immediately received it, and was so irritated by the affront which he thought he had sustained in being foiled with all "his attendants, that he instantly ran Crichton through the heart. Various have been the conjectures concerning the motives which could induce Vincentio di Gonzaga to be guilty of so ungenerous and brutal an action. Some have ascribed it to jealousy, asserting that he suspected Crichton to be more in favour than himself with a lady whom he passionately loved; and sir Thomas Urqnhart has told a story upon this head which is extravagant and ridiculous in the highest degree. Others, with greater probability, represent the whole transaction as the result of a drunken frolic; and it is uncertain, according to Imperiaiis, whether the meeting of the prince and Crichton was by accident or design. However, it is agreed on all hands, that Crichton lost his life in this rencontre. The time of his decease is said, by the generality of his biographers, to have been in the beginning-of July 1583; but lord Buchan, most likely in consequence of a more accurate immiry, fixes it to the same month in the preceding year. There is a difference likewise with regard to the period of life at which Crichton died. The common accounts declare that he was killed in the thirty-second year of his age; but Imperialis asserts that he was only in his twenty-second when that calamitous event took place; and this fact is confirmed by lord Buchan. Criehton’s tragical end excited a very great and general lamentation. If the foolish ravings of sir Thomas Urquhart are to be credited, the whole court of Mantua went three quarters of a year into mourning for him; the epitaphs and elegies that were composed upon his death, and stuck upon his hearse, would exceed, if collected, the bulk of Homer’s works; and, for a long time afterwards, his picture was to be seen in most of the -bed-chambers and galleries of the Italian nobility, representing him on horseback, with a lance in one hand and a book in the other. From all this wonderful account we can only infer, with any degree of confidence, that Crichton was a youth of such lively parts as excited great present admiration, and high expectations with regard to his future attainments. He appears to have had a fine person, to have been adroit in his bodily exercises, to have possessed a peculiar facility in learning languages, to have enjoyed a remarkably quick and retentive memory, and to have excelled in a power of declamation, a fluency of speech, and a readiness of reply. His knowledge likewise was probably very uncommon for his years; and this, in conjunction with his other qualities, enabled him to shine in public disputation. But whether his knowledge were accurate or profound, may justly be questioned; and it may equally be doubted whether he would have arisen to any extraordinary degree of eminence in the literary world, which, however, his early and untimely death prevented from being brought to the test of experiment.

, an eminent philosopher and mathematician, descended from a noble family, was born at Lausanne, April

, an eminent philosopher and mathematician, descended from a noble family, was born at Lausanne, April 13, 1663. His father was Abraham de Crousaz, colonel of a regiment of fusileers: in his youth being of a very delicate habit, he was not too closely confined to his studies, yet left school at the age of thirteen with the reputation of a good scholar. His father, who intended him for the army, had him educated in the branches of knowledge necessary for that profession; but finding him averse to any pursuit unless that of literature, he allowed him to follow his inclination. In his fifteenth year he completed his course of philosophy, and distinguished himself by his theses, but being dissatisfied with the philosophy then taught, he had recourse to the writings of Des Cartes, which he studied with avidity, and applied at the same time to mathematics, but scholastic theology had no more charms for him than the philosophy he had been taught. In his sixteenth year, however, he entered as a student of divinity, attended the best professors, both at Geneva and Lausanne, and read the opinions of other eminent divines on the subjects most involved in controversy. In March 1682 he went to Lcyden, made himself acquainted with the theological disputes, and endeavoured to investigate how far they could be determined by the sacred scriptures. Leaving Holland, he entered France, became acquainted with those celebrated protestant divines Claude and Menard, at Charenton, and fathers Malebranche and le Vassor at Paris, who in vain endeavoured to bring him over to the Roman catholic church, which Vassor himself forsook some years after. On his return to his native country, in J 684, Crousaz married the daughter of John Lewis Loys, comptroller-general, and soon after was ordained, and made honorary professor. He officiated as pastor in the church of Lausanne f >r fourteen years. During this time, in 1691, he was appointed to dispute for the professorship of Hebrew at Berne, which he performed with great credit. In 1699 he was made professor of Greek and philosophy, and although also nominated to the chair of divinity in 1700, he preferred that of philosophy. In 1706 he was appointed rector of the college, which office he held three years, and was again appointed in 1722, but held it then only two years, as it interfered too much with his literary engagements. It was during this second rectorate, that contests arose at Lausanne respecting the obligation of signing the Consensus, a formulary of faith and doctrine maintained in the protestant churches of Swisserland, an account of which may be seen in “Memoires pour servir a l‘histoire des troubles arrives en Suisse a I’occasion du Consensus,” Amst. 1726; and more briefly in Mosheim’s History. In 1705, from his own theses, and those published at the expence of the lords of Berne, he compiled a system of logic, in twenty ­two theses, 4to, and in the same and two following years published an abridgment of this. In 1712 he published in French, a system of logic, entitled “Systeme de reflexions qui peuvent coutribuer a la nettet6 et a Petude de nos connoissances,” Amst. 2 vols. 8vo, reprinted there in 1720, 3 vols. 12mo; in 1725, in 4 vols. and in 1741, in 6 vols. In 1724 he published an abridgment of it in Latin, at Geneva, “Systema Logicæ, juxta principia ab autore in Gallico opere posita.” Some conversations on the subject of beauty in art, led him to an investigation of the subject, and produced in 1715, his “Traité du Beau, ou Ton montre en quoi consiste ce que l'on nomnie ainsi, par des examples tirés de la plupart des arts et des sciences,” reprinted at Amst. 2 vols. 12mo. In 1718, he published an ironical work, “Nouvelles maximes sur l'Education des enfans,” Amst. 8vo; but in 1722, his more serious and better known work on Education, Hague, 1722, 2 vols. 12mo. In 1718 he answered the deistical Collins’s discourse of Freethinking, in “Examen du traite de la Hbert6 de penser,” Amst. 8vo. In the same year he published his first mathematical work, “Geometric des lignes et des surfaces rectilignes et circulaires,” Arnst. 2 vols. 8vo.

, of Alexandria, a famous mathematician about 120 years B. C. was, it is reported, the first inventor

, of Alexandria, a famous mathematician about 120 years B. C. was, it is reported, the first inventor of the pump, which he discovered by accident. On lowering a mirror that was in his father’s shop, he observed that the weight which helped it in moving upwards and downwards, and which was inclosed in a cylinder, made a noise, produced by the friction of the air violently forced by the weight. He set about examining into the cause of this sound, and thought it might be possible to avail himself of it in making an hydraulic organ, in which the air and the water should form the sound; an undertaking which he executed with success. Encouraged by this production, Ctesibius thought of using his mechanical skill in measuring time. He constructed a clepsydra, or waterclock, formed with water, and regulated by cogged wheels; the water by falling turned these wheels, which communicated their motion to a column on which were marked the characters for distinguishing the months and the hours. At the same time that the cogged wheels were put in motion, they raised a little statue, which with a wand pointed to the months and hours marked upon the column. He was also the author of “Geodesia, or the art of dividing and measuring bodies,” which is said to be in the Vatican library; but he must be distinguished from Ctesibius of Chalcis, who was a cynic philosopher, of a sportive disposition and a cheerful temper, who had the art of being agreeable to the great, without submitting to the vile arts of flattery, and made them hearken to truth, and gave them a taste for virtue, under the name of amusement.

man of very extensive erudition, excellently skilled in the learned languages and antiquity, a good mathematician, a subtle philosopher, and a profound metaphysician. The main

Cudworth died at Cambridge, June 26, 1688, and was interred in the chapel of Christ’s college. He was a man of very extensive erudition, excellently skilled in the learned languages and antiquity, a good mathematician, a subtle philosopher, and a profound metaphysician. The main design of his celebrated work, “The Intellectual System,” is to refute the principles of atheism, and in this he has successfully employed a vast fund of learning and reading. But his partiality for the Platonic philosophy, in judging of which, after the example of his contemporaries, he paid too much respect to the writings of the modern Alexandrian Platonists, led him into frequent mistakes. In physics he adopted the atomic system; but, abandoning Democritus and Epicurus as the first patrons of impiety, he added to the doctrine of atoms that of a certain middle substance between matter and spirit, to which he gave the appellation of plastic nature, which he supposed to be the immediate instrument of the divine operation; and this hypothesis gave rise to the controversy above mentioned between Bayle and Le Clerc. Cudworth stands at the head of those divines who, considering the belief in a triune God as a fundamental article of Christian belief, maintain that both the Platonic, and all the other Pagan trinities are only corruptions and mutilations of certain primaeval revelations and patriarchal traditions relative to the asserted distinction in the divine nature; and he has very ably discussed this important subject in his Intellectual System. A great number of writers commend Cudworth’s piety and modesty; and Burnet having observed, that Dr. Henry More studied to consider religion as a seed of a deiform nature, and in order to this, set young students much on reading the ancient philosophers, chiefly Plato, Tully, and Plotinus, and on considering the Christian religion as a doctrine sent from God, both to elevate and sweeten human nature, tells us, that “Cudworth carried this on with a great strength of genius, and a vast compass of learning; and that he was a man of great conduct and prudence; upon which his enemies did very falsely accuse him of craft and dissimulation.” He left several manuscripts which seem to be a continuation of his “Intellectual System,” of which he had given the world only the first part. One of these was published by Chandler, bishop of Durham, 1731, in 8vo, under this title, “A Treatise concerning eternal and immutable Morality.” This piece was levelled against the writings of Hobbes and others, who revived the exploded opinions of Protagoras; taking away the essential and eternal differences of moral good and evil, of just and unjust, and making them all arbitrary productions of divine or human will. He left also several other Mss. with the following titles“: 1. A discourse of moral good and evil.” 2. Another book of morality, wherein Hobbes’s philosophy is explained. 3. A discourse of liberty and necessity, in which the grounds of the atheistical philosophy are confuted, and morality vindicated and explained. 4. Another book “De libero arbitrio.” 5. Upon Daniel’s prophecy of the 70 weeks, wherein all the interpretations of the Jews are considered and confuted, with several of some learned Christians. 6. Of the verity of the Christian religion, against the Jews. 7. A discourse of the creation of the world, and immortality of the soul. 8. Hebrew learning. 9. An explanation of Hobbes’s notion of God, and of the extension of spirits. The history of these Mss. is somewhat curious. Having been left to the care of his daughter, lady Masham , they for a long time quietly reposed in the library at Oates, in Essex. But, about the year 1762, when the late lord Masham married his second lady, his lordship thought proper to remove a number of volumes of ancient learning, which had been bequeathed to the family by Mr. Locke, and the manuscripts of Dr. Cudworih, to make room for books of polite amusement. For this purpose, he sold either the whole, or a considerable part of them, to Mr. Robert Davis, then a bookseller in Piccadilly. Mr. Davis being told, or having concluded, that the manuscripts were the productions of Mr. Locke, it became an object of consideration with him, how to convert them, as a tradesman, to the best advantage. They contained, among other things, sundry notes on scripture. About the same time, a number of manuscript scriptural notes by Dr. Waterland came into the possession of the booksellers. It was therefore projected, by the aid of such celebrated names as Mr. Locke and Dr. Waterland, to fabricate a new Bible with annotations. At a consultation, however, it was suggested, that, though these names were very important, it would be necessary, to the complete success of the design, to join with them some popular living character. The unfortunate Dr. Dodd was then in the height of his reputation as a preacher, and was fixed upon to carry on the undertaking. This was the origin of Dr. Dodd’s Bible, and part of the materials put into his hands the doctor made use of in the “Christian Magazine.” When the manuscripts were returned to Mr. Davis, he carried them down to Barnes in Surry, which was his country retirement, and threw them into a garret, where they lay exposed to the dangers of such a situation. About the beginning of the year 1777, a gentleman, who had a veneration for the name of Mr. Locke, and was concerned to hear that any of his writings were in danger of being lost, went to Barnes, to see these manuscript*; and being positively assured by Mr. Davis, that they were the real compositions of that eminent man, he immediately purchased them fur forty guineas. He was, however, soon, convinced, after an examination of them, that the authority of the bookseller was fallacious, and having remonstrated against the deception, the vender condescended to take them again, upon being paid ten guineas for his disappointment in the negociation. In the investigation of the manuscripts, the gentleman having discovered, by many incontestable proofs, that they were the writings of Dr. Cudworth, he recommended them to the curators of the British Museum, by whom they were purchased; and thus, at last, after many perils and mutilations, they are safely lodged in that noble repository.

, of the same family, probably, with the preceding, and native also of Perugia, was an excellent mathematician, and is memorable for having fitted a pair of wings so exactly

, of the same family, probably, with the preceding, and native also of Perugia, was an excellent mathematician, and is memorable for having fitted a pair of wings so exactly to his body, as to be able to fly with them. He made the experiment several times over the lake Trasimenus; and succeeded so well, that he had the courage to perform before the whole city of Perugia, during the solemnity of the marriage of Bartholomew d'Alviano with the sister of John Paul Baglioni. He shot himself from the highest part of the city, and directed his flight over the square, to the admiration of the spectators: but unfortunately the iron, with which he managed one of his wings, failed; and then, not being able to balance the weight of his body, he fell on a church, and broke his thigh. Bayle fancies, that the history of this Daedalus, for so he was called, will not generally be credited; yet he observes, that it is said to have been practised at other places, for which he refers us to the “Journal des Sgavans” of 1678. Dante was afterwards invited to be professor of the mathematics at Venice. He flourished towards the end of the fifteenth century, and died before he was forty years old.

machines, and composed a commentary on the sphere of Sacrobosco. His grandson Vincent Dante, an able mathematician, like him, was at the same time painter and sculptor. His statue

, a native of Perugia, of the family of Rainaldi, imitated so well the verses of the poet Dante, that he was generally called by his name. He was not less distinguished by the delicacy of his poetry, than by his skill in the mathematics and in architecture. He died in 1512, in an advanced age, after having invented several machines, and composed a commentary on the sphere of Sacrobosco. His grandson Vincent Dante, an able mathematician, like him, was at the same time painter and sculptor. His statue of Julius III. has been generally looked upon as a master-piece of the art. Philip II. king of Spain, offered him a large salary to induce him to come and finish the paintings of the Escurial; but the delicacy of Dante’s constitution would not permit him to quit his natal air. He died at Perugia in 1576, at the age of forty-six. There is extant by him, “The lives of those who have excelled in drawings for statues.

experiments on the charges of powder, &c. and several improvements on Robins (who was not so great a mathematician as he), Darcy continued the experiments to the last moment of

Having published an “Essay on Artillery” in 1760, containing various curious experiments on the charges of powder, &c. and several improvements on Robins (who was not so great a mathematician as he), Darcy continued the experiments to the last moment of his life, but has left nothing behind him. In 1765 he published his “Memoir on the duration of the sensation of 8i^ht,” the most ingenious of his works, and that which shews him in the best light as an accurate and ingenious maker of experiments: the result of these researches was, that a body may souietimes pass by our eyes without being seen, or marking its presence, otherwise than by weakening the brightness of the object it covers; thus, in turning pieces of card painted blue and yellow, you only perceive a continued circle of green; thus the seven prismatic colours, rapidly turned, produce an obscure white, which is the obscurer as the motion is more rapid. As this duration of the sensation increases with the brightness of the object, it would have been interesting to know the laws, according to which the augmentation of the duration follows the intensity of the light, and, contrarywise, what are the gradations of the intensity of the light of an object which motion makes continually visible; but Darcy, now obliged to trust to other eyes than his own, was forced to relinquish this pursuit. Darcy, always employed in comparing mathematical theory and observation, made a particular use of this principle in his “Memoir on Hydraulic Machines,” printed in 1754. In this he shews how easy it is to make mistakes in looking by experiment for the laws of such effects as are susceptible of a maximum or minimum; and indicates at the same time, how a system of experiments may be formed, which shall lead to the discovery of these laws. All Darcy’s works bear the character which results from the union of genius and philosophy; but as he measured every thing upon the largest scale, and required infinite accuracy in experiment, neither his time, fortune, nor avocations allowed him to execute more than a very small part of what he projected. He was amiable, spirited, lively, and a lover of independence; a passion to which he sacrificed even in the midst of literary society, where perhaps a little aristocracy may not be quite so dangerous.

3, 12mo, xvith a dedication to Congreve, who encouraged the publication. He was F. R. S. and an able mathematician. In the dispute concerning elliptical arches, at. the time when

, esq. of the Middle Temple, a barrister at law, afterwards master in chancery, and at the time of his death, Jan. 8, 1763, accomptaiit-general of that court, is noticeable as having translated the “Memoirs of cardinal de Retz,” which were printed in 1723, 12mo, xvith a dedication to Congreve, who encouraged the publication. He was F. R. S. and an able mathematician. In the dispute concerning elliptical arches, at. the time when Bluckfriars bridge was built, application was made by the committee for his opinion on the subject, and his answer may be seen in the London Magazine for March, 1760. He also published in 1761, “A Vindication of the New Calendar Tables, and Rules annexed to the Act for regulating the commencement of the year,” &c. 410.

, an excellent mathematician, mechanic, and astronomer, was born at Chamberry, the capital

, an excellent mathematician, mechanic, and astronomer, was born at Chamberry, the capital of Savoy, in 1611; and descended from a noble family, which had produced several persons creditably distinguished in the church, the law, and the army. He was a great master in all the parts of the mathematics, and printed several books on that subject, which were very well received. His principal performances are, an edition of Euclid’s Elements, where he has struck out the unserviceable propositions, and annexed the use to those he has preserved; a discourse of fortification; and another of navigation. These performances, with some others, were first collected into three volumes in folio, under the title of “Mundus Mathematicus,” comprising a very ample course of mathematics. The first volume includes the first six books of Euclid, with the eleventh and twelfth; an arithmetical tract; Theodosius’s spherics; trigonometry; practical geometry; mechanics; statics; universal geography; a discourse upon the loadstone; civil architecture, and the carpenter’s art. The second volume furnishes directions for stone-cutting; military architecture; hydrostatics; a discourse of fountains and rivers hydraulic machines, or contrivances for waterworks; navigation; optics; perspective; catoptrics, and dioptrics. The third volume has ki it a discourse of music pyrotechnia, or the operations of fire and furnace a discourse of the use of the astrolabe gnomonics, or the art of dialling; astronomy; a tract upon the calendar; astrology; algebra; the method of indivisible and conic sections. The best edition of this work is that of Lyons, printed in 1690; which is more correct than the first, is considerably enlarged, and makes four vols. in folio. Dechales, though not abounding in discoveries of his own, is yet allowed to have made a very good use of those of other men, and to have drawn the several parts of the science of mathematics together with great clearness and judgment. It is said also, that his probity was not inferior to his learning, and that both these qualities made him generally admired and beloved at Paris; where for four years together he read public mathematical lectures in the college of Clermont He then removed to Marseilles, where he taught the art of navigation; and aiterwards became professor of mathematics in the university of Turin, where he died March 28, 1678, aged 67.

, a great mathematician, and greater enthusiast, the son of Rowland Dee, gentleman sewer

, a great mathematician, and greater enthusiast, the son of Rowland Dee, gentleman sewer to Henry VIII. and grandson of Bedo Dee, standard bearer to lord de Ferrars at the battle of Tournay, was born at London, July 13, 1527; and, after some time spent at school there, and at Chelmsford in Essex, sent to John’s college in Cambridge, where he informs us of his progress in the following words: “Anno 1542, I was sent, by my father Rowland Dee, to the university of Cambridge, there to begin with logic, and so to proceed in the learning of good arts and sciences; for I had before been meetly well furnished with understanding of the Latin tongue, I being then somewhat above 15 years old. In the years 1543, 1544, 1545, I was so vehemently bent to study, that for those years I did inviolably keep this order, only to sleep four hours every night; to allow to meat and drink, and some refreshing after, two hours every day; and of the other eighteen hours, all, except the time of going to, and being at, the divine service, was spent in my studies and learning.” In 1547 he went into the Low Countries, on. purpose to converse with Frisius, Mercator, &c. and other learned men, particularly mathematicians; and in about eight months alter returned to Cambridge, where, upon the founding of Trinity college by Henry VIII. he was chosen one of the fellows, but his bias was to the study of mathematics and astronomy. He brought over with him from the Low Countries several instruments “made by the direction of Frisius, together with a pair of large globes made by Mercator; and his reputation was very high. His assiduity, however, in making astronomical observations, which in those days were always understood to be connected with the desire of penetrating into futurity, brought some suspicion upon him; which was so far increased by a very singular accident that befel him, as to draw upon him the imputation of a necromancer, which he deserved afterwards rather mre than now. This affair happened soon after his removal from St. John’s-college, and being chosen one of the fellows of Trinity, where he” was assigned to he the under-reader of the Greek tongue, Mr. Pember being the chief Greek reader then in Trinity-college. Hereupon,“says he,” I did set forth, and it was seen of the university, a Greek comedy of Aristophanes, named in Greek Eijpwij in Latin, Pax; with the performance of the scarabaeus, or beetle, his flying up to Jupiter’s palace with a man and his basket of victuals on his back; whereat was great wondering, and many vain reports spread abroad of the means how that was effected."

large runs thus: “A true and faithful relation of what passed for many years between Dr. John Dee, a mathematician of great fame in queen Elizabeth and king James their reigns,

The noise their adventures made in Europe induced queen Elizabeth to invite Dee home, who, in May 1689, set out from Trebona towards England. He travelled with great pomp and solemnity, was attended by a guard of horse; and, besides waggons for his goods, had uo less than three coaches for the use of his family; for he had married a second wife, and had several children. He landed at Gravesend Nov. 23; and, Dec. 9, presented himself at Richmond to the queen, who received him very graciously. He then retired to his house at Mortlake; and collecting the remains of his library, which had been torn to pieces and scattered in his absence, he sat down to study. He had great friends; received many presents; yet nothing, it seems, could keep him from want. The queen had quickly notice of this, as well as of the vexations he suffered from the common people, who persecuted him as a conjuror, which at that time was not a title equivalent to an impostor. The queen, who certainly listened oftener to him than might have been expected from her good sense, sent him money from time to time: but all would not do. At length he resolved to apply in such a manner as to procure some settled subsistence; and accordingly, Nov. 9, 1592, he sent a memorial to her majesty by the countess of -Warwick, in which he very earnestly pressed her, that commissioners might be appointed to hear his pretensions, and to examine into the justness of his wants and claims. This had a good effect; for, on the 22d, two commissioners, sir Thomas Gorge, knt. and Mr. Secretary Wolley, were actually sent to Mortlake, where Dee exhibited a book, containing a distinct account of all the memorable transactions of his life, those which occurred in his last journey abroad only excepted; and, as he read this historical narration, he produced all the letters, grants, and other evidences requisite to confirm them, and where these were wanting, named living witnesses. The title of this work, the original of which still remains in the Cotton library, and a transcript of it among Dr. Smith’s written collections, runs thus: “The compendious rehearsal of John Dee, his dutiful declaration and proof of the course and race of his studious life for the space of half an hundred years now by God’s favour and help fully spent, and of the very great injuries, damages, and indignities which for these last nine years he hath in England sustained, contrary to her majesty’s very gracious will and express commandment, made unto the two honourable commissioners by her most excellent majesty thereto assigned, according to the intent of the most humble supplication of the said John, exhibited to her most gracious majesty at Hampton-court, ann. 1592, Nov. 9.” Upon the report made by the commissioners to the queen, he received a present, and promises of preferment; but these promises ending like the former in nothing, he engaged his patroness, the countess of Warwick, to present another short Latin petition to the queen, but with what success does not appear. In Dec. 1594, however, he obtained a grant to the chancellorship of St. Paul’s. But this did not answer his end: upon which he applied himself next to Whitgift, archbishop of Canterbury, by a letter, in which he inserted a large account of all the books he had either published or written: and in consequence of this letter, together with other applications, he obtained a grant of the vvardenshipof Manchester-college. Feb. 15D6, he arrived with his wife and family in that town, and was installed in his new charge. He continued there about seven years; which he is said to have spent in a troublesome and unquiet manner. June 1604, he presented a petition to king James, earnestly desiring him that he might be brought to a trial; that, by a formal and judicial sentence, he might be delivered from those suspicions and surmises which had created him so much uneasiness for upwards of fifty years. But the king, although he at first patronized him, being better informed of the nature of his studies, refused him any mark of royal countenance and favour; which must have greatly affected a man of that vain and ambitious spirit, which all his misfortunes could never alter or amend. November the same year he quitted Manchester with his family, in order to return to his house at Mortlake; where he remained but a short time, being now very old, infirm, and destitute of friends and patrons, who had generally forsaken him. We find him at Mortlake in 1607; where he had recourse to his former invocations, and so came to deal again, as he fancied, with spirits. One Hickman served him now, as Kelly had done formerly. Their transactions were continued to Sept. 7, 1607, which is the last date in that journal published by Casaubon, whose title at large runs thus: “A true and faithful relation of what passed for many years between Dr. John Dee, a mathematician of great fame in queen Elizabeth and king James their reigns, and some spirits, tending, had it succeeded, to a general alteration of most states and kingdoms in the world. His private conferences with Rudolph emperor of Germany, Stephen. king of Poland, and divers other princes, about it. The particulars of his cause, as it was agitated in the emperor’s court by the pope’s intervention. His banishment and restoration in part; as also the letters of sundry great men and princes, some whereof were present at some of these conferences, and apparitions of spirits to the said Dr. Dee, out of the original copy written with Dr. Dee’s own hand, kept in the library of sir Thomas Cotton, knt. baronet. With a preface confirming the reality, as to the point of spirits, of this relation, and shewing the several good uses that a sober Christian may make of all. By Meric Casaubon, D. D. Lond. 1659,” fol.

, a celebrated mathematician, of French original, but who spent most of his life in England,

, a celebrated mathematician, of French original, but who spent most of his life in England, was born at Vitri in Champagne May 26, 1667. His father was a surgeon, and spared no pains in his education, and sent him early to school, where he wrote a letter to his parents in 1673, a circumstance which filial affection made him often mention with great pleasure. For some time he was educated under a popish priest, but was afterwards sent to a protestant academy at Sedan, where his predilection for arithmetical calculations so frequently took the place of classical studies, that his master one day pettishly asked, what the “little rogue meant to do with those cyphers?” He afterwards studied at Saumur and Paris, at which last place he began his mathematics under Ozanam. At length the revocation of the edict of Nantz, in 1685, determined him, with many others, to take shelter in England; where he perfected his naathematical studies. A mediocrity of fortune obliged him to employ his talent in this way in giving lessons, and reading public lectures, for his better support: in the latter part of his life too, he chiefly subsisted by giving answers to questions in chances, play, annuities, &c. and it is said many of these responses were delivered at a coffee-, house in St. Martin’s-lane, where he spent much of his time. The “Principia Mathematica” of Newton, which chance is said to have thrown in his way, soon convinced Demoivre how little he had advanced in the science he professed. This induced him to redouble his application; which was attended by a considerable degree of success; and he soon became connected with, and celebrated among, the first-rate mathematicians. His eminence and abilities in this science opened him an entrance into the royal society of London, and into the academies of Berlin and Paris. By the former his merit was so well known and esteemed, that they judged him a fit person to decide the famous contest between Newton and Leibnitz, concerning the invention of Fluxions.

