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, a learned astronomer and mathematician, was born in 1665 at Perinaldo in the county of Nice, a place already honoured by the birth of his maternal uncle, the celebrated Cassini. Having made a considerable progress in mathematics, at the age of twentytwo his uncle, who had been a long time settled in France, invited him there, that he might himself cultivate the promising genius of his nephew. Maraldi no sooner applied himself to the contemplation of the heavens, than he conceived the design of forming a catalogue of the fixed stars, the foundation of the whole astronomical edifice. In consequence of this design, he applied himself to observe them with the most constant attention; and he became by this means so intimate with them, that on being shown any one of them, however small, he could immediately tell what constellation it belonged to, and its place in that constellation. He has been known to discover those small comets, which astronomers often take for the stars of the constellation in which they are seen, for want of knowing precisely what stars the constellation consists f, when others, on the spot, and with eyes directed equally to the same part of the heavens, could not for a long time see any thing of them.

, a physician, mathematician, and poet of Pisa, was born at Pontormo, between Pisa and Florence, March 17, 1633. His talents were early developed, and he became the pupil and intimate friend of the learned Borelli, whom he succeeded in 1679, as professor of mathematics at Pisa. He was a man above prejudices, free to declare his sentiments, preferring experiment to authority, and reason to Aristotle. He produced several excellent disciples, and died at Pontormo, Sept. 6, 1714, aged eighty-one. There are extant by him, 1. “Poems,” 1704, in 4to. 2. Several treatises on philosophical subjects, among which that on the resistance of fluids, is particularly valued, 1669, 4to. After his death appeared, 3. A translation of Lucretius, in Italian verse, much esteemed for its fidelity, ease, and harmony; yet, say* baretti, “the versification, in my opinion, is but indifferent.” It was not allowed to be published in Italy, but was published in London, 1717, in 4to, by Paulo Rolli, the translator of Milton into,blank verse. 4. His free translation of Anacreon is less esteemed; it was published at Venice in 1736. There is an edition of his poems, printed at Venice in 1755, 4to, to which his life is prefixed.

, an eminent French philosopher and mathematician, was born at Dijon, and admitted a member of the academy of sciences of Paris in 1666. His works, however, are better known than his life. He was a good mathematician, and the first French philosopher who applied much to experimental physics. The law of the shock or collision of bodies, the theory of the pressure and motion of fluids, the nature of vision, and of the air, particularly engaged his attention. He carried into his philosophical researches that spirit of scrutiny and investigation so necessary to those who would make any considerable progress in it. He died May 12, 16S4. He communicated a number of curious and valuable papers to the academy of sciences, which were printed in the collection of their Memoirs dated 1666, viz. from volume 1 to volume 10. And all his works were collected into 2 volumes in 4to, and printed at Leyden in 1717.

, an eminent astronomer and mathematician, the son of Edmund Maskelyne, esq. of Purton, in Wiltshire, was born at London in 1732, and educated at Westminster school, where he made a distinguished progress in classical learning. Before he left school his studies appear to have been determined to astronomy by his accidentally seeing the memorable solar eclipse of 1748, exhibited through a large telescope in a camera obscura. From this period he applied himself with ardour to astronomy and optics, and as a necessary preparation, turned his attention to geometry and algebra, the elements of which he learned in a few months without the help of a master. In 1749 he entered of Catherine hall, Cambridge, but soon after removed to Trinity college, where he pursued his favourite studies with increased success; and on taking his degree of B. A. in 1754, received distinguished honours from the university. He took his degrees of A.M. in 1757, B. D. in 1768, and D. D. in 1777. Being admitted into holy orders he officiated for some time as curate of Barnet; and in 1756 became a fellow of his college.

, a celebrated French mathematician and philosopher, was born at St. Malo in 1698, and at first educated there. In 1714 he studied in the college of La Marche, at Paris, where he discovered a strong inclination for mathematics. He fixed, however, on no profession until he arrived at his twentieth year, when he entered into the army, and during the space of five years in which he remained in it, pursued his mathematical studies with great vigour. In 1723 he was received into the royal academy of sciences, and read his first performance, a memoir upon the construction and form of musical instruments. When he commenced his travels, his first visit was to England, and during his residence at London he became a zealous admirer and follower of Newton. His next excursion was to Basil in Switzerland, where he formed a friendship with the celebrated John Bernouilli and his family, which continued till his death. At his return to Paris he applied himself to his favourite studies with greater zeal than ever. And how well he fulfilled the duties of an academician, may be seen in the Memoirs of the academy from 1724 to 1744; where the most sublime questions in the mathematical sciences, received from his hand that elegance, clearness, and precision, so remarkable in all his writings. In 1736 he was sent to the polar circle to measure a degree of the meridian, in order to ascertain the figure of the earth; in which expedition he was accompanied by Messrs. Clairault, Camus, Monnier, Outhier, and Celsus, the celebrated professor of astronomy at Upsal. This business rendered him so famous, that on his return he was admitted a member of almost every academy in Europe.

, a celebrated Italian mathematician, was born in 1494 at Messina, where he afterwards taught mathematics with great success. In that employment he was particularly admired, for the astonishing clearness with which he expressed himself, making the most difficult questions easy, by the manner in which he explained them. He had a penetrating mind, and a prodigious memory. He was abbe of Santa Maria del Porto, in Sicily; but, as mathematicians in his time were generally supposed to be able to read the stars, he could not resist the temptation of assuming to himself such powers; and delivered some predictions to don Juan of Austria, for which, as he happened to guess rightly, he obtained the credit of being a prophet, besides considerable rewards. He died July 21, 1575, at the age of eightyone. His principal works are, 1. An edition of the “Spherics of Theodosius,” 1558, folio. 2. “Emendatio et restitutio Conicorum Apollonii Pergasi,” 1654, folio. 3. “Archimedis monumenta omnia,” 1685, folio. 4. “Euclidis phenomena,” Rome, 1591, 4 to. 5. “Martyrologium, 1566, 4to. 6.” Sinicarum rerum Compendium.“7. Also, in 1552,” Rimes,“in 8vo. He published also, 8.” Opuscula Mathematica,“1575, 4to. 9.” Arithmeticorum libri duo," 1575. These, with a few more, form the list of his works, most of which are upon subjects of a similar nature.

, a very able French mathematician and astronomer, was born at Laon in 17 44, where his father was an architect, and at one time a man of considerable property. At an early age he discovered a strong inclination for mathematical pursuits, and while he was under the instruction of his tutors, corresponded with Lalande, whom he was desirous of assisting in his labours. In 1772, Mechain was invited to Paris, where he was employed at the depot of the marine, and assisted M. Darquier in correcting his observations. Here his merit brought him acquainted with M. Doisy, director of the depot, who gave him a more advantageous situation at Versailles. At this place he diligently observed the heavens, and, in 1774, sent to the Royal Academy of Sciences “A Memoir relative to an Eclipse of Aldebaran,” observed by him on the 15th of April. He calculated the orbit of the comet of 1774, and discovered that of 1781. In 1782, he gained the prize of the academy on the subject of the comet of 1661, the return of which was eagerly expected in 1790; and in the same year he was admitted a member of the academy, and soon selected for the superintendance of the Connoissance des Tems. In 1790, M. Mechain discoveredhis eighth comet, and communicated to the academy his observations on it, together with his calculations of its orbit. In 1792 he undertook, conjointly with M. Delambre, the labour of measuring the degrees of the meridian, for the purpose of more accurately determining the magnitude of the earth and the length of a metre. In the month of June 1792, M. Mechain set out to measure the triangles between Perpignan and Barcelona; and notwithstanding that the war occasioned a temporary suspension of his labours, he was enabled to resume and complete them during the following year. He died on the 20th of September 1805, at Castellon de la Plana, in the sixty-second year of his age. Lalande deplores his loss as that of not only one of the best French astronomers, but one of the most laborious, the most courageous, and the most robust. His last observations and calculations of the eclipse of the sun on the llth of February, are inserted in the Connoissance des Tems for the year 15; and he also published a great many in the Ephemerides of M. Bode, of Berlin, which he preferred to a former work after Lalande became its editor. A more extensive memoir of his labours may be seen in Baron von Zach’s Journal for July 1800, and Lalande’s History of Astronomy for 1804.

By the time he had taken the degree of master of arts, which was in 1610, he had made such progress in all kinds of academical study, that he was universally esteemed an accomplished scholar. He was an acute logician, an accurate philosopher, a skilful mathematician, an excellent anatomist, a great philologer, a master of many languages, and a good proficient in history and chronology. His first public effort was an address that he made to bishop Andrews, in a Latin tract “De sanctitate relativa;” which, in his maturer years, he censured as a juvenile performance, and therefore never published it. That great prelate, however, who was a good judge and patron of learning, liked it so well, that he not only was the author’s firm friend upon an occasion that offered soon after, but also then desired him to be his domestic chaplain. This Mede very civilly refused; valuing the liberty of his studies above any hopes of preferment, wnd esteeming that freedom which he enjoyed in his cell, so he used to call it, as the haven of all his wishes. These thoughts, indeed, had possessed him. betimes: for, when he was a school-boy, he was invited by his uncle, Mr. Richard Mede, a merchant, who, being then without children, offered to adopt him for his son, if he would live with him: but he refused the offer, preferring, as it should seem, a life of study to a life of gain.

, a Jewish philosophical writer, was born at Dessau, in Anhalt, in 1729. After being educated under his father, who was a schoolmaster, he devoted every hour he could spare to literature, and obtained as a scholar a distinguished reputation; but his father ber ing unable to maintain him, he was obliged, in search of labour, or bread, to go on foot, at the age of fourteen, to Berlin, where he lived for some years in indigence, and frequently in want of necessaries. At length he got employment from a rabbi as a transcriber of Mss, who, at the same time that he afforded him the means of subsistence, liberally initiated him into the mysteries of the theology, the jurisprudence, and scholastic philosophy of the Jews. The study of philosophy and general literature became from this time his favourite pursuit, but the fervours of application to learning were by degrees alleviated and animated by the consolations of literary friendship. He formed a strict intimacy with Israel Moses, a Polish Jew, who, without any advantages of education, had become an able, though self-taught, mathematician and naturalist. Hg very readily undertook the office of instructor of Mendelsohn, in subjects of which he was before ignorant; and taught him the Elements of Euclid from his own Hebrew version. The intercourse between these young men was not of long duration, owing to the calumnies propagated against Israel Moses, which occasioned his expulsion from the communion of the orthodox; in consequence of this he became the victim of a gloomy melancholy and despondence, which terminated in a premature death. His loss, which was a grievous affliction to Mendelsohn, was in some measure supplied by Dr. Kisch, a Jewish physician, by whose assistance he was enabled to attain a competent knowledge of the Latin language. In 1748 he became acquainted with another literary Jew, viz. Dr. Solomon Gumperts, by whose encouragement and assistance he attained a general knowledge of the living and modern languages, and particularly the English, by which he was enabled to read the great work of our immortal Locke in his own idiom, which he had before studied through the medium of the Latin language. About the same period he enrolled the celebrated Lessing among his friends, to whom he was likewise indebted for assistance in his literary pursuits. The scholar amply repaid the efforts of his intructor, and soon became his rival and his associate, and after his death the defender of his reputation against Jacobi, a German writer, who had accused Lessing of atheism. Mendelsohn died Jan. 4, 1785, at the age of fifty-seven, highly respected and beloved by a numerous acquaintance, and by persons of very different opinions. When his remains were consigned to the grave, he received those honours from his nation which are commonly paid to their chief rabbies. As an author, the first piece was published in 1755, entitled “Jerusalem,” in which he maintains that the Jews have a revealed law, but not a revealed religion, but that the religion of the Jewish nation is that of nature. His work entitled “Phaedon, a dialogue on the Immortality of the Soul,” in the manner of Plato, gained him much honour: in this hepresents the reader with all the arguments of modern philosophy, stated with great force and perspicuity, and recommended by the charms of elegant writing. From the reputation which he obtained by this masterly performance, he was entitled by various periodical writers the “Jewish Socrates.” It was translated into French in 1773, and into the English, by Charles Cullen, esq. in 1789. Among his other works, which are all creditable to his talents, he wrote “Philosophical Pieces;” “A Commentary on Part of the Old Testament;” “Letters on the Sensation of the Beautiful.”

, an able Italian mathematician in the seventeenth century, concerning whose birth there is no trace, studied mathematics under Cavalieri, to whom the Italians ascribe the invention of the first principles of the infinitesimal calculus. Mengoli was appointed professor of “mechanics” in the college of nobles at Bologna, and acquired high reputation by the success with which he filled that post. His principal works are, “Geometriae SpeciosgR Elementa” “Novae Quadrature Arithmetics, sen de additione Fractionum” “Via regia ad Mathematicas ornata” “Rerrazzione e paralasse Solare” “Speculation! de Musica;” “Arithmetics rationalis Elementa” “Arithmetica realis.” Of these Dr. Burney notices his “Speculationi di Musica,” a desultory and fanciful work, published at Bologna, 1670. An account of this treatise was given in the Phil. Trans, vol. VIII. No. c. p. 6194, seemingly by Birchensha. The speculations contained in Mengoli’s work are some of them specious and ingenious; but the philosophy of sound has been so much more scientifically and clearly treated since its publication, that the difficulty of finding the book is no great impediment to the Advancement of music. He was still living in 1678.

, an eminent geographer and mathematician, was born in 1512, at Ruremonde in the Low Countries. He applied himself with such industry to the sciences of geography and mathematics, that it has been said he often forgot to eat and sleep. The emperor Charles V. encouraged him much in his labours; and the tluke of Juliers made him his cosmographer. He composed and published a chronology; a larger and smaller atlas; and some geographical tables besides other books in philosophy and divinity. He was also so curious, as well as ingenious, that he engraved and coloured his maps himself. He made various maps, globes, and other mathematical instruments for the use of the emperor; and gave the most ample proofs of his uncommon skill in what he professed. His method of laying down charts is still used, which bear the name of “Mercator’s Charts;” also a part of navigation is from him called Mercator’s Sailing. He died at Duisbourg in 1594, at eighty-two years of age.

, an eminent mathematician and astronomer, whose name in High-Dutch was Kauffman, was born about 1640, at Holstein in Denmark. From his works we learn, that he had an early and liberal education, suitable to his distinguished genius, by which he was enabled to extend his researches into the mathematical sciences, and to make very considerable improvements: for it appears from his writings, as well as from the character given of him by other mathematicians, that his talent rather lay in improving, and adapting any discoveries and improvements to use, than invention. However, his genius for the mathematical sciences was very conspicuous, and introduced him to public regard and esteem in his own country, and facilitated a correspondence with such as were eminent in those sciences, in Denmark, Italy, and England, In consequence, some of his correspondents gave him an invitation to this country, which he accepted; and he afterwards continued in England till hi death. In 1666 he was admitted F. R. S. and gave frequent proofs of his close application to study, as well as of his eminent abilities in improving some branch or other of the sciences. But he is charged sometimes with borrowing the inventions of others, and adopting them as his own, and it appeared upon some occasions that he was not of an over-liberal mind in scientific communications. Thus, it had some time before him been observed, that there was an analogy between a scale of logarithmic tangents and Wright’s protraction of the nautical meridian line, which consisted of the sums of the secants; though it does not appear by whom this analogy was first discovered. It appears, however, to have been first published, and introduced into the practice of navigation, by Henry Bond, who mentions this property in an edition of Norwood’s Epitome of Navigation, printed about 1645; and he again treats of it more fully in an edition of Gunter’s works, printed in 1653, where he teaches, from this property, to resolve all the cases of Mercator’s sailing by the logarithmic tangents, independent of the table of meridional parts. This analogy had only been found to be nearly true by trials, but not demonstrated to be a mathematical property. Such demonstration seems to have been first discovered by Mercator, who, desirous of making the most advantage of this and another concealed invention of his in navigation, by a paper in the Philosophical Transactions for June 4, 1666, invites the public to enter into a wager with him on his ability to prove the truth or falsehood of the supposed analogy. This mercenary proposal it seems was not taken up by any one; and Mercator reserved his demonstration. Our author, however, distinguished himself by many valuable pieces on philosophical and mathematical subjects. His first attempt was, to reduce astrology to rational principles, which proved a vain attempt. But his writings of more particular note, are as follow: 1. “Cosmographia, sive Descriptio Cceli & Terrse in Circulos, qua fundamentum sterniter sequentibus ordine Trigonometric Sphericorum Logarithmicse, &c. a” Nicolao Hauffman Holsato,“Dantzic, 1651, 12mo. 2.” Rationes Mathematics subductse anno 1653,“Copenhagen, 4to. 3.” De Emendatione annua Diatribae duae, quibus exponuntur & demonstrantur Cycli Soiis & Lunce,“&c. 4to. 4.” Hypothesis Astronomica nova, et Consensus ejus cum Observationibus,“Lond. 1664, folio. 5.” Logarithmotechnia, sive Method us construendi Logarithmos nova, accurata, et facilis; scripto antehac communicata anno sc. 1667 nonis Augusti; cui nunc accedit, Vera Quadratura Hyperbolae, & inventio summae Logaritbmorum. Auctore Nicolao Mercatore Holsato e Societate Regia. Huic etiam jungitur Michaelis Angeli Riccii Exercitatio Geometrica de Maximis et Minimis, hie ob argument! praestantiam & exemplarium raritatem recusa,“Lond. 1668, 4to. 6.” Institutionum Astronomicarum libri duo, de Motu Astrorum communi & proprio, secundum hypotheses veterum & recentiorum praecipuas deque Hypotheseon ex observatis constructione, cum tabulis Tychonianis, Solaribus, Lunaribus, Lunae-solaribus, & Rudolphinis Solis, Fixarum &*quinque Errantium, earumque usu prajceptis et exemplis commonstrato. Quibus accedit Appendix de iis, quae uovissimis temporibus coelitus innotuerunt,“Lond. 1676, 8vo. 7.” Euclidis Elementa Geometrica, novo ordine ac methodo fere, demonstrata. Una cum Nic. Mercatoris in Geometriam Introductione brevi, qua Magnitudinum Ortus ex genuinis Principiis, & Ortarum Affectiones ex ipsa Genesi derivantur," Lond. 1678, 12mo. His papers in the Philosophical Transactions are, 1. A Problem on some Points of Navigation vol. I. p. 215. 2. Illustrations of the Logarithmo-technia vol. Hi. p. 759. 3. Considerations concerning his Geometrical and Direct Method for finding the Apogees, Excentricities, and Anomalies of the Planets; vol. V. p. 1168. Mercator died in 1594, about fifty-four years of age.

Meston is said to have been one of the best classical scholars of his time, and by no means a contemptible philosopher and mathematician. His wit also was very lively, and shone particularly in jovial meetings, to which unhappily he was rather too strongly addicted. His poems were first published separately, as they were written, and doubtless by way of assisting him in his necessities. That called “the Knight/* appears to have been first printed in 1723; and, after it had received several corrections, a second edition was printed at London. The first decade of” Mother Grim’s Tales,“afterwards appeared; and next, the second part, by Jodocus, her grandson. Some years after, the piece called,” Mob contra Mob.“The whole were first collected in a small volume, 12 mo, at Edinburgh, in 1767, to which a short account of his life is prefixed, whence the present memoirs have been extracted. The Knight,” and several others of his poems, are in the style of Butler, whom he greatly adinired and imitated, perhaps too servilely, yet with some success. In the second decade, written under the name of Jodocus, there are several poems in Latin, and the title was in that language. It runs thus: “Decadem alteram, ex probatissimis auctoribus, in usum Juventutis Jinguse Latinse, prsesertim verse poeseos studiosse, selectam, et in scholis ad propagandam fidem legendam: admixtis subinde nonnullis, in gratiam Pulchrioris Sexus, vernaculis, subjunxit Jodocus Grimmus Aniculae nostrae pronepos.” His Latin poetry is of no great excellence.

, or Meton, a celebrated mathematician of Athens, who flourished 432 B. C. was the son of Pausanias. He observed, in the first year of the 87th olympiad, the solstice at Athens, and published his cycle of 19 years, by which he endeavoured to adjust the course of the sun and moon, and to make the solar and lunar years begin at the same point of time. This is called the Metonic period, or cycle. It is also called the golden number, from its great use in the calendar. Meton was living about the year 412 B. C. for when the Athenian fleet was sent to Sicily, he escaped from being embarked on that disastrous expedition by counterfeiting an appearance of idiotism.

an excellent mathematician and astronomer, was born April 17, 1656, at Dublin, where his father, a gentleman of good family and fortune, lived*. Being of a tender constitution, he was educated under a private tutor at home, till he was near fifteen, and then placed in the university of Dublin, under the care of Dr. PaJliser, afterwards archbishop of Cashell. He distinguished himself here by the probity of his manners as

, an eminent French astronomer and mathematician, was born at Paris, Nov. 23, 1715. His education was chiefly directed to the sciences, to which he manifested an early attachment; and his progress was such that at the age of twenty-one, he was chosen as the co-operator of Maupertuis, in the measure of a degree of the meridian at the polar circle. At the period when the errors in Flamsteed’s catalogue of the stars began to be manifest, he undertook to determine anew the positions of the zodiacal stars as being the most useful to astronomers. In 1743 he traced at St. Sulpice a grand meridian line, in order to ascertain certain solar motions, and also the small variations in the obliquity of the ecliptic.

, an able mathematician, was born at Paris in the year 1678, and intended for the profession of the law, to enable him to qualify for a place in the magistracy. From dislike of this destination, he withdrew into England, whence he passed over into the Low Countries, and travelled into Germany, where he resided with a near relation, M. Chambois, the plenipotentiary of France at the diet of Ratisbon. He returned to France in 1699, and after the death of his father, who left him an ample fortune, devoted his talents to the study of philosophy and the mathematics, under the direction of the celebrated Malehranche, to whom he had, some years before, felt greatly indebted for the conviction of the truth of Christianity, by perusing his work on “The Search after Truth.” In 1700 he went a second time to England, and on his return, assumed the ecclesiastical habit, and was made a canon in the church of Notre-Dame, at Paris. About this time he edited, at his own expence, the works of M. Guisnee on “The Application of Algebra to Geometry,” and that of Newton on the “Quadrature of Curves.” In 1703 he published his “Analytical Essay on Games of Chance,” and an improved edition in 1714. This was most favourably received by men of science in all countries. In 1715 he paid a third visit to England, for the purpose of observing a solar eclipse, and was elected a fellow of the Royal Society, to which learned body he soon afterwards transmitted an important treatise on “Infinite Series,'” which was inserted in the Philosophical Transactions for the year 1717. He was elected an associate of the Royal Academy of Sciences at Paris in 1716, and died at the early age of forty-one, of the small-pox. He sustained all the relations of Hie in the most honourable manner, and though subject to fits’ of passion, yet his anger soon subsided, and he was ever ashamed of the irritability of his temper. Such was his steady attention that he could resolve the most difficult problems in company, and among the noise of playful children. He was employed several years in writing “A History of Geometry,” but he did not live to complete it.