, and that 22 were against them. The pensionary was alone of another opinion; and, as he was a great mathematician, soon discovered the falsity of this notion: he discovered,

He seemed now to have vanquished even Envy herself. In all difficult cases, his ministry was employed: and when the prince of East-Friesland quarrelled with his subjects, he was put at the head of the deputation to terminate the disputes. When war with England, alter the king’s restoration, became necessary, he was one of the deputies that prevailed on the states of Guelder and Overyssel to furnish their quota: he was appointed one of the commissioners for the direction of the navy, and made such vigorous dispositions, that he had a fleet in much better condition, and more ready for sea, than the admirals themselves imagined possible; though naval affairs were quite new to him. When it was thought expedient, after Opdam’s defeat and death, that some of their own deputies should command the fleet, he was one of those three that were put in commission. When he came on board, the fleet was shut up in the Texel, and, in order to secure the outward-bound East India fleet, it was necessary for it to put to sea; which, as the wind then stood, the sailors declared impossible. It was the received doctrine, that there were but 10 points of the compass from which the wind could carry ships out, and that 22 were against them. The pensionary was alone of another opinion; and, as he was a great mathematician, soon discovered the falsity of this notion: he discovered, that there were in reality no less than 28 points for them, and but four against them. He engaged to carry one of their greatest ships through the Spaniard’s-gat with the wind at S. S. W. which he performed Aug. 16, 1665; the greatest part of the fleet followed him without the least accident, and the passage has since been called Witt’s-diep. They met with a dreadful storm on the coast of Norway, which lasted two days: De Witt remained upon deck all the time, never changed his cloaths, nor took any refreshment, but in common with the men; and, when he saw a want of hands, obliged his officers to work by his own example. He wrote a plain and accurate relation of all that happened during the expedition, and at his return verified every article of this account so fully to the States, that they gave him solemn thanks for his good services, and offered him a considerable present, which, however, he declined to accept.

, a disciple of Aristotle, was born at Messina in Sicily. He was a philosopher, historian, and mathematician, and composed a great many books on various subjects, and in

, a disciple of Aristotle, was born at Messina in Sicily. He was a philosopher, historian, and mathematician, and composed a great many books on various subjects, and in all sciences, which were much esteemed. Cicero speaks frequently in the highest terms both of the man and his works. Geography was one of his principal studies; and we have a tieatise, or rather a fragment of a treatise, of his still extant upon that subject. It was first published by Henry Stephens in 1589, with a Latin version and notes; and afterwards by Hudson at Oxford in 1703, among the “Veteris geographiae scriptures Graecos minores, &c.” Pliny tells us that “Dicearchus, a man of extraordinary learning, had received a commission from some princes to take the height of the mountains, and found Pelion, the highest of them, to be 1250 paces perpendicular, from whence he concluded it to bear no proportion which could affect the rotundity of the globe.” He published some good discourses upon politics and government; and the work he composed concerning the republic of Lacedaemon was thought so excellent, that it was read every year before the youth in the assembly of the ephori. As a philosopher, his tenets have little to recommend them* He held that there is no such thing as mind, or soul, either in man or beast; that the principle by which animals perceive and act, is equally diffused throngh the body, is inseparable from it, and expires with it; that the human race always existed; that it is impossible to foretel future events; and that the knowledge of them would be an infelicity.

, an able mathematician, was descended from an ancient family, and born at Digges-court,

, an able mathematician, was descended from an ancient family, and born at Digges-court, in the parish of Barham, in Kent, in the early part of the sixteenth century. He was sent, as Wood conjectures, (for he is doubtful as to the place), to University-college, Oxford, where he laid a good foundation of learning; and retiring from thence without a degree, prosecuted his studies, and composed the following works: 1. “Tectonicum; briefly shewing the exact measuring, and speedy reckoning of all manner of lands, squares, timber, stones, steeples,” &c. 1556, 4to repubiished, with additions, by his son Thomas Digges, 1592, 4to and again in 1647, 4to. 2. “A geometrical practical treatise, named Pantometfia, in three books,” left imperfect in ms. at his death; but his son supplying such parts of it as were obscure and imperfect, published it in 1591, folio; subjoining, “A discourse geometrical of ae iiv< regular and Platonical bodies, containing sundry theoretical and practical propositions, arising by mutual conference of these solids, inscription, circumscription, and transformation.” 3. “Prognostication everlasting of right good effect or, choice rules to judge the weather by the sun, moon, anet stars,” &c. 1555, 1556, and 1564, 4to, corrected and augmented by his son; with general tables, and many compendious rules, 1592, 4to. He died not later than 1573.

, a celebrated mathematician of Alexandria, has been reputed to be the inventor of algebra;

, a celebrated mathematician of Alexandria, has been reputed to be the inventor of algebra; at least his is the earliest work extant on that science. It is not certain when he lived. Some have placed him before Christ, and some after, in the reigns of Nero and the Antonines; Saxius places him in the fourth century. He appears to be the same Diophantus who wrote the “Canon Astronomicus, which Suidas says was commented on by the celebrated Hypatia, daughter of Theon of Alexandria. His reputation must have been very high among the ancients, since they ranked him with Pythagoras and Euclid in mathematical learning. Bachet, in his notes upon the 5th book” De Arithmeticis," has collected, from Diophantus’s epitaph in the Anthologia, the following circumstances of his life; namely, that he was married when he was thirty-three years old, and had asonbornfive years after; that this son died when he was forty-two years of age, and that his father did not survive him above four years; from which it appears, that Diophantus was eighty-four years old when he died.

, an eminent mathematician, was born at Salisbury, on the 29th of May, 1675, being the

, an eminent mathematician, was born at Salisbury, on the 29th of May, 1675, being the fourteenth of that name in a direct line. His father was a gentleman possessed of a small estate in the county of Wilts. His mother was of the family of the Luttrells of Dunstercastle, near Taunton, in Somersetshire, whose fortune made a considerable increase to the family income. Mr. Ditton’s father being of the sect of nonconformists, and extremely tenacious of his opinions, entered much into the religious controversifs of those times, and in supporting such contentions impaired his fortune, almost to the ruin of his family. Mr. Humphrey Ditton was the only son; and his father, observing in him an extraordinary good capacity, was desirous that he should not want the advantage of a good education. Accordingly, he placed him in a private academy, under the direction of Dr. Olive, a clergyman of the established church, who, notwithstanding his religious sentiments were different from those of Mr. Ditton’s family, was much esteemed by them for his candour and moderation in those troublesome times. When Mr. Ditton had finished his studies under Dr. Olive, he at the desire of his father, although contrary to his own inclination, engaged in the professioa of divinity, and began to exercise his function at Tunbridge, in Kent, where he continued to preach some years during which time he married Miss Ball, a lady at that place.

, an ingenious mathematician, was born Feb. 6, 1718, at Bideford, in Devonshire, where his

, an ingenious mathematician, was born Feb. 6, 1718, at Bideford, in Devonshire, where his father kept a mathematical school, and was reputed one of the best teachers of arithmetic, navigation, and dialing, in his time. It appears from some papers in ms. left by the Rev. Mr. Hervey, author of the “Meditations,” that the family name was Donne and that Christopher, the grandfather, was the first that dropped the final e. The subject of the present article was brought up under the care of the Rev. Mr. Mudge, of Plymouth, and his successor White, M. A. with whom he made a very considerable progress in the Latin and Greek languages. When he left the grammar-school, as far as his health would permit, he assisted his father in his mathematical school; and when he was about fourteen years of age, being at play with some of his schoolmates, he fell from a high pile of deals, which, with his soon after going a-swimming in a profuse sweat, laid the foundation for disorders which continued on him till the time of his death; so that, from the fourteenth year of his age to his twenty-eighth, when he died, he can scarcely be said to have had the blessing of health, even for so short an interval as a month. ^Notwithstanding this severe sickness, he studied the mathematics, and acquired some considerable knowledge in those sciences; for he solved several questions in the Diaries. As to astronomy, it seemed to have been his favourite study; and he left behind him the result of hiss calculations of the eclipses of the Sun and Moon, with the transits of Mercury, for more than ten years to come, with their delineations. He was assistant to Mr. Hervey in his studying the use of the globes and that pious clergyman preached his funeral sermon, July 15, 1746. His works were published by his younger brother, Benjamin Donn, who about 1756 opened an academy at Kingston, near Taunton, in Somersetshire, where he taught with great success, and where he died in 1798, after publishing some mathematical treatises.

, a German mathematician, was born at Nuremberg in 1677, and was first intended by his

, a German mathematician, was born at Nuremberg in 1677, and was first intended by his family for the bar, but soon relinquished the study of the law for that of mathematics, in which he was far more qualified to excel. He became professor of mathematics at Nuremberg, after having travelled into Holland and England to profit by the instructions of the most eminent scholars in that science. In England he became acquainted with Flamstead, Wallis, and Gregory, and in 1733, long after he returned home, was elected a fellow of the royal society as he was also of the societies of Petersburgh and Berlin. His works, in German, on astronomy, geography, and mathematics, are numerous. He also published some in Latin: “Nova Methodus parandi Sciaterica Solaria/' 1720.” Physica experimentis illustrata,“4to;” Atlas Ccelestis," 1742, fol. Doppelmaier made some curious experiments in electricity, at the latter part of his life, which he also published; and translated the astronomical tables of Stretius, French and English, into Latin.

ugh the great care of his father, not only a good linguist and poet, but also a good philosopher and mathematician. To all this he afterwards added an exquisite knowledge of the

He left four sons behind him; the eldest of whom, Janus Dousa, would, if he had lived, have been a more extraordinary man than his father. Joseph Scaliger calls him the ornament of the world; and says, that in the flower of his age he had reached the same maturity of wisdom and erudition, as others might expect to attain after a life spent in study. Grotius also assures us, that his poems exceeded those of his father; whom he assisted in composing the Annals of Holland. He was born in 1572; and, before he was well out of infancy, became, through the great care of his father, not only a good linguist and poet, but also a good philosopher and mathematician. To all this he afterwards added an exquisite knowledge of the civil law and of history. Besides a great many poems, which he composed in a very tender age, we have his notes and observations upon several Latin poets. Those upon Plautus were the product of his sixteenth year; and he was not above nineteen when he published his book “De Rebus Ccelestibus,” and his “Echo, sive Lusus imaginis jocose.” His commentaries upon Catullus, Tibullus, and Propertius, were published the same year. His extraordinary fame and merit caused him to be made preceptor to the prince of Orange, and afterwards first librarian of the university of Leyden. He died at the Hague, in his return from Germany in 1597, when he had not quite completed his 26th year.

and, if we may believe his epitaph, which is preserved by Weever, he was not only a musician, but a mathematician, and an eminent astrologer. Of his musical compositions nothing

, “an English musician of the fifteenth century, at an early stage of counterpoint, acquired on the continent the reputation of being its inventor, which, however, Dr. Burney has proved could not belong to him. He was the musician whom the Germans, from a similarity of name, have mistaken for saint Dunstan, and to whom, as erroneously, they have ascribed with others the invention of counterpoint in four parts. He was author of the musical treatise” De Mensurabili Musica,“which is cited by Franchinus, Morley, and Ravenscroft. But though this work is lost, there is still extant in the Bodleian library, a Geographical Tract by this author and, if we may believe his epitaph, which is preserved by Weever, he was not only a musician, but a mathematician, and an eminent astrologer. Of his musical compositions nothing remains but two or three fragments in Franchinus, and Morley. He is very unjustly accused by this last writer of separating the syllables of the same words by rests. Stow calls him” a master of astronomy and music," and says he w;;s buried in the church of St. Stephen, Walbrook, in 1458.

Chandler, to Leyden, where he remained two years. He became an excellent classical scholar, a great mathematician and natural philosopher, was well versed iti the Hebrew, and

, a man of great learning, and the friend and associate of the literati of the last age, was born about 1725, and educated at Northampton, under Dr. Doddridge, and for some time had the additional benefit of being instructed by the learned Dr. John Ward, professor of rhetoric in Gresham -college. He afterwards studied under professor Hutcheson at Glasgow, and to complete his education, his father, an eminent jeweller in London, sent him, by the advice of Dr. Chandler, to Leyden, where he remained two years. He became an excellent classical scholar, a great mathematician and natural philosopher, was well versed iti the Hebrew, and a master of the Latin, Italian, and French languages. Added to these endowments, he was of a temper so mild, and in his conversation so modest and unassuming, that he gained the attention and affection of all around him. In all questions of science, Dr. Johnson looked up to him; and in his life of Dr. Watts (where he calls him “the late learned Mr. Dyer”) has cited an observation of his, that Watts had confounded the idea of space with that of empty space, and did not consider, that though space might be without matter, yet matter, being extended, could not be without space.

, a very eminent mathematician, was born May 14, 1701, at Hurvvorth, a village about three

, a very eminent mathematician, was born May 14, 1701, at Hurvvorth, a village about three miles south of Darlington, on the borders of the county of Durham, at least it is certain he resided here from his childhood. His father, Dutlly Emerson, taught a school, and was a tolerable proficient in the mathematics; and without his books and instructions perhaps his son’s genius might might never have been unfolded. Besides his father’s instructions, our author was assisted in the learned languages by a young clergyman, then curate of Hurworth, who was boarded at his father’s house. In the early part of his life, he attempted to teach a few scholars; but whether from his concise method (for he was not happy in expressing his ideas), or the warmth of his natural temper, he made no progress in his school; he therefore Sood left it oft', and satisfied with a small paternal estate of about 60l. or 70l. a year, devoted himself to study, which he closely pursued in his native place through the course of a long life, being mostly very healthy, till towards the latter part of his days, when he was much afflicted with the stone: towards the close of the year 1781, being sensible of his approaching dissolution, he disposed of the whole of his mathematical library to a bookseller at York, and on May the 26th, 1782, his lingering and painful disorder put an end to his life at his native village, in the eighty-first year of his age. In his person he was rather short, but strong and well-made, with an open countenance and ruddy complexion. He was never known to ask a favour, or seek the acquaintance of a rich man, unless he possessed some eminent qualities of the mind. He was a very good classical scholar, and a tolerable physician, so far as it could be combined with mathematical principles, according to the plan of Keil and Morton. The latter he esteemed above all others as a physician the former as the best anatomist. He was very singular in his behaviour, dress, and conversation. His manners and appearance were that of a rude and rather boorish countryman, he wasof very plain conversation, and indeed seemingly rude, commonly mixing oaths in his sentences. He had strong natural parts, and could discourse sensibly on any subject; but was always positive and impatient of any contradiction. He spent his whole life in close study and writing books; with the profits of which he redeemed his little patrimony from some original incumbrance. He had but one coat, which he always wore open before, except the lower button no waistcoat; his shirt quite the reverse of one in. common use, no opening before, but buttoned close at the collar behind; a kind of flaxen wig which had not a crooked hair in it; and probably had never been tortured with a comb from the time of its being made. This was his dress when he went into company. One hat he made to last him the best part of his lifetime, gradually lessening the flaps, bit by bit, as it lost its elasticity and hung down, till little or nothing but the crown remained. He never rode although he kept a horse, but was frequently seen to lead the horse, with a kind of wallet stuffed with the provisions he had bought at the market. He always walked up to London when he had any thing to publish, revising sheet by sheet himself; trusting no eyes but his own, which was always a favourite maxim with him. He never advanced any mathematical proposition that he had not first tried in practice, constantly making all the different parts himself on a small scale, so that his house was filled with all kinds of mechanical instruments together or disjointed. He would frequently stand up to his middle in water while fishing; a diversion he was remarkably fond of. He used to study incessantly for some time, and then for relaxation take a ramble to any pot ale-house where he could get any body to drink with and talk to. The duke of Manchester was highly pleased with his company, and used often to come to him in the fields and accompany him home, but could never persuade him to get into a carriage. When he wrote his sinall treatise on navigation, he and some of his scholars took a small vessel from Hurworth, and the whole crew soon gotswampt; when Emerson, smiling and alluding to his treatise, said “They must not do as I do, but as I say.” He was a married man; and his wife used to spin on an old-fashioned wheel, of which a very accurate drawing is given in his mechanics. He was deeply skilled in the science of music, the theory of sounds, and the various scales both ancient and modern, but was a very poor performer. He carried that singularity which marked all his actions even into this science. He had, if we may be allowed the expression, two first strings to his violin, which, he said, made the E more melodious when they were drawn up to a perfect unison. His virginal, which is a species of instrument like the modern spinnet, he had cut and twisted into various shapes in the keys, by adding some occasional half-tones in order to regulate the present scale, and to rectify some fraction of discord that will always remain in the tuning. He never could get this regulated to his fancy, and generally concluded by saying, 4< It was a bad instrument, and a foolish thing to be vexed with."

eard the lectures of David Chytraeus, a celebrated divine and historian; and of Henry Bruce, an able mathematician and physician. The death of his father obliged him to return

, a learned professor of Groningen, was born at Gretha, a village in East Friesland, Dec. 5, 1547. He was the son of Emmo Diken, a minister of that village, who had been Luther’s and Melancthon’s disciple; and at nine years of age was sent to study at Embden. He continued there till he was eighteen, and was then sent to Bremen, to improve under the famous John Molanus. Returning to his father, he did not go immediately to the university, but passed some time at Norden. Being turned of twenty-three, he was sent to Rostock, a flourishing university, where he heard the lectures of David Chytraeus, a celebrated divine and historian; and of Henry Bruce, an able mathematician and physician. The death of his father obliged him to return to East Friesland, after he had continued above two years at Rostock.; and his mother’s excessive grief upon this occasion hindered his taking a journey into France, as he had wished, and induced him to continue with her three years, after which he went to Geneva, where he staid two years. Being returned into his own country, he had the choice of two preferments, either to be a minister or the rector of a college: but, from a great degree of natural timidity, he could not venture to engage in the ministry, thoagh it was very much his inclination. He chose therefore to be rector of a college, which was that of Norden and was admitted into that post in 1579. He made his college flourish exceedingly but was turned out of his employment in 1587, through the zeal of some Lutherans, because he would not subscribe the confession of Augsburg. He was chosen the year after to be rector of the college of Leer, whose reputation he raised so high, that it surpassed that of Norden; which the Lutherans could never retrieve from the declining state into which it fell after Emmius was deposed. They had banished from Groningen several persons who followed Calvin’s reformation; and those of the exiles who retired to Leer, meeting with the same fate as Emmius, engaged in a particular friendship with him: so that, when the city of Groningen confederated with the United Provinces, and the magistrates resolved to restore their college, Emmius being recommended by several persons, they chose him to be the rector of that college, and gave him a full power to make or abrogate there such statutes as he should think proper.

tells us, that he was living an ancient man in 1588; but does not know when he died. He was a great mathematician, skilled in vocal and instrumental music, eminent for his knowledge

, or Etheridge, or, as in Latin he writes himself, Edrycus, probably an ancestor of the preceding, was born at Thame in Oxfordshire, and admitted of Corpus Christi college, Oxford, in 1534; of which he was made probationer fellow in 1539. In 1543 he was licensed to proceed in arts; and, two years after, admitted to read any of the books of Hippocrates’s aphorisms. At length, being esteemed an excellent Grecian, he was made the king’s professor of that language about 1553, and so continued till some time after Elizabeth came to the crown, when, on account of his joining in the persecution of the protestants in Mary’s reign, was forced to leave it. He practised medicine with great success in Oxford, where he mostly lived; and also took under his care the sons of many popish gentlemen, to be instructed in the several arts and sciences; among whom was William Gifford, afterwards archbishop of Rheims. He was reckoned a very sincere man, and adhered to the last to the catholic religion, though he suffered exceedingly by it. Wood tells us, that he was living an ancient man in 1588; but does not know when he died. He was a great mathematician, skilled in vocal and instrumental music, eminent for his knowledge of the Greek and Hebrew languages, a poet, and, above all, a physician. There are musical compositions and Latin poems of his still extant in manuscript. In manuscript also he presented to queen Elizabeth, when she was at Oxford in 1566, “Acta Henrici Octavi, carmine Graeco.” He also turned the psalms into a short form of Hebrew verse; and translated the works of Justin Martyn into Latin. In 1588 was published by him in 8vo, “Hypomnemata quasdam in aliquot libros Pauli Æginetae, seu observationes medicamentorum qui hue aetate in usu sunt.” The antiquary Leland was his intimate friend, and in his life-time celebrated his praises in these lines:

, the celebrated mathematician, according to the account of Pappus and Proclus, was born at

, the celebrated mathematician, according to the account of Pappus and Proclus, was born at Alexandria, in Egypt, where he flourished and taught mathematics, with great applause, under the reign of Ptolemy Lagos, about 280 years before Christ. And here, from his time till the conquest of Alexandria by the Saracens, all the eminent mathematicians were either born, or studied; and it is to Euclid, and his scholars, we are beholden for Eratosthenes, Archimedes, Apollonius, Ptolemy, Theon, &c. &c. He reduced into regularity and order all the fundamental principles of pure mathematics, which had been delivered down by Thales, Pythagoras, Eudoxus, and other mathematicians before him, and added many others of his own discovering: on which account it is said he was the first who reduced arithmetic and geometry into the form of a science. He likewise applied himself to the study of mixed mathematics, particularly to astronomy and optics. His works, as we learn from Pappus and Proclus, are the Elements, Data, Introduction to Harmony, Phenomena, Optics, Catoptrics, a Treatise of the Division of Superficies, Porisms, Loci ad Superficiem, Fallacies, and four books of Conies. The most celebrated of these, is the Elements of Geometry, first published at Basil, 1533, by Simon Grynaeus, of which there have been numberless editions, in all languages; and a fine edition of all his works was printed in 1703, by Dr. David Gregory, SaTilian professor of astronomy at Oxford, which is the most complete, and is illustrated by the notes of sir Henry Savile, and dissertations and discussions on the authenticity of the several pieces attributed to Euclid.

onidas was, neither the editor, George Valla, nor any one else pretends to know. It was John Pena, a mathematician in the service of the king of France, who first published this

Euclid, as a writer on music, has ever been held in the highest estimation by all men of science who have treated of harmonics, or the philosophy of sound. As Pythagoras was allowed by the Greeks to have been the first who found out musical ratios, by the division of a monochord, or single string, a discovery which tradition only had preserved, Euclid was the first who wrote upon the subject, and reduced these divisions to mathematical demonstration. His “Introduction to Harmonics,” which in some Mss. was attributed to Cleonidas, is in the Vatican copy given to Pappus; Meibomius, however, accounts for this, by supposing those copies to have been only two different ms editions of Euclid’s work, which had been revised, corrected, and restored from the corruptions incident to frequent transcription by Cleonidas and Pappus, whose names were, on that account, prefixed. It first appeared in print with a Latin version, in 1498, at Venice, under the title of “Cleonidae Harmonicum Introductorium:” who Cleonidas was, neither the editor, George Valla, nor any one else pretends to know. It was John Pena, a mathematician in the service of the king of France, who first published this work at Paris, under the name of Euclid, 1557. After this, it went through several editions with his other works.

, a very eminent mathematician, was born at Basil, on the 14th of April, 1707: he was the son

, a very eminent mathematician, was born at Basil, on the 14th of April, 1707: he was the son of Paul Euler and of Margaret Brucker (of a family illustrious in literature), and spent the first year of his life at the village of Richen, of which place his father was protestant minister. Being intended for the church, his father, who had himself studied under James Bernoulli!, taught him mathematics, as a ground-work of his other studies, or at least a noble and useful secondary occupation. But Euler, assisted and perhaps secretly encouraged by John Bernoulli, who easily discovered that he would be the greatest scholar he should ever educate, soon declared his intention of devoting his life to that pursuit. This intention the wise father did not thwart, but the son did not so blindly adhere to it, as not to connect with it a more than common improvement in every other kind of useful learn-, ing, insomuch that in his latter days men often wondered how with such a superiority in one branch, he could have been so near to eminence in all the rest. Upon the foundation of the academy of sciences at St. Petersburgh, in, 1723, by Catherine I. the two younger Bernouillis, NichoJas and Daniel, had gone thither, promising, when they set out, to endeavour to procure Euler a place in it: they accordingly wrote to him soon after, to apply his mathetics to physiology, which he did, and studied under the best naturalists at Basil, but at the same time, i. e. in 1727, published a dissertation on the nature and propagation of sound; and an answer to the question on the masting of ships, which the academy of sciences at Paris judged worthy of the accessit. Soon after this, he was called to St. Petersburgh, and declared adjutant to the mathematical class in the academy, a class, in which, from the circumstances of the times (Newton, Leibnitz, and so many other eminent scholars being just dead), no easy laurels were to be gathered. Nature, however, who had organized so many mathematical heads at one time, was not yet tired of her miracles and she added Euler to the number. He indeed was much wanted the science of the calculus integralis, hardly come out of the hands of its creators, was still too near the stage of its infancy not to want to be made more perfect. Mechanics, dynamics, and especially hydrodynamics, and the science of the motion of the heavenly bodies, felt the imperfection. The application of the differential calculus, to them, had been sufficiently successful; but there were difficulties whenever it was necessary to go from the fluxional quantity to the fluent. With regard to the nature and properties of numbers, the writings of Fermat (who had been so successful in them), and together with these all his profound researches, were lost. Engineering and navigation were reduced to vague principles, and were founded on a heap of often contradictory observations, rather than a regular theory. The irregularities in the motions of the celestial bodies, and especially the complication of forces whitfh influence that of the moon, were still the disgrace of geometers. Practical astronomy had jet to wrestle with the imperfection of telescopes, insomuch, that it could hardly be said that any rule for making them existed. Euler turned his eyes to all these objects he perfected the calculus integralis he was the inventor of a new kind of calculus, that of sines he simplified analytical operations and, aided by these powerful help-mates, and the astonishing facility with which he knew how to subdue expressions the most intractable, he threw a new light on all the branches of the mathematics. But at Catherine’s death the academy was threatened with extinction, by men who knew not the connection which arts and sciences have with the happiness of a people. Euler was offered and accepted a lieutenancy on board one of the empress’s ships, with the promise of speedy advancement. Luckily things changed, and the learned captain again found his own element, and was named Professor of Natural Philosophy in 1733, in the room of his friend John Bernouilli. The number of memoirs which Euler produced, prior to this period, is astonishing, but what he did in 1735 is almost incredible, An important calculation was to be made, without loss of time; the other academicians had demanded some months to do it. Euler asked three days—in three days he did it; but the fatigne threw him into a fever, and the fever left him not without the loss of an eye, an admonition which would have made an ordinary man more sparing of the other. The great revolution, produced by the discovery of fluxions, had entirely changed the face of mechanics; still, however, there was no complete work on the science of motion, two or three only excepted, of which Euler felt the insufficiency. He saw, with pain, that the best works on the subject, viz. “Newton’s Principia,” and “Herman’s Phoronomia,” concealed the method by which these great men had come at so many wonderful discoveries, under a synthetic veil. In order to lift this up, Euler employed all the resources of that analysis which had served him so well on so many other occasions; and thus uniting his own discoveries to those of other geometers, had them published by the academy in 1736. To say that clearness, precision, and order, are the characters of this work, would be barely to say, that it is, what without these qualities no work can be, classical of its kind. It placed Euler in the rank of the first geometricians then existing, and this at a time when John Bernouilli was still living. Such labours demanded some relaxation; the only one which Euler admitted was music, but even to this he could not go without the spirit of geometry with him. They produced together the essay on a new theory of music, which was published in 1739, but not very well received, probably, because it contains too much geometry for a musician, and too much music for a geometrician. Independently, however, of the theory, which is built on Pythagorean principles, there are many things in it which may be of service, both to composers, and to makers of instruments. The doctrine, likewise, of the genera and the modes of music is here cleared up with all the clearness and precision which mark the works of Euler. Dr. Burney remarks, that upon the whole, Euler seems not to have invented much in this treatise; and to have done little more than arrange and methodize former discoveries in a scientific and geometric manner. He may, indeed, not have known what antecedent writers had discovered before; and though not the first, yet to have imagined himself an inventor. In 1740, his genius was again called forth by the academy of Paris (who, in 1738, had adjudged the prize to his paper on the nature and properties of fire) to discuss the nature of the tides, an important question, which demanded a prodigious extent of calculations, aud an entire new system of the world. This prize Euler did not gain alone; but he divided it with Maclaurin and D. Bernouilli, forming with them a triumvirate of candidates, which the realms of science had not often beheld. The agreement of the several memoirs of Euler and Bernouilli, on this occasion, is very remarkable. Though the one philosopher had set out on the principle of admitting vortices, which the other rejected, they not only arrived at the same end of the journey, but met several times on the road; for instance, in the determination of the tides under the frozen zone. Philosophy, indeed, led these two great men by different paths; Bernouilli, who had more patience than his friend, sanctioned every physical hypothesis he was obliged to make, by painful and laborious experiment. These Euler’s impetuous genius scorned; and, though his natural sagacity did not always supply the loss, he made amends by his superiority in analysis, as often as there was any occasion to simplify expressions, to adapt them to practice, and to recognize, by final formulae, the nature of the result. In 1741, Euler received some very advantageous propositions from Frederic the Second (who had just ascended the Prussian throne), to go and assist him in forming an academy of sciences, out of the wrecks of the Royal Society founded by Leibnitz. With these offers the tottering state of the St. Petersburgh academy, under the regency, made it necessary for the philosopher to comply. He accordingly illumined the last volume of the “Melanges de Berlin,” with five essays, which are, perhaps, the best things in it, and contributed largely to the academical volumes, the first of which was published in 1744. No part of his multifarious labours is, perhaps, a more wonderful proof of the extensiveness and facility of his genius, than what he executed at Berlin, at a time when he contrived also that the Petersburgh acts should not suffer from the loss of him. In 1744, Euler published a complete treatise of isoperimetrical curves. The same year beheld the theory of the motions of tb.e planets and comets; the well-known theory of magnetism, which gained the Paris prize; and the much-amended translation of Robins’ s “Treatise on Gunnery.” In 1746, his “Theory of Light and Colours” overturned Newton’s “System of Emanations;” as did another work, at that time triumphant, the “Monads of Wolfe and Leibnitz.” Navigation was now the only branch of useful knowledge, for which the labours of analysis and geometry had done nothing. The hydrographical part alone, and that which relates to the direction of the course of ships, had been treated by geometricians conjointly with nautical astronomy. Euler was the first who conceived and executed the project of making this a complete science. A memoir on the motion of floating bodies, communicated to the academy of St. Petersburgh, in 1735, by M. le Croix, first gave him this idea. His researches on the equilibrium of ships furnished him with the means of bringing the stability to a determined measure. His success encouraged him to go on, and produced the great work which the academy published in 1749, in which we find, in systematic order, the most sublime notions on the theory of the equilibrium and mo. tion of floating bodies, and on the resistance of fluids. This was followed by a second part, which left nothing to be desired on the subject, except the turning it into a language easy of access, and divesting it of the calculations which prevented its being of general use. Accordingly in 1773, from a conversation with admiral Knowles, and other assistance, out of the “Scientia Navalis,” 2 vols. 4to, was produced, the “Theorie complette de la Construction et de la Manoeuvre des Vaisseaux.” This work was instantly translated into all languages, and the author received a present of 6000 livres from the French king: he had before had 300l. from the English parliament, for the theorems, by the assistance of which Meyer made his lunar tables . And now it was time to collect into one systematical and continued work, all the important discoveries on the infinitesimal analysis, which Euler had been making for thirty years, and which lay dispersed in the memoirs of the different academies. This, accordingly, the professor undertook; but he prepared the way by an elementary work, containing all the previous requisites for this study. This is called “An Introduction to the analysis of Infinitesimals,” and is a work in which the author has exhausted all the doctrine of fractions, whether algebraical or transcendental, by shewing their transformation, their resolution, and their developernent. This introduction was soon, followed by the author’s several lessons on the “calculus integralis, and differentialis.” Having engaged himself to count Orlow, to furnish the academy with papers sufficient to fill their volumes for twenty years after his death, the philosopher is likely to keep his word, having presented seventy papers, through Mr. Golofkin, in the course of his life, and left two hundred and fifty more behind him; nor is there one of these that does not contain a discovery, or something that may lead to one. The most ancient of these memoirs form the collection then published, under the title of “Opuscula Analytica.” Such were Euler’s labours, and these his titles to immortality His memory shall endure till science herself is no more! Few men of letters have written so much as Euler no geometrician, has ever embraced so many objects at one time or has equalled him, either in the variety or magnitude of his discoveries. When we reflect on the good such men do their fellow-creatures, we cannot help indulging a wish (vain, alas as it is) for their illustrious course to be prolonged beyond the term allotted to mankind. Euler’s, though it has had an end, was very long and very honourable; and it affords us some consolation for his loss, to think that he enjoyed it exempt from the ordinary consequences of extraordinary application, and that his last labours abounded in proofs of that vigour of understanding which marked his early days, and which he preserved to his end. Some swimmings in the head, which seized him on the first days of September, 1783, did not prevent his laying hold of a few facts, which reached him through the channel of the public papers, to calculate the motions of the aerostatical globes; and he even compassed a very difficult integration, in which the calculation had engaged him . But the decree was gone forth: on the 7th of September he talked with Mr. Lexell, who had come to dine with him, of the new planet, and discoursed with him upon other subjects, with his usual penetration. He was playing with one of his grand-children at tea-time, when he was seized with an apoplectic fit. “I am dying,” said he, before he lost his senses; and he ended his glorious life a few hours after, aged seventy-six years, five months, and three days. His latter days were tranquil and serene. A few infirmities excepted, which are the inevitable lot of an advanced age, he enjoyed a share of health which allowed him to give little time to repose. Euler possessed to a great degree what is commonly called erudition he had read all the Latin classics was perfect master of ancient mathematical literature and had the history of all ages, and all nations, even to the minutest facts, ever present to his mind. Besides this, he knew much more of physic, botany, and chemistry, than could be expected from any man who had not made these sciences his peculiar occupation. “I have seen,” says his biographer, Mr. Fuss, “strangers go from him with a kind of surprise mixed with admiration; they could not conceive how a man, who for half a century had seemed taken up in making and publishing discoveries in natural philosophy and mathematics, could have found means to preserve so much knowledge that seemed useless to himself, and foreign to the studies in which he was engaged. This was the effect of a happy memory, that lost nothing of what had ever been entrusted to it nor was it a wonder that the man who was able to repeat the whole Æneis, and to point out to his hearers the first and last verses of every page of his own edition of it, should not have lost what he had learned, at an age when the impressions made upon us are the strongest. Nothing can equal the ease with which, without expressing the least degree of ill-humour, he could quit his abstruse meditations, and give himself up to the general amusements of society. The art of not appearing wise above one’s fellows, of descending to the level of those with whom one lives, is too rare in these days not to make it a merit in Euler to have possessed it. A temper ever equal, a natural and easy chearfulness, a species of satirical wit, tempered with urbane humanity, the art of telling a story archly, and with simplicity, made his conversation generally sought. The great fund of vivacity which he had at all times possessed, and without which, indeed, the activity we have just been admiring could not have existed, carried him sometimes away, and he was apt to grow warm, but his anger left him as quickly as it came on, and there never has existed a man to whom he bore malice. He possessed a precious fund of rectitude and probity. The sworn enemy of injustice, whenever or by whomsoever committed, he used to censure and attack it, without the least attention to the rank or riches of the offender. Recent examples of this are in the recollection of all who hear me.” As he was filled with respect for religion, his piety was sincere, and his devotion full of fervour. He went through all his Christian duties with the greatest attention. Euler loved all mankind, and if he ever felt a motion of indignation, it was against the enemy of religion, particularly against the declared apostles of infidelity. He was of a very religious turn of mind. He published a New Demonstration of the Existence of God, and of the Spirituality of the Soul, which last has been admitted into several divinity schools as a standard book. With scrupulous exactness he adhered to the religion of his country, that of Calvinism, and, fortified by its principles, he was a good husband, a good father, a good friend, a good citizen, a good member of private society.

, of Ascalon in Palestine, a Greek mathematician of the sixth century, was one of the most intelligent of those

, of Ascalon in Palestine, a Greek mathematician of the sixth century, was one of the most intelligent of those who lived in the decline of Greek literature. He wrote Commentaries on the Conies of Apollonius, which were addressed to Anthcmius, and are inserted in Halley’s edition of that author, published at Oxford in 1710; and on the most important works of Archimedes, which lately appeared with every advantage of elegance and correctness, in the folio edition of Archimedes, jssued from the Clarendon press in 1792, which was prepared for publication by Torelli of Verona. Eutocius has some of the best qualities of a commentator. He very seldom passes over a difficult passage in his author without explaining it, or a chasm in the reasoning without supplying the defect. His remarks are usually full; and so anxious is he to render th text perspicuous, that sometimes he undertakes to elucidate where his author may be thought sufficiently clear. Writers have differed about his age; Saxius, one of the latest, and generally most accurate, authorities, places him in the fifth century; but Eutocius addresses Anthemius; and we find from his own writings, that Isidorus was his preceptor, both of whom were, according to Procopius, the architects of the church of St. Sophia, built at Constantinople, about the year 532; consequently, Eutocius must have flourished in the middle of the sixth century.

ford, half sheet prints, the heads of the philosophers from Rubens, and a portrait of Dr. Wallis the mathematician, from Kneller. The other John Faber, the younger, was his son,

, is the name of two engravers whose works are held in some estimation among portrait-collectors. The elder was born in Holland, where he learned the art of mezzotinto-scraping, and also drew portraits from the life, on vellum, with a pen. What time he came into England does not appear, but he resided here a considerable time, in Fountain court in the Strand, London. He died at Bristol in May 1721. He drew many of the portraits which he engraved from nature, but they are not remarkable either for taste or execution. His most esteemed works were, a collection of the founders of the colleges of Oxford, half sheet prints, the heads of the philosophers from Rubens, and a portrait of Dr. Wallis the mathematician, from Kneller. The other John Faber, the younger, was his son, and lived in London, at the Golden Head in Bloomsbury-square, where Strutt thinks he died in 1756. Like his father, he confined himself to the engraving of portraits in mezzotinto; but he excelled him in every requisite of the art. The most esteemed works are the portraits of the Kit-Cat club, and the Beauties of Hampton Court. Some of his portraits are bold, free, and beautiful.

p Burnet, in the first letter of his Travels, dated September 1685, speaks of him as an incomparable mathematician and philosopher, who, though only twenty-one years old, was

, a man of considerable learning, but unfortunately connected with the French prophets, was a native of Switzerland, whither his family, originally Italians, were obliged to take refuge, for religion’s sake, in the beginning of the reformation. He was born Feb. 16, 1664. His father intending him for the study of divinity, he was regularly instructed in Greek and Latin, philosophy, mathematics, and astronomy; learned a little of the Hebrew tongue, and began to attend the lectures of the divinity professors of Geneva: but his mother being averse to this, he was left to pursue his own course, and appears to have produced the first fruits of his studies in some letters on subjects of astronomy sent to Cassini, the French king’s astronomer. In 1682 he went to Paris, where Cassini received him very kindly. In the following year he returned to Geneva, where he became particularly acquainted with a count Fenil, who formed the design of seizing, if not assassinating the prince of Orange, afterwards William III. This design Faccio having learned from him communicated it to bishop Burnet about 1686, who of course imparted it to the prince. Bishop Burnet, in the first letter of his Travels, dated September 1685, speaks of him as an incomparable mathematician and philosopher, who, though only twenty-one years old, was already become one of the greatest men of his age, and seemed born to carry learning some sizes beyond what it had hitherto attained. Whilst Dr. Calamy studied at the university of Utrecht, Faccio resided in that city as tutor to two young gentlemen, Mr. Ellys and Mr. Thornton, and conversed freely with the English. At this time he was generally esteemed to be a Spinozist; and his discourse, says Dr. Calamy, very much looked that way. Afterwards, it is probable, that he was professor of mathematics at Geneva. In 1687 he came into England, and was honoured with the friendship of the most eminent mathematicians of that age. Sir Isaac Newton, in particular, was intimately acquainted with him. Dr. Johnstone of Kidderminster had in his possession a manuscript, written by Faccio, containing commentaries and illustrations of different parts of sir Isaac’s Principia. About 1704 he taught mathematics in Spitafnelds, and obtained about that time a patent fora species of jewel-watches. When he unfortunately attached himself to the new prophets, he became their chief secretary, and committed their warnings to writing, many of which were published. The connexion of such a man with these enthusiasts, and their being supported, likewise, by another person of reputed abilities, Maximilian Misson, a French refugee, occasioned a suspicion, though without reason, that there was some deep contrivance and design in the affair. On the second of December, 1707, Faccio stood in the pillory at Charing-cross, with the following words affixed to his hat: “Nicolas Fatio, convicted for abetting and favouring Elias Marion, in his wicked and counterfeit prophecies, and causing them to be printed and published, to terrify the queen’s people.” Nearly at the same time, alike sentence was executed upon Elias Marion, one of the pretended prophets, and John d'Ande, another of their abettors. This mode of treatment did not convince Faccio of his error; and, indeed, the delusion of a man of such abilities, and simplicity of manners, was rather an object of compassion than of public infamy and punishment. Oppressed with the derision and contempt thrown upon himself and his party, he retired at last into the country, and spent the remainder of a long life in silence and obscurity. He died at Worcester in 1753, about eightynine years old. When he became the dupe of fanaticism, he seems to have given up his philosophical studies and connections. Faccio, besides being deeply versed in all branches of mathematical literature, was a great proficient in the learned and oriental languages. He had read much, also, in books of alchymy. To the last, he continued a firm believer in the reality of the inspiration of the French prophets. Dr. Wall of Worcester, who was well acquainted with him, communicated many of the above particulars to Dr. Johnstone, in whose hands were several of Faccio’s fanatical manuscripts and journals; and one of his letters giving an account of count Fenil’s conspiracy, and some particulars of the author’s family was communicated to the late Mr. Seward, and published in the second volume of his Anecdotes. In the Republic of Letters, vol. I. we find a Latin poem by Faccio, in honour of sir Isaac Newton; and in vol. XVIII. a communication on the rules of the ancient Hebrew poesy, on which subject he appears to have corresponded with Whiston. There are also many of his original papers and letters in the British Museum; and among them a Latin poem, entitled “N. Facii Duellerii Auriacus Throno-Servatus,” in which he claims to himself the merit of having saved king William from the above-mentioned conspiracy.

, a very celebrated French mathematician, though by profession a lawyer, was considered by the writers

, a very celebrated French mathematician, though by profession a lawyer, was considered by the writers of his own country as having rendered no less service to mathematical science than Descartes, and as having even prepared the way for the doctrine of infinites, afterwards discovered by Newton and Leibnitz. He was not only the restorer of the ancient geometry, but the introducer of the new. He was born at Toulouse in 1590, educated to the law, and advanced to the dignity of counsellor to the parliament of Toulouse. As a magistrate, his knowledge and integrity were highly esteemed. As a mani of science he was connected with Descartes, Huygens, Pascal, and many others. He is said also to have cultivated poetry. He died in 1664. His mathematical works were published at Toulouse in 1679, in two volumes, folio. The first volume contains the treatise of arithmetic of Diophantus, with a commentary, and several analytical inventions. The second comprises his mathematical discoveries, and his correspondence with the most celebrated geometricians of his age. His son, Samuel Fermat, was also eminent as a literary man, and wrote some learned dissertations.

, he imparted it to a relation, who shewed it to Mr. Halton of Wingfield manor in Derbyshire, a good mathematician, as appears from some pieces of his, in the appendix to Foster’s

Having, however, calculated by these tables an eclipse of the sun, which was to happen June 22, 1666, he imparted it to a relation, who shewed it to Mr. Halton of Wingfield manor in Derbyshire, a good mathematician, as appears from some pieces of his, in the appendix to Foster’s “Mathematical Miscellanies.” He came to see Flamsteed soon after; and finding he was not acquainted with the astronomical performances of others, he sent him Riccioli’s “Almagestum Novum,” and Kepler’s “Tabulae Rudolphinae,” to which he was before a stranger. He prosecuted his astronomical studies from this time with all imaginable vigour and success. In 1669, he collected some remarkable eclipses of the fixed stars, by the moon, which would happen in 1670, calculating them from the Caroline Tables; and directed them to lord Brouncker, president of the royal society. This produced very good effects; for his production being read before that society, was so highly approved, that it procured him letters of thanks, dated Jan. 14, 1669-70, from Oldenburg their secretary, and from Mr. John Collins, one of their members, with whom he corresponded several years. These Jetters were in the hands of William Jones, esq. F. R. S, father of the celebrated sir William Jones. Extracts from them are given in the “Biographia Britannica.

edge wherever knowledge was to be found, Abraham (now Mr.) Fletcher, became a botanist, as well as a mathematician: but he studied the properties, rather than the classification

At about the age of thirty, even his wife began to be persuaded, that learning, according to the old saw, may sometimes be a substitute for house and land, and consented to his relinquishing his manual labours, and setting up as a schoolmaster. For several years, he was a teacher of mathematics of considerable reputation; and many respectable yoimg men were his pupils. Still pursuing knowledge wherever knowledge was to be found, Abraham (now Mr.) Fletcher, became a botanist, as well as a mathematician: but he studied the properties, rather than the classification of plants; and made many experiments to ascertain their medical virtues. Few men, it is believed, have lately made a greater proficiency than he did, in this (now perhaps too much neglected) department of science: and he was soon qualified to commence doctor, as well as schoolmaster. It is true, indeed, he practised chiefly, if not solely, with decoctions, or diet-drinks: yet with these, he either performed, or got the reputation of performing, many extraordinary cures; and had no small practice. Doctor Fletcher was particularly famed for his skill and success in hypochondriacal cases; and, had he been as able to describe, as he was to relieve and cure such cases, many things in this way occurred in his practice, to which even the most learned might have attended with advantage. He was also deeply versant in astrological predictions, and is said to have foretold the time of his own death, within a few days. We have more pleasure, however, in adding that Mr. Fletcher, with all his attention to intellectual attainments, never was inattentive to the duties of his relative station. He was both industrious and economical, and was enabled to leave his large family the sum of 4000l. three-fourths of which were of his own earning. He died Jan. 1, 1793. In 1762 he published a large mathematical work, in 8vo, called “The Universal Measurer,” which, as a collection of mathematical knowledge, is said to possess very great merit.

, an English mathematician, and professor of astronomy at Gresham college, was born in

, an English mathematician, and professor of astronomy at Gresham college, was born in Northamptonshire or as Aubrey says, at Coventry, where he adds that he was some time usher of the school and was sent to Emanuel college, Cambridge, in 1616. He took the degree of B. A. in 1619, and of master in 1623. He applied early to the mathematics, and attained to great proficiency in that kind of knowledge, of which he gave the first specimen in 1624. He had an elder brother at the same college with himself, which precluded him from a fellowship; in consequence of which, he offered himself a candidate for the professorship of astronomy in Gresham college, Feb. 1636, and was elected the 2 d of March. He quitted it again, it does not appear for what reason, Nov. 25, the same year, and was succeeded therein by Mr. Mungo Murray, professor of philosophy at St. Andrew’s in Scotland. Murray marrying in 1641, his professorship was thereby vacated; and as Foster bad before made way for him, so he in his turn made way for Foster, who was re-elected May 22, the same year. The civil war breaking out soon after, he became one of that society of gentlemen, who had stated meetings for cultivating philosophy, and afterwards were established by charter, under the name of the royal society, in the reign of Charles II. In 1646, Dr. Wallis, another member of that society, received from Foster a mathematical theorem, which he afterwards published in his “Mechanics.” Neither was it only in this branch of science that he excelled, but he was likewise well versed in the ancient languages; as appear! from his revising and correcting the “Lemmata” of Archimedes, which had been translated from an Arabic manuscript into Latin, but not published, by Mr. John Greaves. He made also several curious observations upon eclipses, both of the sun and moon, as well at Gresham college, as in Northamptonshire, at Coventry, and in other places; and was particularly famous for inventing, as well as improving, astronomical and other mathematical instruments. After being long in a declining state of health, he died in July 1652, at his own apartment at Gresham college, and, according to Aubrey, was buried in the church of St. Peter le poor. His works are, 1. “The Description and use of -a small portable Quadrant, for the more easy finding of the hour of azimuth/' 1624, 4to, This treatise, which has been reprinted several times, is divided into two parts, and was originally published at the end of Gunter’s” Description of the Cross Staffe in three hooks,“to which it was intended as an appendix. 2.” The Art of Dialling,“1638, 4to. Reprinted in 1675, with several additions and variations from the author’s own manuscript, as also a supplement by the editor William Leybourne. Our author himself published no more, yet left many other treatises, which, though not finished in the manner he intended, were published by his friends after his death as, 3.” Posthuinu Fosteri containing the description of a Ruler, upon which are inscribed divers scales, &c.“1652, 4to. This was published by Edmund Wingate, esq. 4.” Four Treatises of Dialling,“1654, 4to. 5.” The Sector altered, and other scales added, with the description and use thereof, invented and written by Mr. Foster, and now published by William Leybourne, 1661,“4to. This was an improvement of Gunter’s Sector, and therefore published among his works. 6.” Miscellanies, or Mathematical Lucubrations of Mr. Samuel Foster, published, and many of them translated into English, by the care and industry of John Twysden, C. L. M. D. whereunto he hath annexed some things of his own." The treatises in this collection are of different kinds, some of them written in Latin, some in English.

his enlightened design, the founder invited to his new college Ludovicus Vives, Nicholas Crucher the mathematician, Clement Edwards and Nicholas Utten, profes-f ors of Greek;

But what conferred an almost immediate superiority of reputation on this society, was the appointment of two lectures for Greek and Latin, which obtained the praise and admiration of Erasmus and the other learned men who urere now endeavouring to introduce a knowledge of the classics as an essential branch of academic study. With this enlightened design, the founder invited to his new college Ludovicus Vives, Nicholas Crucher the mathematician, Clement Edwards and Nicholas Utten, profes-f ors of Greek; Thomas Lupset, Richard Pace, and other men of -established reputation. This, Mr. Warton observes, was a new and noble departure from the narrow plan of academical education. The course of the Latin lecturer was not confined to the college, but open to the students of Oxford in general. He was expressly directed to drive barbarism from the new college, barbarieme nostro alveario pro virili si quando pullulet cxtirpet et ejiciat. The Greek lecturer was ordered to explain the best Greek classics, and those which Fox specified on this occasion, are the purest in the opinion of modern times. But such was the temper of the age, that Fox was obliged to introduce his Greek lectureship, by pleading that the sacred canons had commanded, that a knowledge of the Greet tongue should not be wanting in public seminaries of education. By the sacred canons he meant a decree of the council of Vienne, in Dauphiny, promulgcd so early as 1311, which enjoined that professorships of Greek, Hebrew, and Arabic, should be instituted in the universities of Oxford, Paris, Bononia, Salamanca, and the court of Rome. This, however, was not entirely satisfactory. The prejudices against the Greek were still, so inveterate, that the university was for some time seriously disturbed by the advocates of the school-learning. The persuasion and example of Erasmus, who resided about this time in St. Mary’s college, had a considerable effect in restoring peace, and more attention was gradually bestowed on the learned languages, and this study, so curiously introduced under the sanction of pope Clement’s decree of Vienne, proved at no great distance of time, a powerful instrument in effecting the reformation. Those who would deprive Clement of the liberality of his edict, state his chief motive to have been a superstitious regard for the Latin, Greek, and Hebrew, because the superscription on the cross was written in these languages.

ttres, but in all arts and sciences. He was a poet, a philosopher, a physician, an astronomer, and a mathematician. He was a man also of great political consequence, as appears

an eminent Italian poet and physician, was born at Verona in 1483. Two singularities are related of him in his infancy; one, that his lips adhered so closely to each other when he came into the world, that a surgeon was obliged to divide them with his knife; the other, that his mother, Camilla Mascarellia, was killed by lightning, while he, though in her arms at the very moment, escaped unhurt. Fracastorio was of parts so exquisite, and made so wonderful a progress in every thing he undertook, that he became eminently skilled, not only in the belles lettres, but in all arts and sciences. He was a poet, a philosopher, a physician, an astronomer, and a mathematician. He was a man also of great political consequence, as appears from pope Paul Ill.'s making use of his authority to remove the council of Trent to Bologna, under the pretext of a contagious distemper, which, as Fracastorio deposed, made it no longer safe for him to continue at Trent. He was intimately acquainted with cardinal Bembo, Julius Scaliger, and all the great men of his time. He died of an apoplexy, at Casi near Verona, in 1553; and in 1559 the town of Verona erected a statue in honour of him.