, a celebrated mathematician, was born at Lyons in the year 1725, and giving early indications of a love of learning, was placed under the instructions of the Jesuits, with whom he acquired an intimate acquaintance with the ancient and modern languages, and some knowledge of the mathematics. At the age of sixteen he went to Toulouse to study the law, and was admitted an advocate, though without much intention of practising at the bar. Having completed his studies, he went to Paris, cultivated an acquaintance with the most distinguished literary characters, and it was owing to his intercourse with them, that he was induced to undertake his “History of the Mathematical Sciences.” But in the interim he published new editions, with additions and improvements, of several mathematical treatises which were already held in the highest estimation. The first of these was “Mathematical Recreations,” by M. Ozanam, which has been since translated into English, and published in London, in 4 vols. 8vo. To all the works which he edited, after Ozanam’s, he gave the initials of his name. He also contributed his assistance for some years to “The French Gazette;” and in 1755 he was elected a member of the Royal Academy of Sciences at Berlin. In the following year, when the experiment of inoculation was about to be tried on the first prince of the blood, Montucla translated from the English an account of all the recent cases of that practice, which had been sent from Constantinople, by lady Mary Wortley Montague. This translation he added to the memoir of De la Condamine on the subject. Previously to this publication, he had given to the world his “History of Inquiries relative to the Quadrature of the Circle.” The encouragement which this met with from very able judges of its merit, afforded him great encouragement to apply with ardour to his grand design, “The History of the Mathematics;” and in 1758 he published this “History,” in two volumes, 4to, which terminates with the close of the 17th century. It answered the expectations of all his friends, and of men of science in all countries, and the author was instantly elevated to a high rank in the learned world. His fame was widely diffused, and he was pressed from all quarters to proceed with the mathematical history of the 18th century, which he had announced for the subject of a third volume, and for which he had made considerable preparations; but he was diverted from his design, by receiving the appointment of secretary to the Intendance at Grenoble. Here he spent his leisure hours chiefly in retirement, and in scientific pursuits. In 1764, Turgot, being appointed to establish a colony at Cayenne, took Montucla with him as his “secretary,” to which was added the title of “astronomer to the king,” and although he returned without attaining any particular object with regard to the astronomical observations, for which he went out, he had an opportunity of collecting some valuable tropical plants, with which he enriched the king’s hothouses at Versailles. Soon after his return, he was appointed chief clerk in an official department, similar to that known in this country by the name of the “Board of Works,” which he retained till the place was abolished in 1792, when he was reduced to considerable pecuniary embarrassments. Under the pressure of these circumstances, he began to prepare a new and much enlarged edition of his “History,” which he presented to the world in 1799, in two volumes, quarto. In this edition are many important improvements; and many facts, which were barely announced in the former impression, are largely detailed and illustrated in this. After the publication of these two volumes, the author proceeded with the printing of the third; but death terminated his labours, when he had arrived at the 336th page. The remainder of the volume, and the whole of the fourth, were printed under the inspection of Lalande. Montucla had been a member of the National Institute from its original establishment. He had obtained various employments under the revolutionary government, though he was but meanly paid for his labour, and had to struggle with many difficulties to furnish his family with the bare necessaries of life. At length he was reduced to seek the scanty means of support by keeping a lottery-office, till the death of Saussure put him in the possession of a pension of about one hundred pounds per annum, which he enjoyed only four months. He died in December 1799, in the 75th year of his age. He was a man of great modesty, and distinguished by acts of generosity and liberality, when it was in his power. He was also friendly, cheerful, and of very amiable manners.

, a very respectable mathematician, fellow of the royal society, and surveyor-general of the ordnance, was born at Whitlee, or Whitle, in Lancashire, Feb. 8, 1617. After enjoying the advantages of a liberal education, he bent his studies principally to the mathematics, to which he had always a strong inclination, and in the early part of his life taught that science in London for his support. In the expedition of king Charles the First into the northern parts of England, our author was introduced to him, as a person studious and learned in those sciences; and the king expressed much approbation of him, and promised him encouragement; which indeed laid the foundation of his fortune. He was afterwards, when the king was at Holdenby-house, in 1647, appointed mathematical master to the king’s second son James, to instruct him in arithmetic, geography, the use of the globes, &c. During Cromwell’s government he appears to have followed the profession of a public teacher of mathematics; for he is styled, in the title-page of some of his publications, “professor of the mathematics;” but his loyalty was a considerable prejudice to his fortune. In his greatest necessity, he was assisted by colonel Giles Strangeways, then a prisoner in the Tower of London, who likewise recommended him to the other eminent persons, his fellow- prisoners, and prosecuted his interest so far as to procure him to be chosen surveyor in the work of draining the great level of the fens’. Having observed in his survey that the sea made a curve line on the beach, he thence took the hint to keep it effectually out of Norfolk. This added much to his reputation. Aubrey informs us, that he made a model of a citadel for Oliver Cromwell “to bridle the city of London,” which was in the possession of Mr. Wild, one of the friends who procured him the surveyorship of the Fens. Aubrey adds, what we do not very clearly understand, that this citadel was to have been the crossbuilding of St. Paul’s church.

, a French mathematician, born in the province of Auvergne about 1643, became a professor of rhetoric and mathematics in different seminaries belonging to the Jesuits, and was at length appointed professor- royal at the university of Toulouse. He died, in 1713, a sacrifice to his exertions in the cause of humanity, during the dreadful pestilential disorder which then raged at Toulouse. To very profound as well as extensive erudition, he united the most polished and amiable manners, and the most ardent piety, which made him zealous in his attempts to reform the age in which he lived. He was a considerable writer: his most celebrated pieces are, “New Elements of Geometry, comprised in less than fifty Propositions;” “A Parallel between Christian Morality and that of the Ancient Philosophers;” “An Explanation of the Theology of the Pythagoreans, and of the other learned Sects in Greece, for the Purpose of illustrating the Writings of the Christian Fathers” and “A Treatise on French Poetry.”

, commonly called Regiomontanus, from his native place, Mons Regius, or Koningsberg, a town in Franconia, was born in 1436, and became the greatest astronomer and mathematician of his time. He was indeed a very prodigy for genius and learning. Having first acquired grammatical learning in his own country, he was admitted, while yet a boy, into the academy at Leipsic, where he formed a strong attachment to the mathematical sciences, arithmetic, geometry, astronomy, &c. But not finding proper assistance in these studies at this place, he removed, at only fifteen years of age, to Vienna, to study under the famous Purbacb, the professor there, who read lectures in those sciences with the highest reputation. A strong and affectionate friendship soon took place between these two, and our author made such rapid improvement in the sciences, that he was able to be assisting to his master, and to become his companion in all his labours. In this manner they spent about ten years together, elucidating obscurities, observing the motions of the heavenly bodies, and comparing and correcting the tables of them, particularly those of Mars, which they found to disagree with the motions, sometimes as much as two degrees.

, an eminent German divine and mathematician, was born at Inghelheim in 1489; and, at fourteen commenced his studies at Heidelberg. Two years after, he entered the convent of the Cordeliers, where he laboured assiduously; yet did not content him self with the studies relating to his profession, but applied himself also to mathematics and cosmography. He was the first who published a “Chaldee Grammar and Lexicon;” and gave the world, a short time after, a “Talmudic Dictionary.” He went afterwards to Basil, and succeeded Pelicanus, of whom he had learned Hebrew, in the professorship of that language. He was one of the first who attached himself to Luther, but meddled little in the controversies of the age, employing his time and attention chiefly to the study of the Hebrew and other Oriental languages, mathematics, and natural philosophy. He published a great number^ of works on these subjects, of which the principal is a Latin version from the Hebrew of all the books of the Old Testament, with learned notes, printed at Basil in 1534 and 1546. This is thought more faithful than the versions of Pagninus and Arias Montanus; and his notes are generally approved, though he dwells a little too long upon the explications of the rabbins. For this version he was called the German Esdras, as he was the German Strabo for an “Universal Cosmography,” in six books, which he printed at Basil in 1550. He published also a treatise on dialling, in fol. 1536, in which is the foundation of the modern art of dialling a translation of Josephus into Latin “Tabulae novae ad geog. Ptolemaei,” “Rudimenta mathematica,” &c. He was a pacific, studious, retired man, and, Dupin allows, one of the most able men that embraced the reformed religion. For this reason Beza and Verheiden have placed him among the heroes of the reformation, although he wrote nothing expressly on the subject. He died at Basil, of the plague, May 23, 1552.

, an eminent mathematician and natural philosopher, was born at Leyden in 1692. He appears first to have studied medicine, as he took his doctor’s degree in that faculty in 1715, but natural philosophy afterwards occupied most of his attention. After visiting London, where he became acquainted with Newton and Desaguliers, probably about 1734, when he was chosen a fellow of the royal society, he returned home, and was appointed professor of mathematics and natural philosophy at Utrecht, which he rendered as celebrated for those sciences as it had long been for law studies. He was afterwards placed in the same chair at Leyden, and obtained great and deserved reputation throughout all Europe. Besides being elected a member of the Paris academy and other learned bodies, the kings of England, Prussia, and Denmark, made him tempting offers to reside in their dominions; but he preferred his native place, where he died in 1761. He published several works in Latin, all of them demonstrating his great penetration and accuracy: 1. “Disputatio de Aeris praesentia in humoribus animalibus,” Leyd. 1715, 4to. 2. “Epitome Elementorum Pbysico-mathematicorum,” ib. 1729, 4to. 3. “Physicx, experimentales, et geometries Dissertationes: ut et Ephemerides meteorologicae Utrajectenses,” ibid. 1729, 4to. 4. “Tentamina Experinientorurn naturalium, in academia del Cimento, ex Ital. in Lat. conversa,” ibid. 1731, 4to. 5. “Elementa Physicsc,” 1734, 8vo, translated into English by Colson, 1744, 2 vols. 8vo. His “Introduction to Natural Philosophy,” which he began to print in 1760, was completed and published at Leyden in 1762 by M. Lulofs, after the death of the author. There is a French translation, of Paris, 1769, 3 vols. 4to. Musschenbroeck is also the author of several papers, chiefly on meteorology, printed in the volumes of the “Memoirs of the Academy of Sciences” for 1734, 1735, 1736, 1753, 1756, and 1760.

, an able mathematician, was born at Paris in 1585, and was educated to the law. He became counsellor to the Chatelet, and afterwards treasurer of France in the generality of Amiens, but was too much attached to mathematical pursuits, and master of too ample a fortune, to pursue his profession as a source of emolument. He was the friend and acquaintance of Des Cartes, and entered into a vindication of him, in the dispute which he had with M. Fermat, and was afterwards a mediator of the peace which was made between those learned men in 1638. In the same year Mydorge published a Lutin treatise “On Conic Sections,” in four bt oks, which Meisenne has inserted in his “Abridgment of Universal Geometry.” In 1642, he and Des Cartes received an invitation from sir Charles Cavendish to settle in England, which he declined, on the approach of the rebellion. He died at Paris in 1647, in the sixty-third year of his age. He was a practical mechanic, as well as an able mathematician, and spent more than a thousand crowns on the fabrication of glasses for telescopes, burning mirrors, mechanical engines, and mathematical instruments.

The following passage, from the life of Lilly the astrologer, contains a curious account of the meeting of those two illustrious men. “I will acquaint you,” says Lilly, “with one memorable story related unto me by John Marr, an excellent mathematician and geometrician, whom I conceive you remember. He was, servant to king James and Charles the First. At first when the lord Napier, or Marchiston, made public his logarithms, Mr. Briggs, then reader of the astronomy lectures at Gresham college in London, was so surprised with admiration of them, that he could have no quietness in himself until he had seen that noble person the lord Marchiston, whose only invention they were: he acquaints John Marr herewith, who went into Scotland before Mr. Briggs, purposely to be there when these two so learned persons should meet. Mr. Briggs appoints a certain day when to meet at Edinburgh; but failing thereof, the lord Napier was doubtful he would not come. It happened one day as John Marr and the lord Napier were speaking of Mr. Briggs; `Ah, John,‘ said Marchiston, `Mr. Briggs will not now come.’ At the very instant one knocks at the gate; John Marr hasted down, and it proved Mr. Briggs, to his great contentment. He brings Mr. Briggs up into my lord’s chamber, where almost one quarter of an hour was spent, each beholding other almost with admiration before one word was spoke. At last Mr. Briggs began: ‘My lord, I have undertaken this long journey purposely to see your person, and to know by what engine of wit or ingenuity you came first to think of this most excellent help into astronomy, viz. the logarithms; but, my lord, being by you found out, I wonder no body else found it out before, when now known it is so easy.’ He was nobly entertained by the lord Napier; and every summer after that, during the lord’s being alive, this venerable man Mr. Briggs went purposely into Scotland to visit him.”

, an able mathematician, was born in 1654, of poor parents, at Metz. He retired to Berlin after the revocation of the edict of Nantes, and there forming a friendship with Langerfield, mathematician to the court, who taught the pages, succeeded him in 1696, was admitted into the society of sciences at Berlin in 1701, and into the academy of the princes, as professor of mathematics, in 1704. He died in 1729, at Berlin. His particular study 'as divinity, on which he has written much more than on mathematics; his only work on that science being a system of geometry, in German, 4to, and some other small pieces in the “Miscellanea,” of the society at Berlin. His theological works are, “Meditationes Saintes,” 12mo, “Morale Evangelique,” 2 vols. 8vo. “La souveraine perfection de Dieu dans ses divins attributs, et la parfaite intégrité de l'Ecriture prise au sens des anciens reformes,” 2 vols. 8vo, against Bayle; “Examen de deux Traités de M. de la Placette,” 2 vols. 12mo. His eldest son distinguished himself as his successor, and died 1745. He was a skilful mathematician, member of the societies of Berlin and London; and several memoirs of his may be found in the “Miscellanea Berolinensia,”

, an eminent English mathematician and divine, the grandson of John Newton, of Axmouth, in Devonshire, and the son of Humphrey Newton of Oundle, in Northamptonshire, was born at Oundle in 1622, and was entered a commoner of St. Edmund’s hall, Oxford, in 1637. He took the degree of B. A. in 1641; and the year following, was created master, in precedence to several gentlemen that belonged to the king and court, then residing in the university, on account of his distinguished talents in the higher branches of science. His genius being inclined to astronomy and the mathematics, he made great proficiency in these sciences, which he found of service during the times of the usurpation, when he continued stedfest to his legal sovereign. After the restoration he was created D. D. at Oxford, Sept. 1661, was made one of the king’s chaplains, and rector of Ross, in Herefordshire, in the place of Mr. John Toombes, ejected for non-conformity. He held this living till his death, which happened at Ross, Dec. 25, 1678. Mr. Wood gives him the character of a capricious and humoursome person; but whatever may be in this, his writings are sufficient monuments of his genius and skill in the mathematics. These are, 1. “Astronomia Britannica, &c. in three parts,” 1656, 4to. 2. “Help to Calculation; with tables of declination, ascension, &c.” 1657, 4to. 3. “Trigonometria Britannica, in two books,” 1658, folio one composed by our author, and the other translated from the Latin of Henry Gellibrand. 4, “Chiliades centum Logarithmorum,” printed with, 5. “Geometrical Trigonometry,” 1659. 6. “Mathematical Elements, three parts,” 1660, 4to. 7. “A perpetual Diary, or Almanac,” 1662. 8. “Description of the use of the Carpenter’s Rule,” 1667. 9. “Ephemerides, shewing the Interest and Rate of Money at six per cent.” &c. 1667. 10. “Chiliades centum Logarithmorum, et tabula partium proportionalium,” 1667. 11. “The Rule of Interest, or the case of Decimal Fractions, &c. part II.” 1668, 8vo. 12. “School-Pastime for young Children,” &c. 1669, 8vo. 13. “Art of practical Gauging,” &c. 1669, 14. “Introduction to the art of Rhetoric,” 1671. 15. “The art of Natural Arithmetic, in whole numbers, and fractions vulgar and decimal,” 1671, 8vo. 16. “The English Academy,” 1677, 8vo. 17. “Cosmography.” 18. “Introduction to Astronomy.” 19. “Introduction to Geography,” 1678, 8vo.

, an able mathematician, was born at Paris in 1613. Having finished his academical studies with the most promising success, he entered into the order of Minims, took the habit in 1632, and as usual, changed the name given him at his baptism for that of Francis, the name of his paternal uncle, who was also a Minim, or Franciscan. The inclination which he had for mathematics appeared early during his philosophical studies; and he devoted to this science all the time he could spare from his other employments, after he had completed his studies in theology. Ah the branches of the mathematics, however, did not equally engage his attention; he confined himself particularly to optics, and studied the rest only as they were subservient to his more favourite pursuit. He informs us in the preface to his “Thaumaturgus Opticus,” that he went twice to Rome; and that, on his return home, he was appointed teacher of theology. He was afterwards chosen to accompany father Francis de la Noue, vica^r-general of the order, in his visitation of the convents throughout all France. Amidst so many employments, it is wonderful that he found so much time to study, for his life was short, and must have been laborious. Being taken sick at Aix, in Provence, he died there, September 22, 1646, aged only thirty-three. He was an intimate acquaintance of Des Cartes, who had a high esteem for him, and presented him with his works. Niceron’s writings are, 1. “L'Interpretation des Chiffres, ou Regies pour bien entendre et expliquer facilement toutes sortes des Chiffres Simples,” &c. Paris, 1641, 8vo. This was only a translation oh the art of decyphering, written by Cospi in Italian, but is much improved by Niceron, who justly conceived it to be a work of utility. 2. “La Perspective curieuse, ou Magie artificielle des effets marveilleux de l'Optique, Catroptique, et Dioptrique,” intended as an introduction to his, 3. “Thaumaturgus Opticus: sive, Admiranda Optices, Catoptrices, et Dioptrices, Pars prima, &c.” 1646, fol. He intended to add two other parts, but was prevented by death.

, a very celebrated French mathematician, was born at Paris, December 23, 1683. His early attachment to the mathematics induced M. Montmortto take the charge of his education, and initiate him in the higher geometry. He first distinguished himself by detecting the fallacy of a pretended quadrature of the circle. A M. Mathulon was so confident that he had discovered this quadrature, as to deposit in the hands of a public notary at Lyons, the sum of 3000 livres, to be paid to any person who in the judgment of the academy of sciences, should demonstrate the falsity of his solution. M. Nicole having undertaken the task, the academy’s judgment was, that he had plainly proved that the rectilineal figure which Mathulon had given as equal to the circle, was not only unequal to it, but that it was even greater than the polygon of 32 sides circumscribed about the circle. It was the love of science, however, and not of money, which inspired Nicole on this occasion, for he presented the prize of 300O livres to the public hospital of Lyons. The academy named Nicole eleve-mechanician, March 12, 1707; adjunct in 1716, associate in 1718, and pensioner in 1724, which he continued till his death, which happened January 18, 1758, at seventy-five years of age.

, an eminent Dutch philosopher and mathematician, was born Aug. 10, 1654, at Westgraafdyk in North Holland, of which place his father vvas minister. He discovered a turn for learning in his first infancy, and his father designed him for the ministry; but when he found him averse from this study, he suffered him to gratify his own taste. He then applied himself to logic, and the art of reasoning justly; in which he grounded himself upon the principles of Des Cartes, with whose philosophy he was greatly delighted. Thence he proceeded to the mathematics, where he made a great proficiency; and added so much to his stock of various knowledge, that he was accounted a good philosopher, a great mathematician, a celebrated physician, and an able and just magistrate. Although naturally of a grave and serious disposition, yet his engaging manner in conversation made him be equally admired as a companion and friend, and frequently drew over to his opinion those who, at first, differed very widely from him. Thus accomplished, he acquired great esteem and credit in the council of the town of Purmerende, where he resided; as he did also in the states of that province, who respected him the more, as he never interfered in any cabals or factions. His disposition inclined him to cultivate the sciences, rather than to obtain the honours of the government and he therefore contented himself with being counsellor and burgomaster of the town, without wishing for more bustling preferments, which might interfere with his studies, and draw him too much out of his library. He died May 30, 1718, in the sixty-third year of his age. His works are, 1. “Considerationes circa Analyseos ad Quantitates infinite parvas applicator principia,” &c. Amst. 1694, 8vo. 2. “Analysis infinitorum seu curvilineorum Proprietates ex Polygpnorum natura deductse,” ibid. 1695, 4to. 3. “Considerationes secundoe circa differentialis Principia r & Responsio ad Yirum nobilissimum G. G. Leibnitium,” ibid. 1696, 8vo. This piece was attacked by John Bernoulli and James Hermant, celebrated geometricians at Basil. 4. “A Treatise upon a New Use of the Tables of Sines and Tangents.” 5. “Le veritable Usage de la Contemplation de TUnivers, pour la conviction des Athees & des Incredules,” in Dutch. This is his most esteemed work; and went through four editions in three or four years. It was translated into English by Mr. John Chamberlaine, and printed three or four times under the title of the “Religious Philosopher,” &c. 3 vols. 8vo. This was, until within these forty years, a very popular book in this country. We have also, by our author, one letter to Bothnia of Burmania, upon the 27th article of his meteors, and a refutation of Spinosa, 1720, 4to, in the Dutch language.

, a very eminent Portuguese mathematician and physician, was born in 1497, at Alcazar in Portugal, anciently a remarkable city, known by the name of Salacia, from whence he was surnamed Salaciensis. He was professor of mathematics in the university of Cojmbra, where he published some pieces which procured him great reputation. He was mathematical preceptor to Don Henry, son to king Emanuel of Portugal, and principal cosmographer to the king. Nonius was very serviceable to the designs which this court entertained of carrying on their maritime expeditions into the East, by the publication of his book “Of the Art of Navigation,” and various other works. He died in 1577, at eighty years of age.

Nonius was the author of several ingenious works and inventions, and justly esteemed one of the most eminent mathematicians of his age. Concerning his “Art of Navigation,” father Dechaies says, “In the year 1530, Peter Nonius, a celebrated Portuguese mathematician, upon occasion of some doubts proposed to him by Martinus Alphonsus Sofa, wrote a treatise on Navigation, divided into two books; in the first he answers some of those doubts, and explains the nature of Loxodromic lines. In the second book he treats of rules and instruments proper for navigation, particularly sea- charts, and instruments serving to find the elevation of the pole” but says he is rather obscure in his manner of writing. Furetiere, in his Dictionary, takes notice that Peter Nonius was the first who, in 1530, invented the angles which the Loxodromic curves make with each meridian, calling them in his language Rhumbs, and which he calculated by spherical triangles. Stevinus acknowledges that Peter Nonius was scarce inferior to the very best mathematicians of the age. And Schottus says he explained a great many problems, and particularly the mechanical problem of Aristotle on the motion of vessels by oars. His Notes upon Purbach’s Theory of the Planets, are very much to be esteemed: he there explains several things, which had either not been noticed before, or not rightly understood.

Christian VI. was desirous of having a circumstantial account of a country so distant and so famous from an intelligent man, and one whose fidelity could not be questioned; and no one was thought more proper than Norden. He was then in the flower of his age, of great abilities, of a good taste, and of a courage that no danger or fatigue could dishearten; a skilful observer, a great designer, and a good mathematician: to all which qualities may be added an enthusiastic desire of examining, upon the spot, the wonders of Egypt, even prior to the order of his master. How he acquitted himself in this business appears amply from his “Travels in Egypt and Nubia.” In these countries he stayed about a year and, at his return, when the count of Danneskiold-Samsoe, who was at the head of the marine, presented him to his majesty, the king was much pleased with the masterly designs he had made of the objects in his travels, and desired he would draw up an account of his voyage, for the instruction of the curious and learned. At this time he was made captain-lieutenant, and soon after captain of the royal navy, and one of the commissioners for building ships.