, a celebrated French mathematician of the seventeenth century, was the contemporary and companion

, a celebrated French mathematician of the seventeenth century, was the contemporary and companion of Des Cartes, Fermat, and the other learned mathematicians of their time. He was admitted geometrician of the French academy in 1666; and died in 1675. He had many papers inserted in the ancient memoirs of the academy, of 1666, particularly in vol. V. of that collection, viz. 1. “A method of resolving problems by Exclusions.” 2. “Treatise of right-angled Triangles in Numbers.” 3. “Short tract on Combinations.” 4. “Tables of Magic Squares.” 5. “General method of making Tables of Magic Squares.” His brother Nicolas

, a very eminent philosopher and mathematician, was born in Milan, April 13, 1727. He was first educated in

, a very eminent philosopher and mathematician, was born in Milan, April 13, 1727. He was first educated in the schools of the Barnabite fathers in that metropolis; and so uncommon was his progress in the classes, that it was soon predicted by his teachers and schoolfellows, that he would one day excel in polite literature, in poetry, and in pulpit eloquence; nature, however, had more unequivocally designed him to be what he really proved, a philosopher and a mathematician. In 1743, (the sixteenth of his age) he embraced the monastic life among the Barnabites of Lombardy, where he passed so rapidly through all the remainder of his studies, that he had the honour of being appointed, while still in the inferior orders, to the professorship of philosophy in the college of Lodi, and afterwards promoted, in the same capacity, to the royal school of Casale, in Monferrat, as a successor to the late celebrated cardinal Gerdil.,

, the celebrated astronomer and mathematician, was the son of Vincenzo Galilei, a nobleman of Florence, not

, the celebrated astronomer and mathematician, was the son of Vincenzo Galilei, a nobleman of Florence, not less distinguished by his quality and fortune, than conspicuous for his skill and knowledge in music; about some points in which science he maintained a dispute with the famous Zarlinas. His wife brought him this son, Feb. 10, 1564, either at Pisa, or, which is more probable, at Florence. Galileo received an education suitable to his birth, his taste, and his abilities. He went through his studies early, and his father then wished that he should apply himself to medicine;. but having obtained at college some knowledge of mathematics, his genius declared itself decisively for that study. He needed no directions where to begin. Euclid’s Elements were well known to be the best foundation in this science. He therefore set out with studying that work, of which he made himself master without assistance, and proceeded thence to such authors as were in most esteem, ancient and modern. His progress in these sciences was so extraordinary, that in 1589, he was appointed professor of mathematics in the university of Pisa, but being there continually harrasted by the scholastic professors, for opposing some maxims of their favourite Aristotle, he quitted that place at the latter end of 1592, for Padua, whither he was invited very handsomely to accept a similar professorship; soon after which, by the esteem arising from his genius and erudition, he was recommended to the friendship of Tycho Brache. He had already, even long before 1586, written his “Mechanics,” or a treatise of the benefits derived from that science and from its instruments, together with a fragment concerning percussion, the first published by Mersennus, at Paris, in 1G34-, in “Mersenni Opera,” vol. I. and both by Menoless, vol. I. as also his “Balance,” in which, after Archimedes’s problem of the crown, he shewed how to find the proportion of alloy, or mixt metals, and how to make theuaid instrument. These he had read to his pupils soon after his arrival at Padua, in 1593.

having lately invited him to Florence, gave him the post and title of his principal philosopher and mathematician.

While he was professor at Padua, in 1609, visiting Ve>­nice, then famous for the nrt of making glass, he heard of the invention of the telescope by James Metius, in Holland. This notice was sufficient for Galileo; his curiosity was raised; and the result of his inquiry was a telescope of his own, produced from this hint, without having seen the Dutch glass. All the discoveries he made in astronomy were the easy and natural consequences of this invention, which opening a way, till then unknown, into the heavens, gave that science an entirely new face. Galileo, in one of his works, ridicules the unwillingness of the Aristotelians to allow of any discoveries not known to their master, by introducing a speaker who attributes the telescope to him, on account of what he says of seeing the stars from the bottom of a deep well. “The well,” says he, “is the tube of the telescope, the intervening vapours answer to the glasses.” He began by observing the moon, and calculating the height of her mountains. He then discovered four of Jupiter’s satellites, which he called the Medicean stars or planets, in honour of Cosmo II. grand duke of Tuscany, who was of that noble family. Cosmo now recalled him from Padua, re-established him at Pisa, with a very handsome stipend, in 1610; and the same year, having lately invited him to Florence, gave him the post and title of his principal philosopher and mathematician.

lems, were printed at Bologna in 4to. His last disciple, Vincenzo Viviani, who proved a very eminent mathematician, methodized a piece of his master’s, and published it under

Galileo wrote a number of treatises, many of which were published in his life-time. Most of them were also collected after his death, and published by Mendessi in 2 vols. 4to, under the title of “L'Opere di Galileo Galilei Lynceo,” in 1656. Some of these, with others of his pieces, were translated into English and published by Thomas Salisbury, in his Mathematical Collections, in 2 vols. folio. A volume also of his letters to several learned men, and solutions of several problems, were printed at Bologna in 4to. His last disciple, Vincenzo Viviani, who proved a very eminent mathematician, methodized a piece of his master’s, and published it under this title, “Quinto libro de gli Elementi d' Euclidi,” &c. at Florence in 1674, 4to. Viviani published some more of Galileo’s things, being extracts from his letters to a learned Frenchman, where he gives an account of the works which he intended to have published, and a passage from a letter of Galileo dated at Arcetri, Oct. 30, 1635, to John Camillo, a mathematician of Naples, concerning the angle of contact. Besides all these, he wrote many other pieces, which were unfortunately lost. Galileo had two daughters and a son by a Greek woman he lived with; the daughters became nuns; one son continued the family, which, Frisi says, is but lately extinct; one turned missionary, and was induced from religious scruples to burn many of his grandfather’s works and the third ran away.

was placed as an apprentice under the tuition of Mr. Dawson, at Sedbergh, in Yorkshire, a celebrated mathematician, who was at that time a surgeon and apothecary, Here he laid

, an ingenious English physician, was born at Caste rton, near Kivkby Lonsda'le, Westmoreland, April 21, 1766. About the age of fourteen, after having received the first rudiments of education at his native village, he was placed as an apprentice under the tuition of Mr. Dawson, at Sedbergh, in Yorkshire, a celebrated mathematician, who was at that time a surgeon and apothecary, Here he laid the foundation of his medical and philosophical knowledge. After this he proceeded to Edinburgh, and took his degree about 1758. During his residence there, he became the pupil of Dr. Brown, whose new system of medicine Dr. Garnet, from this time, held in the highest estimation. Soon after he visited London, and attended the practice of the hospitals. He had now arrived at an age which made it necessary for him to think of some permanent establishment. With this view he left London, and settled at Bradford in Yorkshire, where he gave private lectures on philosophy and chemistry, and wrote a treatise on the Horley Green Spa. In 179J he removed to Knaresborough, and in summer to Harrogate, and was soon engaged in an extensive practice. As this, however, was necessarily limited to the length of the season, which lasted only three or four months, Dr. G. soon after his marriage, which took place in 1795, formed the design of emigrating to America. At Liverpool, where he was waiting to embark, he was strongly solicited to give a chemical course of lectures, which met with a most welcome reception, as did also another course on experimental philosophy. He then received a pressing invitation from Manchester, where he delivered the same lectures with equal success. These circumstances happily operated to prevent his departure to America, and he became a successful candidate for the vacant professorship of Anderson’s institution at Glasgow, in 1796. In Scotland, his leisure hours were employed in collecting materials for his “Tour through the Highlands;” which work was in some degree impeded by the sudden death of his wife in child-birth; an event which so strongly affected his feelings, that he never thought of it but with agony. Dr. G. was induced to relinquish the institution at Glasgow, by favourable offers from the new Royal Institution in London, where, for one season, he was professor of natural philosophy and che-p mistry, and delivered the whole of the lectures. On retiring from this situation, which was far too laborious for the state of his health, at the close of 1801, he devoted himself to his professional practice, and took a house in Great Marlborough-street, where he built a new and convenient apartment, completed an expensive apparatus, and during the winter of 1801 and 1802, he gave regular courses on experimental philosophy and chemistry, and a new course on “Zoonomia,” or, “the Laws of Animal Life, arranged according to the Brunonian theory.” These were interrupted in February, for some weeks, by a dangerous illness, which left him in a languid state; though he not only resumed and finished the lectures he had begun, but also commenced two courses on botany, one at his own house, and the other at Brompton. In the midst of these, he received, by infection, from a patient whom he had attended, the fever which terminated his life, June 28, 1802. His “Zoonomia” was afterwards published for the benefit of his family. “Thus,” says his biographer, “was lost to society a man, the ornament of his country, and the general friend of humanity. In his personal attachments, he was warm and zealous. In his religion he was sincere, yet liberal to the professors of contrary doctrines. In his political principles he saw no end, but the general good of mankind; and, conscious of the infirmity of human judgment, he never failed to make allowances for error. As a philosopher and a man of science, he was candid, ingenuous, and open to conviction; he never dealt in mystery, or pretended to any secret in art; he was always ready in explanation, and desirous of assisting every person willing to acquire knowledge.” Besides his “Tour in Scotland,” and the other works mentioned before. Dr. Garnet contributed many papers to the Memoirs of the Medical Society of London, the Royal Irish Academy, and other scientific societies.

iderable fortune, was Garrick’s friend upon this occasion, recommended him to Mr. Colson, an eminent mathematician, to be boarded and instructed by him in mathematics, philosophy,

About the beginning of 1735, Mr. (afterwards Dr.) Samuel Johnson, undertook to instruct some young gentlemen of Lichfield in the belles lettres; and David Garrick, then turned eighteen, became one of his scholars, or (to speak more properly) his friend and companion. But the master, however qualified, was not more disposed to teach, than Garrick was to learn; and, therefore, both growing weary, after a trial of six months, agreed to try the,ir fortunes in the metropolis. Mr. Walmsley, register of the ecclesiastical court at Lichfield, a gentleman much respected, and of considerable fortune, was Garrick’s friend upon this occasion, recommended him to Mr. Colson, an eminent mathematician, to be boarded and instructed by him in mathematics, philosophy, and polite learning; with a view of being sent within two or tlireft years to the Temple, and bred to the law. But when Garrick arrived in London, he found that his finances would not suffice to put him under Mr. Colson, till the death of his uncle; who, about 1737, left Portugal, and died in London soon after. He bequeathed his nephew 1000l. with the interest of which, he prudently embraced the means of acquiring useful knowledge under Mr. Colson. His proficiency, however, in mathematics and philosophy was not extensive; his mind was still theatrically disposed; and, both father and mother living but a short time after, he gave himself up to his darling passion for acting from which, says his historian, “nothing but his tenderness for so dear a relation as a mother had hitherto restrained him.” During the short interval, however, between his mother’s death and his commencing comedian, he engaged in the wine trade, with his brother Peter Garrick; and they hired vaults in Durham-yard.

, a very eminent mathematician and philosopher, was born Jan. 22, N. S. 1592, at a village

, a very eminent mathematician and philosopher, was born Jan. 22, N. S. 1592, at a village called Chantersier, about three miles from Digne in Provence, in France. His father, Antony Gassendi, a Roman catholic, educated him with great piety, and the first words he learned to pronounce were those of his prayers. This practice made such an impression upon his infant mind, that at four years of age he demonstrated the good effects of it in reproving or exhorting his playfellows, as occasion prompted. In these first years of his youth he likewise took particular delight in gazing at the moon and stars, in clear uncloudy weather, and was so intent on these observations in solitary places, that his parents had him often to seek, not without many anxious fears. At a proper age they put him to school at Digne, to Godfrey Wendeline, an excellent master, under whose care he made a quick and extraordinary progress in learning. In a very short time he learned not only the elements of the Latin language, but was so far advanced in rhetoric as to be superior to all the boys in that school; and some friends who had witnessed his proficiency, recommended to have him removed, in order to study philosophy under Fesay, a very learned Minorite friar, then at Aix. This proposal was not much relished by his father, whose design was to breed up his son in his own way to country business, or farming, as a more profitable employment than that of a scholar, nor would he consent but upon condition that the boy should return home in two years at farthest. Young Gassendi accordingly, at the end of his allotted time, repaired to Chantersier; but he did not stay there long, being invited to be a teacher of rhetoric at Digne, before he was full sixteen years of age; and he had been engaged in this not above three years, when his master Fesay dying, he was made professor of philosophy in his room at Aix.

, an able divine and mathematician, was born at Lindau, in Swabia, in 1667, and after some education

, an able divine and mathematician, was born at Lindau, in Swabia, in 1667, and after some education here, was sent to Ulm, and afterwards to the university of Jena, where he took the degree of M. A. and became a considerable proficient in mathematics. After this he spent some time in different German universities, improving himself in theology and mathematics, and then visited Amsterdam and London. In 16y3 he was ordained, and appointed in 1728 principal pastor of Lindau. His leisure hours he devoted to mathematical and philosophical pursuits, became a lecturer in these branches of science, in which character his reputation procured him the correspondence of many of the most learned mathematicians in foreign countries. He was a practical mechanic, as well as an able illustrator of the higher branches of science; and many of the instruments which he made use of were constructed by himself. He had begun the erection of an observatory, but death terminated his labours in 1738. He was the author of “Gnomonica Mechanica Universalis;” of various calendars, and calculations and descriptions of eclipses; of other philosophical treatises, and of sermons. His Ephemerides and astronomical observations were received by the royal academies of sciences at Paris and Berlin, and several of them were inserted in the Memoirs of those learned societies.

As to his character in the learned world, which is that of a mathematician, it must be confessed, that whatever progress he made, was chiefly

As to his character in the learned world, which is that of a mathematician, it must be confessed, that whatever progress he made, was chiefly the produce of a plodding industry, without much genius. Hence we see, that he was wot capable of discerning the true weight and force of the reasoning on which the Copernican system was built in his time; and to the same cause must be ascribed that confusion and amazement he was thrown into, upon considering the change (then, indeed, but just discovered) in the variation of the magnetic needle.

llant knight and all his men perished with her. He was a man of quick parts, a brave soldier, a good mathematician, and of a very enterprizing genius. He was also remarkable for

, a brave officer and navigator, was born in 1539, in Devonshire, of an ancient family, and though a second son, inherited a considerable fortune from his father. He was educated at Eton, and afterwards at Oxford, but is not mentioned by Wood, and probably did not remain long there. His destination was the law, for which purpose he was to have been sent to finish his studies in the Temple; but being introduced at court by his aunt, Mrs. Catherine Ashley, then in the queen’s service, he was encouraged to embrace a military life. Having distinguished himself in several expeditions, particularly in that to Newhaven, in 1563, he was sent over to Ireland to assist in suppressing a rebellion excited by James Fitzmorris; and for his signal services he was made commander in chief and governor of Munster, and knighted by the lord-deputy, sir Henry Sidney, on Jan. 1, 1570, and not by queen Elizabeth in 1577, as Prince asserts. He returned soon after to England, where he married a rich heiress. In 1572 he sailed with a squadron of nine ships, to reinforce colonel Morgan, who at that time meditated the recovery of Flushing; and when he came home he published in 1576, his “Discourse to prove a passage by the North-west to Cathaia, and the East Indies,” Lond. This treatise, which is a masterly performance, is preserved in Hakluyt’s Voyages. The style is superior to most writers of that age, and shows the author to have been a man of considerable reading. The celebrated Frobisher sailed the same year, probably in consequence of this publication. In 1578, sir Humphrey obtained from the queen a very ample patent, empowering him to discover and possess in North America any lands then unsettled. He accordingly sailed to Newfoundland, but soon returned to England without success; yet, in 1583, he embarked a second time with five ships, the largest of which put back on occasion of a contagious distemper on board. Gilbert landed at Newfoundland, Aug. 3, and two days after took possession of the harbour of St. John’s. By virtue of his patent he granted leases to several people; but though none of them remained there at that time, they settled afterwards in consequence of these leases, so that sir Humphrey deserves to be remembered as the real founder of our American possessions. His half-brother, sir Walter Raleigh, was a joint adventurer on this expedition, and upon sir Humphrey’s death took out a patent of the same nature, and sailed to Virginia. On the 20th August in the above year (1583), sir Humphrey put to sea again, on board of a small sloop, for the purpose of exploring the coast. After this he steered homeward in the midst of a tempestuous sea, and on the 9th of September, when his small bark was in the utmost danger of foundering, he was seen by the crew of the other ship sitting in the stern of the vessel, with a book in his hand, and was heard to cry out, “Courage, my lads! we are as sear heaven at sea as at land.” About midnight the bark was swallowed up by the ocean; the gallant knight and all his men perished with her. He was a man of quick parts, a brave soldier, a good mathematician, and of a very enterprizing genius. He was also remarkable for his eloquent and patriotic speeches both in the English and Irish parliaments. At the close of the work above-mentioned, he speaks of another treatise “On Navigation,” which he intended to publish, but which is probably lost.

, a skilful mathematician, was born December 13, 1633, at Bitonto. He spent his youth

, a skilful mathematician, was born December 13, 1633, at Bitonto. He spent his youth in idleness and debauchery, and married a young woman without any fortune; and having killed one of his brothersin-law, who reproached him with his indolence and laziness, he entered as a soldier in a fleet fitted out by the pope against the Turks. The admiral, finding that he did not want genius, gave him a writer’s place which happened to be vacant; and Giordani, being obliged in consequence to learn arithmetic, eagerly studied that of Clavius, and acquired a taste for mathematics. Returning to Rome, in 1659, he was made keeper of the castle of St. Angelo, and devoted the leisure that office afforded him to mathematical studies, in which he made so rapid a progress, that queen Christina chose him for her mathematician during her stay at Rome; and Louis XIV, appointed him to teach mathematics in the academy of painting and sculpture which he had founded in that city, 1666. Giordani was made engineer to the castle of St. Angelo by pope Clement X., appointed mathematical professor at the college della Sapienza 1685, and admitted into the academy of the Arcadi, May 5, 1691. He died November 3, 1711. His principal works are, “Euclide restitute,” foiio; “De componendis gravium momentis,” folio; “Fundamentum doctrines motus gravium,1705, folio; “Ad Hyacinthum Christophorum Epistola,1705, folio.

, a mathematician, was born at Breslaw, in Silesia, in 1623, and died at Leyden

, a mathematician, was born at Breslaw, in Silesia, in 1623, and died at Leyden in 1665. The works by which he is generally known are “Elementa Architecture Militaris,1643, 8vo “De Usu Proportionarii Circuli” “De Stylometricis,1662 and another treatise “On Architecture,” published in 1696, by Christopher Sturm, with numerous engravings, and the life of the author. He had also improved the description of Solomon’s Temple by Villapandus, but this was never published.

, a French mathematician, was born Sept. 18, 1650, at Dieppe, and entered among the Jesuits

, a French mathematician, was born Sept. 18, 1650, at Dieppe, and entered among the Jesuits in 1667. He early acquired reputation for his skill in mathematics, and was admitted into the academy of sciences in 1699. He assisted constantly at the meetings of that academy, whose members entertained a high opinion of his genius. He died at Paris, in the professed house of the Jesuits, March 24, 1725, aged seventy-five. His principal work is entitled, “Observations Physiques et Mathematiques pour servir a la perfection de TAstronomie, et de la geographic, envoyees de Siam, a Pacademie des sciences de Paris, par ies P. P. Jesuites missionaires;” with notes and remarks, in 2 vols. the first, 8vo, the second, 4to. These remarks may also be found in torn. 7. of the “Memoires” of the above academy.

, a philosopher and mathematician, was born Oct. 1, 1671, at Cremona, where his father, a branch

, a philosopher and mathematician, was born Oct. 1, 1671, at Cremona, where his father, a branch of a decayed family, carried on the business of ai> embroiderer. His mother, a woman of considerable talents, taught him Latin, and gave him some taste for poetry. Being disposed to a studious life, he cliose the profession of theology, that he might freely indulge his inclination. He entered into the religious order of Camaldolitesj at Raverrna, in 1687, where he was distinguished for his proficiency in the different branches of literature and science, but was much dissatisfied with the Peripatetic philosophy of the schools. He had not been here long before he established an academy of students of his own age, which he called the Certanti, in opposition to another juvenile society called the Concordi. To his philosophical studies he added those of the belles lettres, music, and history. It appears to have been his early ambition to introduce a new system in education, and with that view he obtained the professorship of philosophy at Florence, by the influence of father Caramelli, although not without some opposition from the adherents to the old opinions. He now applied himself to the introduction of the Cartesian philosophy, while, at the same time, he became zealously attached to mathematical studies. The works of the great Torricelli, of our countryman Wallis, and of other celebrated mathematicians, were his favourite companions, and the objects of his familiar intercourse. His first publication was a treatise to resolve the problems of Viviani on the construction of arcs, entitled “Geometrica Demonstnuio Vivianeorum problematum,” Florence, 1609, 4to. He dedicated this work to the grand duke. Cosmo Til. who appointed the author professor of philosophy in the university of Pisa. From this time Grandius pursued the higher branches of mathematics with the stmost ardour, and had the honour of ranking the ablest mathematicians among his friends and correspondents. Of the number may be named the illustrious Newton, Leibnitz, and Bernoulli. His next publications were, “Geometrica dernonslratio theorematum Hugenianorum circa logisticam, seu Logarithmicam lineatn,1701, 4to, and “Quadratura circuii et hyperbola3 per infinitas hyperbolas et parabolas geometrice exhibita,” Pisa, 1703, 8vo. He then published “Sejani et Rufini dialogus de Laderchiana historia S. Petri Damiani,” Paris, 1705, awd “Dissertationes Camaldu lenses,” embracing inquiries into the history of the Camaldolites, both which gave so much offence to the community, that he was deposed from the dignity of abbot of St. Michael at Pisa; but the grand duke immediately appointed him his professor of mathematics in the university. He now resolved some curious and difficult problems for the improvement of acoustics, which had been presented to the royal society in Dublin, and having accomplished his objecvt, he transmitted the solutions, by means of the British minister at the court of Florence, to the Royal Society at London. This was published under the title of “Disquisitio geometrica in systema sonorum D. Narcissi (Marsh) archiepiscopi Armachani,” in 1709, when he was chosen a fellow of the royal society. This was followed by his principal work, “De infinitis infinitorum, et infinite parvorum ordinibus disquisitio geometrica,” Pisa, 1710, 4to, and by many other works enumerated by his biographer, few of which appear in the catalogues of the public libraries in this country. Among other subjects he defended Galileo’s doctrine respecting the earth’s motion, and obtained a complete victory over those who opposed it. He was deeply versed in subjects of political economy; and various disputes were referred to his decision respecting the rights of fishery, &c. He was appointed commissioner from the grand duke and the court of Rome jointly, to settle some differences between the inhabitants of Ferrara and Bologna, concerning the works necessary to preserve their territories from the ravages of inundation. For these and other important public services, he was liberally rewarded by his employers. He died at the age of sevejity-two, in July 1742.

, an eminent mathematician and antiquary, was eldest son of John Greaves, rector of Colmore,

, an eminent mathematician and antiquary, was eldest son of John Greaves, rector of Colmore, near Alresford, in Hampshire, where, his son was born in 1602, and probably instructed in grammar learning by his father, who was the most celebrated school-master in that country. At fi/teen years of age he was sent to Baliol college, in Oxford, where he proceeded B. A. July 6, 1621. -Three years after, his superiority in classical learning procured him the first place of five in an election to a fellowship of Merton-college. On June 25, 1628, he commenced M. A. and, having completed his fellowship, was more at liberty to pursue the bent of his inclination, which leading him chiefly to oriental learning and the mathematics, he quickly distinguished himself in each of these studies; and his eminent skill in the latter procured him the professorship of geometry in Gresham college, which he obtained February 22^ 1630.

d, intended to have given you a visit with us. You will find him a very ingenious person, and a good mathematician, worth your acquaintance.” In proceeding, he mentions our author

He continued at Edinburgh till 1691, when, hearing of Dr. Bernard’s intention to resign the Savilian professorship of astronomy at Oxford, he left Scotland, and, coming to London, was admitted a member of the royal society: and paid his addresses to sir Isaac Newton, who took the first opportunity of recommending him to Mr. Flamstead (master of the mathematical school in Christ’s-hospital, London), with a letter, recommending his mathematical merit above all exception in these terms: “Sir, it. is almost a fortnight since I intended, with Mr. Paget and another friend or two, to have given you a visit at Greenwich; but sending to the Temple coffee-house, I understood you had not been in London for two or three weeks before, which made me think you were retired to your living for a time. The bearer hereof, Mr. Gregory, mathematic professor of Edinburgh college, in Scotland, intended to have given you a visit with us. You will find him a very ingenious person, and a good mathematician, worth your acquaintance.” In proceeding, he mentions our author as a fit person, in case of Mr. Flamstead’s death, to carry on his astronomical views. Thus recommended, the royal astronomer used his best interest to procure him success at Oxford, where he was elected astronomy-professor this year, having been first admitted of Baliol college, and incorporated M. A. February 8, and he was created M. D. on the

, he was succeeded in the professorship at that university by his brother James, likewise an eminent mathematician; who held that office for thirty-three years, and, retiring

When Dr. David Gregory, the Savilian professor, quitted Edinburgh, he was succeeded in the professorship at that university by his brother James, likewise an eminent mathematician; who held that office for thirty-three years, and, retiring in 1725, was succeeded by the celebrated Maclaurin. A daughter of this professor James Gregory, a young lady of great beauty and accomplishments, was the victim of an unfortunate attachment, that furnished the subject of Mallet’s well-known ballad of “William and Margaret.” Another brother, Charles, was created professor of mathematics at St. Andrew’s by queen Anne, in 1707. This office he held with reputation and ability for thirty-two years; and, resigning in 1739, was succeeded by his son, who eminently inherited the talents of his family, and died in 1763.

m and friendship of' some of the most distinguished literati there. Edward Montague, esq. an eminent mathematician, maintained a firm friendship for the doctor, founded on a similarity

, professor of medicine in the university of Edinburgh, was born at Aberdeen in 1724. He was the third son of James Gregory, M. D. professor of medicine in King’s college, Aberdeen, by Anne, daughter of the rev. George Chalmers, principal of King’s college there. His grandfather was David Gregory of Kinardie, and his grand-uncle the James Gregory, whose life we have first given, the inventor of the reflecting telescope. Though the father of Dr. John Gregory died when he was very young, his education was carefully superintended, and he made a rapid progress in his studies, and like the rest of his ancestors became deeply versed in mathematical knowledge. He also cultivated an elegant and just taste, clearness -and beauty of expression, with precision of judgment, and extensive knowledge. He was the early, intimate, and constant friend and associate of Drs. Gerard, Beattie, and the other eminent men who belonged to the university of Aberdeen. In 1742, he went to Edinburgh, to prosecute the study of medicine, and thence to Leyden in 1745, and to Paris in 1746, for further improvement. On his return he was appointed professor of philosophy in King’s college, Aberdeen, and had at the same time the degree of M. D. conferred upon him. He held this professorship for a few years. In 1754, he went to London, where he. cultivated the acquaintance, and fixed the esteem and friendship of' some of the most distinguished literati there. Edward Montague, esq. an eminent mathematician, maintained a firm friendship for the doctor, founded on a similarity of manners and studies. His, lady the celebrated Mrs. Montague? and George lord Lyttelton, were of the number of his friends; and it is not improbable that he would have continued in London, and practised there in his profession, if the death of his brother Dr. James Gregory, professor of physic in King’s college, Aberdeen, in 1756, had not occasioned his being recalled to his native university to fill that chair. His occupations in physic now began to be active; he gave a course of lectures in physic, and practised in his profession, with great success. In the above-mentioned year, while at London, he was elected a fellow of the royal society. In 1766, on the death of Dr. Robert Whytt, the ingenious professor of the theory of physic at Edinburgh, Dr. Gregory was called to succeed him, as his majesty’s first physician in Scotland; and about the same time he was chosen to fill the chair of professor of the practice of physic, which was just resigned by Dr. Rutherford. Dr. Gregory gave three successive courses of practical lectures. Afterwards by agreement with his ingenious colleague, Dr. Cullen, they lectured alternate sessions, on the practice and institutions of medicine, with just and universal approbation, till the time of Dr. Gregory’s death.

, a. physician, astronomer, and mathematician, and like his countryman, friar Bacon, violently suspected of

, a. physician, astronomer, and mathematician, and like his countryman, friar Bacon, violently suspected of magic, lived in the fourteenth century, He studied at Merton college, Oxford; and, probably to escape the disagreeable consequences of such suspicions, went into France, where he devoted himself entirely to the study of medicine, first at Montpelier, and then at Marseilles. In this eity he fixed his residence, and lived by the practice of his profession, in which he acquired much skill and eminence. There is no greater proof of his genius, besides the imputations he laboured under in his youth, than his assiduously pursuing the method instituted by the Greek physicians, of investigating the nature and cause of the disease and the constitution of the patient. The time of his death is not known; but we are told that he was an old man in 1350, and that he had a son, who was first an abbot of canons regular at Marseilles, and at length arrived at the pontificate under the name of Urban V. Bale and Pits both give lists of his works, none of which are known to be extant.

owledge of the abstract sciences in particular as the former did of his learning in general. Stevin, mathematician to prince Maurice of Nassau, composed a small treatise for the

Grotius, having chosen the law for his profession, had taken an opportunity before he left France, to obtain a doctor’s degree in that faculty; and upon his return he attended the law-courts, and pleaded his first cause at Delft with universal applause, though he was scarcely seventeen; and he maintained the same reputation as lung as he continued at the bar. This employment, however, not filling up his whole time, he found leisure to publish the same year, 1599, another work, which discovered as much knowledge of the abstract sciences in particular as the former did of his learning in general. Stevin, mathematician to prince Maurice of Nassau, composed a small treatise for the instruction of pilots in finding a ship’s place at sea; in which he drew up a table of the variations of the needle, according to the observations of Plancius, a celebrated geographer, and added directions how to use it. Grotius translated into Latin this work, which prince Maurice had recommended to the college of admiralty, to be studied by all officers of the navy; and, because it might be equally useful to Venice, he dedicated his translation to that republic. In 1600, he published his “of Aratus,” which discovers a great knowledge in physics, and especially astronomy. The corrections he made in the Greek are esteemed very judicious: the notes shew that he had reviewed several of the rabhies, and had some knowledge of the Arabic tongue; and the verses he made to supply those of Cicero that were lost have been thought very happy ‘imitations of that writer’s style. In the midst of these profound studies, this extraordinary young man found time to cultivate the muses, and with such success, that he was esteemed one of the best Latin poets in Europe. The prosopopoeia, in which he makes the city of Ostend speak, after having been three years besieged by the Spaniards, was reckoned a masterpiece, and was translated intoJFrench by Du Vae’r, Rapin, Pasquier, and Malherbe; and Casanbon turned it into Greek. Neither did Grotius content himself with writing small pieces of verse; he rose to tragedy, of which he produced three specimens; the first, called “Adamus Exul,” was printed in Leyden, in 1601, with which, however, he became afterwards dissatisfied, and would not let it appear in the collection of hi* poems published by his brother. “Christus patiens,” his second tragedy, was printed at Leyden in 1608, and much approved: Casaubon greatly admires its poetical fire. Sandys translated it into English verse, and dedicated it to Charles I. It was favourably received in England, and in Germany proposed as the model of perfect tragedy. His third was the story of Joseph, and its title “Sophornphanceus,” which, in the language of Egypt, signifies the Saviour of the World; he finished this in 1633, and the following year, at Hamburgh.

ed men, Erasmus recommends him as a man perfectly skilled in Latin and Greek, a good philosopher and mathematician, and a man of humble manners, whose object was to visit the

, a very learned German, was thg son of a peasant of Suabia, and born at Veringen in the county of Hohenzollern in 1493. He pursued his studies in Pfortsheim at the same time with Melancthon, which gave rise to a lasting friendship between them. He then went for farther instruction to Vienna, and there taking the degree of master in philosophy* was appointed Greek professor. Having embraced the protestant religion, he was exposed to many dangers; and particularly in Baden, of which he was some years rector of the school. He was thrown into prison at the instigation of the friars; but at the solicitation of the nobles of Hungary, was set at liberty, and retired to Wittemberg, where he had a conference with Luther and Melancthon. Being returned to his native country, he was invited to Heidelberg, to be Greek professor in that city, in 1523. He exercised this employment till 1529, when he was invited to Basil to teach publicly in that city. In 1531, he took a journey into England, and carried with him a recommendatory letter from Erasmus to William Montjoy, dated Friburg, March 18, 1531. After desiring Montjoy to assist Grynaeus as much as he could, in shewing him libraries, and introducing him to learned men, Erasmus recommends him as a man perfectly skilled in Latin and Greek, a good philosopher and mathematician, and a man of humble manners, whose object was to visit the libraries, &c. Erasmus recommended him also to sir Thomas More, from whom he received the highest civilities, In 1534, he was employed, in conjunction with other persons, in reforming the church and school of Tubingen. He returned to Basil in 1536, and in 1540 was appointed to go to the conferences of Worms, with Melancthon, Capito, Bucer, Calvin, &c. He died, of the plague at Basil in 1541.

, an eminent Italian mathematician, was born at Bologna, September 27, 1655. The great progress

, an eminent Italian mathematician, was born at Bologna, September 27, 1655. The great progress which he had made in mathematics, was evinced by his publications at the age of twenty-one years, immediately after which he was admitted doctor of medicine, and was permitted to teach the mathematics, although he did not obtain the title of professor until 1694. In 1696 he was elected a member of the principal learned societies of Europe; and in 1702 the university of Padua offered him the professorship of the theory of medicine, an office which he filled with great reputation. He died July 12, 1710. His numerous publications were collected and edited by Morgagni, under the title of “Opera omnia Mathematica, Hydraulica, Medica, et Physica. Accessit vita auctoris a J. B. Morgagni,” Geneva, 1719, 2 vols. 4to. They principally consist of a Treatise on Hydrostatics, in Latin a large work entitled “Delia Natura de Fiumi,” which is esteemed his master-piece a dissertation “de Sanguinis Natura et Constitutione” a treatise on comets, written on the appearance of the comet in 1681, and two Letters on Hydrostatics, occasioned by a dispute which he had with M. Papin, respecting his work on that subject.

, an English mathematician, was of Welsh extraction, from a family at Gunter’s-town, in

, an English mathematician, was of Welsh extraction, from a family at Gunter’s-town, in Brecknockshire but his father being settled in the county of Hereford, had this son born to him there in 1581. As he was a gentleman possessed of a handsome fortune, he thought proper to give him a liberal education, to which end he was placed by Dr. Busby at Westminster-school, where he was admitted a scholar on the foundation, and elected student of Christ-church, Oxford, in 1599. Having taken both his degrees in arts at the regular times, he entered into orders, and became a preacher in 1614, and proceeded B. D. November 23, 1615. But genius and inclination leading him chiefly to mathematics, he applied early to that study; and about 1606, merited the title of an inventor by the new projection of his sector, which he then described, together with its use, in a Latin treatise; and several of the instruments were actually made according to his directions. These being greatly approved, as being more extensively useful than any that had appeared before, on account of the greater number of lines upon them, and those better contrived, spread our author’s fame universally their uses also were more largely and clearly shewn than had been done by others and though he did not print them, yet many copies being transcribed and dispersed abroad, carried his reputation along with them, recommended him to the patronage of the earl of Bridgewater, brought him into the acquaintance of the celebrated Mr. Oughtred, and Mr. Henry Briggs, professor of geometry at Gresham; and thus, his fame daily increasing the more he became known, he was preferred to the astronomy-chair at Gresham-college, on March 6, 1619.

In 1616 he held a correspondence with Mr. Oughtred, as appears by a letter of his to that excellent mathematician, printed in the General Dictionary, hi 1618 he accompanied sir

On May 24 of this year, Mr. Hales quitted his fellowship at Merton, and was admitted fellow of Eton college. He was then in orders, and had acquired fame as a preacher. In 1616 he held a correspondence with Mr. Oughtred, as appears by a letter of his to that excellent mathematician, printed in the General Dictionary, hi 1618 he accompanied sir Dudley Carlton, ambassador to the Hague, as his chaplain, by which means he procured admission into the synod of Dort, though he was not properly a member. This indeed seems to have been his principal view in accompanying sir Dudley, who, besides his brother the bishop of Llandaff, first English commissioner, recommended him to Bogerman, president of the synod, and some other leading men. Ail this afforded him a favourable opportunity of collecting that information respecting the proceedings of the synod, which was afterwards published in his “Golden Remains.” The effect of these proceedings on his own mind was, that he became a convert to Arminianism. His friend Mr. Faringdon. informs us that “in his younger days he was a Calvinist, but that some explanation given by Episcopius* of the text in St. John iii. 16, induced him, as he said, to” bid John Calvin good night.“It does not appear, however, from his sermons, that he became a decided anti-predestinarian, although he pleads strongly for a toleration between the two parties, and thinks they may remain in Christian charity with each other. It is more remarkable that he should be induced by the arguments advanced in this synod, to think with indifference of the divinity of Jesus Christ as a necessary article of faith. This, however, seems obvious from some passages in his” Tract on Schism;“and such was his free and open manner both of talking and writing on these subjects, that he soon incurred the suspicion of inclining to Socinianism. Dr. Heylin went so far as to attribute two works to him, published with fictitious names, which have been since printed in the” Phoenix;" but it has been proved that they were written by Socinian authors. His biographers, however, all allow that he may be classed among those divines who were afterwards called Latitudinarians. He returned from the synod Feb. 8, 1619.

, bishop of Ossory, and an eminent mathematician, was born in the county of Dublin, March 26, 1729. He entered

, bishop of Ossory, and an eminent mathematician, was born in the county of Dublin, March 26, 1729. He entered of Trinity-college, Dublin, Dublin, Nov. 17, 1742, and in 1751 was elected a fellow that college. In 1758 he published his treatise on conic ions, < De Sectionibus Conicis," and in 1759 was elected Erasmus Smith’s professor of natural philosophy. In 1764 he resigned his fellowship, having accepted a college living; and in 1767 obtained the living of St. Anne’s, Dublin, which in the following year he resigned at the proposal of the primate Robinson, for the deanery of Armagh. In 1772 he married an Irish lady of good family of the name of Wood. In 1796 he was consecrated 'bishop of Clonfert, having been recommended to that dignity without his solicitation or knowledge; and in 1799 was removed to the see of Ossory, where he continued till his death, Dec. 1, 1805.

, an eminent mathematician, was born at Oxford, or, as Anthony Wood expresses it, “turn-;

, an eminent mathematician, was born at Oxford, or, as Anthony Wood expresses it, “turn-; bled out of his mother’s womb in the lap of the Oxonian Muses,” in 1560. Having been instructed in grammarlearning in that city, he became a commoner of St. Maryhall, where he took the degree of B. A. in 1579. He had then so distinguished himself, by his uncommon skill in mathematics, as to be recommended soon after to sir Walter Raleigh as a proper preceptor to him in that science. Accordingly, that noble knight became his first patron, took him into his family, and allowed him a handsome pension. In 1585 he was sent over by sir Walter with his first colony to Virginia; where, being settled, he was employed in discovering and surveying that country, in observing what commodities it produced, together with the manners and customs of its inhabitants. He published an account of it under this title, “A brief and true Report of the Newfoundland of Virginia;” which was reprinted in the third voyage of Hakluyt’s “Voyages.” Upon his return to England, he was introduced by his patron to the acquaintance of Henry earl of Northumberland who, “finding him,” says Wood, “to be a gentleman of an affable and peaceable nature, and well read in the obscure pan of learning,” allowed him a yearly pension of 120l. About the same time, Robert Hues, well known by his ' Treatise upon the Globes,“and Walter Warner, who is said to have communicated to the famous Harvey the first hint concerning the circulation of the blood, being both of them mathematicians, received pensions from him of less value, ^o that in 1606, when the earl was committed to the Tower for life, Harriot, Hues, and Warner, were his constant companions, and were usually called the earl of Northumberland’s Magi. They had a table at the earl’s charge, who did constantly converse with them, to divert the melancholy of his confinement; as did also sir Walter Raleigh, who was then in the Tower. Harriot lived for some time at Sion-college, and died in London, July 2, 1621, of a cancer in his lip. He was universally esteemed on account of his learning. When he was but a young man, he was styled by Mr. Hakluyt” Juvenis in disciplinis mathematicis excellens;“and by Camden,” Mathematicus insignis.“A ms. of his, entitled” Ephemeris Chryrometrica,“is preserved in Sion-college library and his” Artis Analytic* Praxis“was printed after his death, in a thin folio, and dedicated to Henry earl of Northumberland. Des Cartes is said to have been obliged to this book for a great many improvements in algebra, which he published to the world as his own, a fact that has been amply proved, in the astronomical ephemeris for 17vS8, by Dr. Zach, astronomer to the duke of Saxe Gotha, from manuscripts which he found in 1784 at the seat of the earl of Egremont at Petworth, a descendant of the above-mentioned earl of Northumberland. These papers also show that Mr. Harriot was an astronomer as well as an algebraist, As to his religion, Wood says, that,” notwithstanding his great skill in mathematics, he had strange thoughts of the Scripture, always undervalued the old story of the Creation of the World, and could never believe that trite position, * Ex nihilo nihil fit.‘ He made a Philosophical Theology, wherein he cast off the Old Testament, so that consequently the New would have uo foundation. He was a deist; and his doctrine he did impart to the earl, and to sir Walter Raleigh, when he was compiling the ’ History of the World,' and would controvert the matter with eminent divines of those times: who, therefore, having no good opinion of him, did look on the manner of his death, as a judgment upon him for those matters, and for nullify, ing the Scripture.“Wood borrowed all this from Aubrey, without mentioning his authority; and it has been answered, that Harriot assures us himself, that when he was with the first colony settled in Virginia, in every town where he came,” he explained to them the contents of the Bible, &c. And though I told them,“says he,” the book materially and of itself was not of such virtue as I thought they did conceive, but only the doctrine therein contained; yet would many be glad to touch it, to embrace it, to kiss it, to hold it to their breasts and heads, and stroke over all their bodies with it, to shew their hungry desires of that knowledge which was spoken of." To which we may add, that, if Harriot was reputed a deist, it is by no means probable that Dr. Corbet, an orthodox divine* and successively bishop of Oxford and Norwich, sending a poem, dated December 9, 1618, to sir Thomas Aylesbury, when the comet appeared, should speak of

so left above eighty “Academical Discourses.” He must be distinguished from George Hartman, a German mathematician, who, in 1540, invented the bombarding-staff, “Baculus Bombardicus,”

, a learned divine, was born in 1680, at Minister, of catholic parents. After having been several years a Je.uit, he turned protestant at Cassel in 1715, was soon after made professor of philosophy and poetry, and, in 1722, appointed professor of history nnd rhetoric at Marpurg, where he died in 1744. His most esteemed works are, “Hist. Hassiaca,” 3 vols. “Vita? Pontificum Romanorum Victoris III. Urbani II. Pascalis II. Gelasii II. Callisti II. Honorii II.;” “State of the Sciences in Hesse,” in German; “Praecepta eloquentiae rationalis,” &c. He has also left above eighty “Academical Discourses.” He must be distinguished from George Hartman, a German mathematician, who, in 1540, invented the bombarding-staff, “Baculus Bombardicus,” and was author of a treatise on perspective, reprinted at Paris, 1556, 4to and from Wolfgang Hartman, who published the Annals of Augsburg, in folio, 1596.

, an eminent mathematician, was born at Goud?, in Holland, March 26, 1656. His father intended

, an eminent mathematician, was born at Goud?, in Holland, March 26, 1656. His father intended him for the ministry, but the young man had an early disposition for contemplating the heavenly bodies, which engrossed his whole attention, and finding, at the age of thirteen or fourteen, that without some knowledge of the mathematics he could make no satisfactory progress in this study, he saved his boyish allowance and presents in money, and applied to a teacher of the mathematics, who promised to be very expeditious, and kept his word. Under him he first learned to grind optic glasses, and at length, partly by accident, was enabled to improve single microscopes by using small globules of glass, melted in the flame of a candle. By these he discovered the animalculse in semine humano, which laid the foundation of a new system of generation.

successful attempt on the enemies possessions in the West Indies, and in the Canaries. He was a good mathematician, and understood every thing that related to his profession as

, an able naval commander, was born at Plymouth about 1520. Being the son of a seaman, captain William Hawkins, he imbibed a love for the profession, and when a youth made several voyages to Spain, Portugal, and the Canaries. In the spring of 1562 he formed the design of his first famous voyage, the consequence of which was very important to his country, as he then began that traffic in slaves, which after two centuries and a half we have seen abolished. At that time, however, this trade was accounted honourable and useful, and sir John bore the badge of his exploits in a crest of arms granted him by patent, consisting of a “demi-moor in his proper colour, bound with a cord,” not unlike a device which we have seen employed to excite an abhorrence of the slave-trade when its abolition was first agitated. In returning from a third expedition of this kind he was attacked and defeated by a Spanish fleet. After undergoing many hardships, he reached home in Jair. 1568; and it is said that his ill-success in this instance damped his ardour for maritime enterprise. In 1573 he was appointed treasurer of the navy, and in a few months he had nearly lost his life by a wound from an enthusiastic assassin, who mistook him for another person. He was now consulted on every important occasion, and in 1588; was appointed rear-admiral on-board the Victory, to confront the famous armada. His conduct on this occasion obtained for him the high commendations of his illustrious queen, the honour of knighthood, and other important commands in the navy. He died in 1595, it is said of vexation, on account of an unsuccessful attempt on the enemies possessions in the West Indies, and in the Canaries. He was a good mathematician, and understood every thing that related to his profession as a seaman. He possessed much personal courage, and had a presence of mind that set him above fear, and which enabled him frequently to deliver himself and others out of the reach of the most imminent dangers; he had great sagacity, and formed his plans so judiciously, and executed the orders committed to him with so much punctuality and accuracy, that he ever obtained the applause of his superiors. He was submissive to those above him, and courteous to his inferiors, extremely affable to his seamen, and much beloved by them. He sat twice in parliament as burgess for Plymouth, and once for some other borough. He erected an hospital at Chatham for the relief of disabled and diseased seamen, and is highly applauded by his contemporaries and by historians, who lived after him. His son, sir Richard Hawkins, was brought up to a maritime life, and in 1582, when very young, he had the command of a vessel in an expedition under his uncle to the West Indies; he also commanded a ship in the action against the Spanish armada, in which he was greatly distinguished. About 1593, he sailed with three ships, his own property, to the coast of Brazil, at the commencement of a much longer voyage; but he was obliged to burn one of his little squadron, another deserted their commander, so that he was under the necessity of sailing alone through the straits of Magellan. To satisfy the desires of his men, he made prizes of some vessels, which drew upon him the whole force of a Spanish squadron, to which he was compelled to yield. After a confinement of two years in Peru and the adjacent provinces, he was sent back to Europe. He died in 1622, as he was attending, on business, the privycouncil. He left behind him a work of considerable value, which was printed and ready for publication it is entitled “The Observations of sir Richard Hawkins, knight, into the South-sea, A.D. 1593.” From this piece, which the author dedicated to prince Charles, afterwards king Charles I., it appears that the issue of his voyage to the South-seas, his long confinement, and the disasters which naturally attended it, brought him into great distress. His nautical observations, his description of the passage through the straits of Magellan, and his remarks on the sea-scurvy, and on the best methods of preserving his men in health, were considered at that period of very great importance. He intended to have published a second part of his observations, in which he meant to have given an account of what happened to him and his companions during their stay in Peru, and in Terra Firma, but which death prevented him from accomplishing.

, a learned mathematician of the academy of Berlin, and member of the academy of sciences

, a learned mathematician of the academy of Berlin, and member of the academy of sciences at Paris, was born at Basil in 1678. He was a great traveller; and for six years was professor of mathematics at Padua. He afterwards went to Russia, being iovited thither by the Czar Peter I. in 1724, as well as his compatriot Daniel Bernoulli. On his return to his native country he was appointed professor of morality and natural law at Basil, where he died in 1733, at fifty-five years of age. He wrote several mathematical and philosophical pieces, in the Memoirs of different academies, and elsewhere; but his principal work is the “Phoronomia, or two books oh the forces and motions of both solid and fluid bodies,1716, 4to a very learned work on the new mathematical physics.

, or Hevelke, a celebrated astronomer and mathematician, was born at Dantzic January 28, 1611. His parents, who were

, or Hevelke, a celebrated astronomer and mathematician, was born at Dantzic January 28, 1611. His parents, who were of rank and fortune, gave him a liberal education; in which he discovered early a propensity to natural philosophy and astronomy. He studied mathematics under Peter Crugerus, in which he made a wonderful progress; and learned also to draw, to engrave, and to work both in wood and iron in such a manner as to be able to frame mechanical instruments. In 1630 he set out upon his travels, on which he spent four years, visiting Holland, England, France, and Germany; and on his return was so taken up with civil affairs, that he was obliged to intermit his studies for some years, until his master, Crugerus, who foresaw his future fame, recalled him to the study of astronomy; and in 1639 Hevelius began to apply himself entirely to it, by building an observatory upon the top of his house, which he furnished with instruments for making the most accurate observations. He constructed excellent telescopes himself, and began his observations with the moon, whose various phases and spots he noted very accurately; “with a view,” as he says, “of taking lunar eclipses with greater exactness, and removing those difficulties which frequently arise for want of being able to settle more precisely the quantity of an eclipse.” When he had finished his course of observations, and prepared a great number of fine engravings, he published his work at Dantzick, 1647, under the title of “Selenographia, sive, Luna3 descriptio;” to which he added, by way of appendix, the phases of the other planets, as they are seen through the telescope, with observations upon them, upon the spots of the sun and Jupiter in particular; all engraved by himself upon copper, and distinctly placed before the eyes of the reader. At the entrance of this work there is a handsome mezzotinto of himself by Falek, as he then was, in his thirty-sixth year, with a just encomium, although in bad Latin verse.