, a learned traveller, whose German name was Oelschlager, was born in 1599, or 1600, at Aschersieben, a small town in the principality of Anhalt. 43is parents were very poor, and scarcely able to maintain him, yet by some means he was enabled to enter as a student at Leipsic, where he took his degrees in arts and philosophy, but never was a professor, as some biographers have asserted. He quitted Leipsic for Holsteiu, where the duke Frederic, hearing of his merit and capacity, wished to employ him. This prince having a wish to extend the commerce of his country to the East, determined to send an embassy to the Czar Michael Federowitz, and the king of Persia, and having chosen for this purpose two of his counsellors, Philip Crusius and Otto Bruggeman, he appointed Olearius to accompany them as secretary. Their travels lasted six years, during which Olearius collected a great fund of information respecting the various countries they visited. The Czar of Moscovy on his return wished to have retained him in his service, with the appointment of astronomer and mathematician; not, however, his biographers tell us, so much on account of his skill in these sciences, as because the Czar knew that Olearius had very exactly traced the course of the Volga, which the Russians then wished to keep a secret from foreigners. Olearius had an inclination, however, to have accepted this offer, but after his return to the court of Holstein, he was dissuaded from it, and the duke having apologized to the Czar, attached him to himself as mathematician and antiquary. In 1643, the duke sent him on a commission to Moscow, where, as before, his ingenuity made him be taken for a magician, especially as on this occasion he exhibited a camera obscura. In 1650 the duke appointed him his librarian, and keeper of his curiosities. The library he enriched with many Oriental Mss. which he had procured in his travels, and made also considerable additions to the duke’s museum, particularly of the collection of Paludanns, a Dutch physician, which the duke sent him to Holland ta purchase; and he drew up a description of the whole, which was published at Sleswick in 1666, 4to. He also constructed the famous globe of Gottorp, and an armillary sphere of copper, which was not less admired, and proved how much mathematics had been his study. He died Feb. 22, 1671. He published, in German, his travels, 1647, 1656, 1669, fol. Besides these three editions, they were translated into English by Davies, and into Dutch and Italian. The most complete translation is that, in French, by Wicquefort, Amst. 1727, 2 vols. fol. who also translated Olearius’s edition of Mandelso’s “Voyages to Persia,” c. fol. Among his other and less known works, are some lives of eminent Germans “The Valley of Persian Roses,” from the Persian; “An abridged Chronicle of Holstein,” &c

, a celebrated cardinal, and one of the greatest men of his time, was born at a small village in the county of Almagnac, Aug. 23, 1526. He was descended of indigent parents, and left an orphan at nine years of age, in very hopeless circumstances; but Thomas de Marca, a neighbouring gentleman, having observed his promising genius, took the care of his education, and placed him under the tutors of the young lord of Castlenau de Mugnone, his nephew and ward. D'Ossat made such a quick progress, that he became preceptor to his companion; and was sent in that character with the young nobleman and two other youths to Paris, where they arrived in May 1559. He discharged this trust with fidelity and care, till they had completed their course of study; and then sent them back to Gascony, in 1562. During this time he had made himself master of rhetoric and philosophy, and became a good mathematician; and being now at leisure to improve himself, he repaired to Bourges, where he studied the law under Cujacius. About this time he wrote a defence of Peter Rarnus, under whom he had studied philosophy, against James Charpentier, entitled “Expositio in disputationem Jacobi Carpenterii de Methodo,” Parisi 1564, to which Charpentier published a scurrilous reply, “Ad expositionem disputationis de methodo, contra Thessalum Ossatum responsio.” D'Ossat, having obtained his diploma at Bourges, returned to Paris in 1568, and applied himself to the bar. In this station his merit procured him the acquaintance and esteem of many distinguished persons; and, among the rest, of Paul de Foix, then counsellor to the parliament of Paris, took him in his company to Rome, in 1574.

Notwithstanding all Oughtred’s mathematical merit, he was, in 1646, in danger of a sequestration by the committee for plundering ministers; in order to which, several articles were deposed and sworn against him; but, upon his day of hearing, William Lilly, the famous astrologer, applied to sir Bulstrode Whitelocke and all his old friends, who appeared so numerous in his behalf, that though the chairman and many other presbyterian members were active against him, yet he was cleared by the majority. This Lilly tells us himself, in the “History of his own Life,” where he styles Oughtred the most famous mathematician then of Europe. “The truth is,” continues this writer, “he had a considerable parsonage and that alone was enough to sequester any moderate judgment besides, he was also well known to affect his majesty.” His merit, however, appeared so much neglected, and his situation was made so uneasy at home, that his friends procured several invitations to him from abroad, to live either in Italy, France, or Holland, but he chose to encounter all his difficulties at Albury. Aubrey informs us that the grand duke invited him to Florence, and offered him 500l. a year, but he would not accept it because of his religion. From the same author we learn that he was thought a very indifferent preacher, so bent were his thoughts on mathematics; but, when he found himself in danger of being sequestered for a royalist, " he fell to the study of divinity, and preached (they sayd) admirably well, even in his old age.

Although, according to Aubrey, he burnt “a world of papers” just before his death, yet it is certain that he also left behind him a great number of papers upon mathematical subjects; and, in most of his Greek and Latin mathematical books there were found notes in his own handwriting, with an abridgment of almost every proposition and demonstration in the margin, which came into the museum of the late William Jones, esq. F. R. S. father to sir William Jones. These books and manuscripts then passed into the hands of sir Charles Scarborough, the physician; the latter of which were carefully looked over, and all that were found fit for the press, printed at Oxford, 1676, under the title of “Opuscula Mathematica hactenus inedita.” This collection contains the following pieces: 1. “Institutiones mechanics.” 2. “De variis corporum generibus gravitate et magnitudine comparatis.” 3. “Automata.” 4. “Qusestiones Diophanti Alexandrini, libri tres.” 5. “De triangulis planis rectangulis.” 6. “t)e divisione superficiorum.” 7. “Musicae elemental 8.” De propugnaculornm munitionibus.“9.” Sectiones angulares.“In 1660, sir Jonas Moore annexed to his arithmetic, then printed in octavo, a treatise entitled” Conical sections; or, the several sections of a cone; being an analysis or methodical contraction of the two first books of Mydorgius, and whereby the nature of the parabola, hyperbola, and ellipsis, is very clearly laid down. Translated from the papers of the learned William Oughtred." Oughtred, says Dr. Hutton, though undoubtedly a very great mathematician, was yet far from having the happiest method of treating the subjects he wrote upon. His style and manner were very concise, obscure, and dry and his rules and precepts so involved in symbols and abbreviations, as rendered his mathematical writings very troublesome to read, and difficult to be understood.

, a learned French ecclesiastic, of the seventeenth century, was a native of Chinon in Tourraine, and a canon of Tours, He enjoyed the reputation of an universal scholar; was a poet, mathematician, divine, a controversial writer, and even a musician, although in the latter character he appears to have escaped the very minute researches of Dr. Burney in his valuable history of that art. He had been music- master of the holy chapel at Paris for ten years, before he became a canon of Tours. He wrote a great many works, among which some of his controversial pieces against the protestants, his “History of Music from its origin to the present time,” and his dissertation on Vossius’s treatise “De poematum cantu et viribus rythmi,” remain in manuscript. Those which were published, are, 1. “Secret pour composer en musique par un art nouveau,” Paris, 1660. 2. “Studiosis sanctarum scripturarum Biblia Sacra in lectiones ad singulos dies, per legem, prophetas, et evangelium distributa, et 529 carminibus mnemonicis comprehensa,” ibid. 1668; of this a French edition was published in 1669. 3. “Motifs de reunion a l‘eglise catholique, presentes a ceux de la religion pretendue-reforme*e de France, avec un avertissement sur la reponse d’un ministre a Poffice du saint Sacrement,” ibid. 1668. 4. “Le motifs de la conversion du comte de Lorges Montgommery,” dedicated to Louis XIV. ibid. 1670. 5. “Defense de Tancienne tradition des eglises de France, sur la mission des premiers predicateurs evangeliques dans les Gaules, du temps des apotres ou de leurs disciples immediats, et de Pusage des ecrits des S. S. Severe-Sulpice, et Gregoire de Tours, et de Tabus qu‘on en faiten cette rnatiere et en d’autres pareilles,” ibid. 178. This was addressed to the clergy and people of To'irs by the author, who held the same sentiments as M.de Ma re a, respecting St. Denis. 6. “L‘Art de la science des Nombres, en Francois et en Latin, avec un preface de i’excellence de Farithmetique,” ibid. 1677. 7. “Architecture harmonique, ou application de la doctrine des proportions, de la musique a ^architecture, avec un addition a cet ecrit,” ibid. 1679, 4to. 8. “Calendarium novum, perpetuum, et irrevocable,” 1682; but this work he was induced to suppress by the advice of his friend M. Arnauld, who thought that his ideas in it were too crude to do credit to his character. His last publication was, 9. “Breviarium Turonense, renovatum, et in melius restitutum,” 1685. He died at Tours, July 19, 1694, and the following lines,

, an eminent French mathematician, was descended from a family of Jewish extraction, but which had long been convertsto the Romish faith and some of whom had held considerable places in the parliaments of Provence. He was born at Boligneux, in Brescia, in 1640; and being a younger son, though his father had a good estate, it was thought proper to breed him to the church, that he might enjoy some small benefices which belonged to the family, to serve as a provision for him. Accordingly he studied divinity four years; but, on the death of his father, devoted himself entirely to the mathematics, to which he had always been strongly attached. Some mathematical books, which fell into his hands, first excited his curiosity; and by his extraordinary genius, without the aid of a master, he made so great a progress, that at the age of fifteen he wrote a treatise of that kind, of which, although it was not published, he inserted the principal parts in some of his subsequent works.

Ozanam was of a mild and calm disposition, a cheerful and pleasant temper, endeared by a generosity almost unparalleled. His manners were irreproachable after marriage; and he was sincerely pious, and zealously devout, though studiously avoiding to meddle in theological questions. He used to say, that it was the business of the Sorbonne to discuss, of the pope to decide, and of a mathematician to go straight to heaven in a perpendicular line. He wrote a great number of useful books; a list of which is as follows 1. “La Geometric-pratique, contenant la Trigonometric theorique & pratique, la Longimetrie, la Planimetrie, & la Stereometric,” Paris, 1684, 12mo., 2. “Tables des Sinus, Tangentes, & Secantes, & des Logarithmes des Sinus & des Tangentes, & des nombres depuis T unite jusqu'a dix mille, avec un traite de Trigonometric, par de nouvelles demonstrations & des pratiques tres faciles,” Paris, 1685, 8vo reprinted, with additions, in 1710. 3. “Traite des 'Lignes du premier genre, de la construction des equations, et des lieux Geometriques, expliquees par une methode nouveile & facile,” Paris, 1687, 4to. 4. “L‘usage du Compas de proportion, explique & demontre d’une maniere courte & facile, & augmente d'un Traite de la division des champs,” Paris, 1688, 8vo, reprinted in 1700. 5. “Usage de l'instrument universel pour resoudre promptement & tres-exactement tous les problemes de la Geometric- pratique sans aucun calcul,” Paris, 1688, 12mo; reprinted in 1700. 6. “Dictionaire Mathematique, ou Idee generale des Mathematiques,” Paris, 1690, 4to. 7. “Methode Generale pour tracer des Cadrans sur toutes sortes de plans,” Paris, 1673, 12mo, reprinted and enlarged in 1685. 8. “Cours de Mathematiques, qui comprend toutes les parties de cette science les plus utiles & les plus necessaires,” Paris, 1693, 5 vols. 8vo. 9. “Traite” 4e la Fortification, contenant les methodes anciennes & modernes pour la construction & defense des Places, & la maniere de les attaquer, expliquees plus au long qu‘elles n’on jusqu' a present,“Paris, 1694, 4to. 10.” Recreations Mathematiques & Physiques, qui contiennent plusieurs problemes utiles & agreables de PArithmetiquej de Geometric, d'Optique, de Gnomonique, de Cosmographie, de Mechanique, de Pyrotecnie, & de Physique, avec un Traite des Horloges elementaires,“Paris, 1694, 2 vols. 8vo. There was a new edition, with additions, at Paris, in 1724, 4 vols. 8vo; and in 1803, Dr. Hutton published a very enlarged edition, in 4 vols. 8vo, with Montucla’s and his own additions and improvements. 11.” Nouvelle Trigonometric, oil Ton trouve la maniere de calculer toutes sortes de Triangles rectilignes, sans les tables des Sinus, & aussi par les Tables des Sinus, avec un application de la Trigonometric a la mesure de Lignes droites accessibles & inaccessibles sur la terre,“Paris, 1699, 12mo. 12.” Methode facile pour arpenter ou mesurer toutes sortes de superficies, & pour toiser exactement la Ma^onnerie, les Vuidanges des terres, & tous les autres corps, avec le toise du bois de charpente, & un traite dela Separation des Terres,“Paris, 1699, 12mo; reprinted, with corrections, in 1725. 13.” Nouveaux Elemens d'Algebre, ou Principes generaux pour resoudre toutes sortes de problemes de Mathematiques,“Amsterdam, 1702, 8vo, Mr. Leibnitz, in the Journal des Savans of 1703, speaks thus of this work of our author:” Monsieur Ozanam’s Algebra seems to me greatly preferable to most of those which have been published a long time, and are only copies from Des Cartes and his commentators. I am well pleased that he has revived part of Vieta’s precepts, which deserve not to be forgotten.“14.” Les Elemens d'Euclide, par le P. Dechales. Nouvelle edition corrigee & augmentee,“Paris, 1709, in 12mo; reprinted in 1720. 15.” GeometriePratique du Pieur Boulanger, augmentee de plusieurs notes & d‘un Traite de l’Arithmetique par Geometric, par M. Ozanam,“Paris, 1691, 12mo. 16.” Traite de la Sphere du Monde, par Boulanger, revu, corrige*, & augmente, par M. Ozanam,“Paris, 12mo. 17.” La Perspective Theorique & Pratique, ou Ton enseigne la maniere de mettre toutes sortes d‘objets en perspective, & d’en representer les ombres causees par le Soleil, ou par une petite Lumiere,“Paris, 1711, 8vo. 18. * e Le Geographic & Cosmographie, qui traite de la Sphere, des Corps celestes, des differens Systmes du Monde, du Globe, & de ses usages,” Paris, 1711, 8vb. 19. In the Journal des Ssavans, our author has the following pieces I. “Demonstration de ce Theoreme que la somme ou la. difference de deux quarre”-quarrez ne peut etre un quarre-quarre,“Journal of May 20, 1680. II.” Response a un probleme propose“par M.'Comiers,” Journal of Nov. 17, 1681. III. “Demonstration d'un problSaie touchant les racines fausses imaginaires,” Journal of the 2d and 9th of April, 1685. IV. “Methode pour trouver en nombres la racine cubique, & la racme sursolide d'un binoine, quand ii y en a une,” Journal of April 9th, 1691. 20. In the “Me mo ires de Trevoux,” he has this piece, “Reponse aux principaux articles, qui sont dans le 23 Journal de Paris de Tan 1703, touchant la premiere partie de son Algebre,” inserted in the Me. noire* of December 1703, p. 2214. And lastly, in the Memoirs of the Academy of Sciences of 1707, he has Observations on a Problem of Spherical Trigonometry.

, an eminent French mathematician, was born at Avignon, in Provence, March 3, 1604, and entered the army at fourteen, for which he had been educated with extraordinary care. Ir> 1620 he was engaged at the siege of Caen, in the battle of the bridge of Ce, and other exploits, in which he signalized himself, and acquired a reputation above his years. He was present, in 1G21, at the siege of St. John d'Angeli, as also at that of Clerac and Montauban, where he lost his left eye by a musket-shot. At this siege he had another loss, which he felt with no less sensibility, viz. that of the constable of Luynes, who died there of a scarlet fever. The constable was a near relation to him, and had been his patron at court. He did not, however, sink under his misfortune, but on the contrary seemed to acquire fresh energy from the reflection that he must now trust solely to himself. Accordingly, there was after this time, no siege, battle, or any other occasion, in which he did not signalize himself by some effort of courage and conduct. At the passage of the Alps, and the barricade of Suza, he put himself at the head of the forlorn hope, consisting of the bravest youths among the guards; and undertook to arrive the first at the attack by a private way which was extremely dangerous; but, having gained the top of a very steep mountain, he cried out to his followers, “See the way to glory!” and sliding down the mountain, his companions followed him, and coming first to the attack, as they wished to do, immediately began a furious assault; and when the army came up to their support, forced the barricades. He had afterwards the pleasure of standing on the left hand of the king when his majesty related this heroic action to the duke of Savoy, with extraordinary commendations, in the presence of a very full court. When the king laid siege to Nancy in 1633, our hero had the honour to attend his sovereign in drawing the lines and forts of circumvallation. In 1642 his majesty sent him to the service in Portugal, in the post of field-marshal; but that year he had the misfortune to lose his eye-sight.

, a very eminent Greek of Alexandria, flourished, according to Suidas, under the emperor Theodosius the Great, from the year 379 to* 395, and acquired deserved fame as a consummate mathematician. Many of his works are lost, or at least have not yet been discovered. Suidas and Vossius mention as the principal of them, his “Mathematical Collections,” in 8 books, of which the first and part of the second are lost; a “Commentary upon Ptolomy’s Almagest;” an “Universal Chorography;” “A Description of the Rivers of Libya;” a treatise or' “Military Engines;” “Commentaries upon Aristarchus of Samos, concerning the Magnitude and Distance of the Sun and Moon,” &c. Of these, there have been published, “The Mathematical Collections,” in a Latin translation, with a large commentary, by Commandine, in 1588, folio; reprinted in 1660. In 1644, Mersenne exhibited an abridgment of them in his <c Synopsis JVIathematica,“in 4to, containing only such propositions as could be understood without figure*. In 1655, Meibomius gave some of the Lemmata of the seventh book, in his” Dialogue upon Proportions.“In 1688, Dr. Wallis printed the last twelve propositions of the second book, at the end of his” Aristarchus Samius.“In 1703, Dr. David Gregory gave part of the preface of the seventh book, in the Prolegomena to his Euclid. And in 1706, Dr. Halley exhibited that preface entire, in the beginning of his” Apollonius." Dr. Ilutton, in his Dictionary, has given an excellent analysis of the “Mathematical Collections.”

, or rather Deparcieux (Anthony), an able mathematician, was born in 1703, at a hamlet near Nismes, of industrious but poor parents, who were unable to give him education; he soon, however, found a patron, who placed him in the college at Lyons, where he made astonishing progress in mathematics. On his arrival at Paris, he was obliged to accept of humble employment from the mathematical instrument makers, until his works brought him into notice. These were, 1. “Table astronomiques,” 1740, 4to. 2. “Traite” de trigonometric rectiligne et spherique, avec un trait6 de gnomonique et des tables de logarithmes,“1741, 4to. 3.” Essai sur les probabilites de la dnre de la vie humame,“1746, 4to. 4.” Reponse aux objections contrtr ce livre,“1746, 4to. 5.” Additions a I'essai, c.“1760, 4to. 6.” Memoires sur la possibility et la facilit^ d‘amener aiipres de PEstrapade, a Paris, les eaux de la riviere d’Yvette,“1763, 4to, reprinted, with additions, in 1777. It was always Deparcieux’s object to turn his knowledge of mathematics to practical purposes, and in the memoirs of the academy of sciences are many excellent papers which he contributed with this view. He also introduced some ingenious improvements in machinery. He was censor- royal and member of the academy of sciences at Paris, and of those of Berlin, Stockholm, Metz, Lyons, and Montpelher. He died at Paris Sept. 2, 1768, aged sixty-five. He had a nephew of the same name, born in 1753, who was educated at the college of Navarre at Paris, where he studied mathematics and philosophy, and at the age of twentyfour gave public lectures. In 177y he began a course of experimental philosophy, in the military school of Brienne; after which, he occupied the philosophical professorship at the Lyceum in Paris, where he died June 23, 1799, in a state bordering on indigence. He wrote a” Traité elementaire de Mathematiques,“for the use of students; ”Traite* des annuites, ou des rentes a terme,“1781, 4to” Dissertation snr le moyen d‘elever l’eau par la rotation d'une curde verticale sans fin,“Amst. 1782, 8vo” Dissertation sur ies globes areostatiques,“Paris, 1783, 8vo. He left also some unfinished works; and a” Cours complet de physique et de chimie," was in the press when he died.

, an ingenious French mathematician and philosopher, was born at Pau, in the province of Gascony, in 1636; his faiher being a counsellor of the parliament of that city. At the age of sixteen he entered into the order of Jesuits, and made so great proficiency in his studies, that he taught polite literature, and composed many pieces in prose and v< rse with considerable delicacy of thought and style before he was well arrived at the age of manhood. Propriety and elegance of language appear to have been his first pursuits, lor which purpose he studied the belles lettres; but afterwards he devoted himself to mathematical and philosophical studies, and read, with due attention, the most valuable authors, ancient and modern, in those sciences. By such assiduity in a short time he made himself master of the Peripatetic and Cartesian philosophy, and taught them both with great reputation. Notwithstanding he embraced Cartesianism, yet he affected to be rather an inventor in philosophy himself. In this spirit he sometimes advanced very bold opinions in natural philosophy, which met with opposers, who charged him with starting absurdities: but he was ingenious enough to give his notions a plausible turn, so as to clear them seemingly from contradictions. His reputation procured him a call to Paris, as professor of rhetoric in the college of Louis the Great. He also taught the mathematics in that city, as he had before done in other places; but the high expectations which his writings very reasonably created, were all disappointed by his early death, in 1673, at thirty-seven years of age. He fell a victim to his zeal, having caught a contagious disorder by preaching to the prisoners in the Bicetre.

, a French mathematician, was born at Paris in 1666. He shewed early a propensity to mathematics, eagerly perusing such books as fell in his way. His custom was to write remarks upon the margins of the books which he read; and he had filled some of these with a kind of commentary at the age of thirteen. At fourteen he was put under a master who taught rhetoric at Chartres. Here he happened to see a Dodecaedron, upon every face of which was delineated a sun-dial, except the lowest, on which it stood. Struck immediately with the curiosity of these dials, he set about drawing one himself; but, having a book which only shewed the practical part without the theory, it was not till some time after, when his rhetoric-master came to explain the doctrine of the sphere to him, that he began to understand how the projection of the circles of the sphere formed sundials. He then undertook to write a “Treatise upon Gnomonics,” anr the piece was rude and unpolished enough; but it was entirely his own. About the same time he wrote also a book of “Geometry,” at Beauvais.

At length his friends sent for him to Paris, to study the law; and, in obedience to them he went through a course in that faculty, but this was no sooner finished, than, his passion for mathematics returning, he shut himself up in the college of Dormans, and, with an allowance of less than 200 livres a year, he lived content in this retreat, which he never left but to go to the royal college, in order to hear the lectures of M. de la Hire, or M. de Sauveur. As soon as he found himself able enough to teach others, he took pupils; and, fortification being a part of mathematics which the war had rendered very necessary, he turned his attention to that branch; but after some time began to entertain scruples about teaching what he knew only in books, having never examined a fortification elsewhere, and communicating these scruples to M. Sauveur, that friend recommended him to the marquis d'Aligre, who happened at that time to want a mathematician in his suite. Parent accordingly made two campaigns with the marquis, and instructed himself thoroughly by viewing fortified places, of which he drew a number of plans, though hq had never received any instruction in that branch. From this time he assiduously cultivated natural philosophy, and the mathematics in all its branches, both speculative and practical; to which he joined anatomy, botany, and chemistry, and never appears to have been satisfied while there was any thing to learn. M. de Billettes being admitted into the academy of sciences at Paris in 1699, with the title of their mechanician, nominated for his eleve or disciple, Parent, who excelled chiefly in that branch. It was soon found in this society, that he engaged in all the various subjects which were brought before them, but often with an eagerness and impetuosity, and an impatience of contradiction, which involved him in unpleasant disputes with the members, who, on their parts, exerted a pettish fastidiousness in examining his papers. He was in particular charged with obscurity in his productions; and indeed the fault was so notorious, that he perceived it himself, and could not avoid correcting it.