, an eminent French mathematician and astronomer, was born at Paris, March 18, 1640. His father

, an eminent French mathematician and astronomer, was born at Paris, March 18, 1640. His father Laurence, who was painter in ordinary to dm king, professor in the academy of painting and sculpture, and much celebrated, intended him also for the same occupation; and with that view taught him the principles of design, and some branches of mathematics, but died when Philip was no more than seventeen. Falling afterward* into a bad habit of body, he projected a journey into Italy; which he conceived might contribute not less to the recovery of his health, than to bring him to perfection in his art. He accordingly set out in 1660, and soon found himself well enough to contemplate the remains of antiquity, with which Italy abounds, and also to study geometry, to which he had indeed more propensity than to painting, and which soon afterwards engrossed him entirely. The retired manner in which he spent his time in Italy, very much suited his disposition; and he would willingly have continued longer in that country, but for the importunity of his mother, who prevailed upon him to return, after an absence of about four years.

versy about the quadrature of the circle, became so celebrated, although certainly undeservedly as a mathematician, that, in 1647, he was recommended to instruct Charles prince

Among many illustrious persons who upon the shipwreck of the royal cause retired to France for safety, was sir Charles Cavendish, brother to the duke of Newcastle, who, being skilled in every branch of mathematics, proved a constant friend and patron to Hobbes: and Hobbes himself, by embarking, in 1645, in a controversy about the quadrature of the circle, became so celebrated, although certainly undeservedly as a mathematician, that, in 1647, he was recommended to instruct Charles prince of Wales, afterwards Charles II. in that branch of study. His care in the discharge of this office gained him the esteem of that prince in a very great degree: and though he afterwards withdrew his public favour from Hobbes on account of his writings, yet he always retained a sense of the services he had done him, shewed him various marks of his favour after he was restored to his dominions, and, as some say, had his picture hanging in his closet. This year also was printed in Holland, by the care of M. Sorbiere, a second and more complete edition of his book “De Cive,” to which are prefixed two Latin letters to the editor, one by Gassendi, the other by Mersenne, in commendation of it. While Hobbes was thus employed at Paris, he was attacked by a violent fit of illness, which brought him so low that his friends began to despair of his recovery. Among those who visited him in this weak condition was his friend Mersenne, who, taking this for a favourable opportunity, began, after a few general compliments of condolence, to mention the power of the church of Rome to forgive sins; but Hobbes immediately replied, “Father, all these matters I have debated with myself long ago. Such kind of business would be troublesome to me now; and you can entertain me on subjects more agreeable; when did you see Mr. Gassendi?” Mersenne easily understood his meaning, and, without troubling him any farther, suffered the conversation to turn upon general topics. Yet some days afterwards, when Dr. Cosin, afterwards bishop of Durham, came to pray with him, he very readily accepted the proposal, and received the sacrament at his hands, according to the forms appointed by the church of England.

the learned as well as the modern languages; hath long had the reputation of a great philosopher and mathematician; and in his age hath had conversation with very many worthy

After this account of Hobbes, which, though undoubtedly true in the main, may be thought too strongly coloured, it will be but justice to subjoin what lord Clarendon has said of him. This noble person, during his banishment, wrote a book in 1670, which was printed six years after at Oxford with this title, “A brief View of the dangerous and pernicious Errors to Church and State in Mr. Hobbes’s book entitled Leviathan.” In the introduction the earl observes, that Mr. Hobbes’s *' Leviathan“” cohtains in it good learning of all kinds, politely extracted, and very wittily and cunningly digested in a very commendable, and in a vigorous and pleasant style: and that Mr. Hobbes himself was a man of excellent parts, of great wit, some reading, and somewhat more thinking; one who has spent many years in foreign parts and observations; understands the learned as well as the modern languages; hath long had the reputation of a great philosopher and mathematician; and in his age hath had conversation with very many worthy and extraordinary men: to which it may be, if he had been more indulgent in the more vigorous part of his life, it might have had greater influence upon the temper of his mind; whereas age seldom submits to those questions, inquiries, and contradictions, which the laws and liberty of conversation require. And it hath been always a lamentation among Mr. Hobbes’s friends, that he spent too much time in thinking, and too little in exercising those thoughts in the company of other men of the same, or of as good faculties; for want whereof his natural constitution, with age, contracted such a morosity, that doubting-and contradicting men were never grateful to him. In a word, Mr. Hobbes is one of the most ancient acquaintance I have in the world; and of whom I have always had a great esteem, as a man, who, besides his eminent parts, learning, and knowledge, hath been always looked upon as a man of probity, and of a life free from scandal.“There have been few persons, whose writings have had a more pernicious influence in spreading irreligion and infidelity than those of Hobbes; and yet none of his treatises are directly levelled against revealed religion. He sometimes affects to speak with veneration of the sacred writings, and expressly declares, that though the laws of nature are not laws as they proceed from nature, yet” as they are given by God in Holy Scripture, they are properly called laws; for the Holy Scripture is the voice of God, ruling all things by the greatest right.“But though ha, seems here to make the laws of Scripture the Jaws of God, and to derive their force from his supreme authority, yet elsewhere he supposes them to have no authority, but what they derive from the prince or civil power. He sometimes seems to acknowledge inspiration to be a supernatural gift, and the immediate hand of God: at other times he treats the pretence to it as a sign of madness, and represents God’s speaking to the prophets in a dream, to be no more than the prophets dreaming that God spake unto them. He asserts, that we have no assurance of the certainty of Scripture but the authority of the church f, and this he resolves into the authority of the commonwealth; and declares, that till the sovereign ruler had prescribed them,” the precepts of Scripture were not obligatory laws, but only counsel or advice, which he that was counselled might without injustice refuse to observe, and being contrary to the laws could not without injustice observe;“that the word of the interpreter of Scripture is the word of God, and that the sovereign magistrate is the interpreter of Scripture, and of all doctrines, to whose authority we must stand. Nay, he carries it so far as to pronounce that Christians are bound in conscience to obey the laws of an infidel king in matters of religion; that” thought is free, but when it comes to confession of faith, the private reason must submit to the public, that is to say, to God’s lieutenant.“Accordingly he allows the subject, being commanded by the sovereign, to deny Christ in words, holding the faith of him firmly in his heart; it being in this” not he, that denieth Christ before men, but his governor and the laws of his country.“In the mean time he acknowledges the existence of God, and that we must of necessity ascribe the effects we behold to the eternal power of all powers, and cause of all causes; and he reproaches those as absurd, who call the world, or the soul of the world, God. But then he denies that we know any thing more of him than, that he exists, and seems plainly to make him corporeal; for he affirms, that whatever is not body is nothing at all. And though he sometimes seems to acknowledge religion and its obligations, and that there is an honour and worship due to God; prayer, thanksgivings, oblations, &c. yet he advances principles, which evidently tend to subvert all religion. The account he gives of it is this, that” from the fear of power invisible, feigned by the mind, or imagined from tales, publicly allowed, ariseth religion; not allowed, superstition:“and he resolves religion into things which he himself derides, namely,” opinions of ghosts, ignorance of second causes, devotion to what men fear, and taking of things casual for prognostics.“He takes pains in many places to prove man a necessary agent, and openly derides the doctrine of a future state: for he says, that the belief of a future state after death,” is a belief grounded upon other men’s saying, that they knew it supernaturally; or, that they knew those, that knew them, that knew others that knew it supernaturally.“But it is not revealed religion only, of which Hobbes makes light; he goes farther, as will appear by running over a few more of his maxims. He asserts,” that, by the law of nature, every man hath a right to all things, and over all persons; and that the natural condition of man is a state of war, a war of all men against all men: that there is no way so reasonable for any man, as by force or wiles to gain a mastery over all other persons that he can, till he sees no other power strong enough to endanger him: that the civtt laws are the only rules of good and evil, just and unjust, honest and dishonest; and that, antecedently to such laws, every action is in its own nature indifferent; that there is nothing good or evil in itself, nor any common laws constituting what is naturally just and unjust: that all things are measured by what every man judgeth fit, where there is no civil government, and by the laws of society, where there is: that the power of the sovereign is absolute, and that he is not bound by^ any compacts with his subjects: that nothing the sovereign can do to the subject, can properly be called injurious or wrong; and that the, king’s word is sufficient to take any thing from the subject if need be, and that the king is judge of that need." This scheme evidently strikes at the foundation of all religion, natural and revealed. It tends not only to subvert the authority of Scripture, but to destroy God’s moral government of the world. It confounds the natural differences of good and evil, virtue and vice. It destroys the best principles of the human nature; and instead of that innate benevolence and social disposition which should unite men together, supposes all men to be naturally in a state of war with one another. It erects an absolute tyranny in the state and church, which it confounds, and maKes the will of the prince or governing power the sole standard of right and wrong.

was contemporary with Roger Bacon, but probably older by about 20 years. He was certainly the first mathematician of his time; and he wrote, 1. “De Sphaera Mundi,” Venice, 1478,

Holywood was contemporary with Roger Bacon, but probably older by about 20 years. He was certainly the first mathematician of his time; and he wrote, 1. “De Sphaera Mundi,” Venice, 1478, 1490, 4to, a work often reprinted, and illustrated by various commentators. 2. “De Anni Ratione, seu de Computo Ecclesiastico.” 3. “De Algorismo,” printed with “Comm. Petri Cirvilli Hisp.” Paris, 1498.

, an eminent English mathematician, and one of the most inventive geniuses that the world has ever

, an eminent English mathematician, and one of the most inventive geniuses that the world has ever seen, was son of Mr. John Hooke, rector of Freshwater in the Isle of Wight, and born there July 18, 1635. He was designed for the church; but being of a weakly constitution, and very subject to the head-ache, he was left to follow the bent of his genius, which led him to mechanics, and first appeared in his making little toys, which he did with wonderful art and dexterity. Seeing, on one occasion, an old brass clock taken to pieces, he made a wooden one that would go: he made likewise a small ship about a yard long, fitly shaped, masted, and rigged, with a contrivance to make it fire small guns, as it was sailing across a haven of some breadth. These indications led his friends to think of some trade for him in which such talents might be useful; and after his father’s death in 1648, as he had also a turn for drawing, he was placed with sir Peter Lely, but the smell of the oil-colours increased his headaches, and he quitted painting in a very short time. Afterwards he was kindly taken by Dr. Busby into his house, and supported there while he attended Westminster-school. Here he not only acquired Greek and Latin, together with some knowledge of Hebrew and other oriental languages, but also made himself master of a good part of Euclid’s Elements; and Wood adds, that while he lived with Dr. Busby he “learned of his own accord to play twenty lessons on the organ, and invented thirty several ways of flying as himself and Dr. Wilkins of Wadham- college have reported.” About 1653 he went to Christ-church, Oxford, and in 1655 was introduced to the philosophical society there; where, discovering his mechanic genius, he was first employed to assist Dr. Willis in his operations of chemistry, and afterwards recommended to Mr. Boyle, whom he served many years in the same capacity. He was also instructed about this time by Dr. Seth Ward, Savilian professor of astronomy, in that science; and from henceforward distinguished himself by a greater number of important inventions and improvements of the mechanic kind, than any one man had ever discovered. Among these were several astronomical instruments for making observations both at sea and land; and he was particularly serviceable to Boyle, in completing the air-pump. Wood tells us, that he also explained “Euclid’s Elements,” and “Des Cartes’s Philosophy,” to Boyle. In Nov. 1662, sir Robert Moray, then president, having proposed him for curator of experiments to the Royal Society, he was unanimously accepted, and it was ordered that Boyle should have the thanks of the society for dispensing with him for their use; and that he should come and sit among them, and both exhibit every day three or four of his own experiments, and take care of such others as should be mentioned to him by the society. He executed this office so much to their satisfaction, that when that body was established by the royal charter, his name was in the list of those who were first nominated by the council, May 20, 1663; and he was admitted accordingly, June 3, with a peculiar exemption from all payments. Sept. 28 of the same year, he was nominated by Clarendon, chancellor of Oxford, for the degree of M.A.; and Oct. 19, it was ordered that the repository of the Royal Society should be committed to his care, the white gallery in Gresham-college being appointed for that use. In May 1664, he began to read the astronomical lecture at Gresham for the professor, Dr. Pope, theri in Italy; and the same year was made professor of mechanics to the Royal Society by Sir John Cutler, with a salary of 50l. per annum, which that gentleman, the founder, v settled upon him for life. On Jan. 11, 1664-5, he was elected by that society curator of experiments for life, with an additional salary of“30l. per annum to sir John Cutler’s annuity, settled on him” pro tempore:“and, March folJowing, was elected professor of geometry in Greshamcollege. In 1665, he published in folio his” Micrographia, or some philosophical descriptions of minute bodies, made by magnifying glasses, with observations and enquiries thereupon:" and the same year, during the recess of the Royal Society on account of the plague, attended Dr. Wilkins and other ingenious gentlemen into Surrey, where they made several experiments. In Sept. 1666, he produced his plan for rebuilding the city of London, then destroyed by the great fire; which was approved by the lord -may or and court of aldermen. According to it, all the chief streets were to have been built in regular lines; all the other cross streets to have turned out of them at right angles; and all the churches, public buildings, marketplacesj &c. to have beetl fixed in proper and convenient places; but the nature of the property, and the impossibility of raising funds to indemnify the landholders who would be injured by this scheme, prevented its being carried into execution. The rebuilding of the city, however, according to the act of parliament, requiring an able person to set out the ground to the several proprietors, Hooke was appointed one of the city surveyors, and Oliver, a glass-painter, the other. In this employment he acquired -the greatest part of that estate of which he died possessed; as appeared sufficiently evident from a large iron chest of money found after his death, locked down with a key in it, and a date of the time, which shewed that the contents had been so shut up for above thirty years, and seldom disturbed, for he almost starved himself and all in his house.

, an English mathematician, was son of sir Arthur Hopton, and born in Somersetshire. He

, an English mathematician, was son of sir Arthur Hopton, and born in Somersetshire. He was educated at Lincoln college, Oxford, and after taking his degree of B. A. removed to the Temple, where he lived in habits of friendship with the learned Selden. He died in 1614, a very young man, not having attained to more than his twenty-sixth year. He wrote a treatise on the “Geodetical Staff;” “The Topographical Glass, containing the uses of that instrument, the theodolite, plane table, and circumferentor;” “A Concordance of Years, containing a new and a most exact computation of time, according to the English accompt;” “Prognostications for the years 1607 and 1614.

orrect two or three important errors and inaccuracies that had been introduced, by Israel Lyons, the mathematician employed on the voyage, in the numerous mathematical calculations

In 1768 he went to Christ church, Oxford, as private tutor to Heneage earl of Aylesbury, then lord Guernsey. To this university he appears to have become attached; and his first mathematical publication was elegantly printed at the Clarendon press, “Apollonii Pergaci inclinationum libri duo. Resthuebat S. Horsley,1770. This work was criticised with some severity at the time, but does not appear to have injured his rising reputation, especially wnh the members of the royal society, who chose him to the office of secretary in November 1773. In 1774 he was incorporated B.C. L. at Oxford, and immediately proceeded to the degree of D. C. L. and was presented by his patron, the earl of Aylesbury, to the rectory of Aldbiiry in. Surrey, with which he obtained a dispensation to hold the rectory of Newington. In the same year he published “Remarks on the Observations made in the late Voyage towards the North Pole, for determining the acceleration, of the Pendulum, in latitude 79 51'. In a letter to the hon. Constantinefohn Phipps,” 4to. His intention in this pamphlet, which ought ever to be bound up with “Phipps’s Voyage,” is to correct two or three important errors and inaccuracies that had been introduced, by Israel Lyons, the mathematician employed on the voyage, in the numerous mathematical calculations which appear in that valuable work; and this it was acknowledged, was performed by our learned author with equal skill, delicacy, and candour. I>r. Horsley had long meditated a complete edition of the works of sir Isaac Newton, and in 1776 issued proposals for printing it, by subscription, in 5 vote. 4to, having obtained the royal permission to dedicate it to his majesty; but the commencement of it was for a considerable time delayed by severe domestic affliction, arising from the illness of his wife, for whom he had the tenderest regard. She died in the following year, and some time after, the works of Newton were put to press, but were not finally completed until 1785. In the mean time his great diligence and proficiency in various sciences attracted the notice of an excellent judge of literary merit, the late Dr. Lowth, bishop of London, who on his promotion to that see in 1777, appointed Dr. Horsley his domestic chaplain; and collated him to a prebend in St. Paul’s cathedral. He also, by the same interest, succeeded his father as clerk in orders at St. Martin’s in the Fields.

, a great mathematician of France, was born of a branch of the preceding family, in

, a great mathematician of France, was born of a branch of the preceding family, in 1661. He was a geometrician almost from his infancy; for one day being at the duke de Rohan’s, where some able mathematicians were speaking of a problem of PaschaPs, which appeared to them extremely difficult, he ventured to say, that he, believed he could solve it. They were amazed at what appeared such unpardonable presumption in a boy of fifteen, for he was then no more, yet it a few days be sent them the solution. He entered early into the army, but always preserved his love for the mathematics, and studied them even in his tent; whither he used to retire, it is said, not only to study, but also to conceal his application to study: for in those days, to be knowing in the sciences was thought to derogate from nobility; and a soldier of quality, to preserve his dignity, was in some measure obliged to hide his literary attainments. De l'Hospital was a captain of horse; but, being extremely short-sighted, and exposed on that account to perpetual inconveniences and errors, he at length quitted the army, and applied himself entirely to his favourite amusement. He contracted a friendship with Malbranche, judging by his “Recherche de la Verite*,” that he must be an excellent guide in the sciences; and he took his opinion upon all occasions. His abilities and knowledge were no longer a secret: and at the age of thirty-two he gave a public solution of problems, drawn from the deepest geometry, which had been proposed to mathematicians in the acts of Leipsic. In 1693 he was received an honorary member of the academy of sciences at Paris; and published a work upon sir Isaac Newton’s calculations, entitled “L'Analyse des iniinimens petits.” He was the first in France who wrote on this subject: and on this account was regarded almost as a prodigy. He engaged afterwards in another work of the mathematical kind, in which he included “Les Sectiones coniques, les Lieux georoetriques, la Construction des Equations,” and “Une Theorie des Courbes mechaniques:” but a little before he had finished it, he was seized with a fever, of which he died Feb. 2, 1704, aged 49. It was published after his death, viz. in 1707. There are also six of his pieces inserted in different volumes of the memoirs of the academy of sciences.

, or L'Hoste (John), a learned mathematician of Nancy, towards the end of the sixteenth century, taught law

, or L'Hoste (John), a learned mathematician of Nancy, towards the end of the sixteenth century, taught law and mathematics with uncommon reputation at Pont-a-Mousson, and was appointed superintendant of fortifications, and counsellor of war by Henry duke of Lorrain. His genius was extensive, penetrating, and formed for the sciences. He died in 1631, leaving several valuable works the principal ones are, “Le sommaire et l'usage de la Sphere Artificielle,” 4to “La Pratique de Géométrie,” 4to “Description et usage des principaux instrumens de Géométrie,” 4to “Du Quadran et quarré; Rayon astronomique Bâton de Jacob; interpretation du grand art de Raymond Lulle,” &c.

, a very celebrated mathematician and astronomer, was born at the Hague April 14, 1629, and was

, a very celebrated mathematician and astronomer, was born at the Hague April 14, 1629, and was son of Constantino Huygens, lord of Zuylichem, who had served three successive princes of Orange in the quality of secretary, and had spent his whole life in cultivating the mathematics not in the speculative way only, but in making them subservient to the uses of life., From his infancy our author applied himself to this study, and made a considerable progress in it, even at nine years of age, as well as in music, arithmetic, and geography; in all which he was instructed by his father, who in the mean time did not suffer him to neglect the belles lettres. At thirteen he was initiated in the study of mechanics; having discovered a wonderful curiosity in examining machines and other pieces of mechanism; and two years after had the assistance of a master in mathematics, under whom he made surprising progress. In 1645 he went to study law at Leyden, under Vinnius; yet did not attach himself so closely to that science, but that he found time to continue his mathematics under the professor Schooten. He left this university at the end of one year, and went to Breda, where an university had just been founded, and placed under the direction of his father; and here, for two or three years, he made the law his chief study. In 1649 he went to Holstein and Denmark, in the retinue of Henry count of Nassau; and was extremely desirous of going to Sweden to visit Des Cartes, who was then in that country with the queen Christina, but the count’s short stay in Denmark would not permit him. In 1651, he gave the world a specimen of his genius for mathematics, in a treatise entitled “Theoremata de quadratura Hyperboles, Ellipsis, & Circuli, ex dato portionum gravitatis centro” in which he shewed very evidently what might be expected from him afterwards.

st to Mr. Burnett, of EIrick, in the county of Aberdeen; afterwards to James Gregory, the celebrated mathematician; and lastly to Mr. Eddie, one of the magistrates of Aberdeen.

Mr. Jameson died at Edinburgh in 1644, and was interred in the churchyard of the Grey Friars, but without, any monument. By his will, written witli his own hand in 1641, and breathing a spirit of much piety and benevolence, he provides kindly for his wife and children, and leaves many legacies to his relations and friends. Of his family, his daughter Mary was thrice married: first to Mr. Burnett, of EIrick, in the county of Aberdeen; afterwards to James Gregory, the celebrated mathematician; and lastly to Mr. Eddie, one of the magistrates of Aberdeen. By all these gentlemen she had children, and many of the descendants of the two first have numerous families in the county of Aberdeen. Mary seems to have inherited a portion of her father’s genius. Several specimens of her needle-work remain, particularly Jephtha’s rash vow; Susannah and the Elders, &c. probably from a design of her father’s; these now adorn the East end of St. Nicholas church, Aberdeen. Though Jameson was little known in England, and has not been noticed by any English writer on the arts, except lord Orford, his character, as well as his works, were highly esteemed in his own country. Arthur Johnston, the poet, addressed to him an elegant Latin epigram, on the picture of the marchioness of Huntley, which may be seen in the works of that author, printed at Middleburgh in 1642.

law, which he once thought of making his profession, even after he had studied physic. He was also a mathematician and philosopher, and was concerned with two friends in publishing

Amidst the cares of his new profession, he did not decline his attention to theological study, nor to what he considered as the cause of true liberty. He was, as he had been for many years, zealous for the abolition of subscription, a warm friend to the cause of America against England, an incessant advocate for annual parliaments and universal suffrage (those pernicious engines for destroying the British constitution), a writer in newspapers, and a speaker in public meetings. So many eager pursuits seem to have exhausted his constitution, and he died, apparently of a decline, in March 1786. Dr. John Jebb was a man of various and extensive learning, master of many languages, among which were Hebrew and Arabic; and during his last illness, he studied the Saxon, with the Anglo-Saxon laws and antiquities. He was twice a candidate for the professorship of Arabic at Cambridge. Besides his theological and medical knowledge, he was not a little versed in the science of law, which he once thought of making his profession, even after he had studied physic. He was also a mathematician and philosopher, and was concerned with two friends in publishing at Cambridge a small quarto, entitled “Excerpta quaedam e Newtonii principiis Philosophise naturalis, cum notis variorum;” which was received as a standard book of education in that university. His other works have been collected into 3 vols. 8vo, published in 17S7 by Dr. Disney, and contain chiefly, (besides the plan of his lectures, and harmony of the gospels, six sermons, and a medical treatise on paralysis,) controversial tracts and letters, on his intended improvements at Cambridge, on subscription, on parliamentary reform, &c. He seems to have been an active, enterprising, and rather turbulent, but a sincere man.

of St. John’s college he not only was always in the first class, but was without comparison the best mathematician of his year. His first summer vacation was devoted entirely

, an eminent and learned tutor of the university of Cambridge, was born at Beriew in Montgomeryshire, June 23, 1756. His education, till he entered on his twelfth year, was confined to the instruction of a common country school, first at Beriew, and afterwards in the neighbouring parish of Kerry. During the time that he frequented the latter school, the vicar of the parish, discovering in him those talents which he afterwards so eminently displayed, advised his mother (for he lost his father at an early age) to send him to the grammar-school at Shrewsbury, where he continued nearly seven years, and was inferior to none of his schoolfellows, either in attention to study or in regularity of conduct. In May 1774, he was admitted of St. John’s college, Cambridge, and came to reside there in October following. From that time the excellence of his genius became more particularly conspicuous. He had acquired, indeed, at school, a competent share of classical learning; but his mind was less adapted to Greek and Latin composition than to the investigation of philosophical truths. At the public examinations of St. John’s college he not only was always in the first class, but was without comparison the best mathematician of his year. His first summer vacation was devoted entirely to his favourite pursuit; and at that early period he became acquainted with mathematical works, which are seldom attempted before the third year of academical study. He remained at St. John’s college till after the public examination in June 1776, when, having no prospect of obtaining a fellowship, there being already a fellow of the diocese of St. Asaph in that college, and the statutes limiting the fellowships to one from each diocese, he removed to Trinity college. Here he took his bachelor’s degree in 1779, and his superiority was so decided, that no one ventured to contend with him. The honour of senior wrangler, as it is called in academical phrase, was conceded before the examination began, and the second place became the highest object of competition. If any thing was wanting to shew his superiority, it would be rendered sufficiently conspicuous by the circumstance, that he was tutor to the second wrangler, now the learned Dr. Herbert Marsh, professor of divinity at Cambridge, who acknowledged that for the honour which he then obtained, he was indebted to the instruction of his friend. In the same year in which Mr. Jones took his bachelor’s degree he was appointed assistant tutor at Trinity college. In Oct. 1781 he was elected fellow, and in Oct. 1787, on the resignation of Mr. Cranke, he was appointed to the office of head tutor, which he held to the day of his death. In 1786 and 1787 he presided as moderator in the philosophical schools, where his acuteness and impartiality were equally conspicuous. It was about this time that he introduced a grace, by which fellow-commoners, who used to obtain the degree of bachelor of arts with little or no examination, were subjected to the same academical exercises as other under-graduates. During many years he continued to take an active part in the senate-house examinations; but for some years before his death confined himself to the duties of college- tutor. These, indeed, were sufficiently numerous to engage his whole attention and he displayed in them an ability which was rarely equalled, with an integrity which never was surpassed. Being perfect master of his subjects, he always placed them in the clearest point of view; and by his manner of treating them he made them interesting even to those who had otherwise no relish for mathematical inquiries. His lectures on astronomy attracted more than usual attention, since that branch of philosophy afforded the most ample scope for inculcating (what, indeed, he never neglected in other branches) his favourite doctrine of final causes; for arguing from the contrivance to the contriver, from the structure of the universe to the being and attributes of God. And this doctrine he enforced, not merely by explaining the harmony which results from the established Jaws of nature, but by shewing the confusion which would have arisen from the adoption of other laws. His lectures on the principles of fluxions were delivered with unusual clearness; and there was so much originality in them, that his pupils often expressed a wish that they might be printed. But such was his modesty, that though frequently urged, he never would consent; and when he signed his will a short time before his death, he made the most earnest request to Dr. Marsh, that none of his manuscripts should be printed. But it is a consolation to know, that his lectures in philosophy will not be buried in oblivion: all his writings on those subjects were delivered to his successor in the tuition, and, though less amply than by publication, will continue to benefit mankind. The only things he ever published were “A Sermon on Duelling,” and “An Address to the Volunteers of Montgomeryshire.” The former was published as a warning to the young men of the university, soon after a fatal duel had taken place there. The latter, which he wrote with great animation (for he was a zealous advocate of the volunteer system) was calculated to rouse the volunteers to a vigorous defence of their country.

, an eminent mathematician, was born in 1680, in the island of Anglesey, North Wales. His

, an eminent mathematician, was born in 1680, in the island of Anglesey, North Wales. His parents were yeomen, or little farmers, in that island, and gave to their son the best education which their circumstances would allow; but he owed his future fame and fortune to the diligent cultivation of the intellectual powers by which he was eminently distinguished. Addicted from early life to the study of mathematics, he commenced his career of advancement in the humble office of a teacher of these sciences on board a man of war. In this situation he attracted the notice, and obtained the friendship of lord Anson. He appeared as an author in his 22d year; when his treatise on the art of navigation was much approved. We may judge of his predominant taste for literature and science by a trivial circumstance which occurred at the capture of Vigo, in 1702. Having joined his comrades in pillaging the town, he selected a bookseller’s shop, in hope of obtaining some valuable plunder; but, disappointed in his expectations, he took up a pair of scissars, which was his only booty, and which he afterwards exhibited' to his friends as a trophy of his military success. On his return to England, he established himself as a teacher of mathematics in London; and here, in 1706, he published his “Synopsis Palmariorum Matheseos; or, a new Introduction to the Mathematics,” a work which has ever since been held in the highest estimation as a compendious but comprehensive summary of mathematical science. Mr. Jones was no less esteemed and respected on account of his private character and pleasing manners, than for his natural talents and scientific attainments; so that he reckoned among his friends the most eminent persons of the period in which he lived. Lord Hardwicke selected him as a companion on the circuit, when he was chief justice; and when he afterwards held the great seal, conferred upon him the office of secretary for the peace, as a testimony of his friendship and regard. He was also in habits of intimate acquaintance with lord Parker, president of the royal society, sir Isaac Newton, Halley, Mead, and Samuel Johnson. So highly was his merit appreciated by sir Isaac Newton, that he prepared, with his permission, and very much to his satisfaction, a very elegant edition of small tracts in the higher mathematics. Upon the retirement of lord Mace lesfi eld to Sherborne castle, Mr. Jones resided in his family, and instructed his lordship in the sciences. Whilst he occupied this situation he had the misfortune, by the failure of a banker, to lose the greatest part of that property which he had accumulated Uy the most laudable industry and economy; but the loss was in a great measure repaired to him by the kind attention of his lordship, who procured for him a sinecure place of considerable emolument. He was afterwards offered, by the same nobleman, a more lucrative situation; which, however, he declined, that he might be more at leisure to devote himself to his favourite scientific pursuits. In this retreat he formed an acquaintance with miss Mary Nix, the daughter of a cabinet-maker, who had become eminent in his profession, and whose talents and manners had recommended him to an intimacy with lord Macclesfield. This acquaintance terminated in marriage; and the connection proved a source of personal satisfaction to Mr. Jones himself, and of permanent honour to his name and family. By this lady Mr. Jones had three children two sons and a daughter. One son died in infancy the other will be the subject of the next article and the daughter, who was married to Mr. Rainsford, an opulent merchant retired from business, perished miserably, in 1802, in consequence of her clothes accidentally taking fire. The death of Mr. Jones was occasioned by n polypus in the heart, which, notwithstanding the medical attention and assistance of Dr. Mead, proved incurable. He died in July 1749. Mr. Jones’s papers in the Philosophical Transactions are: “A compendious disposition of Equations for exhibiting, the relations of Goniometrical Lines,” vol. XLIV. “A Tract on Logarithms,” vol. LXI. “Account of the person killed by lightning in Tottenham-court-chapel, and its effects on the building,” vol. LXII. “Properties of the Conic Sections, deduced by a compendious method,” vol. LXIII. In all these works of Mr. Jones, a remarkable neatness, brevity, and accuracy, everywhere prevails. He seemed to delight in a very^ short and comprehensive mode of expression and arrangement; insomuch that sometimes what he has contrived to express in two or three pages, would occupy a little volume in the ordinary style of writing. Mr. Jones, it is said, possessed the best mathematical library in England; which by will he left to lord Macclesfield. He had collected also a great quantity of manuscript papers and letters of former mathematicians, which have often proved useful to writers of their lives, &c. After his death, these were dispersed, and fell into different persons hands many of them, as well as of Mr. Jones’s own papers, were possessed by the late Mr. John Robertson, librarian and clerk to the royal society at whose death Dr. Hutton purchased a considerable quantity of them. From such collections as these it was that Mr. Jones was enabled to give that first and elegant edition, 1711, in 4to, of several of Newton’s papers, that might otherwise have been lost, entitled “Analysis per quantitatum Series, Fluxiones, ac Differentias: cum Enumeratione Linearum Tertii Ordinis.