, an English historian, was a Benedictine monk of the congregation of Clugny, in the monastery of St. Alban’s, the habit of which order he took in 1217. He was an universal scholar; understood, and had a good taste both in painting and architecture. He was also a mathematician, a poet, an orator, a divine, an historian, and a man of distinguished probity. Such rare accomplishments and qualities as these, did not fail to place him very high in the esteem of his contemporaries; and he was frequently employed in reforming some monasteries, visiting others, and establishing the monastic discipline in all. He reproved vice without distinction of persons, and did not even spare the English court itself; at the same time he shewed a hearty affection for his country in maintaining its privileges against the encroachments of the pope. Of this we have a clear, though unwilling, evidence in Baronius, who observes, that this author remonstrated with too sharp and bitter a spirit against the court of Rome; and that, except in this particular only, his history was an incomparable work. He died at St. Alban’s in 1259. His principal work, entitled “Historia Major,” consists of two parts: The first, from the creation of the world to William the Conqueror; the second, from that king’s reign to 1250. He carried on this history afterwards to the year of his death in 1259. Rishanger, a monk of the monastery of St. Alban’s, continued it to 1272 or 1273, the year of the death of Henry III. It was first printed at London in 1571, and reprinted 1640, 1684, fol. besides several foreign editions. There are various ms copies in our public libraries, particularly one which he presented to Henry III. and which is now in the British Museum. From Jiis Mss. have also been published “Vitas duorum Offarum, Merciae regum, S, Albani fundatorum” <c Gesta viginti duo abbatum S. Albani“”Additamenta chronicorum ad historian) majorern,“all which accompany the editions of his” Historia Major“printed in 1640 -and 1684. Among his unpublished Mss. are an epitome of his” Historia Major," and a history from Adam to the conquest, principally from Matthew of Westminster. This is in the library of Bene't college, Cambridge. The titles of some other works, but of doubtful authority, may be seen in Bale and Pits.

, a French mathematician and philosopher, and one of the greatest geniuses and best writers that country has produced, was born at Clermont in Auvergne, June 19, 1623. His father, Stephen Pascal, was president of the Court of Aids in his province, and was also a very learned man, an able mathematician, and a friend of Des Cartes. Having an extraordinary tenderness for this child, his only son, he quitted his office and settled at Paris in 1631, that he might be quite at leisure to attend to his son’s education, of which he was the sole superintendant, young Pascal never having had any other roaster. From his infancy Blaise gave proofs of a very extraordinary capacity. He was extremely inquisitive; desiring to know the reason of every thing; and when, good reasons were not given him, he would seek for better; nor would he ever yield his assent but upon such as appeared to him well grounded. What is told of his manner of learning the mathematics, as well as the progress he quickly made in that science, seems almost miraculous, liis father, perceiving in him an extraordinary inclination to reasoning, was afraid lest the knowledge of the mathematics might hinder his learning the languages, so necessary as a foundation to all sound learning. He therefore kept him as much as he could from all notions of geometry, locked up all his books of that kind, and refrained even from speaking of it in his presence. He could not however prevent his son from musing on that science; and one day in particular he surprised him at work with charcoal upon his chamber floor, and in the midst of figures. The father asked him what he was doing: “I am searching,” says Pascal, “for such a thing;” which was just the same as the 32d proposition of the 1st book of Euclid. He asked him then how he came to think of this: “It was,” says Blaise, “because I found out such another thing;” and so, going backward, and using the names of bar and round, he came at length to the definitions and axioms he had formed to himself. Of this singular progress we are assured by his sister, madame Perier, and several other persons, the credit of whose testimony cannot reasonably be questioned.

, an eminent English mathematician, descended from an ancient family in Lincolnshire, was bora at Southwyke in Sussex, March t, 1610; and educated in grammar-learning at the free-school, then newly founded, at Steyning in that county. At thirteen, he was sent to Trinity college in Cambridge, where he pursued his studies with unusual diligence, but although capable of undergoing any trials, and one of the best classical scholars of his age, he never offered himself a candidate at the election of scholars or fellows of this college. After taking the degree of B. A. in 1628, he drew up the “Description and Use of the Quadrant, written for the use of a friend, in two books;” the original ms. of which is still extant among his papers in the Royal Society; and the same year he held a correspondence with Mr. Henry Briggs on logarithms. In 1630 he wrote “Modus supputatidi Ephemerides Astronomicas (quantum ad motum solis attinet) paradigmate ad an. 1630 accommodate;” and “A Key to unlock the Meaning of Johannes Trithemius, in his Discourse of Ste^anography;” which key Pell the same year imparted to Mr. Samuel Hartlib and Mr. Jacob Homedae. The same year, he took the degree of master of arts at Cambridge, and the year following was incorporated in the university of Oxford. In June he wrote “A Letter to Mr. Edward Win gate on Logarithms;” and, Oct. 5, 1631, “Commentationes in Cosmographiam Alstedii.” July 3, 1632', he married Ithamaria, second daughter of IVtr. Henry Reginolles of London, by whom he had four sons and four daughters. In 1633 he finished his “Astronomical History of Observations of heavenly Motions and Appearances;” and his “Eclipticus Prognostica or Foreknower of the Eclipses; teaching how, by calculation, to foreknow and foretell all sorts of Eclipses of the heavenly lights.” In 1634, he translated “The everlasting Tables of Heavenly Motions, grounded upon the observations of all times, and agreeing with them all, by Philip Lansberg, of Ghent in Flanders” and the same year he committed to writing, “The Manner of deducing his Astronomical Tables out of the Tables and axioms of Philip Lansberg.” In March 1635, he wrote “A Letter of Remarks on Gellibrand’s Mathematical Discourse on the Variation of the Magnetic Needle; and, June following, another on the same subject. Such were the employments of the first six years of Mr. Pell’s public life, during which mathematics entirely engrossed his attention. Conceiving this science of the utmost importance, he drew up a scheme for a mathematical school on an extensive scale of utility and emulation*, Which was much approved by Des Cartes^ but so censured by Mersenne in France, that our author was obliged to write in its defence. The controversy may be seen in Hooke’s Philosophical Collections, and with Pell’s” Idea of the Mathematics."

Some of his manuscripts he left at Brereton in Cheshire", where he resided some years, being the seat of William lord Brereton, who had been his pupil at Breda. A great many others came into the hands of Dr. Busby; which Mr. Hook was desired to use his endeavours to obtain for the society. But they continued buried under dust, and mixed with the papers and pamphlets of Dr. Busby, in four large boxes, till 1755; when Dr. Birch, secretary to the Royal Society, procured them for that body, from the trustees of Dfr. Busby. The collection contains not only Pell’s mathematical papers, letters to him, and copies of those from him, &c. but also several manuscripts of Walter Warner, the mathematician and philosopher, who lived in the reignS of James the First and Charles the First.

, a learned physician, mathematician, and mechanist, was born at London, in 1694. After studying grammar at a school, and the higher classics under Mr. John Ward, afterwards professor of rhetoric at Gresham college, he went to Leyden, and attended the lectures of the celebrated Boerhaave, to qualify himself for the profession of medicine. Here also, as well as in England, he constantly mixed with his professional studies those of the best mathematical authors, whom he contemplated with great effect. From hence he went to Paris, to perfect himself in the practice of anatomy, to which he readily attained, being naturally dexterous in all manual operations. Having obtained his main object, he returned to London, enriched also with other branches of scientific knowledge, and a choice collection of mathematical books, both ancient and modern, from the sale of the valuable library of the abbe Gallois, which took place during his stay in Paris. After his return he assiduously attended St. Thomas’s hospital, to acquire the London practice of physic, though he seldom afterwards practised, owing to his delicate state of health. In 1719 he returned to Leyden, to take his degree of M. D where he was kindly entertained by his friend Dr. Boerhaave. After his return to London, he became more intimately acquainted with Dr. Mead, sir I. Newton, and other eminent men, with whom he afterwards cultivated the most friendly connexions. Hence he was useful in assisting sir I. Newton in preparing a new edition of his “Principia,” in writing an account of his philosophical discoveries, in bringing forward Mr. Robins, and writing some pieces printed in the 2d volume of that gentleman’s collection of tracts, in Dr. Mead’s * Treatise on the Plague," and in his edition of Cowper on the Muscles, &c. Being chosen professor of physic in Gresham-college, he undertook to give a course of lectures on chemistry, which was improved every time he exhibited it, and was publisned in 1771, by his friend Dr. James Wilson. In this situation too, at the request of the college of physicians, he revised and reformed their pharmacopoeia, in a new and much improved edition. After a long and laborious life, spent in improving science, and assisting its cultivators, Dr. Pemberton died in 1771, at seventy-seven years of age.

, a learned divine, was born, according to Fuller, in Sussex, but more probably at Egerton, in Kent, in 1591, and was educated at Magdalen college, Oxford, on one of the exhibitions of John Baker, of Mayfield, in Sussex, esq. Wood informs us that having completed his degree of bachelor by determination, in 1613, he removed to Magdalen-hall, where he became a noted reader and tutor, took the degree of M. A. entered into orders, was made divinity reader of that house, became a famous preacher, a well-studied artist, a skilful linguist, a good orator, an expert mathematician, and an ornament to the society. “All which accomplishments,” he adds, “were knit together in a body of about thirtytwo years of age, which had it lived to the age of man, might have proved a prodigy of learning.” As he was a zealous Calvinist, he may be ranked among the puritans, but he was not a nonconformist. He died while on a visit to his tutor, Richard Capel, who was at this time minister of Eastington, in Gloucestershire, in the thirty-second year of his age, April 14, 1623. His works, all of which were separately printed after his death, were collected in 1 vol. fol. in 1635, and reprinted four or five times; but this volume does not include his Latin works, “De formarum origine;” “De Sensibus internis,” and “Enchiridion Oratorium,” Bishop Wilkins includes Pemble’s Sermons in the list of the best of his age.

, a celebrated mathematician, who descended from an illustrious family of Aix, was born at Moustiers, in the diocese of Riez, in Provence, in 1530. He studied the belles lettres under Ramus, but is said to have afterwards instructed his master in mathematics, which science he taught with great credit in the royal college at Paris. He died Aug. 23, 1560, aged thirty. M. Pena left a Latin translation of Euclid’s “Catoptrica,” with a curious preface, and also employed his pen upon that geometrician’s other works, and upon an edition of the “Spherica” of Theodosius, Greek and Latin, Paris, 1558, 4to, c.

The sole ambition bf Pepus’ch, during the last years of his life, seems to have been the obtaining the reputation of a profound theorist, perfectly skilled in the music of the ancients; and attaching himself to the mathematician De Moivre and Geo. Lewis Scot, who helped him to calculate ratios, and to construe the Greek writers on music, he bewildered himself and some of his scholars with the Greek genera, scales, diagrams, geometrical, arithmetical, and harmonical proportions, surd quantities, apotomes, lemmas, and every thing concerning ancient harmonics, that was dark, unintelligible, and foreign to common and useful practice. But with all his pedantry and ideal admiration of the music of the ancients, he certainly had read more books on the theory of modern music, and examined more curious compositions, than any of the musicians of his time; and though totally devoid of fancy and invention, he was able to correct the productions of his contemporaries, and to assign reasons for whatever had been done by the greatest masters who preceded him. But when he is called the most learned musician of his time, it should be said, in the music of the sixteenth century. Indeed, he had at last such a partiality for musical mysteries, and a spirit so truly antiquarian, that he allowed no composition to be music but what was old and obscure. Yet, though he fettered the genius of his scholars by antiquated rules, he knew the mechanical laws of harmony so well, that in glancing his eye over a score, he could by a stroke of his pen smooth the wildest and most incoherent notes into melody, and make them submissive to harmony; instantly seeing the superfluous or deficient notes, and suggesting a bass from which there was no appeal. His “Treatise on Harmony” has lately been praised, as it deserves, in Mr. Shield’s valuable “Introduction to Harmony.”

, a considerable mathematician and philosopher of France, was born at Montlugon, in the diocese of Bourges, in 1598, according to some, but in 1600 according to others. He first cultivated the mathematics and philosophy in the place of his nativity; but in 1633 he repaired to Paris, to which place his reputation had procured him an invitation. Here he became highly celebrated for his ingenious writings, and for his connections with Pascal, Des Cartes, Mersenne, and the other great men of that time. He was employed on several occasions by cardinal Richelieu; particularly to visit the sea-ports, with the title of the king’s engineer; and was also sent into Italy upon the king’s business. He was at Tours in 1640, where he married; and was afterwards made intendant of the fortifications. Baillet, in his Life of Des Cartes, says, that Petit had a great genius for mathematics; that he excelled particularly in astronomy; and had a singular passion for experimental philosophy. About 1637 he returned to Paris from Italy, when the dioptrics of Des Cartes were much spoken of. He read them, and communicated his objections to Mersenne, with whom he was intimately acquainted, and yet soon after embraced the principles of Des Cartes, becoming not only his friend, but his partisan and defender. He was intimately connected with Pascal, with whom he made at Rouen the same experiments concerning the vacuum, which Torricelli had before made in Italy; and was assured of their truth by frequent repetitions. This was in 1646 and 1647; and though there appears to be a long interval from this date to the time of his death, we meet with no other memoirs of his life. He died August 20, 1667, at Lagny, near Paris, whither he had retired for some time before his decease. Petit was the author of several works upon physical and astronomical subjects; the principal of which are, 1. “Chronological Discourse,” &c. 1636, 4to, in defence of Scaliger. 2. “Treatise on the Proportional Compasses.” 3. “On the Weight and Magnitude of Metals.” 4. “Construction and Use of the Artillery Calibers.” 5. “On a Vacuum.” 6. “On Eclipses.” 7. “On Remedies against the Inundations of the Seine at Paris.” 8. “On the Junction of the Ocean with the Mediterranean Sea, by means of the rivers Aude and Garonne.” 9. “On Comets.” 10. “On the proper Day for celebrating Easter.” 11. “On the nature of Heat and Cold,” &c.

, a singular instance of an almost universal genius, and of learning, mechanical ingenuity, and ceconomy, applied to useful purposes, was the eldest son of Anthony Petty, a clothier at Rumsey, in Hampshire, and was born May 16, 1623. It does not appear that his father was a man of much property, as he left this son none at his death, in 1641, and contributed very little to his maintenance. When young, the boy took extraordinary pleasure in viewing various mechanics at their work, and so readily conceived the natjure of their employment, and the use of their tools, that he was, at the age of twelve, able to iiandle the latter with dexterity not much inferior to that of the most expert workmen in any trade which he had ever seen. What education he had was first at the grammar-school at Rum?ey, where, according to his own account, he acquired, before the age of fifteen, a competent knowledge of the Latin, Greek, and French languages, and became master of the common rules of arithmetic, geometry, dialling, and the astronomical part of navigation. With this uncommon fund of various knowledge he removed, at the above age of fifteen, to the university of Caen in Normandy. This circumstance is mentioned among those particulars of his early life which he has given in his will, although, by a blunder of the transcriber, Oxford is put for Caen in Collir.s’s Peerage. Wood says that, when he went to Caen, “with a little stock of merchandizing which he then improved, he maintained himself there, learning the French tongue, and at eighteen years of age, the arts and mathematics.” Mr. Aubrey’s account is in these not very perspicuous words: “He has told me, there happened to him the most remarkable accident of life (which he did not tell me), and which was the foundation of all the rest of his greatness and acquiring riches. He informed me that about fifteen, in March, he went over to Caen, in Normandy, in a vessel that went hence, with a little stock, and began to play the merchant, and had so good successe that he maintained himselfe, and also educated himselfe: this I guesse was that most remarkable accident that he meant. Here he learned the French tongue, and perfected himself in Latin, and had Greeke enough to serve his turne. At Caen he studyed the arts. At eighteen, he was (I have heard him say) a better mathematician than he is now; but when occasion is, he knows how to recurre to more mathematical knowledge.” These accounts agree in the main points, and we may learn from both that he had at a very early period begun that money-making system which enabled him to realize a vast fortune. He appears to have been of opinion, that “there are few ways in which a man can be more harmlessly employed than in making money.” On his return to his native country, he speaks of being 1 preferred to^the king’s navy, but in what capacity is not known. This he attributes to the knowledge he had acquired, and his “having been at the university of Caen.” In the navy, however, before he was twenty years of age, he got together about 60l. and the civil war raging at this time, he determined to set out on his travels, for further improvement in his studies. He had now chosen medicine as a profession, and in the year 1643, visited Leyden, Utrecht, Amsterdam, and Paris, at which last city he studied anatomy, and read Vesalixis with the celebrated Hobbes, who was partial to him. Hobbes was then writing on optics, and Mr. Petty, who had a turn that way, drew his diagrams, &c. for him. While at Paris, he informed Aubrey that “at one time he was driven to a great streight for money, and told him, that he lived a week or two on three pennyworths of walnuts.” Aubrey likewise queries whether he was not some time a prisoner there. His ingenuity and industry, however, appear to have extricated him from his difficulties, for we have his own authority that; he returned home in 1646, a richer man by IQl. than he set out, and yet had maintained his brother Anthony as well as himself.

, a celebrated physician and mathematician, was born at Bautzen in Lusatia in 1525, and became a doctor and professor of medicine at Wirtemberg. He married a daughter of Melancthon, whose principles he contributed to diffuse, and whose works he published at Wirtemberg in 1601, in five volumes folio. He had an extreme ardour for study. Being for ten years in close imprisonment, on account of his opinions, he wrote his thoughts on the margins of old books which they gave him for amusement, making his ink of burnt crusts of bread, infused in wine. He died at seventy-eight, on the 25th of September, 1602. He wrote several tracts, 1. “De praecipuis divinationum generibus,” 1584, 4to. 2. Methodus curatidi morbos internes,“Francfort, 1614, 8vo. 3.” De Febribus,“1614, 4to. 4.” Vita? illustrium medicowjm.“5.” Hypotheses astronomicas.“6.” Les no, us des Monnoies, des Poids, et Mesures," 8vo. His character, as drawn by himself, is that of a man who did no injury to any one, but, on the contrary, gave all the aid in his power to all who might require it. For these things he calls God to witness.

, a learned Jesuit, born at Avignon in 1692, where he died some little time after 1770, was for a long time professor of physics and hydrography at Marseilles. His works and translations on these and similar subjects are very numerous: 1. “Elemens du Pilotages,” 1737, 12mo. 2. A translation of Maclaurin’s Fluxions, 1749, 2 vols. 4to. 3. “Pratique du pilotage,” 1749, 8vo. 4. “Theory and practice of gauging,” 8vo. 5. “Maclaurin’s Algebra translated,” 1750, 8vo. He translated also the Course of Experimental Philosophy by Desaguliers, Dyche’s Dictionary of Arts and Sciences, which was supplanted by Prevot’s “Manuel Lexique,” Ward’s Young Mathematician’s Guide, and Smith’s Optics. From the German he translated Baker’s Treatise of the Microscope, 1754. His ideas and language were clear, and he was esteemed for the mildness and agreeableness of his character, as well as for his talents.

, an able mathematician of France, aud one of the most learned astronomers of the seventeenth century, was born at Fleche, and became priest and prior of Rillie in Anjou. Coming afterwards to Paris, his superior talents for mathematics and astronomy soon made him known and respected. In 1666 he was appointed astronomer in the Academy of Sciences. And five years after, he was sent, by order of the king, to the castle of Urani burgh, built by Tycho Brahe in Denmark, to make astronomical observations there; and from thence he brought the original manuscripts written by Tycho Brahe; which are the more valuable, as they differ in many places from the printed copies, and contain a book more than lias yet appeared. These discoveries were followed by many others, particularly in astronomy: he was one of the first who applied the telescope to astronomical quadrants: he first executed the work called “La Connoissance des Temps,” which he calculated from 1679 to 1683 inclusively: he first observed the light in the vacuum of the barometer, or the mercurial phosphorus: he also first of any went through several parts of France, to measure the degrees of the French meridian, and first gave a chart of the country, which the Cassini’s afterwards carried to a great degree of perfection. He died in 1682 or 1683, leaving a name dear to his friends, and respectable to his contemporaries and to posterity. His works are: 1. “A treatise on Levelling.” 2. “Practical Dialling by calculation.” 3. “Fragments of Dioptrics.” 4. “Experiments on Running Water.” 5. “Of Measurements.” 6. “Mensuration of Fluids and Solids.” 7. ' Abridgment of the Measure of the Earth.“8.” Journey to Uraniburgh, or Astronomical Observations made in Denmark.“9.” Astronomical Observations made in divers parts of France.“10” La Connoissance des Temps," from 1679 to 1683.

, a Dutch divine and mathematician, was born at Campen in Overyssell, towards the close of the fifteenth century, and was educated at Louvain. He acquired considerable distinction by his publications against Luther, Melancthon, Bucer, and Calvin, and was much esteemed, as indeed he deserved, by popes Adrian VI. Clement VII. and Paul III for, even by the confession of the catholic historians, he was most blindly attached to the powers, privileges, and usurpations of the Romish pontiffs. He died at Utrecht, where he was provost of the church of St. John the Baptist, Dec. 29, 1542, leaving many works; the most considerable among which is entitled “Assertio Hierarchiae Ecclesiastical,” Colog. 1572, folio. His mathematical treatises, which do him most credit, were, “De Ratione Paschalis celebrationis,” 1520; “De Æquinoctiorum Solstitiorumque inventione” a defence of the Alphonsine tables, and “Astrologiae Defensio” against the pretenders to prognostics, and annual predictions.

, a French mathematician and astronomer, was born at Paris, in 1711. In 1727 he became a member of the canons regular of the congregation of France. He was intended for the church, hut the freedom of his opinions displeased his superiors, and after a few years’ study of theology, he devoted himself entirely to the sciences. In 1749 he was appointed a member of the academy of sciences in Rouen, and was elected to fill the office of astronomer, and attained to first-rate excellence. His earliest production, as an author, was the “Calculation of an Eclipse of the Moon,” on the 23d of December 1749. Lacaille had calculated it at Paris; but the calculations differed by four minutes: Lacaille., however confessed his error, and received Pingre into his friendship. In May 1753 he was elected correspondent of the Academy of Sciences at Paris, after having sent them an observation of the transit of Mercury, which he made at Rouen. He was next appointed librarian of the abbey of St. Genevieve, obtained the construction of an observatory, and was furnished by the abbot and chapter with a six-foot telescope, while he had the loan of an excellent quadrant from the academy. At the desire of Le Monnier, he next engaged in calculating “A Nautical Almanack,” to enable navigators more easily to ascertain the longitude by means of lunar observations. He calculated a table of the eclipses visible of the sun and moon from the commencement of the Christian aera to 1900, and afterwards a table of the eclipses visible from the northern pole to the equator, for a thousand years before our aera. The utility of these labours for verifying historical dates, induced the Academy of Inscriptions to insert a part of them in the forty-second volume of their Memoirs. He published the “State of the Heavens” for 1754: in this the moon’s place was calculated with the utmost exactness according to the tables of Dr. Halley for noon and midnight, with the right ascension in seconds of time twice a day. In 1753 he published “A Memoir relating to the Discoveries made in the South Sea, during the Voyages of the English and French round the World.” In 1760, Pingre left France for the island of Rodriguez, in the Indian ocean, to observe the transit of Venus, that was to take place in the following year; and on the 6th of June of that year he made his observations, from which he concluded that the parallax, of the sun was 10“. 2. At the same time the English astronomer Mason concluded, from the observations which he made at the Cape of Good Hope, that the parallax was 8”. 2. La Lande, in his “Astronomy,” published in 1764, adopted a medium between these conclusions, and supposed l,he parallax to be 9“, in which he was followed by astronomers in general, till more numerous observations, made on the transit of 1769, led to a different result. After the return of Pingre from the East, he published a description of Pekin, in which he shewed the position of that capital from the result of a number of calculations of eclipses; and ascertained its longitude by other calculations, with a degree of precision to which none of the labours of the scientific missionaries had any pretensions. In 1769 he sailed for the island of St. Domingo, on board the Isis man of war, to observe the transit of Venus, and performed the service committed to him in the most able and satisfactory manner possible. An account of this voyage, which proved of considerable importance to the science of geography, as well as astronomy, appeared in 1773, in two vols. 4to. After comparing the results of the immense number of calculations made by the observers of the transit in 1769J the sun’s parallax has been concluded to be about 8”. 6. In 1771, Pingre made another voyage, on board the Flora frigate, with a view of extending the interests of geographical and astronomical knowledge, having with him, as the companion of his pursuits, the chevalier de Borda, a celebrated engineer and geometrician. The account of their proceedings, observations, and experiments, was published in 1778, in two vols. 4to. In 1784, M. Pingre published his “Cometography, or historical and theoretical treatise on Comets,” in two vols. 4tc, which is his most considerable work, and contains calculations of the orbits of all the comets of which an. account has been preserved. After a long life, spent in the most important services to the world, he died in the month of May 179tf, leaving behind him a high character for integrity, having enjoyed the esteem of the public, as well as that of his friends. He was author of many other works besides those that have been already noticed.

, an ingenious mathematician, descended of a noble family of Languedoc, was born in 1695. In his early mathematical studies, he appears to have had no instructor; but going, in his twenty-third year, to Paris, he formed an acquaintance with Reaumur. In 1724 he was received into the academy of sciences, in the Memoirs of which he wrote a great many papers, He wrote a valuable work, entitled “The Theory of working Ships,” 1731, which procured him to be elected a member of the Royal Society of London. In 1740, the states-general of Languedoc gave him the appointment of principal engineer to the province, and also that of inspector- general of the famous canal which forms a navigable junction between the Mediterranean sea and the bay of Biscay. One of his greatest works Was that for supplying Montpelier with water from sources at the distance of three leagues. For this and other services the king honoured him with the order of St. Michael. He died in 1771, at the age of seventy-six.

, an Italian marquis, and a learned mathematician, was born at Padua in 1683. He was appointed professor of astronomy and mathematics in the university of his native city, and filled that post with high reputation. In three instances he gained prizes from the Royal Academy of Sciences, and in 1739 he was elected an associate of that body. He was also a member of the academy of Berlin, a fellow of the London Royal Society, and a member of the Institutes of Padua and Bologna, and contributed many valuable mathematical and astronomical papers to the Memoirs of these Societies. As he was celebrated for his skill and deep knowledge of hydraulic architecture, he was nominated by the Venetian government, superintendant of the rivers and waters throughout the republic; other states also applied to him for advice, in business belonging to the same science. He was sent for by pope Benedict XIV. to survey the state of St. Peter’s church at Rome, and drew up a memoir on what he conceived necessary to be done. He died at Padua in 1761, at the age of 7S. He appears to have acquired very distinguished reputation in his day, and was the correspondent of many learned contemporaries, particularly sir Isaac Newton, Leibnitz, the Bernoulli’s, Wolff, Cassini, Gravesande, Muschenbroeck, Fontenelle, and others. Nor was he more esteemed as a mathematician than as an antiquary, and the learned world is indebted to him for a valuable supplement to the collections of Graerius and Gronovius, Venice, 1737, 5 vols. fol. but these volumes are rather scarce. Among his other most valued publications are, “Exercitationes Vitruvianae, seu Commentarius Criticus de Vitruvii architectura,” Venice, 1739, 4to and “Dissertazione sopra al Tempio di Diana di Efeso,” Rome, 1742. Fabroni gives a long list of his mathematical and astronomical essays, and of the Mss. he left behind him.

, successively bishop of Rochester and Winchester, in the reign of Edward VI. was born in the county of Kent, about the year 1516, and was educated in King’s college, Cambridge, where his adversaries allow he was distinguished for his learning;. He was not only skilled in Greek and Latin, but in some of the modern languages, particularly Italian and Dutch. In early life he proved himself an able mathematician and mechanist. He constructed a clock, which pointed both to the hours of the day, the day of the month, the sign of the Zodiack, the lunar variations, and the tides, which was presented to Henry VIII. and considered by him and others as a very extraordinary performance. Heylin, who is seldom partial to the early English reformers, tells us, that he was “well-studied with the ancient fathers.”

, a great geographer, mathematician, and astronomer of antiquity, was born at Pelusium, in Egypt, about the year 70, and flourished in the reigns of Adrian and Marcus Antoninus. He tells us himself, in one place, that he made a great number of ob* servations upon the fixed stars at Alexandria, in the second year of Antoninus Pius and in another, that he observed an eclipse of the moon in the ninth year of Adrian, whence it is reasonable to conclude that this astronomer’s observations upon the heavens were made between A. D. 125, and A. D. 140. Hence appears the error of some authors in supposing that this Claudius Ptolemy was the same with the astrologer Ptolemy, who constantly attended Galba, promised Otho that he should survive Nero, and afterwards that he should obtain the empire; which is as improbable as what Isidorus, an ecclesiastical writer of the seventh century, and some modems after him, have asserted; namely, that this astronomer was one of the kings of Egypt. We know no circumstances of the life of Ptolemy but it is noted in his Canon, that Antoninus Pius reigned three-and-twenty years, which shews that himself survived him.

, a very eminent mathematician and astronomer, was born at Purbach, a town upon the confines of Bavaria and Austria, in 1423, and educated at Vienna. He afterwards visited the most celebrated universities in Germany, France, and Italy; and found a particular friend and patron in cardinal Cusa, at Rome. Returning to Vienna, he was appointed mathematical professor, in which office he continued till his death, which happened in 1461, in the 39th year of his age only, to the great loss of the learned world.

, or La Ramme'E, a celebrated French mathematician and philosopher, was born in 1515, in a village of Vermandois, in Picardy, of a family so greatly reduced by the ravages of war, that his grandfather, having lost all his possessions, was obliged to turn collier for a livelihood. His father followed husbandry, but appears to have been unable to give any education to this son, whose 4 arly years were spent in mean occupations. At length he obtained the place of servant in the college of Navarre, at Paris, where he picked up the rudiments of learning, and became acquainted with the logic of Aristotle. All his leisure time he devoted to study, so that what is related in the first Scaligerana of his living to nineteen without learning to read, and of his being very dull and stupid, is totally inconsistent with the truth. On the contrary, his talents and perseverance at last procured him to be regularly educated in the college, and having finished classical learning and rhetoric, he went through a course of philosophy, which took him up three years and a half. The thesis which he made for his master’s degree denied the authority of Aristotle, and this he maintained with great ability, and very ingeniously replied to the objections of the professors. This success inclined him to examine the doctrine of Aristotle more closely, and to combat it vigorously: but he confined himself principally to his logic. All this, however, was little less than heresy; and the two first books he published, the one entitled “Institutiones Dialecticae,” the other “Aristotelicse Animadversiones,” so irritated the professors of the university of Paris, that, besides many effusions of spleen and calumny, they prosecuted this anti- peripatetic before the civil magistrate, as a man who was at war with religion and learning. The cause was then carried before the parliament of Paris, but his enemies dreading either the delay or the fairness of a trial there, brought it before the king, Francis I. who ordered that Ramus, and Antony Govea, who was his principal adversary, should chuse two judges each, to pronounce on the controversy after they should have ended their disputation; while he himself appointed an umpire. Ramus, in obedience to the king’s orders, appeared before the five judges, though three of them were his declared enemies. The dispute lasted two days; and Govea had all the advantage he could desire, Ramus’s books being prohibited in all parts of the kingdom, and their author sentenced not to write or teach philosophy any longer. This sentence, which elated his enemies beyond all bounds of moderation, was published in Latin and French in all the streets of Paris, and in all parts of Europe, whither it could be sent. Plays were acted with great pomp, in which Ramus was ridiculed in various ways amidst the applauses and acclamations of the Aristotelians. This happened in 1543. The year after, the plague made great havoc in Paris, and forced most of the students to quit the university, and cut off several of the professors. On their return, Ramus, being prevailed upon to teach in it, soon drew together a great number of auditors, and through the patronage and protection of the cardinal of Lorrain he obtained in 1547 from Henry II. the liberty of speaking and writing, and the royal professorship of philosophy aad eloquence in 1551. The parliament of Paris had, before this, maintained him in the liberty of joining philosophical lectures to those of eloquence; and this arret or decree had put an end to several prosecutions, which Ramus and his pupils had suffered. As soon as he was made regius professor, he was fired with new zeal for improving the sciences; and was extremely laborious and active on this occasion, notwithstanding the machinations of his enemies. He bore at that time a part in a very singular aflair, which deserves to be mentioned. About 1550 the royal professors corrected, among other abuses, that which had crept into the pronunciation of the Latin tongue. Some of the clergy followed this regulation; but the Sorbonnists were much offended at it as an innovation, and defended the old pronunciation with great zeal. Things at length were carried so far, that a clergyman who had a good living was ejected from his benefice for having pronounced qm’squis, quanquaw, according to the new way, instead of kiskis, kankam, according to the old. The clergyman applied to the parliament; and the royal professors, with Ramus among them, fearing he would fall a victim to the credit and authority of the faculty of divines, for presuming to pronounce the Latin tongue according to their regulations, thought it incumbent on them to assist him. Accordingly they went to the court of justice, and represented in such strong terms the indignity of the prosecution, that the person accused was acquitted, and the pronunciation of Latin recovered its liberty.

, a French mathematician and astronomer, was born at Montpellier, Sept. 1, 1722, and from his earliest years became attached to the study of the sciences, particularly mathematics. When very young, he was appointed secretary to the Montpellier academy of sciences, which office he held until all academies in France were dissolved. In the course of his office, he published two volumes of their “Memoirs/' and was preparing a third at the time of the revolution. He also contributed many valuable papers himself on philosophical and mathematical subjects, and furnished some articles for the” Dictionnaire Encyclopedique.“The comet of 1759, the subject of so much prediction and expectation, so far altered his pursuits as to make them afterwards centre in astronomy. He was for a long time considered as the only good astronomer at Montpellier, and made many useful observations, particularly on the famous transit of Venus in 1761. Such was his zeal, that when old age prevented him from making observations with his usual accuracy, he maintained a person for that purpose at his own expence as keeper of the observatory at Montpellier. On the death of his father, in 1770, he became counsellor of the court of aids, and was often the organ of that company on remarkable occasions. In 1793, when such members of the old academy as had esdaped the murderous period of the revolution attempted to revive it under the name of” Societe* Libre des sciences et belles lettres de Montpeliier,“De Ratte was chosen president. Some volumes of their transactions have been published under the title of” Bulletins." When the national institute was formed, De Ratte was chosen an associate, and also a member of other learned societies in France, and at last one of the legion of honour. He died Aug. 15, 1805, aged eighty-three. His astronomical observations have been collected for publication by M. De Flaugergues, an astronomer of Viviers; but our authority does not mdntipn whether they haV yet appeared.

, a learned physician and mathematician, was born of a good family in Wales, and flourished in the reigns of Henry VIII., Edward VI., and Mary. There is no account of the exact time of his birth, though it must have been early in the sixteenth century, as he was entered of the university of Oxford about 1525, where he was elected fellow of All Souls college in 1531, being then B. A. but Wood is doubtful as to the degree of master. Making physic his profession, he went to Cambridge, where he was honoured with the degree of doctor in that faculty, in 1545, and highly esteemed by all that knew him for his great knowledge in several arts and sciences. He afterwards returned to Oxford, where, as he had done before he went to Cambridge, he publicly taught arithmetic, and other branches of the mathematics, with great applause. It seems he afterwards repaired to London, and it has been said he was physician to Edward VI. and Mary, to which princes he dedicates some of his books; and yet he ended his days in the King’s Bench prison, Southwark, where he was confined for debt, in 155.S, at a very immature age. Pits gives him a very high character, as excelling in every branch of knowledge, philosophy, polite literature, astronomy, natural history, &c. &c. And Tanner observes that he had a knowledge of the Saxon language, as appears from his marginal notes on Alexander Essebiens, a ms. in Corpus Christi college, Cambridge.

In 1736, he resigned this office, and, accompanied by Dr. John Stewart, afterwards professor of mathematics in Marischal college, and author of a “Commentary on Newton’s Quadrature of Curves,” on an excursion to England. They visited together London, Oxford, and Cambridge, and were introduced to the acquaintance of many persons of the first literary eminence. His relation to David Gregory procured him a ready access to Martin Folkes, whose house concentrated the most interesting objects which the metropolis had to offer to his curiosity. At Cambridge he saw Dr. Bentley, who delighted him with his learning, and amused him with his vanity; and enjoyed repeatedly the conversation of the blind mathematician Saunderson; a phenomenon in the history of the human mind, to which he has referred more than once in his philosophical speculations. With the learned and amiable Dr. Stewart he maintained an uninterrupted friendship till 1766, when Mr. Stewart died of a malignant fever. His death was accompanied with circumstances deeply affecting to Dr. Reid’s sensibility; the same disorder proving fatal to his wife and daughter, both of whom were buried with him the same day in the same grave.

, an eminent astronomer and mathematician, was born at Salfeldt in Thuringia, a province in Upper Saxony, the llth of October, 1511. H^ studied mathematics under James Milichi at Wittemberg, in which university he afterwards became professor of those sciences, which he taught with great applause. After writing a number of useful and learned works, he died February 19, 1553, at 42 years of age only. His writings are chiefly the following: 1. “Theorize novae Planetarum G. Purbachii,” augmented and illustrated with diagrams and Scholia in 8vo, 1542; and again in 1580. In this work, among other things worthy of notice, he teaches (p. 75 and 76) that the centre of the lunar epicycle describes an ovalfgure in each monthly period, and that the or hit of Mercury is also of the same oval figure. 2. “Ptolomy’s Almagest,” the first book, in Greek, with a Latin version, and Scholia, explaining the more obscure passages, 1549, 8vo. At the end of p. 123 he promises an edition of Theon’s Commentaries, which are wry useful for understanding Ptolomy’s meaning; but his immature death prevented Reinhold from giving this and other works which he had projected. 3. “Prutenicse Tabulae Ccelestiurn Motuum,” 1551, 4to; again in 1571; and also iii 1585. Reinhold spent seven years labour upon this work, in which he was assisted by the munificence of Albert, duke of Prussia, from whence the tables had their name. Reinhold compared the observations of Copernicus with those of Ptolomy and Hipparchus, from whence he constructed these new tables, the uses of which he has fully explained in a great number of precepts and canons, forming a complete introduction to practical astronomy. 4. “Primus liber Tabularum Directionum” to which are added, the “Canon Fcecundus,” or Table of Tangents, to every minute of the quadrant and New Tables of Climates, Parallels, and Shadows, with an Appendix containing the second Book of the Canon of Directions; 1554, 4to. Reinhold here supplies what was omitted by Regiomontanus in his Table of Directions, &c.; shewing the finding of the sines, and the construction of the tangents, the sines being found to every minute of the quadrant, to the radius 10,000,000; and he produced the Oblique Ascensions from 60 degrees to the end of the quadrant. He teaches also the use of these tables in the solution of spherical problems.

Reinhold left a son, named also Erasmus after himself, an eminent mathematician and physician at Salfeldt. He wrote a small work in the German language, on Subterranean Geometry, printed in 4to at Erfurt, 1575. He wrote also concerning the New Star which appeared in Cassiopeia in 1572; with an Astrological Prognostication, published in 1574, in the German language.

, a German lawyer and mathematician, was born April 19, 1635, at Schleusingen in the county of Henneberg, and was educated at Leipsic and Leyden. He was afterwards appointed preceptor to the young prince of Gotha, then professor of mathematics at Kiel, 1655, and some years after professor of law in the same place, where he died Nov. 22, 1714, being then counsellor to the duke of Saxe Gotha, and member of the Royal Academy of Sciences at Berlin. Reyher translated Euclid’s works into German with algebraical demonstrations, and wrote several works in Latin, among which, that entitled “Mathesis Biblica,” and a very curious Dissertation on the Inscriptions upon our Saviour’s cross and the hour of his crucifixion, are particularly esteemed.

, commonly called Father Reyneau, a noted French mathematician, was born at Brissac, in the province of Anjou, in 1656. At twenty years of age he entered himself in the congregation of the Oratory at Paris, and was soon after sent, by his superiors, to teach philosophy at Pezenas, and then at Toulon. His employment requiring some acquaintance with geometry, he contracted a great affection for this science, which he cultivated and improved to so great an extent, that he was called to Angers in 1683, to fill the mathematical chair; and the academy of Angers elected him a member in 1694.

, a celebrated German astronomer and mathematician, was born at Feldkirk in Tyrol, February 15, 1514. After imbibing the elements of the mathematics at Zurick with Oswald Mycone, he went to Wittemberg, where he diligently cultivated that science, and was made master of philosophy in 1535, and professor in 1537. He quitted this situation, however, two years after, and went to Fruenburg to profit by the instructions of the celebrated Copernicus, who had then acquired great fame. Rheticus assisted this astronomer for some years, and constantly exhorted him to perfect his work “De Revolutionibus,” which he published after the death of Copernicus, viz. in 1543, folio, atNorimberg, together with an illustration of the same, dedicated to Schoner. Here too, to render astronomical calculations more accurate, he began his very elaborate canon of sines, tangents and secants, to 15 places of figures, and to every 10 seconds of the quadrant, a design which he did not live quite to complete. The canon of sines however to that radius, for every 10 seconds, and for every single second in the first and last degree of the quadrant, computed by him, was published in folio at Francfort, 1613, by Pitiscus, who himself added a few of the first sines computed to 22 places of figures. But the larger work, or canon of sines, tangents, and secants, to every 10 seconds, was perfected and published after his death, viz. in 1596, by his disciple Valentine Otho, mathematician to the electoral prince palatine; a particular account and analysis of which work may be seen in the Historical Introduction to Dr. Button’s Logarithms.

, an able mathematician, was born in 1707 at Castel Franco, in the territory of Treviso, and in 1726 entered among the Jesuits, and taught mathematics at Bologna, till the suppression of his order in 1773. At this period he returned to his native place, and died there of a cholic, in 1775, aged sixty-eight, leaving some good mathematical works among others, a large treatise on the “Integral Calculus,” 3 vols. 4to. He had been much employed in hydraulics, and such was the importance of his services in this branch, that the republic of Venice ordered a gold medal, worth a thousand livres, to be struck in honour of him, in 1774.

, a learned Italian astronomer, philosopher, and mathematician, was born in 1598, at Ferrara, a city in Italy, in the dominions of the pope. At sixteen years of age he was admitted into the society of the Jesuits, and the progress he made in every branch of literature and science was surprising. He was first appointed to teach rhetoric, poetry, philosophy, and scholastic divinity, in the Jesuits’ colleges at Parma and Bologna; yet applied himself in the mean time to making observations in geography, chronology, and astronomy. This was his natural bent, and at length he obtained leave from his superiors to quit all other employment, that he might devote himself entirely to those sciences.

, in German Sterck, an eminent Flemish philosopher and mathematician, was born at Antwerp, and first studied in the emperor Maximilian the First’s palace, and afterwards at the university of Lou vain, where he acquired the learned languages, philosophy, and the mathematical sciences. He became a public professor in that university, and taught various sciences; and in 1528 went into Germany, and taught the mathematical sciences and the Greek tongue in various seminaries of that country, and afterwards at Parig, Orleans, and Bourdeaux, and other places. He died about 1536. Among his most esteemed works were, “De Ratione Studii,” Antwerp, 1529, in which are many particulars of his own studies; various treatises on grammar; Dialectica, et Tabulae Dialectics,“Ley den, 1547;” De conscribendis Epistolis Lib.“” Rhetoricae, et quat ad earn spectant“” Sententiae“” Sphiera, sive Institutionum Astronomicarum, Lib. III.,“Basil, 1528, 8vo;” Cosmographia“” Optica“” Chaos Mathematicum“”Arithraetica" all which were collected and published at Leyden, in 1531.

, an American philosopher and mathematician, was born in Pennsylvania in 1732. By the dint of genius and application, he was enabled to mingle the pursuits of science with the active employments of a farmer and watch-maker. The latter of these occupations he filled with unrivalled eminence among his countrymen. In 17t9 he was with others invited by the American Philosophical Society to observe the transit of Venus, when he particularly distinguished himself by his observations and calculations. He afterwards constructed an observatory, where he made such valuable discoveries, as tended to the general diffusion of science. After the American war, as he was a strenuous advocate for independence, he successively filled the offices of treasurer of the state of Pennsylvania, and director of the national mint; in the first of which he manifested incorruptible integrity, and in the last, the rare talent of combining theories in such a way as to produce correct practical effects. He succeeded Dr. Franklin in the office of president of the American Philosophical Society; but towards the close of his days he withdrew from public life, and spent his time in retirement. After a very severe illness, but of no long continuance, he died July 10, 1796, about the age of 64. He had the degree of LL. D. conferred upon him. To the “Transactions” of the American Philosophical Society he contributed several excellent papers, chiefly on astronomical subjects.

, an eminent French mathematician, was born in 1602, at Roberval, a parish in the diocese of Beauvais. He was first professor of mathematics at the college of Maitre-Gervais, and afterwards at the college-royal. A similarity of taste connected him with Gassendi andMorin; the latter of whom he succeeded in the mathematical chair at the royal college? without quitting, however, that of Ramus. Roberval made experiments on the Torricellian vacuum: he invented two new kinds of balance, one of which was proper for weighing air; and made many other curious experiments. He was one of the first members of the ancient academy of sciences of 1666; but died in 1675, at seventy-thre years of age. His principal works are, 1. “A treatise on Mechanics.” 2. A work entitled “Aristarchus Samos.” Several memoirs inserted in the volumes ofl the academy of sciences of 1666; viz. 1. Experiments concerning the pressure of the air. 2. Observations on the composition of motion, and on the tangents of curve lines. 3. The recognition of equations. 4. The geometrical resolution of plane and cubic equations. 5. Treatise on indivisibles. 6. On the Trochoicl, or Cycloid. 7. A letter to father Mersenne. 8. Two letters from Torricelli. 9. A new kind of balance. Robervallian Lines were his, for the transformation of figures. They bound spaces that are infinitely extended in length, which are nevertheless equal to other spaces that are terminated on all sides. The abbot Gallois, in the Memoirs of the Royal Academy, anno 1693, observes, that the method of transforming figures, explained at the latter end of RobervaPs treatise of indivisibles, was the same with that afterwards published by James Gregory, in his Geometria Ujiiversalis, and also by Barrow in his LectiotteV Geometric^; and that, by a letter of Torricelli, it appears, that Roberval was the inventor of this manner of transforming figures, by means of certain lines, which Torricelli therefore called Robervaliian Lines. He adds, that it is highly probable, that J. Gregory first learned the method in the journey he made to Padua in 1668, the method itself having been known in Italy from 164-6, though the book was not published till 1692. This account David Gregory has endeavoured to refute, in vindication of his uncle James. His answer is inserted in the Philos. Trans, of 1694, and the abbot rejoined in the French Memoirs of the Academy of 1703.