We learn from the “Anecdotes of Bowyer,” that the plan of another work was formed by this eminent mathematician, intended to be of the same nature with the “Synopsis,” but

We learn from the “Anecdotes of Bowyer,” that the plan of another work was formed by this eminent mathematician, intended to be of the same nature with the “Synopsis,” but far more copious and diffusive, and to serve as a general introduction to the sciences, or, which is the same thing, to the mathematical and philosophical works of Newton. A work of this kind had long been a desideratum in literature, and it required a geometrician of the first class to sustain the weight of so important an undertaking; for which, as M. d'Alembert justly observes, “the combined force of the greatest mathematicians would not have been more than sufficient.” The ingenious author was conscious how arduous a task he had begun; but his very numerous acquaintance, and particularly his friend the earl of Macclesfield, never ceased importuning and urging him to persist, till he had finished the whole work, the result of all his knowledge and experience through a life of near 7O years, and a standing monument, as he had reason to hope, of his talents and industry. He had scarcely sent the first sheet to the press, when a fatal illness obliged him to discontinue the impression; and a few days before his death, he intrusted the ms. fairly transcribed by an amanuensis, to the care of lord Macclesfield, who promised to publish it, as well for the honour of the author as for the benefit of his family, to whom the property of the book belonged. The earl survived his friend many years but the “Introduction to the Mathetics” was forgotten or neglected and, after his death, the ms. was not to be found whether it was accidentally destroyed, which is hardly credible, or whether, as hath been suggested, it had been lent to some geometrician, unworthy to bear the name either of a philosopher or a man, who has since concealed it, or possibly burned the original for fear of detection. Lord Teignmouth, however, informs us, in his life of Mr. Jones’s illustrious Son, that there is no evidence in his memoranda to confirm or disprove this account.

, a learned Spanish mathematician, knight of Malta, and commander of the band of gentlemen marine

, a learned Spanish mathematician, knight of Malta, and commander of the band of gentlemen marine guards, was chosen, with Ulloa, to attend the French academicians, who went to Peru', for the purpose of measuring a degree on the meridian, in order to determine the earth’s figure. They embarked May 26, 1735. Ulloa undertook the historical part of the voyage, which appeared translated into French, Amsterdam, 1752, 2 vols. 4to; and D. George Juan the astronomical part, who accordingly published a large work on the earth’s figure, printed in Spanish. On his return he went to Paris, 171 where the academy of sciences admitted him a member. He died at Madrid, 1773, leaving several works in Spanish on naval affairs, a translation of which would be useful.

, in Italian Giuntino, a celebrated mathematician and astrologer of the sixteenth century, was born 1523, at Florence.

, in Italian Giuntino, a celebrated mathematician and astrologer of the sixteenth century, was born 1523, at Florence. He published Commentaries, in Latin, on the Sphaera of Holywood or Sacro Bosco, 1577 and 1578, 2 vols. 8vi; “Speculum Astrologiae,” Lngd. 1581, 2 vols. fol. and other works relating to astronomy. There is also a treatise written by him in French on the comet which appeared in 1577, 8vi; and another on the reformation of the calendar by Gregory XIII. 8vi, in Latin. He had quitted the Carmelite order, and became a protestant, but returned afterwards to the Catholic church, and spent the chief of his life at Lyons, where his conduct was very irregular. He died 1590. a

, an eminent mathematician, physician, and botanist, the son of a schoolmaster at Lubec,

, an eminent mathematician, physician, and botanist, the son of a schoolmaster at Lubec, in Germany, was born October 21, 1587. His mother was daughter to a clergyman of the cathedral church at Lubec. Jungius, having unfortunately been deprived of his father very early in life (for he was stabbed one evening upon his return home from a convivial party), was obliged to depend almost entirely upon his own exertions for knowledge; yet in his youth, he became a very subtle logician, and ingenious disputant, and thus prepared his mind for that clearness of investigation and accuracy of judgment, which were so eminently conspicuous in the works which he published at a more advanced period of his life. Selecting the study of medicine as a profession, he travelled over a great part of Italy and Germany, in order to cultivate the acquaintance of the most distinguished physicians of that time. He had previously graduated with distinguished honour at the university of Giessen A. D. 1607, and remained there a few years as mathematical tutor. In 1625 he was chosen professor of physic at Helmstadt, but, on account of the Danish war, he was obliged, soon after his appointment, to fly to Brunswick, whence he soon returned to Helmstadt, and in 1629 was appointed rector of the school at Hamburgh.

, an eminent mathematician, and professor of mathematics at Gottingen, was born at Leipsic,

, an eminent mathematician, and professor of mathematics at Gottingen, was born at Leipsic, Sept. 27, 1719. He had part of his education at home, under his father and uncle, both of whom were lecturers on jurisprudence, and men of general literature. In 1731 he attended the philosophical lectures of the celebrated Winkler, and next year studied mathematics under G. F. Richter, and afterwards under Hausen; but practical astronomy being at that period very little encouraged at Leipsic, he laboured for some years under great difficulties for want of instruments, and does not appear to have made any great progress until, in 1742, he formed an acquaintance with J. C. Baumann, and by degrees acquired such helps as enabled him to make several observations. Heinsius was his first preceptor in algebra; and, in 1756, he was invited to Gottingen, to be professor of mathematics and moral philosophy, and afterwards became secretary of the royal society, and had the care of the observatory on the resignation of Lowitz in 1763; but, notwithstanding his talents in astronomy and geography, the services he rendered to the mathematical sciences in general are more likely to convey his name to posterity. He exerted himself with the most celebrated geometers of Germany, Segner, and Karsten, to restore to geometry its ancient rights, and to introduce more precision and accuracy of demonstration into the whole of mathematical analysis. The doctrine of binomials that of the higher equations the laws of the equilibrium of two forces on the lever, and their composition are some of the most important points in the doctrine of mathematical analysis and mathematics, which Kastner illustrated and explained in such a manner as to excel all his predecessors. Germany is in particular indebted to him for his classical works on every part of the pure and practical mathematics. They unite that solidity peculiar to the old Grecian geometry with great brevity and clearness, and a fund of erudition, by which Kastner has greatly contributed to promote the study and knowledge of the mathematics. Kiistner’s talents, however, were not confined to mathematics: his poetical and humorous works, as well as his epigrams, are a proof of the extent of his genius; especially as these talents seldom fall to the lot of a mathematician. How Kastner acquired a taste for these pursuits, we are told by himself in one of his letters. In the early part of his life he resided at Leipsic, among friends who were neither mathematicians nor acquainted with the sciences; he then, as he tells us, contracted “the bad habit of laughing at others;”' but he used always to say, Hanc veniam damns petimusque vicissim.

, an eminent mathematician and philosopher, was born Dec. 1, 1671, at Edinburgh, where

, an eminent mathematician and philosopher, was born Dec. 1, 1671, at Edinburgh, where he received the first rudiments of learning; and, being educated in that university, continued there till he took the degree of M. A. His genius leading him to the mathematics, he studied that science very successfully under David Gregory the professor there, who was one of the first that had embraced the Newtonian philosophy; and, in 1694, he followed his tutor to Oxford, where, being admitted of Baliol, he obtained one of the Scotch exhibitions in that college. He is said to have been the first who taught Newton’s principles by the experiments on which they are grounded, -which he was enabled to do by an apparatus of instruments of his own providing; and the lectures he delivered in his chambers upon natural and experimental philosophy, procured him very great reputation. The first public specimen he gave of his skill in mathematical and philosophical knowledge, was his “Examination of Burnet’s Theory of the Earth,” which appeared in 1698, and was universally applauded by the men of science, and allowed to be decisive against the doctor’s “Theory.” To this piece he subjoined “Remarks upon Whiston’s New Theory of the Earth;” and these theories, being defended by their respective inventors, drew from Keill, in 1699, another performance entitled “An Examination of the Reflections of the Theory of the Earth, together with ‘ a Defence of the Remarks on Mr. Whiston’s New Theory’.” Dr. Burnet was a man of grea.t humanity, moderation, and candour; and it was therefore supposed that Keill had treated him too roughly, considering the great disparity of years between them. Keill, however, left the doctor in possession of that which has since been thought the great characteristic and excellence of his work: and, though he disclaimed him as a philosopher, yet allowed him to be a man of a fine imagination. “Perhaps,” says he, “many of his readers will be sorry to be undeceived about his Theory; for, as I believe never any book was fuller of mistakes and errors in philosophy, so none ever abounded *vith more beautiful scenes and surprizing images of nature. But I write only to those who might expect to find a true philosophy in it: the*y who read it as an ingenious romance will still be pleased with their entertainment.

essor of astronomy at Oxford. In 1711, being attacked by Leibnitz, he entered the lists against that mathematician, in the dispute about the invention of fluxions. Leibnitz wrote

In Feb. 1701 he was admitted a fellow of the royal society; and, in 1708, published, in the “Philosophical Transactions,” a paper “Of the Laws of Attraction, and its Physical Principles.” At the same time, being offended at a passage in the “Acta Eruditorum” at Leipsic, in which Sir Jsaac Newton’s claim to the first invention of the method of fluxions was called in question, he communicated to the royal society another paper, in which he asserted the justice of that claim. In 1709 he was appointed treasurer to the Palatines, and in that station attended them in their passage to New England; and, soon after his return in 1710, was chosen Savilian professor of astronomy at Oxford. In 1711, being attacked by Leibnitz, he entered the lists against that mathematician, in the dispute about the invention of fluxions. Leibnitz wrote a letter to Dr. Hans Sloane, then secretary to the royal society, dated March 4, 1711, in which he required Keill, in effect, to give him satisfaction for the injury he had done him in his paper relating to the passage in the “Acta Eruditorum” at Leipsic. He protested, that he was far from assuming to himself Sir Isaac Newton’s method of fluxions; and desired, therefore, that Keill might be obliged to retract his false assertion. Keill desired, on the other hand, that he might be permitted to justify what he had asserted which he performed to the approbation of Sir Isaac, and other members of the society and a copy of his defence was sent to Leibnitz, who, in a second letter, remonstrated still more loudly against Keill’s want of candour and sincerity; adding, that it was not fit for one of his age and experience to enter into a dispute with an upstart, who acted without any authority from Sir Isaac Newton and desiring that the royal society would enjoin him silence. Upon this, a special committee was appointed who, after examining the facts, concluded their report with “reckoning Mr. Newton the inventor of fluxions; and that Mr. Keill, in asserting the same, had been no ways injurious to Mr. Leibnitz.” In the mean time, Keill behaved himself with great firmness and spirit; which he also shewed afterwards in a Latin epistle, written in 172O, to Bernoulli, mathematical professor at Basil, on account of the same usage shewn to Sir Isaac Newton; in the title-page of which he put the arms of Scotland, viz. a thistle, with this motto, “Nemo me impune lacessit.” The particulars of the contest are recorded in Collins’s “Commercium Epistolicum.

condition that Kepler had consented to leave Gratz), who received him very kindly, and made him his mathematician, upon condition that he should serve Tycho as an arithmetician.

, the greatest astronomer perhaps that any age has produced, was born at Wiel in the dutchy of Wirtemberg, Dec. 27, 1571. His father, Henry Kepler, was descended from a family which had raised themselves under the emperors by their military services, and was himself an officer of rank in the army; but afterwards, experiencing ill fortune, was obliged to sell all he had, and support himself and his family by keeping a public-house. He died in 1590, and' left his son John without provision. His education had be^n therefore neglected, but, by the favour of his prince, he was enabled to enter upon hi* studies in philosophy at Tubingen, immediately upon his father’s death, and, two years after, pursued the mathematics in the same university, under the famous Michael Maestlinus, an astronomer of eminence, and of the Copernican school, but at this time Kepler informs us he had. no particular predilection for astronomy. His passion was rather for studies more fluttering to the ambition of a youthful mind; and when his prince selected him, in 1591, to fill the vacant astronomical chair, it was purely from deference to his authority, and the persuasions of Masstlinu^ who had high expectations from his talents, that he reluctantly accepted of the office. He appears to have thought it unsuitable to his pretensions; and the state of astronomy was besides so low, uncertain, and in many respects visionary, that he had no hope of attaining to eminence in it. But what he undertook with reluctance, and as a temporary provision conferred on a dependant by his prince, soon engaged his ardour, and engrossed almost his whole attention. The first fruit? of his application to astronomical studies appeared in his “Mysterium Cosmographicum,” published about two years after his settlement in Gratz; and hasty and juvenile as this production was, it displayed so many marks of genius, and such indefatigable patience in the toil of calculation, that on presenting it to Tycho Brahe, it procured him the esteem of that illustrious astronomer, and even excited his anxiety for the proper direction of talents go uncommon. Accordingly, not contented with exhorting Kepler to prefer the road of observation to the more uncertain one of theory, Tycho added an invitation to live with him at Uraniburg, where his whole observations should be open to Kepler’s perusal, and those advantages provided for making others, which his situation at Gratz denied. This after some time was accepted. In 1597, Kepler entered into the married state, which at first created him great uneasiness, from a dispute which arose about his wife’s fortune; and, the year after, he was banished from Gratz on account of his religion, but afterwards recalled, and restored to his former dignity. However, the growing troubles and confusions of that place inclined him to think of a residence elsewhere; and he now determined to accept T. Brahe’s invitation, and accordingly left the university of Gratz, and removed into Bohemia with his family in 1600. In his journey he was seized with a quartan ague, which continued seven or eight months; and prevented his profiting by Tycho’s kindness, and, what was worse, some petty differences interrupted their connection. Kepler was offended at Tycho, for refusing some services to his family, which he had occasion for: he was also dissatisfied with his reserved ness; for, Tycho did not communicate to him all that he knew; and, as he died in 1601, he did not give Kepler time to be very useful to him, or to receive any considerable advantages from him. Before his death, however, he introduced him to the emperor Rodolphus at Prague (for, it was upon this condition that Kepler had consented to leave Gratz), who received him very kindly, and made him his mathematician, upon condition that he should serve Tycho as an arithmetician. From that time Kepler enjoyed the title of mathematician to the emperor all his life, and gained more and more reputation every year by his works. Rodolphus ordered him to finish the tables begun by Tycho, which were to be called the “Rodolphine Tables” and he applied himself very vigorously to this work but such difficulties arose in a short time, partly from the nature of it, and partly from the delay of the treasurers, that the tables were not finished and published till 1627. He complained, that, from 1602 and 1603, he. was looked upon by the treasurers with a very invidious eye; and when, in 1609, he had published a noble specimen o/ the work, and the emperor had given orders that, besides the expence of the edition, he should immediately be paid the arrears of his pension, which, he said, amounted to 2000 crowns, and likewise 2000 more; yet, that it was not till two years after, that the generous orders of Rodolphus, in his favour, were put in execution. He met with no less discouragement from the financiers under the emperoc Matthias, than under Rodolphus; and therefore, after struggling with poverty for ten years at Prague, began to think of quitting his quarters again. He was then fixed at Lints by the emperor Matthias, who appointed him a salary from the states of Upper Austria, which was paid for sixteen years. In 1613 he went to the assembly at Ratisbon, to assist in the reformation of the calendar; but returned to Lints, where he continued to 1626. In November of that year, he went to Ulm, in order to publish the “Rodolphine Tables;” and afterwards, in 1629, with the emperor’s leave, settled at Sagan in Silesia, where he published the second part of his “Ephemerides;” fot the first had been published at Lints in 1617. In 1630, he went to Ratisbon, to solicit the payment of the arrears of his pension; but, being seized with a fever, which, it is said, was brought upon him by too hard riding, he died there in November, in his 59th year.

, a philosopher and mathematician of considerable learning, was born at Fulde, in Germany, 1601.

, a philosopher and mathematician of considerable learning, was born at Fulde, in Germany, 1601. He entered into the society of Jesuits 1618; and after going through the regular course of studies, during which his talents and industry were equally conspicuous, he taught philosophy, mathematics, the Hebrew and Syriac languages, in the university of Wirtzburg, in Franconia. The war which Gustavus Adolphus of Sweden made in Germany, disturbing his repose here, he retired into France, and settled in the Jesuits college at Avignon, where he was in 1635. He was afterwards called to Rome to teach mathematics in the Roman college; which he did six years. He spent the remainder of his life in that city; and for some time professed the Hebrew language. He died in 1680, after having published no less than twenty-two volumes in folio, eleven in quarto, and three in octavo, in all which, however, he discovers too much of that species of learning which is of little use. He was always credulous, inaccurate, and careless of what he asserted. Some reckon as his principal work, his “Oedipus Ægyptiacus: hoc est, universalis hieroglyphicae veterum doctrinse temporum injuria abolitae, instauratio. Romas, 1652, &c.” in 4 vols. folio. Kircher was more than ordinarily addicted to the study of hieroglyphical characters; and could always find a plausible, if not a true meaning for thm. As his rage for hieroglyphics was justly esteemed ridiculous, some young scholars resolved to divert themselves a little at his expence. With this view they engraved some unmeaning fantastic characters, or figures, upon a shapeless piece of stone, and had it buried in a place which was shortly to be dug up. It was then carried to Kircher, as a most singular curiosity; and he, enraptured at the discovery, applied himself instantly to explain the hieroglyphic, and made it, at length, in his opinion, very intelligible. Among Kircher’s other works are, “Praelusiones Magnetic,1654, fol. “Primitice Gnomonicae Catopticae,” 4to “Ars magna lucis et umbrae,” Romae, 1646, fol. “Musurgia Universalis,1650, 2 vols. folio. Dr. Burney says this, which treats of music, is a large book but a much larger might be composed in pointing out its errors and absurdities. For what is useful in it he was obliged to father Mersenne, in his “Harmonic Universelle.” “Obeliscus Pamphilius,1650, fol. “Itinerarium extaticum,” 4to; “Obeliscus Ægyptianus,” fol.; “Mundus subterraneus,” 1678, 2 vols. fol. “China illustrata,1667, fol. translated into French by F. S. d'Alquie, 1670, fol. “Turris Babel,” fol. “Area Noe,” fol. “Latium,1671, fol. a valuable work; “Phonurgia nova,” 16 73, fol.; “Ars sciendi combinatorial,1669, fol.; “Polygraphia,1663, fol. &c.

, a learned philosopher and mathematician, was a Swiss by birth, and came early into eminence by his

, a learned philosopher and mathematician, was a Swiss by birth, and came early into eminence by his mathematical abilities. He was professor of philosophy and natural law at Franeker, and afterwards at the Hague, where he became also librarian to the stadtholder, and to the princess of Orange; and where he died in 1757. The academy of Berlin enrolled him among her members; but afterwards expelled him on the following occasion. Maupertuis, the president, had inserted in the volume of the Memoirs for 1746, a discourse upon the laws of motion; which Koenig not only attacked, but also attributed the memoir to Leibnitz. Maupertuis, stung with the imputation of plagiarism, engaged the academy of Berlin to call upon him for his proof; which Koenig failing to produce, he was struck out of the academy. All Europe was interested in the quarrel which this occasioned between Koenig and Maupertuis. The former appealed to the public; and his appeal, written with the animation of resentment, procured him many friends. He was author of some other works, and had the character of being one of the best mathematicians of the age. He had a brother, Daniel, who was murdered at the age of twenty-two, at Franekei 4 The populace, overhearing him talk in French, imagined that he was a French spy, and would have killed him on the spot, if the academicians had not rescued him from their fury: but the wounds which he received hurried him to the grave in a few months. He translated into Latin Dr. Arbuthnot’s “Tables of Ancient Coins,” which remained in ms. till 1756, when it was published at Utrecht, with a curious and useful preface, by professor Reitz.

, an eminent mathematician, was born at Lyons in 1660. Being intended for the bar, he was

, an eminent mathematician, was born at Lyons in 1660. Being intended for the bar, he was sent to study the law first at the college of Lyons, and next at the university of Thoulouse but having accidentally met with Fournier’s Euclid, and a treatise on algebra, mathematics became his favourite science. In 1686 he came to Paris, was soon after appointed tutor to the duke de Noailles, elected a member of the academy of sciences, and was appointed by Louis XIV, royal hydrographer at Rochefort; but sixteen years afterwards, he was recalled to Paris, and made librarian to the king with a considerable pension. He died April 11, 1734, and in his last moments, when he no longer knew the persons who surrounded his bed, one of them, through a foolish curiosity, asked him “What is the square of 12” to which he replied, as it were mechanically, 144. His works are, 1. “New Methods for the Extraction and Approximation of Roots,1692, 4to, 2. “Elements of Arithmetic and Algebra,1697, 12mo. 3. “On the Cubature of the, Sphere,1702, 12mo. 4. “A general Analysis, or Method of resolving Problems,” published by Richer in 1733, 4to. 5. Several Papers in the Memoirs of the Academy. Lagny excelled in arithmetic, algebra, and geometry, in which he made many important discoveries.

, a very eminent mathematician and philosopher, was born at Turin, Nov. 25, 1736, where his

, a very eminent mathematician and philosopher, was born at Turin, Nov. 25, 1736, where his father, who had been treasurer of war, was in reduced circumstances. In his early days his taste was more inclined to classical than mathematical studies, and his attention to the latter is said to have been first incited by a memoir that the celebrated Halley had composed for the purpose of demonstrating the superiority of analysis. From this time Lagrange devoted himself to his new study with such acknowledged success, that at the age of sixteen he became professor of mathematics in the royal school of artillery at Turin. When he had discovered the talents of his pupils, all of whom were older than himself, he selected some as his more intimate friends, and -from this early association arose an important institution, the academy of Turin, which published in 1759 a first volume under the title of “Actes de la Socie*te* Prive*e.” It is there seen that young 'Lagrange superintended the philosophical researches of Cigna, the physician, and the labours of the chevalier de Saluces. He furnished Foncenex with the analytical part of his memoirs, leaving to him the task of developing the reasoning upon which the formulae depended. In these memoirs, which do not bear his name, may be observed that pure analytical style which characterizes his greatest productions. He discovered a new theory of the lever, which makes the third part of a memoir that had much celebrity. The first two parts are in the same style, and are known to be also by Lagrange, although he did not positively acknowledge them, and they were generally ascribed to Foncenex.

Euler’s admiration of our young mathematician involves the origin of Lagrange' s discoveries, as he himself

Euler’s admiration of our young mathematician involves the origin of Lagrange' s discoveries, as he himself after^ wards related. The first attempts to determine the maxima and minima in all indefinite integral formulae were made by means of a curve of the quickest descent, and by the Isoperimeters of Bernouilli. Euler reduced them to a general method, which, however, had not that simplicity which is desirable in a work of pure analysis. Euler himself thought so, but thought at the same time that it was conformable to truth, and that by means of sound metaphysics it might be made extremely evident; but this task, he said, he left to those who made metaphysics their study. While the metaphysicians took no notice of this appeal, Lagrange’s emulation was excited, and he soon discovered the solution that Euler had despaired of, by analysis; and in giving an account of his process, he said that he considered it not as a metaphysical principle, but as a necessary result of the laws of mechanism, as a mere corollary of a more general law, which he afterwards made the basis of his celebrated work, entitled “Mecanique analytique.” We see also the germ of this work in the paper he wrote when the Academy of sciences proposed as a prize question, the theory of the moon’s libration, on which subject he had an opportunity to apply the principles of his analytical discoveries. He wrote also an equally able memoir on another prize subject by the same academy, the theory of Jupiter’s satellites; and as the subject was not exhausted in this memoir, it was his intention to return to it and enlarge his researches, but his other more pressing engagements prevented him.

, an eminent mathematician and astronomer, was born at Muhlhausen, in the Sundgaw, a town

, an eminent mathematician and astronomer, was born at Muhlhausen, in the Sundgaw, a town in alliance with the Swiss cantons, Aug. 29th, 1728. His father was a poor tradesman, who, intending to bring him up to his own business, sent him to a public school, where he was taught the rudiments of learning, at the expence of the corporation, till he was twelve years old. Here he distinguished himself among his school-fellows, and some attempts were made to provide him with the means of studying theology as a profession, but for want of encouragement, he was under the necessity of learning his father’s trade. In this laborious occupation, however, he continued to devote a considerable part of the night to the prosecution of his studies; and to furnish himself with candles, he sold for half-pence or farthings small drawings which he delineated while employed in rocking his infant sister in a cradle. He met with an old book on the mathematics which gave him inexpressible pleasure, and which proved that he had a genius for scientific pursuits. Seeing the turn which the young man had for knowledge, several learned men afforded him assistance and advice; and they had the pleasure of finding him improve, under their patronage, with a rapidity beyond their most sanguine expectations. He was now taken from the drudgery of the shop-board, and M. Iselin, of Basil, engaged him as his amanuensis, a situation which afforded him an opportunity of making further progress in the belles-lettres, as well as philosophy and mathematics. In 1748, his patron recommended him to baron Salis, president of the Swiss confederacy, to become tutor to his children, in which office he gladly engaged. His talents as a philosopher and mechanician began to display themselves in his inventions and compositions. After living eight years at Coire, he repaired, in 1756, with his pupils, to the university of Gottingen, where he was nominated a corresponding member of the scientific society in that place, and from thence he removed, in the following year, to Utrecht, where he continued twelve months. In 1758, he went with his pupils to Paris, where he acquired the esteem and friendship of D' Alembert and Messier; and from thence he travelled to Marseilles, and formed the plan of his work “On Perspective,” which he published in the following year at Zurich. In 1760 he published his “Photometry,” a master-piece of sagacity, which contains a vast quantity of information of the most curious and important nature. In the same year he was elected a member of the Electoral Bavarian Scientific Society. Lambert was author of many other pieces besides those which have been already mentioned: among these were his “Letters on the Construction of the Universe,” which were afterwards digested, translated, and published under the title of “The System of the World.” In 1764 he made an excursion to Berlin, and was introduced to Frederic II., who, sensible of his great services to science, gave directions to have him admitted a regular member of the academy; this appointment enabled him to devote himself wholly to the pursuit of his favourite studies. He enriched the transactions of several learned societies with his papers and treatises, some of which he published separately. He died Sept. 25th, 1777, when he was in the 50th year of his age. Most of his mathematical pieces were published in a collective form by himself in three volumes, in which almost every branch of mathematical science has been enriched with additions and improvements.