, an English mathematician of great genius and eminence, was born at Bath in Somersetshire in 1707. His parents, who were quakers, were of low condition, and consequently neither able, from their circumstances, nor willing from their religious profession, to have him much instructed in that kind of learning which they are taught to despise as human. Yet he made an early and surprising progress in various branches of science and literature, in the mathematics particularly; and his friends, being desirous that he might continue his pursuits, and that his merit might not be buried in obscurity, wished that he could be properly recommended to teach this science in London. Accordingly, a specimen of his abilities was shewn to Dr. Pemberton, the author of the “View of Sir Isaac Newton’s Philosophy;” who conceiving a good opinion of the writer, for a farther trial of his proficiency, sent him some problems, which Robins solved very much to his satisfaction. He then came to London, where he confirmed the opinion which had been formed of his abilities and knowledge.

, an English mathematician, was born in Staffordshire about the close of the 15th century, as he was entered a student at Oxford in 1516, and was in 1620 elected a fellow of All Souls college, where he took his degrees in arts, and was ordained. But the bent of his genius lay to the sciences, and he soon made such a progress, says Wood, in “the pleasant studies of mathematics and astrology, that he became the ablest person in his time for those studies, not excepted his friend Record, whose learning was more general. At length, taking the degree of B. D. in 1531, he was the year following made by king Henry the VIIIth (to whom he was chaplain) one of the canons of his college in Oxon, and in December 1543, canon of Windsor, and in fine chaplain to queen Mary, who had him in great veneration for his learning. Among several things that he hath written relating to astrology (or astronomy) I find these following: `De culminatione Fixarum Stellarum,‘ &c.; `De ortu et occasu Stellarum Fixarum,’ &c.; ‘Annotationes Astrologicæ,’ &c. lib. 3;‘ `Annotationes Edwardo VI.;’ `Tractatus de prognosticatione per Eclipsin.‘ All which books, that are in ms. were some time in the choice library of Mr. Thomas Allen of Glocester Hall. After his death, coming into the hands of Sir Kenelm Digby, they were by him given to the Bodleian library, where they yet remain. It is also said, that he the said Robyns hath written a book entitled `De Portentosis Cometis;’ but such a thing I have not yet seen, nor do I know any thing else of the author, only that paying his last debt to nature the 25th of August 1558, he was buried in the chapel of St. George, at Windsore.” This treatise “De Portentosis Cometis,” which Wood had not seen, is in the royal library (12 B. xv.); and in the British museum (Ayscough’s Cat.) are other works by Robins; and one “De sterilitatem generantibus,” in the Ashmolean museum.

, an eminent natural philosopher and mathematician, was born at Boghall, in the county of Stirling, in Scotland, in 1739. His father, a merchant in Glasgow, having, by a course of successful industry, acquired considerable property, employed it in the purchase of an estate to which he retired during the latter part of his life. His son was educated at Glasgow, and before entering on his nineteenth year had completed his course of study at that university, but had manifested a peculiar predilection for the mathematics. Though he went deep into algebra and fluxions, yet he derived frm the celebrated Simson, and always retained, a disposition to prefer the more accurate though less comprehensive system of ancient geometry. The first thing which is said to have obtained him the notice of that eminent professor, was his having produced a geometrical solution of a problem which had been given out to the class in an algebraic form.

, or Rømer (Olaus), a Danish astronomer and mathematician, was born at Arhusen in Jutland in 1644; and, at eighteen, was sent to the university of Copenhagen. He applied himself assiduously to the study of mathematics and astronomy, and became such an adept in those sciences, that, when Picard was sent by Lewis XIV. in 1671, to make observations in the North, he was so pleased with him, that he engaged him to return with him to France, and had him presented to the king, who ordered him to teach the dauphin mathematics, and settled a pension on him. He was joined with Picard and Cassini, in making astronomical observations; and, in 1672, was admitted a member of the academy of sciences. During the ten years he resided at Paris, he gained a prodigious reputation by his discoveries; yet is said. to have complained afterwards that his coadjutors ran away with the honour of many things which belonged to him. In 1681, Christian V. king of Denmark called him back to his own country, and made him professor of astronomy at Copenhagen. He employed him also in reforming the coin and the architecture, in regulating the weights and measures, and in measuring the high roads throughout the kingdom. Frederic IV. the successor of Christian, shewed the same favour to Roemer, and conferred new dignities on him. He was preparing to publish the result of his observations, when he died Sept. 19, 1710, aged 66; but some of his observations, with his manner of making those observations, were published in 1735, under the title of “Basis Astronomise,” by his scholar Peter Horrebow, then professor of astronomy at Copenhagen. Roemer was the first who found out the velocity with which light moves, by means of the eclipses of Jupiter’s satellites. He had observed for many years that, when Jupiter was at his greatest distance from the earth, where he could be observed, the emersions of his first satellite happened constantly 15 or J 6 minutes later than the calculation gave them. Hence he concluded that the light reflected by Jupiter took up this time in running over the excess of distance, and consequently that it took up 16 or 18 minutes in running over the diameter of the earth’s orbit, and 8 or in coming from the sun to us, provided its velocity was nearly uniform. This discovery had at first many opposers but it was afterwards confirmed by Dr. Bradley in the most ingenious and beautiful manner.

, a French mathematician, was born at Ambert, a small town in Auvergne, April 21, 1652. His first studies and employments were under notaries and attorneys occupations but little suited to his genius, and therefore he quitted them and went to Paris in 1675, with no other recommendation than that of writing a fine hand, and subsisted by giving lessons in penmanship. But as it was his inclination for the mathematics which had drawn him to that city, he attended the masters in this science, and soon became one himself. Ozanam proposed a question in arithmetic to him, to which Rolle gave a solution so clear and good, that the minister Colbert made him a handsome gratuity, which at last became a fixed pension. He then abandoned penmanship, and gave himself up entirely to algebra and other branches of the mathematics. His conduct in life gained him many friends; in which his scientific merit, his peaceable and regular behaviour, with an exact and scrupulous probity of manners, were conspicuous. He was chosen a member of the ancient academy of sciences in 1685, and named second geometrical-pensionary on its renewal in 1699; which he enjoyed till his death, which happened July 5, 1719, at the age of 67.

, a worthy French priest, a doctor in divinity and member of the academy of Besançon, was born at Quingey, Feb. 7, 1716. Of his early history we find no account, previous to his appearing as an author in 1767, when he published, 1. “Traité elementaire de Morale,” 2 vols. 12mo, which had the year before gained the prize offered by the academy of Dijon, and was thought a performance of very superior merit. 2. “La Morale evangelique, comparée à celle des differentes sectes de religion et de philosophie,” 1772, 2 vols. 12mo. 3. “Traité sur le Providence,” which was read in ms. and approved by cardinal de Choiseul, previous to its being published. 4. “L'Esprit des Peres, comparé aux plus celebres ecrivains, sur les matieres interessantes de la philosophie et de la religion,” 1791, 3 vols. 12mo. In this work he attempts to prove that the fathers are unanimous in all the essential doctrines of religion. M. Rose was also a good mathematician, and in 1778 sent to the academy of sciences at Paris, a “Memoire sur une courbe à double courbure,” of which it is sufficient to say that it was approved by La Place, and, printed in 1779 at Besançon. In the same year he sent to the same academy, a memoir, which had been read in that of Besançon, relative to “the passage of Venus over the Sun.” In 1791 he published a small work on “the organization of the Clergy,” and left some valuable papers in manuscript. He appears to have escaped the dangers of the revolution, although an orthodox and pious priest. He died August 12, 1805, and the tears of the poor spoke his eulogium.

, an ingenious English mathematician and philosopher, was fellow of Magdalen college, Cambridge, and afterwards rector of Anderby in Lincolnshire, in the gift of that society. He was a constant attendant at the meetings of the Spalding Society, and was a man of a philosophical turn of mind, though of a cheerful and companionable disposition. He had a good genius for mechanical contrivances in particular. In 1738 he printed at Cambridge, in 8vo, “A Compendious System of Natural Philosophy,” in 2 vols. 8vo; a very ingenious work, which has gone through several editions. He had also two pieces inserted in the Philosophical Transactions, viz. I. “A Description of a Barometer wherein the Scale of Variation may be increased at pleasure;” vol. 38, p. 39. And 2. “Directions for making a Machine for finding the Roots of Kquations universally, with the manner of using it;” vol. 60, p. 240. Mr. Rowning died at his lodgings in Carey -street, near Lincoln’s-Inn Fields, the latter end of November 1771, at the age of seventy-two. Though a very ingenious and pleasant man, he had but an unpromising and forbidding appearance: he was tall, stooping in the shoulders, and of a sallow down-looking countenance*.

Prince Rupert, who never was married, left a natural son, usually called Dudley Rupert, by a daughter of Henry Bard viscount Beilemont, though styled in his father’s last will and testament Dudley Bard. He was educated at Eton school, and afterwards placed under the care of that celebrated mathematician sir Jonas Moore at the Tower. Here he continued till the demise of the prince, when he made a tour into Germany to take possession of a considerable fortune which had been bequeathed to him. He was very kindly received by the Palatine family, to whom he had the honour of being so nearly allied. In 1686 he made a campaign in Hungary, and distinguished himself at the siege of Buda, where he had the misfortune to lose his life, in the month of July or August, in a desperate attempt made by some English gentlemen upon the fortifications of that city, in the twentieth year of his age; and, though so young, he had signalized his courage in such an extraordinary manner, that his death was exceedingly regretted.

Father Fulgentio, his friend and companion, who was a man of great abilities and integrity, and is allowed on all hands to have drawn up Paul’s life with great judgment and impartiality, observes, that, notwithstanding the animosity of the court of Rome against him, the most eminent prelates of it always expressed the highest regard for him; and Protestants of all communities have justly supposed him one of the wisest and best men that ever lived. ther Paul,“says sir Henry Wotton,” was one of the humblest things that could be seen within the bounds of humanity; the very pattern of that precept, quanta doctior, tanto submissior, and enough alone to demonstrate, that knowledge well digested non wflat. Excellent in positive, excellent in scholastical and polemical, divinity: a rare mathematician, even in the most abstruse parts thereof, as in algebra and the theoriques; and yet withal so expert in the history of plants, as if he had never perused any book but nature. Lastly, a great canonist, which was the title of his ordinary service with the state; and certainly, in the time of the pope’s interdict, they had their principal light from him. When he was either reading or writing alone, his manner was to sit fenced with a castle of paper about his chair and over his head; for he was of our lord St. Alban’s opinion, that all air is predatory, and especially hurtful, when the spirits are most employed. He was of a quiet and settled temper, which made him prompt in his counsels and answers; and the same in consultation which Themistocles was in action, ayro-xE&aÆiv ivavoTarogj as will appear unto you in a passage between him and the prince of Conde. The said prince, in a voluntary journey to Home, came by Venice, where, to give some vent to his own humours, he would often divest himself of his greatness; and after other less laudable curiosities, not long before his departure, a desire took him to visit the famous obscure Servite. To whose cloyster coming twice, he was the first time denied to be within; and at the second it was intimated, that, by reason of his daily admission to their deliberations in the palace, he could not receive the visit of so illustrious a personage, without leave from the senate, which he would seek to procure. This set a greater edge upon the prince, when he saw he should confer with one participant of more than monkish speculations. So, after Jeave gotten, he came the third time; and then, besides other voluntary discourse, desired to be told by him, who was the true unmasked author of the late Tridentine History? To whom father Paul said, that he understood he was going to Rome, where he might learn at ease, who was the author of that book."

A blind man moving in the sphere of a mathematician, seems a phenomenon difficult to be accounted for, and has excited the admiration of every age in which it has appeared. Tuliy mentions it as a thing scarce credible in his own master in philosophy, Diodotus, that “he exercised himself in that science with more assiduity after he became blind; and, what he thought almost impossible to be done without sight, that he described his geometrical diagrams so expressly to his scholars, that they could draw every line in its proper direction.” Jerome relates a more remarkable instance in Didymus of Alexandria, who, “though blind from his infancy, and therefore ignorant of the very letters, appeared so great a miracle to the world, as not only to learn logic, but geometry also, to perfection, which seems the most of any thing to require the help of sight.” But, if we consider that the ideas of extended quantity, which are the chief objects of mathematics, may as well be acquired from the sense of feeling, as that of sight; that a fixed and steady attention is the principal qualification for this study; and that the blind are by necessity more abstracted than others, for which reason Democritus is said to have put out his eyes, that he might think more intensely; we shall perhaps be of opinion, that there is no other branch of science better adapted to their circumstances.

, a French mathematician, was born in 165S* at Courtuson, in the principality of Orange. He was educated by his father, and was at a very early age made a minister at Eure in Dauphiny. But he was compelled to retire to Geneva in 1633, in consecpence of having given offence in a sermon, which he afterwards heightened at Berne by preaching against some of the established doctrines of the church. He then withdrew to Holland, but was so ill received by his brethren, that he determined to turn Roman catholic; with this design, in 1690 he went to Paris, and made an abjuration of his supposed errors under the famous Bossuet, rather, it is believed, to have an opportunity of pursuing his studies unmolested at Paris than from any motives of conscience or mental conviction. After this he had a pension from the king, and was admitted a member of the academy of sciences in 1707, as a geometrician. The decline of Saurin’s life was spent in the peaceable prosecution of his mathematical studies, occasionally interrupted by literary controversies with Rousseau and others. He was a man of a daring and impetuous spirit, and of a lofty and independent mind. Saurin died at Paris in 1737. Voltaire undertook the vindication of his memory, but has not been sufficiently successful to clear it from every unfavourable impression. It was even said he had been guilty of crimes, by his own confession, that ought to have been punished with death.

Sauvages was much loved by his pupils, to whom he communicated freely all that he knew, and received with equal readiness whatever information any one was enabled to give him. He was an able mathematician, an. accurate observer of phenomena, and ingenious in devising experiments; but had too much bias to systems, so that he did not always consult facts uninfluenced by prepossession. He was a member of the most learned societies of Europe, viz. of the Royal Society of London, of those of Berlin, Upsal, Stockholm, and Montpellier, of the Academy “Naturae Curiosorum,” of the Physico-Botanical Academy of Florence, and of the Institute of Bologna. He obtained the prizes given by many public bodies to the best essays oil given subjects; and a collection of these prize-essays was published at Lyons in 1770, in two volumes, with the title of.“Chef d'Œuvres de M. de Sauvages.”

, an eminent French mathematician, was born at La Fleche, March 24, 1653. He was totally dumb till he was seven years of age; and ever after was obliged to speak very slowly and with difficulty. He very early discovered a great turn for mechanics, and when sent to the college of the Jesuits to learn polite literature, made very little progress, but read with greediness books of arithmetic and geometry. He was, however, prevailed on, to go to Paris in 1670, and, being intended for the church, applied himself for a time to the study of philosophy and theology; but mathematics was the only study he cultivated with any success; and during his course of philosophy, he learned the first six books of Euclid in the space of a month, without the help of a master.

In 1681 he was sent with M, Mariotte to Chantilli, to make some experiments upon the waters there, in which he gave great satisfaction. The frequent visits he made to this place inspired him with the design of writing a treatise on fortification; and, in order to join practice with theory, he went to the siege of Mons in 1691, where he continued all the while in the trenches. With the same view also he visited all the towns of FUnders; and on his return he became the mathematician in ordinary at the court, with a pension for life. In 1680 he had been chosen to teach mathematics to the pages of the Dauphiness. In 1686 he was "appointed mathematical professor in the Royal College. And in 1696 admitted a member of the Academy of Sciences, where he was in high esteem with the members of that society. He became also particularly acquainted with the prince of Conde, from whom he received many marks of favour and affection. In 1703, M. Vanban having been made marshal of France, he proposed Sauveur to the king as his successor in the office of examiner of the engineers; to which the king agreed, and honoured him with a pension, which our author enjoyed till his death, winch happened. July 9, 1716, in the sixty-fourth year of his age.

Sauveur was of an obliging disposition, and of a good temper; humble in his deportment, and of simple manners. He was twice married. The first time he took a precaution more like a mathematician than a lover; for he would not meet the lady till he had been with a notary to have the conditions he intended to insist on, reduced into a written form for fear the sight of her should not leave him enough master of himself. He had children by both his wives anJ by the latter a son, who, like himself, was dumb for the first seven years of his life.

, an eminent physician and mathematician, was born about 1616. After the usual classical education he was admitted of Caius college, Cambridge, in 1632, and took his first degree in arts in 1636. He was then elected to a fellowship, and commencing A. M. in 1640, he took pupils. In the mean time, intending to pursue medicine as his profession, he applied himself to all the preparatory studies necessary for that art. Mathematics constituted one of these studies: and the prosecution of this science having obtained him the acquaintance of Mr. (afterwards bishop) Seth Ward, then of Emanuel college, they mutually assisted each other in their researches. Having met with some difficulties in Mr. Ougbtred’s “Clavis Mathematical which appeared to them insuperable, they made a joint visit to the author, then at his living of Aldbury, in Surrey. Mr. Oughtred (See Oughtred) treated them with great politeness, being much gratified to see these ingenious young men apply so zealously to these studies, and in a short time fully resolved all their questions. They returned to Cambridge complete masters of that excellent treatise, and were the first that read lectures upon it there. In the ensuing civil wars, Mr. Scarborough became likewise a joint sufferer with his fellow-student for the royal cause, being ejected from his fellowship at Caius. Upon this reverse of fortune he withdrew to Oxford, and entering himself at Merton college, was incorporated A.M. of that university, 23d of June, 1646. The celebrated Dr. Harvey was then warden of that college, and being employed in writing his treatise” De Generatione Animaiium,“gladly accepted the assistance of Mr. Scarborough. The latter also became acquainted with sir Christopher Wren, then a gentleman commoner of Wadham college, and engaged him to translate” Oughtred’s Geometrical Dialling" into Latin, which was printed in 1649.

, a considerable mathematician and astronomer, was born at Mundeilheitn in Schwaben, in 1575. He entered into the society of the Jesuits whenhe was twenty; and afterwards taught the Hebrew tongue and the mathematics at Ingolstadt, Friburg, Brisac, and Rome. At length, he became rector of the college of the Jesuits at Neisse in Silesia, and confessor to the archduke Charles. He died in 1650, at the age of seventylive.

, a noted German philosopher and mathematician, was born at Carolostadt in 1477, and died in 1547, aged seventy. From his uncommon acquirements, he was chosen mathematical professor at Nuremberg when he was but a young man. He wrote a great many works, and was particularly famous for his astronomical tables, which he published after the manner of those of Regiomontanus, and to which he gave the title of Resolute, on account of their clearness. But, notwithstanding his great knowledge, he was, after the fashion of the times, much addicted to judicial astrology, which he took great pains to improve. The list of his writings is chiefly as follows: I. “Three Books of Judicial Astrology.” 2. “The astronomical tables named Resolutoj.” 3. “De Usu Globi Stelliferi; De Compositione Giobi Ccelestis De Usu Globi Terrestris, et de Compositione ejusdem.” 4. “Æquatorium Astronomicum.” 5. “Libeilus de Distantiis Locorum per Instrumenturn et Numeros investigandis.” 6. “De Compositione Torqueti.” 7. “In Constructionem et Usum Rectangnli sive Radii Astronomic! Annotationes.” S. “Horarii Cylindri Canones.” 9. “Planisphserium, sen Meteoriscopium.” 10. “Organum Uranicum.” 11.“Instrumentum Impedimentorum Luna3.” All printed at Nuremberg, in 1551, folio. Of these, the large treatise of dialling rendered him more known in the learned world than all his other works besides, in which he discovers a surprising genius and fund of learning of that kind; but some have attributed this to his son.

, an ancient mathematician and geographer, was a native of Caryanda, in Caria, and is noticed by Herodotus, and by Suidas, who, however, has evidently confounded different persons of the same name. There is a Periplus which still remains, bearing the name of Scylax, and which is a brief survey of the countries along the shores of the Mediterranean and Euxine seas, together with part of the western coast of Africa surveyed by Hanno; but it seems doubtful to what Scylax it belongs. This Periplus has come down to us in a corrupted state: it was first published from a palatine ms by Hoeschelius and others in 1600. It was afterwards edited by Isaac Vossius in 1639, by Hudson in 1698, and by Gronovius in 1700.

, an eminent mathematician, mechanist, and astronomer, was descended from an ancient family at Little-Horton, near Bradford, in the West Riding of Yorkshire, where he was born about 1651. He was at first apprenticed to a merchant at Manchester, but his inclination and genius being decidedly for mathematics, he obtained a release from his master, and removed to Liverpool, where be gave himself up wholly to the study of mathematics, astronomy, &c. and for a subsistence, opened a school, and taught writing and accounts, &c. Before he had been long at Liverpool, he accidentally met with a merchant or tradesman visiting that town from London, in whose house the astronomer Mr. Flamsteed then lodged; and such was Sharp’s enthusiasm for his favourite studies, that with the view of becoming acquainted with this emiment man, he engaged himself to the merchant as a bookkeeper. Having been thus introduced, he acquired the friendship of Mr. Flamsteed, who obtained for him a profitable employment in the dock-yard at Chatham. In this he continued till his friend and patron, knowing his great merit in astronomy and mechanics, called him to his assistance, in completing the astronomical apparatus in the royal observatory at Greenwich, which had been built about the year 1676.

The mathematician meets with something extraordinary in Sharp’s elaborate treatise of “Geometry Improved,” (1717, 4to, signed A. S. Philomath.) 1st, by a large and accurate table of segments of circles, its construction and various uses in the solution of several difficult problems, with compendious tables for finding a true proportional part; and their use in these or any other tables exemplified in making logarithms’, or their natural numbers, to 60 places of figures; there being a table of them for all primes to 1100, true to 61 figures. 2d. His concise treatise of Polyedra, or solid bodies of many bases, both the regular ones and others: to which are added twelve new ones, with various methods of forming them, and their exact dimensions in surds, or species, and in numbers: illustrated with a variety of copper-plates, neatly engraved with his own hands. Also the models of these polyedra he cut out in box- wood with amazing neatness and accuracy. Indeed few or none of the mathematical instrument-makers could exceed him in exactly graduating or neatly engraving any mathematical or astronomical instrument, as may be seen in the equatorial instrument above mentioned, or in his sextant, quadrants and dials of various sorts; also in a curious armillary sphere, which, beside the common properties, has moveable circles, c. for exhibiting and resolving all spherical triangles; also his double sector, with many other instruments, all contrived, graduated, and finished, in a most elegant manner, by himself. In short, he possessed at once a remarkably clear head for contriving, and an extraordinary hand for executing, any thing, not only in mechanics, but likewise in drawing, writing, and making the most exact and beautiful schemes or figures in all his calculations and geometrical constructions. The quadrature of the circle was undertaken by him for his own private amusement, in 1699, deduced from two different series, by which the truth of it was proved to 72 places of figures as may be seen in the introduction to S'herwin’s tables of logarithms and in Sherwin may also be seen his ingenious improvements on the making of logarithms, and the constructing of the natural sines, tangents, and secants. He calculated the natural and logarithmic sines, tangents, and secants, to every second in the first minute of the quadrant: the laborious investigation of which may probably be seen in the archives of the Royal Society, as they were presented to Mr. Patrick Murdoch for that purpose; exhibiting his very neat and accurate manner of writing and arranging his figures, not to be equalled perhaps by the best penman now living.

The late ingenious Mr. Smea‘ton says (Philos. Trans, an. 1786, p. 5, &c). ’ In the year 1689, Mr. Flamsteed com^ pleted his mural arc at Greenwich; and, in the prolegomena to his “Historia Ccelestis,” he makes an ample acknowledgment of the particular assistance, care, and industry of Mr. Abraham Sharp; whom, in the month of Aug. 1688, he brought into the observatory as his amanuensis, and being, as Mr. Flamsteed tells us, not only a very skilful mathematician, but exceedingly expert in mechanical operations, he was principally employed in the construction of the mural arc; which in the compass of fourteen months he finished, so greatly to the satisfaction of Mr. Flamsteed, that he speaks of him in the highest terms of praise.

In his retirement at Little Horton, he employed four or five rooms or apartments in his house for different purposes, into which none of his family, could possibly enter at any time without his permission. He was seldom visited by any persons, except two gentlemen of Bradford, the one a mathematician, and the other an ingenious apothecary: these were admitted, when he chose to be seen by them, by the signal of rubbing a stone against a certain part of the outside wall of the house. He duly attended the dissenting chapel at Bradford, of which he was a member, every Sunday; at which time he took care to be provided with plenty of halfpence, which he very charitably suffered to be taken singly out of his hand, held behind him during his walk to the chapel, by a number of poor people who followed him, without his ever looking back, or asking a single question.

It has also been commonly supposed that he was the real editor of, or had a principal share in, two other periodical works of a miscellaneous mathematical nature; viz. the “Mathematician,” and “Turner’s Mathematical Exercises,” two volumes, in 8vo, which came out in periodical numbers, in 1750 and 1751, &c. The latter of these seems especially to have been set on foot to afford a proper place for exposing the errors and absurdities of Mr. Robert Heath, the then conductor of the “Ladies Diary” and the “Palladium;” and which controversy between them ended in the disgrace of Mr. Heath, and expulsion from his office of editor to the “Ladies Diary,” and the substitution of Mr. Simpson in his stead, in 1753.

, an eminent mathematician, was the eldest son of Mr. John Simson, of Kirton-hall in Ayrshire, and was born Oct. 14, 1687. Being intended for the church, he was sent to the university of Glasgow in 1701, where he made great progress in classical learning and the sciences, and also contracted a fondness for the study of geometry, although at this time, from a temporary cause, no mathematical lectures were given in the college. Having procured a copy of Euclid’s Elements, with the aid only of a few preliminary explanations from some more advanced students, he soon came to understand them, and laid the foundation of his future eminence. He did not, however, neglect the other sciences then taught in college, but in proceeding through the regular course of academic study, acquired that variety of knowledge which was visible in his conversation throughout life. In the mean time his reputation as a mathematician became so high, that in 1710, when only twenty-two years of age, themembersof the college voluntarily made him an offer of the mathematical chair, in which a vacancy in a short time was expected to take place. From his natural modesty, however, he felt much reluctance, at so early an age to advance abruptly from the state of a student, to that of a professor in the same college, and therefore solicited permission to spend one year at least in London. Being indulged in this, he proceeded to the metropolis, and there diligently employed himself in improving his mathematical knowledge. He also enjoyed the opportunity of forming an acquaintance with some eminent mathematicians of that day, particularly Mr. Jones, Mr. Caswell, Dr. Jurin, and Mr. Ditton. With the latter, indeed, who was then mathematical master of Christ’s Hospital, and well esteemed for his learning, &c. he was more particularly connected. It appears from Mr. Simson’s own account, in his letter, dated London, Nov. 1710, that he expected to have had an assistant in his studies chosen by Mr. Caswell; but, from some mistake, it was omitted, and Mr. Simson himself applied to Mr. Ditton. He went to him not as a scholar (his own words), but to have general information and advice about his mathematical studies. Mr. Caswell afterwards mentioned to Mr. Simson that he meant to have procured Mr. Jones’s assistance, if he had not been engaged.

After he returned to his curacy, he was offered a school xvorth 500l. a year, arising from the benefit of the scholars, but refused it as interfering with the plan of literary improvement and labour which he had marked out for himself; and when told that he might employ ushers, he said he could not in conscience take the money, without giving up his whole time and attention to his scholars. In 1744, he published “The Candid Reader, addressed to his terraqueous majesty, the WorUl.” The objects of his ridicule in this are Hill, the mathematician, who proposed making verses by an arithmetical table, lord Shaftesbury, and Johnson, the author of a play called “Hurlothrumbo,” with a parallel between Hurlothrumbo and the rhapsody of Shaftesbury. In the same year he also published “A Letter to the authors of Divine Analogy and the Minute Philosopher, from an old officer,” a plain, sensible letter, advising the two polemics to turn their arms from one another against the common enemies of the Christian faith. During the rebellion in 1745, he published a very seasonable and shrewd pamphlet, entitled the “Chevalier’s hopes.” On the death of Dr. Sterne, the see of Clogher was filled by Dr. Clayton, author of the “Essay on Spirit,” a decided Arian; and between him and Skelton there could consequently be no coincidence of opinion, or mutuality of respect. In 1748, Mr. Skelton having prepared for the press his valuable work entitled “Deism revealed,” he conceived it too important to be published in Ireland, and therefore determined to go to London, and dispose of it there. On his arrival, he submitted his manuscript to Andrew Millar, the bookseller, to know if he would purchase it, and have it printed at his own expence. The bookseller desired him, as is usual, to leave it with him for a day or two, until he could get a certain gentleman of great abilities to examine it. Hume is said to have come in accidentally into the shop, and Millar shewed him the ms. Hume took it into a room adjoining the shop, examined it here and there for about an hour, and then said to Andrew, print. By this work Skelton made about 200l. The bookseller allowed him for the manuscript a great many copies, which he disposed of among the citizens of London, with whom, on account of his preaching, he was a great favourite. He always spake with high approbation of the kindness with which he was received by many eminent merchants. When in London he spent a great part of his time in going through the city, purchasing books at a cheap rate, with the greater part of the money he got by his “Deism revealed,” and formed a good library. This work was published in 1749, in two volumes, large octavo, and a second edition was called for in 1751, which waacomprized in two volumes 12mo. It has ever been considered as a masterly answer to the cavils of deists; but the style in this, as in some other of his works, is not uniform, and his attempts at wit are rather too frequent, and certainly not very successful. A few months after its publication the bishop of Clogher, Dr. Clayton, was asked by Sherlock, bishop of London, if he knew the author. “O yes, he has been a curate in my diocese near these twenty years.” “More shame for your lordship,” answered Sherlock, “to let a man of his merit continue so long a curate in your diocese.”

, a mathematician, was born in 1620, at Vise, a small town in the county of Liege. He became abbe of Amas, canon, councillor, and chancellor of Liege, and made his name famous for his knowledge in theology, physics, and mathematics. The Royal Society of London elected him one of their members, and inserted several of his compositions in their Transactions. This very ingenious and learned man died at Liege in 1683, at the age of sixty-three. Of his works there have been published, some learned letters, and a work entitled “Mesolabium et Problemata solida;” besides the following pieces in the Philosophical Transactions: viz. I. Short and easy Method of drawing Tangents to all Geometrical Curves; vol. VII. p. 5143. 2. Demonstration of the same; vol. VIII. pp. 6059, 6119. 3. On the Optic Angle of Alhaz, n vol. VIII. p. 6139.

, son of the preceding, and an excellent mathematician, was born at Leyden in 1591, where he succeeded his father in the mathematical chair in 1613, and where he died in 1626, at only thirty-five years of age. He was author of several ingenious works and discoveries, and was the first who discovered the true law of the refraction of the rays of light; a discovery which he made before it was announced by Des Cartes, as Huygens assures us. Though the work which Snell prepared upon this subject, and upon optics in general, was never published, yet the discovery was very well known to belong to him, by several authors about his time, who had seen it in his manuscripts. He undertook also to measure the earth. This he effected by measuring a space between Alcmaer and Bergen-op-zoom, the difference of latitude between these places being 1° 1′ 30″. He also measured another distance between the parallels of Alcmaer and Leyden; and from the mean of both these measurements, he made a degree to consist of 55,021 French toises or fathoms. These measures were afterwards repeated and corrected by Musschenbroek, who found the degree to contain 57,033 toises. He was author of a great many learned mathematical works, the principal of which are, 1. “Apollonius Batavus;” being the restoration of some lost pieces of Apollonius, concerning Determinate Section, with the Section of a Ratio and Space, in 1608, 4to, published in his seventeenth year; but on the best authority this work is attributed to his father. The present might perhaps be a second edition. 2. “Eratosthenes Batavus,” in 1617, 4to; being the work in which he gives an account of his operations in measuring the earth. 3. A translation out of the Dutch language, into Latin, of Ludolph van Collen’s book “De Circulo & Adscriptis,” &c. in 1619, 4to. 4. “Cyclometricus, De Circuli Dimensione,” &c. 1621, 4to. In this work, the author gives several ingenious approximations to the measure of the circle, both arithmetical and geometrical. 5. “Tiphis Batavus;” being a treatise on Navigation and naval affairs, in 1624, 4to. 6. A posthumous treatise, being four books “Doctrinæ Triangulorum Canonicæ,” in 1627, 8vo: in which are contained the canon of secants; and in which the construction of sines, tangents, and secants, with the dimension or calculation of triangles, both plane and spherical, are briefly and clearly treated. 7. Hessian and Bohemian Observations; with his own notes. 8. “Libra Astronomica & Philosophica;” in which he undertakes the examination of the principles of Galileo concerning comets, 9. “Concerning the Comet which appeared in 1618, &c.”

, an Egyptian mathematician, whose principal studies were chronology and the mathematics in general, and who flourished in the time of Julius Cxsar, is represented as well versed in the mathematics and astronomy of the ancients; particularly of those celebrated mathematicians, Thales, Archimedes, Hipparchus, Calippus, and many others, who had undertaken to determine the quantity of the solar year; which they had ascertained much nearer the truth than one can well imagine they could, with instruments so very imperfect; as may appear by reference to Ptolomy’s Almagest. It seems Sosigenes made great improvements, and gave proofs of his being able to demonstrate the certainty of his discoveries; by which means he became popular, and obtained repute with those who had a genius to understand and relish such inquiries. Hence he was sent for by Julius Caesar, who being convinced of his capacity, employed him in reforming the calendar; and it was he who formed the Julian year, which begins 45 years before the birth of Christ. His other works are lost since that period.

, a Flemish mathematician of Bruges, who died in 1633, was master of mathematics to prince Maurice of Nassau, and inspector of the dykes in Holland. It is said he was the inventor of the sailing chariots, sometimes made use of in Holland. He was a good practical mathematician and mechanist, and was author of several useful works: as, treatises on arithmetic, algebra, geometry, statics, optics, trigonometry, geography, astronomy, fortification, and many others, in the Dutch language, which were translated into Latin, by Snellius, and printed in two volumes folio. There are also two editions in the French language, in folio, both printed at Leyden, the one in 1608, and the other in 1634, with curious notes and additions, by Albert Girard. In Dr. Hutton’s Dictionary, art. Algebra, there is a particular account of Stevin’s inventions and improvements, which were many and ingenious.

, an eminent mathematician, and professor of mathematics in the university of Edinburgh, was the son of the reverend Mr. Dugald Stewart, minister of Rothsay in the Isle of Bute, and was born at that place in 1717. After having finished his course at the grammar school, being intended by his father for the church, he was sent to the university of Glasgow, and was entered there as a student in 1734. His academical studies were prosecuted with diligence and success; and he uas particularly distinguished by the friendship of Dr. Hutcheson, and Dr. Simson the celebrated geometrician, under whom he made great progress in that science.

, a protestant minister, and very skilful mathematician, was born at Eslingen, a town in Germany; and died at Jena in Thuringia, in I 567, at fifty-eight years of age, according to Vossius, but some others say eighty. Stitels was one of the best mathematicians ol his time. He published, in the German language, a treatise on algebra, and another on the Calendar or ecclesiastical computation. But his chief work is the “Arithmetica Integra,” a complete and exct llent treatise, in Latin, on Arithmetic and Algebra, printed in 4to, at Norimberg, 1544. In this work there are a number of ingenious inventions, both in common arithmetic, and in algebra, and many curious things, some of which have been ascribed to a much later date, such as the triangular table for constructing progressional and figurate numbers, logarithms, &c. Stifels was a zealous, but weak uisciple of Luther, and took it into his head to become a prophet. He predicted that the end of the world would happen on a certain day in 1553, by which he terrified many people, but lived to see its fallacy, and to experience the resentment of those whom he had deluded.

, a German mathematician, was born at Justingen in Suabia, in 1452, and died in 1531. He taught mathematics at Tubingen, wnere he acquired a great reputation, which however he lost again in a great measure, by intermeddling with the prediction of future events. He announced a great deluge, which he said would happen in the year 1524, a prediction with which he terrified all Germany, where many persons prepared vessels proper to escape with from the floods. But the prediction failing, served to convince him of the absurdity of his prognostications. He was author of several works in mathematics and astrology, full of foolish and chimerical ideas; such as, 1. “Elucidatio Fabric. Ususque Astrolabii,” 1513, fol. 2. “Procli sphaeram comment.” 1541, fol. 3. “Cosmographies aliquot Descriptiones,” 1537, 4to.

, an eminent, though self-taught mathematician, was a native of Scotland, and son of a gardener in the service of the duke of Argyle. Neither the time nor place of his birth is exactly known, but from a ms memorandum in our possession it appears that he died in March or April 1768. The chief account of him that is extant is contained in a letter written by the celebrated chevalier Ramsay to father Castel, a Jesuit at Paris, and published in the Journal de Trevoux, p. 109. From this it appears, that when he was about eighteen years of age, his singular talents were discovered accidentally by the duke of Argyle, who found that he had been reading Newton’s Principia. The duke was surprised, entered into conversation with him, and was astonished at the force, accuracy, and candour of his answers. The instructions he had received amounted to no more than having been taught to read by a servant of the duke’s, about ten years before. “I first learned to read,” said Stone; “the masons were then at work upon your house: I went near them one day, and I saw that the architect used a rule and compasses, and that he made calculations. I inquired what might be the use of these things; and I was informed, that there was a science called arithmetic: I purchased a book of arithmetic, and I learned it. I was told there was another science called geometry: I bought the books, and I learned geometry. By reading I found that there were good books in these two sciences in Latin: I bought a dictionary, and 1 learnt Latin. I understood that there were good books of the same kind in French: I bought a dictionary, and I learned French. And this, my lord, is what I have done. It seems to me that we may learn every thing, when we know the twenty-four letters of the aipiuibet.” Delighted with this account, the duke drew him from obscurity, and placed him in a situation which enabled him to pursue his favourite objects. Stone was author and translator of several useful works 1 “A new Mathematical Dictionary, 1726, 8vo. 2.” Fluxions,“1730, 8vo. The direct method is a translation of L' Hospital’s Analyse des infiniment petits, from the French; and the inverse method was supplied by Stone himself. 3.” The Elements of Euclid," 1731, 2 vols. 8vo. This is a neat and useful edition of the Elements of Euclid, with an account of the life and writings of that mathematician, and a defence of his elements against modern objectors. 4. ' A paper in the Philosophical Transactions, vol. xli. p. 218, containing an account of two species of lines of the third order, not mentioned by sir Isaac Newton, or Mr. Sterling; and some other small productions.

, a German Luthe-an divine and mathematician, but in this country known only as a chronologist, was born in 1632, at Wittemberg. He studied at Leipsic, and was afterwards professor of theology at Wittemberg, and at Dantzick. He was frequently involved in theological disputes, both with the Roman catholics and the Calvinists, from his intemperate zeal in favour of Lutheranism. He died at Wittemberg in 1682. He published some mathematical works; but was chiefly distinguished for his chronological and historical disquisitions, of which he published a considerable number from 1652 to 1680. One of the best and most useful, his “Breviarium Chronologicum,” was long known in this country by three editions (with improvements in each) of an English translation, by Richard Sault, called in the title F. R. S. but his name does not occur in Dr. Thomson’s list of the members of the Royal Society. Locke’s high commendation of this work probably introduced it as a useful manual of chronology. The edition of 1745, which, we believe, was the last, received many improvements and corrections, but it has since given way to lesser chronological systems.

Wood was contemporary with Stubbe at Oxford, and has given him this character: that, “he was a person of most admirable parts, and had a most prodigious memory; was the most noted Latinist and Grecian of his age; was a singular mathematician, and thoroughly read in all political matters, councils, ecclesiastical and profane histories; had a voluble tongue, and seldom hesitated either in public disputes or common discourse; had a voice big and magisterial, and a mind equal to it; was of an high generous nature, scorned money and riches, and the adorers of them; was accounted a very good physician, and excellent in the things belonging to that profession, as botany, anatomy, and chemistry. Yet, with all these noble accomplishments, he was extremely rash and imprudent, and even wanted common discretion. He was a very bold man, uttered any thing that came into his mind, not only among his companions, but in public coffee-houses, of which he was a great frequenter: and would often speak freely of persons then present, for which he used to be threatened with kicking and beating. He had a hot and restless head, his hair being carrot-coloured, and was ever ready to undergo any enterprise, which was the chief reason that macerated his body almost to a skeleton. He was also a person of no fixed principles; and whether he believed those things which every good Christian doth, is not for me to resolve. Had he been endowed with common sobriety and discretion, and not have made himself and his learning: mercenary and cheap to every ordinary and ignorant fellow, he would have been admired by all, and might have picked and chused his preferment; but all these things being wanting, he became a ridicule, and undervalued by sober and knowing scholars, and others too.”

, a noted German mathematician and philosopher, was born at Hippo! stein in 1635. He was a professor of philosophy and mathematics at Altdorf, and died there Dec. 26, 1703. In 1670, he published, 1. A German translation of the works of Archimedes; and afterwards produced many other books of his own. 2. “Collegium experimental curiosum,” Nuremberg, 1676, 4to; reprinted in 1701, 4to, a very curious work, containing a multitude of interesting experiments, neatly illustrated by copper-plate figures printed upon almost every page, by the side of the letter-press. Of these, the 10th experiment is an improvement on father Lana’s project for navigating a small vessel suspended in the atmosphere by several globes exhausted of air. '6. “Physica electiva, et Hypothetica,” Nuremberg, 1675, 2 vols. 4to; reprinted at Altdorf, 1730. 4.“Scientia Cosmica,” Altdorf, 1670, folio. 5. “Architecture militaris Tyrocinia,” at the same place, 1682, folio. 6. “Epistola de veritate proposiiionum Borellide motu animalium,” 4to, Nuremb. 1684. 7. “Physicae conciliatricis Conamina,” Altdorf, 1684, 8vo. 8. “Mathesis enucleata,” Nuremb. 1695, 8vo. 9. “Mathesis Juvenilis,” Nureiwb. 1699, 2 vols. 8vo, 10. “Physicae modernae compendium,” Nuremb. 1704, 8vo. 11. “Tyrocinia mathematica,” Leipsic, 1707, folio. 12. “Praelectiones Academics,” 1722, 4to. 13. “Praelectiones Academics,” Strasburg, 12mo. The works of this author are still more numerous, but the most important of them are here enumerated.

, a noted mathematician, was born at Brescia in Italy, probably towards the conclusion of the fifteenth century, as we find he was a considerable master or preceptor in mathematics in 1521, when the first of his collection of questions and answers was written, which heafterwards published in 1546, under the title of “Quesiti et Invention! diverse,” at Venice, where he then resided as a public lecturer on mathematics, he having removed to this place about 1534. This work consists of nine chapters, containing answers to a number of questions on all the different branches of mathematics and philosophy then in vogue. The last or ninth of these, contains the questions in algebra, among which are those celebrated letters and communications between Tartalea and Cardan, by which our author put the latter in possession of the rules for cubic equations, which he first discovered in 1530.

, a celebrated philosopher and mathematician, was born at Edmonton in Middlesex, Aug. 28, 1685. His grandfather, Nathaniel Taylor, was one of the Puritans whom Cromwell elected by later, June 14, 1653, to represent the county of Bedford in parliament. His father, John Taylor, esq. of Bifrons in Kent, is said to have still retained some of the austerity of the puritanic character, but was sensible of the power of music; in consequence of which, his son Brook studied that science early, and became a proficient in it, as he did also in drawing. He studied the classics and mathematics with a private tutor at home, and made so successful a progress, that at fifteen he was thought to be qualified for the university. In 1701 he went to St. John’s college, Cambridge, in the rank of a fellow-commoner, and immediately applied himself with zeal to the study of mathematical science, which alone could gain distinction there. It was not long before he became an author in that science, for, in 1708, he wro e his “Treatise on the Centre of Oscillation,” though it was not published till it appeared some years after in the Philosophical Transactions. In 1709, he took the degree of bachelor of laws; and about the same time commenced a correspondence with professor Keil, on subjects of the most abstruse mathematical disquisition. In 1712 he was elected into the Royal Society, to which in that year he presented three papers, one, “On the Ascent of Water betwetMi two Glass Planes.” 2. “On the Centre of Oscillation.” 3. “On the Motion of a stretched String.” He presented also, in 1713, a paper on his favourite science of music; but this, though mentioned in his correspondence with iteil, does not appear in the Transactions.

His distinguished abilities as a mathematician had now recommended him particularly to the esteem of the Royal Society, who, in 1714, elected him to the office of secretary. In the same year, he took the degree of doctor of laws, at Cambridge. In 1715, he published his “Methodus incrementorum,” and a curious essay in the Philosophical Transactions, entitled, “An Account of an Experiment for the Discovery of the Laws of Magnetic Attraction;” and, besides these, his celebrated work on perspective, entitled “New Principles of Linear Perspective: or the art of designing, on a plane, the representations of all sorts of objects, in a more general and simple method than has hitherto been done.' 7 This work has gone through several editions, and received some improvements from Mr. Colson, Lucasian professor at Cambridge. In the same; year Taylor conducted a controversy, in a correspondence with Raymond count de Montmort, respecting the tenets of Malbranche, which occasioned him to be noticed afterwards in the eulogium pronounced on that celebrated metaphysician. In 1716, by invitation from several learned men, to whom his merits were well known, Dr. Taylor visited Paris, where he was received with every mark of respect and distinction. Early in 1717, he returned to London, and composed three treatises, which are in the thirtieth volume of the Philosophical Transactions. But his health having been impaired by intense application, he was now advised to go to Aix-la-chapelle, and resigned his office of secretary to the Royal Society. After his return to England in 1719, it appears that he applied his mind to studies of a religious nature, the result of which were found in some dissertations preserved among his papers,” On the Jewish Sacrifices,' 7 &c. He did not, however, neglect his former pursuits, but amused himself with drawing, improved his treatise on linear perspective, and wrote a defence of it against the attacks of J. Bernoulli!, in a paper which appears in the thirtieth volume of the Philosophical Transactions, Bernouilli objected to the work as too abstruse, and denied the author the merit of inventing his system. It is indeed acknowledged, that though Dr. B. Taylor discovered it for himself, he was not the first who had trod the same path, as it had been done by Guido Ubaldi, in a book on perspective, published at Pesaro in 1600. The abstruseness of his work has been obviated by another author, in a work entitled, “Dr. Brook Taylor’s method of Perspective made easy, both in theory and practice, &c. by Joshua Kirby, painter;” and this publication has continued to be the manual both of artists and dilettanti. Towards the end of 1720, Dr. Taylor visited lord Bolingbroke, near Orleans, hut returned the next year, and published his last paper in the Philosophical Transactions, which described, “An Experiment made to ascertain the Proportion of Expansion in the Thermometer, with regard to the Degree of Heat.”