, an eminent mathematician, was born at Peakirk, near Peterborough in Northamptonshire,

, an eminent mathematician, was born at Peakirk, near Peterborough in Northamptonshire, in January 1719. He became very early a proficient in the mathematics, as we find him a contributor to the “Ladies Diary” in 1744, to which useful publication he continued to send articles until a few years before his death. In the “Philosophical Transactions” for 1754, he wrote “An investigation of some theorems, which suggest several very remarkable properties of the circle, and are at the same time of considerable use in resolving Fractions, &c.” In 1755, he published a small volume, entitled “Mathematical Lucubrations,” and containing a variety of tracts relative to the rectification of curve lines, the summation of series, the finding of fluents, and many other points in the higher parts of the mathematics. The title “Lucubrations,” was supposed to intimate that mathematical science was at that time rather the pursuit of his leisure hours, than his principal employment and indeed it continued to be so during the greatest part of his life for about the year 1762 he was appointed agent to earl Fitzwilliam an employment which he resigned only two years before his death.

t was not the only one who had considered the matter before him; for d’Alembert there speaks of some mathematician, though he does not mention his name, who, after reading what

In the 67th volume, for 1777, he gave “A New Theory of the Motion of bodies revolving about an axis in free space, when that motion is disturbed by some extraneous force, either percussive or accelerative.” At that time he did not know that the subject had been treated by any person before him, and he considered only the motion of a sphere, spheroid, and cylinder. After the publication of of this paper, however, he was informed, that the doctrine of rotatory motion had been considered by d'Alembert; and upon procuring that author’s “Opuscules Mathematiques,” he there learned that d‘Alembert was not the only one who had considered the matter before him; for d’Alembert there speaks of some mathematician, though he does not mention his name, who, after reading what had been written on the subject, doubted whether there be any solid whatever, beside the sphere, in which any line, passing through the centre of gravity, will be a permanent axis of rotation. In consequence of this, Mr. Landen took up the subject again; and though he did not then give a solution to the general problem, viz. “to determine the motions of a body of any form whatever, revolving without restraint about any axis passing through its centre of gravity,” he fully removed every doubt of the kind which had been started by the person alluded to by d'Alembert, and pointed out several bodies which, under certain dimensions, have that remarkable property. This paper is given, among many others equally curious, in a volume of “Memoirs,” which he published in 1780. That volume is also enriched with a very extensive appendix, containing “Theorems for the calculation of Fluents;” which are more complete and extensive than those that are found in any author before him. In 1781, 1782, and 1783, he published three small tracts on the “Summation of Converging Series;” in which he explained and shewed the extent of some theorems which had been given for that purpose by De Moivre, Stirling, and his old friend Thomas Simpson, iii answer to some things which he thought had been written to the disparagement of those excellent mathematicians. It was the opinion of some, that Mr. Landen did not shew less mathematical skill in explaining and illustrating these theorems, than he has done in his writings on original subjects; and that the authors of them were as little aware of the extent of their own theorems, as the rest of the world were before Mr. Landen’s ingenuity made it obvious to all.

, a learned mathematician of the sixteenth century, was a native of Keiserberg in Upper

, a learned mathematician of the sixteenth century, was a native of Keiserberg in Upper Alsatia, and was professor of Greek and mathematics at Friburg about the year 1610. Two years after, he wrote his “Elementale Mathematicum,” which, according to Vossius, was not printed until five years afterwards. It was, in 1625, much improved and published by Isaac Habrecht, a philosopher and physician. Langius’s previous works were, an edition of “Martial,” Strasburgh, 1595, 12mo, and a “Florilegium,” in 1598, 8vo, which, at the distance of some years, was followed by a folio, entitled, “Polyanthea nova.” This, which Bayle reckons the third compilation of the kind, was printed at Geneva, in 1600, and often since. Langius also published an edition of “Juvenal and Persius,” at Friburgh, in 1608. A “Tyrocinium Graecarum Literarum,” in 1607; and a collection entitled “Adagia, sive Sententise proverbiales.” We have no account of his personal history, unless that, after living many years in the Protestant communion, he became a Roman Catholic; but when he died is not specified.

, a mathematician, was born in Zealand, in 1561, and was a preacher at Antwerp,

, a mathematician, was born in Zealand, in 1561, and was a preacher at Antwerp, in 1586, and afterwards for several years; Vossius mentions that he was minister at Goese in Zealand, twenty-nine years; and being then discharged of his functions, on account of his old age, he retired to Middleburgh, where he died in 1632. His works were principally the following: 1. “Six Books of sacred Chronology,” printed in 1626. 2. “Essays on the Restitution of Astronomy,” printed at Middleburgh, 1629. 3. “Four Books of Geometrical Triangles,” printed in 1631. 4. “Of Measuring the Heavens,” in three books, in the same year. 5. “An Account of the diurnal and annual Motion of the Earth and of the true Situation of the visible celestial Bodies.” In this work he declares himself openly for Copernicus’s System, and even pretends to improve it. He composed this work in Dutch, and it was translated into Latin by M-minus Hortensius, and printed at Middleburgh, 1630. Fromond, a doctor of Louvain, wrote an answer to it, and endeavoured to prove the earth stood still; and his son published an answer not only to Fromond, but to Morin, regius professor at Paris, and to Peter Bartholinus, which is entitled “A Defence of the Account,” &c. This occasioned a controversy, but of no long duration.

itation to Vienna from the empress Maria Teresa, who honoured him with her esteem, and appointed him mathematician to the court, with a pension of 500 florins. What rendered him

, a learned Italian mathe. matician, was born at Milan, Nov. 17, 1702. He was educated among the Jesuits, and entered into their order in 1718. He afterwards taught the belles-lettres at Vercelli and Pavia, and was appointed rhetoric- professor in the university of Brera, in Milan. In 1733 the senate of Milan appointed him professor of mathematics at Pavia, and afterwards removed him to the same office at Milan, the duties of which he executed with reputation for twenty years. In F75J) his fame procured him an invitation to Vienna from the empress Maria Teresa, who honoured him with her esteem, and appointed him mathematician to the court, with a pension of 500 florins. What rendered him most celebrated, was the skill he displayed as superintendant and chief director of the processes for measuring the bed of the Reno and other less considerable rivers belonging to Bologna, Ferrara, and Ravenna. On this he was employed for six years, under Clement XIII.; and Clement XIV. ordered that these experiments should be continued upon Leccln’s plans. He died August 24, 1776, aged seventy-three years. Fabroni, who has given an excellent personal character of Lecchi, and celebrates his skill in hydraulics, has, contrary to his usual practice, mentioned his works only in a general way; and for the following list we have therefore been obliged to have recourse to a less accurate authority: 1. “Theoria lucis,” Milan, 1739. 2. “Arithmetica universalis Jsaaci Newton, sive de compositione, et resolutione arithmetica perpetuis commentariis illustrata et aucta,” Milan, 1752, 3 vols. 8vo. 3. “Elementa geometrise theoricx et practices,” ibid. 1753, 2 vols. 8vo. 4. “Elementa Trigonometric,” &c. ibid. 1756. 5. “De sectionibus conicis,” ibid. 1758. 6. “Idrostatica csaaiinata,” &c. ibid. 1765, 4 to. 7. “Relazione della visita alle terre dannegiate dalle acque di Bologna, Ferrara, e Ravenna,” &c. Rome, 17G7, 4to. 8. “Memorie idrostatico-storiche delle operazioni esequite nella inalveazione del Reno di Bologna, e degli altri minori torrenti per la linea di primaro al mare dalP anno 1765 al 1772,” Modena, 1775, 2 vols. 4to. 9. “Trattato de' canali navigabili,” Milan, 1776, 4to.

, a very eminent mathematician and philosopher, was born at Leipsic, July 4, 1646. His father,

, a very eminent mathematician and philosopher, was born at Leipsic, July 4, 1646. His father, Frederic Leibnitz, was professor of moral philosophy, and secretary to that university; but did not survive the birth of his son above six years. His mother put him under messieurs Homschucius and Bachuchius, to teach him Greek and Latin; and he made so quick a progress as to surpass the expectations of his master; and not content with their tasks, when at home, where there was a well-chosen library left by his father, he read with attention the ancient authors, and “especially Livy. The poets also had a share in his studies, particularly Virgil, many of whose verses he could repeat in his old age, with fluency and accuracy. He had himself also a talent for versifying, and is said to have composed in one day’s time, a poem of three hundred lines, without an elision. This early and assiduous attention to classical learning laid the foundation of that correct and elegant taste which appears in all his writings. At the age of fifteen, he became a student in the university of Leipsic, and to polite literature joining philosophy and the mathematics, he studied the former under James Thomasius, and the latter under John Kuhnius, at Leipsic. He afterwards went to Jena, where he heard the lectures of professor Bohnius upon polite learning and history, and those of Falcknerius in the law. At his return to Leipsic, in 1663, he maintained, under Thomasius, a thesis,” De Principiis Individuationis.“In 1664, he was admitted M. A.; and observing how useful philosophy might be in illustrating the law, he maintained several philosophical questions taken out of the” Corpus Juris." At the same time he applied himself particularly to the study of the Greek philosophers, and engaged in the task of reconciling Plato with Aristotle; as he afterwards attempted a like reconciliation between Aristotle and Des Cartes. He was so intent on these studies, that he spent whole days in meditating upon them, in a forest near Leipsic.

n, which prefers the agency of fire to that of water. “I am not worthy,” adds Gibbon, “to praise the mathematician; but his name is mingled in all the problems and discoveries

Gibbon has drawn the character of Leibnitz with great force and precision, as a man whose genius and studies have ranked his name with the first philosophic names of his age and country; but he thinks his reputation, perhaps, would have been more pure and permanent, if he had not ambitiously grasped the whole circle of human science. As a theologian, says Gibbon (who is not, perhaps, the most impartial judge of this subject), he successively contended with the sceptics, who believe too little, and with the papists who believe too much; and with the heretics, who believe otherwise than is inculcated by the Lutheran confession of Augsburgh. Yet the philosopher betrayed his love of union and toleration* his faith in revelation was accused, while he proved the Trinity by the principles of logic; and in the defence of the attributes and providence of the Deity, he was suspected of a secret correspondence with his adversary Bayle. The metaphysician expatiated in the fields of air; his pre-established harmony of the soul and body might have provoked the jealousy of Plato; and his optimism, the best of all possible worlds, seems an idea too vast for a mortal mind. He was a physician, in the large and genuine sense of the word like his brethren, he amused him with creating a globe and his Protogæa, or primitive earth, has not been useless to the last hypothesis of Buffon, which prefers the agency of fire to that of water. “I am not worthy,” adds Gibbon, “to praise the mathematician; but his name is mingled in all the problems and discoveries of the times; the masters of the art were his rivals or disciples; and if he borrowed from sir Isaac Newton, the sublime method of fluxions, Leibnitz was at least the Prometheus who imparted to mankind the sacred fire which he had stolen from the gods. His curiosity extended to every branch of chemistry, mechanics, and the arts; and the thirst of knowledge was always accompanied with the spirit of improvement. The vigour of his youth had been exercised in the schools of jurisprudence; and while he taught, he aspired to reform the laws of nature and nations, of Rome and Germany. The annals of Brunswick, and of the empire, of the ancient and modern world, were presented to the mind of the historian; and he could turn from the solution of a problem, to the dusty parchments and barbarous style of the records of the middle age. His genius was more nobly directed to investigate the origin of languages and nations; nor could he assume the character of a grammarian, without forming the project of an universal idiom and alphabet. These various studies were often interrupted by the occasional politics of the times; and his pen was always ready in the cause of the princes and patrons to whose service he was attached; many hours were consumed in a learned correspondence with all Europe; and the philosopher amused his leisure in the composition of French and Latin poetry. Such an example may display the exte^nt and powers of the human understanding, but even his powers were dissipated by the multiplicity of his pursuits. He attempted more than he could finish; he designed more than he could execute: his imagination was too easily satisfied with a bold and rapid glance on the subject, which he was impatient to leave; and Leibnitz may be compared to those heroes, whose empire has been lost in the ambition of universal conquest.

, an Italian mathematician, who flourished at the commencement of the thirteenth century,

, an Italian mathematician, who flourished at the commencement of the thirteenth century, was the first person who brought into Europe the knowledge of the Arabic cyphers and algebra. He travelled into the East for instruction, and being at Bugia, a town in Africa, was taught the Arabic method of keeping accounts, and finding it more convenient and preferable to the European method, he drew up a treatise for the purpose of introducing it into Italy, where it was cultivated with success, and became speedily known to all mathematicians From Italy the knowledge of the Arabic cyphers and algebra was afterwards communicated to the other countries of Europe. He was author of a treatise on surveying,preserved in the Magliabecchi library at Florence.

, a celebrated astronomer in the sixteenth century, was born in Bohemia, and was appointed mathematician to Otho Henry, elector palatine. He acquired a high reputation

, a celebrated astronomer in the sixteenth century, was born in Bohemia, and was appointed mathematician to Otho Henry, elector palatine. He acquired a high reputation by his astronomical productions, of which the principal were, “Ephemerides ab anno 1556 ad ann. 1606;” “Expedita Ratio constituendi Tin-mat is coelestis” “Loca stellarum fixarum ab anno Dom. 1549 usque in ann. 2029” and “De Eclipsibus Liber.” Tycho Brahe paid him a visit in 1569, when they had several conversations on their favourite subjects. Notwithstanding the great learning of Leowitz, he was weak enough to become the dupe of judicial astrology. He died in Swabia 1574. He had predicted that the world would come to an end in 1584; and of this prophecy many priests and preachers took advantage as the important period approached, and enriched themselves at the expence of the fears of their people.

college. He afterwards became an eminent author himself, and appears to have been the most universal mathematician of his time. He published many mathematical treatises in the

, who was originally a printer in London, published several of the mathematical works of Samuel Foster, astronomical professor in Gresham college. He afterwards became an eminent author himself, and appears to have been the most universal mathematician of his time. He published many mathematical treatises in the seventeenth century. Among these his “Cursus Mathematicus” was esteemed the best system of the kind extant. His “Panarithmologia; or, Trader’s sure Guide,” being tables ready cast up, was long in use. It was formed upon a plan of his own, and has been adopted by Mr. Bareme in France. The seventh edition was published in 1741. We have no account of his birth or death.

ith these learned men he lived more like a companion than a pupil; and Brucxus, himself an excellent mathematician, acknowledged that he was instructed by Liddel in the more perfect

In 1584 Liddel returned to Francfort, and again applied to physic, and at the same time instructed some pupils in various branches of mathematics and philosophy. In 1587, being obliged to leave Francfort on account of the plague, he retired to the university of Rostock, where his talents attracted the esteem of Brucseus, and Caselius, which last observes, that, as far as he knew, Liddel was the first person in Germany who explained the motions of the heavenly bodies according to the three different hypotheses of Ptolemy, Copernicus, and Tycho Brahe. With these learned men he lived more like a companion than a pupil; and Brucxus, himself an excellent mathematician, acknowledged that he was instructed by Liddel in the more perfect knowledge of the Copernican system, and other astronomical questions. It was probably during his residence here that Licldel became acquainted with Tycho Brahe. In 1590, having taken his master’s degree at Rostock, he returned once more to Francfort; but, hearing of the increasing reputation of the new university at Helmstadt, where his friend Caselius had accepted the chair of philosophy, he removed thither, and in 1591 was appointed to the first or lower professorship of mathematics, and in 1594 to the second and more dignified mathematical chair, which he filled with great reputation to himself and to the university. In 1596 he obtained the degree of doctor of medicine, and both taught and practised physic, and was employed as first physician at the court of Brunswick. His reputation being now at its height, he was several times chosen dean of the faculties, both of philosophy and physic, and in 1604, pro-rector of the university, the year before he resigned his mathematical professorship.

lled in the Latin language, in which he made good verses, and he had much reputation as an orator, a mathematician, and a divine. He published several books, namely, 1. “Antiquarius,

, one of the most learned protestants of his time, was born at Westersted, in the county of Oldenburg, March 24, 1556, of which place his father was minister, who sent him first to Leipsic, where he prosecuted his studies with great success, and for further improvement went thence to Cologne. After this he visited the several universities of Helmstadt, Strasburg, Jena, Marpurg, and, last of all, Rostock, where he was made professor of poetry in 1595. Having there read lectures with great applause for ten years, he was advanced to the divinity chair in the same university, in 1605. In 1620 he was seized with a tertian ague, under which he laboured for ten months before it put a period to his life in June 162 1. He has the character of having been a good Greek scholar, and was well skilled in the Latin language, in which he made good verses, and he had much reputation as an orator, a mathematician, and a divine. He published several books, namely, 1. “Antiquarius, sive priscorum et minus usitatorum vocabulorum brevis et dilucida interpretatio.” 2. “Clavis Graecae linguae.” 3. “Anacreon, Juvenal, and Persius, with notes.” 4. “Horace and Juvenal, with a paraphrase.” 5. “The Anthologia, with a Latin version,1604, 4to. 6. “Epistolae veterum Grsecorum, Greece et Latine, cum methodo conscribendarum epistolarum.” 7. “Commentaiies upon some of the Epistles of St. Paul.” 8. “Monotessaion,sive historia evangelica,” &c. &c. i. e. a harmony of the four Evangelists. 9. “Nonni Dionysiaca,” in Greek and Latin, at Francfort, 1605, 8vo. 10. “Latin Poems,” inserted in the third volume of “Deliciae ^oetarum Germanorum.

, an eminent mathematician and philosopher, was the son of a clergyman, and born at Kilmodan,

, an eminent mathematician and philosopher, was the son of a clergyman, and born at Kilmodan, near Inverary, in Scotland, Feb. 1698. His family was originally from Tirey, one of the western islands. He was sent to the university of Glasgow in 1709, where he continued five years, and applied himself to study in a most intense manner, particularly to the mathematics. His great genius for this science discovered itself so early as at twelve years of age; when, having accidentally met with a copy of Euclid’s Elements in a friend’s chamber, he became in a few days master of the first six books without any assistance: and it is certain, that in his sixteenth year he had invented many of the propositions, which were afterwards published as part of his work entitled “Geometria Organica.” In his fifteenth year, he took the degree of master of arts; on which occasion he composed and publicly defended a thesis “On the power of gravity,” with great applause. After this he quitted the university, and retired to a country-seat of his uncle, who had the care of his education, his parents being dead some time. Here he spent two or three years in pursuing his favourite studies; and such was his acknowledged merit, that having in 1717 offered himself a candidate for the professorship of mathematics in the Marischal college of Aberdeen, he obtained it after a ten days trial against a very able competitor. In 1719 he went to London, where he left his “Geometria Organica” in the press, and where he became acquainted with Dr. Hoadly, bishop of Bangor, Dr. Clarke, sir Isaac Newton, and other eminent men. At the same time he was admitted a member of the royal society; and in another journey in 1721, he contracted an intimacy with Martin Folkes, esq. the president of it, which lasted to his death.

, a celebrated philosopher and mathematician, was born at Rome Octqber 23, 1637. After studying jurisprudence,

, a celebrated philosopher and mathematician, was born at Rome Octqber 23, 1637. After studying jurisprudence, in which he made a great and very rapid progress at Pisa, he began to devote his main attention to mathematics and natural philosophy, which he cultivated at Florence, during three years, under the celebrated Vincent Viviani, and was made secretary to the academy del Cimento, the duties of which office he discharged with the utmost assiduity and care. Being directed by the prince to draw up an account of the experiments made there, he published it in 1666, when it was received with universal applause by men of science. While engaged on this work, he obtained leave from Leopold to pay a visit to his father at Rome, and with a view to obtain some ecclesiastical promotion. Having failed in this object, he returned to Florence, and obtained a place at the court of the grand duke Ferdinand II.; and shortly after a pension was given him by pope Alexander VII. About 1666 he drew up and published a small volume relative to the history of China, which was received with great applause; and at the same time he published a small, but elegant compendium of the Moral Doctrine of Confucius. Having considerable poetical talents, he was the first person who published a good translation of the Odes of Anacreon in Italian verse. He was very conversant in many of the modern languages, and could write and speak French, Spanish, and English, with the correctness and ease of the natives of those countries. When in England he became the intimate friend of the illustrious Mr. Robert Boyle, whom he vainly attempted to convert from the errors of the protestant faith. After being employed in several missions to foreign princes, he was in 1674 appointed ambassador to the imperial court, where he acquired the particular favour of the emperor, and formed connections with the men most eminent for science and literature; but, finding a very inconvenient delay of the necessary pecuniary remittances from his court, he determined to return to Florence without waiting the permission of the duke. Shortly after, that prince recalled him, and gave him apartments in his palace, with a considerable pension, but Magalotti preferred retirement, and the quiet prosecution of his studies. In 1684 he composed fifteen Italian odes, in which he has drawn the picture of a woman of noble birth and exquisite beauty, distinguished not only by every personal, but by every mental charm, and yet rendering herself chiefly the object of admiration and delight by her manners and conduct, whom, with no great gallantry, he entitled “The Imaginary Lady.” His next work consisted of Letters against Atheists, in which his learning and philosophy appear to great advantage. In 169 he was appointed a counsellor of state to the grand duke, who sent him his ambassador into Spain to negotiate a marriage between one of his daughters and king Charles II.; but soon after he had accomplished the object of this mission, he sunk into a temporary melancholy. After recovering in about a year, he resumed his literary labours, and published works upon various subjects, and left others which were given to the world after his decease, which happened in 1712, when he had attained the age of 75. Magalotti was as eminent for his piety as he was for his literary talents; unimpeachable in his morals, liberal, beneficent, friendly, polite, and a lively and cheerful, as well as very instructive companion. His house was the constant resort of men of letters from all countries, whom he treated with elegant hospitality. He was deeply conversant with the writings of the ancient philosophers, and was a follower of the Platonic doctrine in his poems. In his natural and philosophical investigations he discarded all authority, and submitted to no other guide but experiment. Among the moderns he was particularly attached to Galileo. After his death a medal was struck in honour of his memory, with the figure of Apollo raised on the reverse, and the inscription Omnia Lustrat.

, a poet and mathematician, but less known in the latter character, was born at Mons in

, a poet and mathematician, but less known in the latter character, was born at Mons in Kainault, in 1581, and entered into the order of the Jesuits. He taught philosophy at Pont-a-Mousson, whence he went to Poland, where he was appointed professor of mathematics, and afterwards filled the same office at Doway. His reputation induced Philip IV. to give him an invitation to Madrid, as professor of mathematics in his newly-founded college, which he accepted, but died on his way to Vittoria, Nov. 5, 1630. His Latin poems were printed at Antwerp in 1634, and have been praised for purity of style, and imagery. Of his mathematical works one is entitled “Oratio de Laudibus Mathematicis,” in which he treats of the phenomena of the newly-discovered Dutch telescope. The others are, “Institutions of Practical Arithmetic;” the “Elements of Geometry” “A Paraphrase on the Dialectics of Aristotle” and “Commentaries on the first six Books of Euclid.

, a distinguished mathematician, philosopher, and military engineer, was born at Paris July

, a distinguished mathematician, philosopher, and military engineer, was born at Paris July 23, 1775. His first education was principally directe'd to classical and polite literature, and at seventeen years of age he composed a tragedy in five acts, called “The Death of Cato.” These pursuits, however, did not prevent him from a study apparently not very compatible, that of the mathematics; for at the above age he passed an examination which gained him admittance into the school of engineers. After having distinguished himself there by his genius for analysis, he was about to leave it in quality of officer of military engineers, but was rejected on political grounds, and as this repulse deprived him of all hope of promotion there, he repaired to the army in the north, where he was incorporated in the 15th battalion of Paris, and was employed as a common soldier in the fortifications of Dunkirk. The officer of engineers, who superintended those works, perceiving that Malus was deserving of a better station, represented his merits to the government, and he was recalled and sent to the Polytechnic school, where he was soon appointed to the analytic course in the absence of M. Monge. Being now re-established in his former rank at the date of his first nomination, he succeeded almost immediately to that of captain, and was employed at the school at Metz as professor of mathematics.

, a celebrated astronomer and mathematician, was born at Bologna in 1674, and soon displayed a genius above

, a celebrated astronomer and mathematician, was born at Bologna in 1674, and soon displayed a genius above his age. He wrote ingenious verses while he was but a child, and while very young formed in his father’s house an academy of youth of his own age, which in time became the Academy of Sciences, or the Institute, there. He was appointed professor of mathematics at Bologna in 1698, and superintendant of the waters there in 1704. The same year he was placed at the head of the college of Montalto, founded at Bologna for young men intended for the church. In 1711 he obtained the office of astronomer to the institute of Bologna. He became member of the Academy of Sciences of Paris in 1726, and of the Royal Society of London in 1729; and died on the 15th of February 1739. His works are: 1. “Ephemerides Motuum Coelestium ab anno 17 15 ad annum 1750;” 4 vols. 4to. The first volume is an excellent introduction to astronomy; and the other three contain numerous calculations. His two sisters were greatly assisting to him in composing this work. 2. “De Transitu Mercurii per Solem, anno 1723,” Bologna, 1724, 4to. 3. “De annuls Inerrantium Stellarum aberrationibus,” Bologna, 1729, in 4to; besides a number of papers in the Memoirs of the Academy of Sciences, and in other places, which are enumerated by Fabroni. The best edition of his Poems, which are still in repute, is that by Bodoni, in 1793, 8vo, with a life of the author.

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