In the interval between 1721 and his death, he appears to have been in part disabled by ill health, and in part diverted by other objects from severe study. “A Treatise on Logarithms,” addressed to his friend lord Paisley, afterwards lord Abercorn, is almost the only fruit of his labour which has been found to belong to that period; and 'this has never been published. After the loss of his second wife, he seems to have endeavoured to divert his mind by study; and an essay, entitled “Contemplatio Philosophica,” printed, but not published, by his grandson, sir William Young, in 1793, was probably written at this time, and for this purpose. It was the effort of a strong mind, and affords a most remarkable example of the close logic of the mathematician, applied to metaphysics. The effort, however, was Tain, and equally vain were the earnest endeavours of his friends to amuse and comfort him by social gratifications. Dr. Taylor is proved by his writings to have been a finished scholar, and a profound mathematician: he is recorded to have been no less a polished gentleman, and a sound and serious Christian. It is said of him, that “he inspired partiality on his first address; he gained imperceptibly on acquaintance; and the favourable impressions which he made from genius and accomplishments, he fixed in further intimacy, by the fundamental qualities of benevolence and integrity.” His skill in drawing is also commended in the highest terms. “He drew figures,” says his biographer, “with extraordinary precision and beauty of pencil. Landscape was yet his favourite branch of design. His original landscapes are mostly painted in water-colours, but with all the richness and strength of oils. They have a. force of colour, a freedom of touch, a varied disposition of planes of distance, and a learned use of aerial as well as linear perspective, which all professional men who have seen these paintings have admired. Some pieces are compositions; some are drawn from nature: and the general characteristic of their effect may be exemplified, by supposing the bold fore-grounds of Salvator Rosa to be backed by the ession of distances, and mellowed by the sober harmony which distinguishes the productions of Caspar Poussin. The small figures, interspersed in the landscapes, would not have disgraced the pencil of the correct and classic Nicolas.”

, called Tripolites, or of Tripoli, was a celebrated mathematician, who flourished, as Saxius seems inclined to think, in the first century. He is mentioned by Suidas, as probably the same with Theodosius, the philosopher of Bythinia, who, Strabo says, excelled in mathematics. He appears to have cultivated chiefly that part of geometry which relates to the doctrine of the sphere, on which he wrote three books containing fifty-nine propositions, all demonstrated in the pure geometrical manner of the ancients, and of which Ptolomy as well as all succeeding writers made great use. These three books were translated by the Arabians out of the Greek into their own language, and from the Arabic the work was again translated into Latin, and printed at Venice. But the Arabic rersion being very defective, a more complete edition was published in Greek and Latin at Paris, in 1558, by John Pena (See Pena) professor of astronomy. Theodosius’s works were also commented upon by others, and lastly by De Chales, in his “Cursus Mathematicus.” But that edition of Theodosius’ s spherics which is now most in use, was translated and published by our countryman the learned Dr. Barrow, in 1675, illustrated and demonstrated in anew and concise method. By this author’s’ account, Theodosius appears not only to he a great master in this more difficult part of geometry, but the first considerable author of antiquity who has written on thai subject. Theodosius also wrote concerning the celestial houses; and of dnys and nights; copies of which, in Greek, are in the king’s library at Paris, and of which there was a Latin edition, published by Peter Dasypody in 1572.

, of Alexandria, a celebrated Greek philosopher and mathematician, flourished in the fourth century, about the year 380, in the time of Theodosius the Great; but the time and manner of his death are unknown. His genius and disposition for the study of philosophy were very early improved by a close application to study; so that he acquired such a proficiency in the sciences as to render his name venerable in history; and to procure him the honour of being president of the famous Alexandrian school. One of his pupils was the celebrated Hypatia, his daughter, who succeeded him in the presidency of the school; a trust, which, like, himself, she discharged with the greatest honour and usefulness. (See Hypatia.)

, an Italian mathematician, was born at Verona, Nov. 4, 1721, and was educated at Padua, principally in jurisprudence, in which faculty he took his doctor’s degree, but he did not confine himself to that science. The knowledge which he acquired was so general, that upon whatever subject the conversation happened to turn, he delivered his sentiments upon it as if it had formed the only object of his study. On his return from the university, he entered on the possession of a considerable fortune, and determined to devote himself entirely to literary pursuits. The Hebrew, Greek, Latin, and Italian languages occupied much of his time, his object being to understand accurately the two first, and to be able to write and speak the two last with -propriety and elegance. He also learned French, Spanish, and English, the last particularly, for he was eager to peruse the best English writers, and was enabled to enter into their spirit. Ethics, metaphysics, divinity, and history, also shared much of his attention, and he displayed considerable taste in the fine arts, music, painting, and architecture. Nor did he neglect the study of antiquities, but made himself familiarly acquainted with coins, gems, medals, engravings, &c. Scarce any monumental inscriptions were engraved at Verona which he had not either composed or corrected. With the antiquities of his own country he was so intimately acquainted, that every person of eminence, who visited Verona, took care to have him in their company when they examined the curiosities of the city.

But these pursuits he considered merely as amusements; mathematics and the belles lettres were his serious studies. These studies are in general thought incompatible; but Torelli was one of the few who could combine the gravity of the mathematician with the amenity of the muses and graces. Of his progress in mathematics we have a sufficient proof in his edition of the collected works of Archimedes, printed at Oxford in 1792, folio, Greek and Latin. The preparation of this work had been the labour of most part of his life. Having been completely ready for publication, and even the diagrams cut which were to accompany the demonstration, the manuscript was disposed of after his death to the curators of the Clarendon press, by whose order it was printed under the immediate care of Dr. Robertson, the present very learned professor of astronomy. It seems to be the general opinion that there have been few persons in any country, or in any period of time, who were better qualified, than Torelli, for preparing a correct edition of Archimedes. As a Greek scholar he was capable of correcting the mistakes, supplying the defects, and illustrating the obscure passages that occurred in treatises originally written in the Greek tongue; his knowledge of Latin, and a facility, acquired by habit, of writing in this language, rendered him a fit person to translate the Greek into pure and correct Latin, and his comprehensive acquaintance with mathematics and philosophy qualified him for conducting the whole with judgment and accuracy. Torelli wrote the Italian language with the classic elegance of the fourteenth and fifteenth centuries, as appears by his different works in that language, both in prose and verse. He translated the whole of jtsop’s fables into Latin, and Theocritus, the epithalamium of Catullus, and the comedy of Plautus, called “Pseudolus,” into Italian verse. The first two books of the Æneid were also translated by him with great exactness, and much in the style of the original. Among his other Italian tanslations was Gray’s Elegy.

an illustrious mathematician and philosopher of Italy, was born at Faenza, in 1608, and was trained in Greek and Latin literature by an uncle who was a monk, Natural inclination led him to cultivate mathematical knowledge, which he pursued some time without a master; but, at about twenty years of age, he went to Rome, where he continued the pursuit of it under father Benedict Castelli. Castelli had been a scholar of the great Galilei, and had been called by pope Urban VIII. to be a professor of mathematics at Rome. Torricelli made so extraordinary a progress under this master, that, having read Galilei’s “Dialogues,” he composed a “Treatise concerning Motion” upon his principles. Castelli, astonished at the performance, carried it and read it to Galilei, who heard it with much pleasure, and conceived a high esteem and friendship for the author. Upon this Castelli proposed to Galilei, that Torricelli should come and live with him; recommending him as the most proper person he could have, since he was the most capable of comprehending those sublime speculations which his own great age, infirmities, and, above all, want of sight, prevented him from giving to the world. Galilei accepted the proposal, and Torricelli the employment, as things of all others the most advantageous to each. Galilei was at Florence, whither Torricelli arrived in 1641, and began to take down what Galilei dictated, to regulate his papers, and to act in every respect according to his directions. But he did not enjoy the advantages of this situation long, for at the end of three months Galilei died. Torricelli was then about returning to Rome. But the grand duke Ferdinand II. engaged him to continue at Florence, making him his own mathematician for the present, and promising him the chair as soon as it should be vacant. Here he applied himself intensely to the study of mathematics, physics, and astronomy, making many improvements and some discoveries. Among others, he greatly improved the art of making microscopes and telescopes; and it is generally acknowledged that he first found out the method of ascertaining the weight of the atmosphere by a proportionate column of quicksilver, the barometer being called from him the Torricellian tube, and Torricellian experiment. In short, great things were expected from him, and great things would probably have been farther performed by him if he had lived; but he died, after a few days illness, in 1647, when he was but just entered the fortieth year of his age.

, an ingenious mathematician, lord of Killingswald and of Stolzenberg in Lusatia, was born April 10, 1651.After having served as a volunteer in the army of Holland in 1672, be travelled into most parts of Europe, as England, Germany, Italy, France, &c. He went to Paris for the third time in 1682; where he communicated to the Academy of Sciences, the discovery of the curves called from him Tschirnhausen’s Caustics; and the academy in consequence elected the inventor one of its foreign members. On returning to Italy, he was desirous of perfecting the science of optics; for which purpose he established two glass-works, from whence resulted many new improvements in dioptrics and physics, particularly the noted burning-glass which he presented to the regent. It was to him too that Saxony owed its porcelain manufactory.

, the second baronet of the family, of Roydon hall, East Peckham, in Kent, was born in 1597. His father, William Twysden, esq. was one of those who conducted king James to London, when he first came from Scotland, to take possession of the English crown, and was first knighted and afterwards created a baronet by his majesty. Sir William had a learned education, understood Greek and Hebrew well, and accumulated a valuable collection of books and Mss. which he made useful to the public, both in defence of the protestant religion and the ancient constitutions of the kingdom. He died in January 1627-8. Sir Roger, his eldest son, had also a learned education, and was a good antiquary. He assisted Mr. Philpot in his Survey of Kent, who returns him acknowledgments, as a person to whom, “for his learned conduct of these his imperfect labours, through the gloomy and perplexed paths of antiquity, and the many difficulties that assaulted him, he was signally obliged.” He was a man of great accomplishments, well versed in the learned languages, and exemplary in his attachment to the church of England. He made many important additions to his father’s library, which seems seldom to have been unemployed by his family or his descendants. His brother, Thomas, was brought up to the profession of the law, and became one of the justices of the King’s Bench after the restoration, and was created a baronet, by which he became the founder of the family of Twisdens (for he altered the spelling of the name) of Bradbourn in Kent. Another brother, John, was a physician, and a good mathematician, and wrote on both sciences.

, was an eminent mathematician irt Italy, in the end of the sixteenth and early part of the seventeenth century, but no particulars are known of his life, nor when he died. The following occur in catalogues as his works: 1. “Mechanica,” Pis. 1577, fol. and Yen. 1615. 2. “Pianisphaeriorum universalium Theorica,” Pis. 1579, fol. and Col. 1581, 8vo. 3. “Paraphrasis in ArchimedisSquiponderantia,” Pis. 1588, fol. 4. Perspectiva,“ibid. 1600, fol. 5.” Problemata Astronomica,“Ven. 1609, fol. 6.” De Cochlaea," ibid. 1615, fol.

, a celebrated Spanish mathematician, and a commander of the order of St. Jago, was born at Seville Jan. 12, 1716. He was brought up in the service of the royal marines, in which he at length obtained the rank of lieutenant-general. In 1735 he was appointed, with Don George Juan, to sail to South America, and accompany the French academicians who were going to Peru to measure a degree of the meridian. On his return home in 1745, in a French ship, he was taken by two English vessels, and after being detained some time at Louisbourg in Cape Breton, was brought to England, where his talents recommended him to Martin Folkes, president of the Royal Society, and he was the same year elected a member of that learned body. On his return to Madrid he published his “Voyage to South America,” which was afterwards translated into German and French. There is also an English translation, in two vols. 8vo, 1758, but miserably garbled and inaccurate. In 1755 he made a second voyage to America, where he collected materials for another work, which however did not appear until 1772, under the title of “Entretenimientos Physico-historicos.” He travelled afterwards over a considerable part of Europe to collect information respecting such improvements in arts and manufactures as might be serviceable to Spain, and was the means of introducing many which had not before been known in Spain, or very imperfectly carried on. He died on July 5, 1795. There are a few of his papers in the “Philosophical Transactions.”

, a celebrated French mathematician and priest, was born at Caen in 1654. He was the son of an architect in middling circumstances, but had a college education, being intended for the church. Having accidentally met with a copy of Euclid’s Elements, he was inclined to study it, and this led him to the works of Des Cartes, which confirmed his taste for geometry, and he even abridged himself of the necessaries of life to purchase books which treated on this science. What contributed to heighten this passion in him was, that he studied in private: for his relations observing that the books he studied were not such as were commonly used by others, strongly opposed his application to them; and as there was a necessity for his being an ecclesiastic, he continued his theological studies, yet not entirely sacrificing his favourite subject to them. At this time the Abbé St. Pierre, who studied philosophy in the same college, became acquainted with him. A taste in common for rational subjects, whether physics or metaphysics, and continued disputations, formed the bonds of their friendship, and they became mutually serviceable to each other in their studies. The abbe, to enjoy Varignon’s company with greater ease, lodged in the same house with him; and being in time more sensible of his merit, he resolved to give him a fortune, that he might fully pursue his inclination. Out of only 18 hundred livres a year, which he had himself, he conferred 300 of them upon Varignon; and when determined to go to Paris to study philosophy, he settled there in 1686, with M. Varignon, in the suburbs of St. Jacques. There each studied in his own way; the abbé applying himself to the study of men, manners, and the principles of government whilst Varignon was wholly occupied with the mathematics. Fontenelie, who was their countryman, often went to see them, sometimes spending two or three days with them. They had also room for a couple of visitors, who came from the same province. “We joined together,” says Fontenelle, “with the greatest pleasure. We were young, full of the first ardour for knowledge, strongly united, and, what we were not then perhaps disposed to think so great a happiness, little known. Varignon, who had a strong constitution, at least in his youth, spent whole days in study, without any amusement or recreation, except walking sometimes in fine weather. I' have heard him say, that in studying after supper, as he usually did, he was often surprised to hear the clock strike two in the morning; and was much pleased that four hours rest were sufficient to refresh him. He did not leave his studies with that heaviness which they usually create; nor with that weariness that a long application might occasion. He left off gay and lively, filled with pleasure, and impatient to renew it. In speaking of mathematics, he would laugh so freely, that it seemed as if he had studied for diversion. No condition was so much to be envied as his; his life was a continual enjoyment, delighting in quietness.” In the solitary suburb of St. Jacques, he formed however a connection with many other learned men; as Du Hamel, Du Verney, De la Hire, &c. Du Verney often asked his assistance in those parts of anatomy connected with mechanics: they examined together the positions of the muscles, and their directions; hence Varignon learned a good deal of anatomy from Du Verney, which he repaid by the application of mathematical reasoning to that subject. At length, in 1687, Varignon made himself known to the public by a “Treatise on New Mechanics,” dedicated to the Academy of Sciences. His thoughts on this subject were, in effect, quite new. He discovered truths, and laid open their sources. In this work, he demonstrated the necessity of an equilibrium, in such cases as it happens in, though the cause of it is not exactly known. This discovery Varignon made by the theory of compound motions, and his treatise was greatly admired by the mathematicians, and procured the author two considerable places, the one of geometrician in the Academy of Sciences, the other of professor of mathematics in the college of Mazarine, to which he was the first person raised.

As soon as the science of Infinitesimals appeared in the world, Varignon became one of its most early cultivators. When that sublime and beautiful method was attacked in the academy itself (for it could not escape the fate of all innovations) he became one of its most zealous defenders, and in its favour he put a violence upon his natural character, which abhorred all contention. He sometimes lamented, that this dispute had interrupted him in his inquiries into the Integral Calculation so far, that it would be difficult for him to resume his disquisition where he had left it off. He therefore sacrificed Infinitesimals to the Interest of Infinitesimals, and gave up the pleasure and glory of making a farther progress in them when called upon by duty to undertake their defence. All the printed volumes of the Academy bear witness to his application and industry. His works are never detached pieces, but complete theories of the laws of motion, central forces, and the resistance of mediums to motion. In these he makes such use of his rules, that nothing escapes him that has any connection with the subject he treats. In all his works he makes it his chief care to place every thing in the clearest light; he never consults his ease by declining to take the trouble of being methodical, a trouble much greater than that of composition itself; nor does he endeavour to acquire a reputation for profoundness, by leaving a great deal to be guessed by the reader. He learned the history of mathematics, not merely out of curiosity, but because he was desirous of acquiring knowledge from, every quarter. This historical knowledge is doubtless an ornament in a mathematician; but it is an ornament which, is by no means without its utilityThough Varignon’s constitution did not seem easy to be impaired, assiduity and constant application brought upon him a severe disease in 1705. He was six months in clanger, and three years in a languid state, which proceeded from his spirits being almost entirely exhausted. He said that sometimes when delirious with a fever, he thought himself in the midst of a forest, where all the leaves of the trees were covered with algebraical calculations. Condemned by his physicians, his friends, and himself, to lay aside all study, he could not, when alone in his chamber, avoid taking up a book of mathematics, which he bid as soon as he heard any person coming, and again resumed the attitude and behaviour of a sick man, which unfortunately he seldom had occasion to counterfeit.

His works that were published separately, were, 1. “Projet d'une Nouvelle Mechanique,” Paris, 1687, 4to. 2. “Dcs Nouvelles conjectures sur la Pesanteur. 3. <c Nouvelle Mechanique ou Statique,” 1725, 2 vols. 4to. 4. “UnTraite du Mouvement et de laMesure des Eaux Courantes, &c.” 1725, 4to. 5. “Eclaircissement sur l'Analyse des Infiniment-petits,” 4to. 6. “De Cahiers de Matheraatiques, ou Elemens de iVlathematiques,” 1731. 7. “Une Demonstration de la possibilit6 de la presence reelle du Corps de Jesus Christ dans PEucbariste,” printed in a collection entitled “Pieces fugitives sur I'Eucharistie,” published in 1730; an extraordinary thing for a mathematician to undertake to demonstrate; which he does, as may be expected, not mathematically but sophistically. His “Mamoirs” in the volumes of the Academy of Sciences are extremely numerous, and extend through almost all the, volumes down to the time of his death in 1722.

His son, John, whom we have mentioned as the late rector of Clapham, was born in that parish March 9, 1759, and received the early part of his education under Mr. Shute at Leeds. He was then removed to Hippasholme school, where he was well grounded in classics by the care of Mr. Sutcliffe. He had afterwards the benefit of the rev. Joseph Milner’s instruction at the grammar-school at Hull; and of the rev. Thomas Robinson’s and the rev. William Ludlam’s, the last an eminent mathematician at Leicester. He was admitted a member of Sidney Sussex college, Cambridge, where he took the degree of A. B. in 1781. In September 1782, he was ordained deacon, as curate to his father; he entered into priest’s orders in March 1783, and two days afterwards was instituted to the living of little Dunham, in Norfolk. In Oct. 1789, he married Miss Catherine King, of Hull, who died April 15, 1803, leaving a family of seven children. In June 1792, on the death of sir James Stonehouse (predecessor in the baronetcy to the sir James Stonehouse recorded in our vol. XXVIII.) he was instituted to the rectory of Clapham. In August Is 12, he married Miss Turton, daughter of John Turton, esq. of Clapham, and resided at this place from the beginning of 1793, to the day of his death, July 1, 1813, aged fifty-four. Mr. Venn never appeared in the character of an author, nor prepared any sermons for the press; but two volumes have since been published, selected from his manuscripts, and may be considered “as a fair exhibition of his manner, sentiments, and doctrine.” They are more polished in style than his father’s, but there is a perceptible difference in their opinions on some points, the father being a more decided Calvinist. Prefixed to these sermons, is a brief account of the author, from which we have extracted the above particulars.

, a very celebrated French mathematician, was born in 1540, at Fontenai, or Fontenai-le-­Comte, in Lower Poitou, a province of France. He was master of requests at Paris, where he died in 1603, in the sixty-third year of his age. Among other branches of learning in which he excelled, he was one of the most respectable mathematicians of the sixteenth century, or indeed of any age. His writings abound with marks of great originality and genius, as well as intense application. His application was such, that he has sometimes remained in his study for three days together, without eating or sleeping. His inventions and improvements in all parts of the mathematics were very considerable. He was in a manner the inventor and introducer of Specious Algebra, in which letters are used instead of numbers, as well as of many beautiful theorems in that science. He made also corir siderable improvements in geometry and trigonometry. His angular sections are a very ingenious and masterly performance: by these he was enabled to resolve the problem of Adrian Roman, proposed to all mathematicians, amounting to an equation of the 45th degree. Romanus was so struck with his sagacity, that he immediately quitted his residence of Wirtzbourg in Franconia, and came to France to visit him, and solicit his friendship. His “Apollonius Gallus,” being a restoration of Apollonius’s tract on Tangencies, and many other geometrical pieces to be found in his works, shew the finest taste and genius for true geometrical speculations. He gave some masterly tracts on Trigonometry, both plane and spherical, which may be found in the collection of his works, published at Leyden in 1646, by Schooten, besides another large and separate volume in folio, published in the author’s life-time at Paris 1579, containing extensive trigonometrical tables, with the construction aad use of the same, which are particularly described in the introduction to Dr. Hutton’s Logarithms, p. 4, &c. To this complete treatise on Trigonometry, plane and spherical, are subjoined several miscellaneous problems and observations, such as, the quadrature of the circle, the duplication of the cube, &c. Vieta having observed that there were many faults in the Gregorian Calendar, as it then existed, he composed a new form of it, to which he added perpetual canons, and an explication of it, with remarks and objections against Clavius, whom he accused of having deformed the true Lelian reformation, by not rightly understanding it. Besides those, it seems, a work greatly esteemed, and the loss of which cannot be sufficiently deplored, was his “Harmonicon Cceleste,” which, being communicated to father Mersenne, was, by some perfidious acquaintance of that honest-minded person, surreptitiously taken from him, and irrecoverably lost, or suppressed, to the great detriment of the learned world. There were also, it is said, other works of an astronomical kind, that have been buried in the ruins of time, Vieta was also a profound decypherer, an accomplishment that proved very useful to his country. As the different parts of the Spanish monarchy lay very distant from one another, when they had occasion to communicate any secret designs, they wrote them in cyphers and unknown characters, during the disorders of the league: the cypher was composed of more than five hundred different Characters, which yielded their hidden contents to the penetrating genius of Vieta alone. His skill so disconcerted the Spanish councils for two years, that they reported at Rome, and other parts of Europe, that the French king had only discovered their cyphers by means of magic.

, or Vitello, a Polish mathematician of the 13th century, flourished about 1254. We have of his a large “Treatise on Optics,” the best edition of which is that of 1572, fol. Vitello was the first optical writer of any consequence among the modern Europeans. He collected all that was given by Euclid, Archimedes, Ptolomy, and Alhazen; though his work is but of little use now.

, a celebrated Italian mathematician, was born at Florence in 1621, or, according to some, in 1622. He was a disciple of the illustrious Galileo, and lived with him from the seventeenth to the twentieth year of his age. After the death of his great master he passed two or three years more in prosecuting geometrical studies without interruption, and in this time it was that he formed the design of his Restoration of Aristeus. This ancient geometrician, who was contemporary with Euclid, had composed five books of problems “De Locis Solidis,” the bare propositions of which were collected by Pappus, but the books are entirely lost; which Viviani undertook to restore by the force of his genius. He discontinued his labour, however, in order to apply himself to another of the same kind, which was, to restore the fifth book of Apollonius’s Conic Sections. While he was engaged in this, the famous Borelli found, in the library of the grand duke of Tuscany, an Arabic manuscript, with a Latin inscription, which imported, that it contained the eight books of Apollonius’s Conic Sections; of which the eighth however was not found to be there. He carried this manuscript to Rome, in order to translate it, with the assistance of a professor of the Oriental languages. Viviani, very unwilling to lose the fruits of his labours, procured a certificate that he did not understand the Arabic language, and knew nothing of that manuscript: he was so jealous on this head, that he would not even suffer Borelli to send him an account of any thing relating to it. At length he finished his book, and published it 1659, in folio, with this title, “De Maximis et Minimis Geometrica Divinatio in quintum Conicorum Apollonii Fergsei.” It was found that he had more than divined; as he seemed superior to Apollonius himself. After this he was obliged to interrupt his studies for the service of his prince, in an affair of great importance, which was, to prevent the inundations of the Tiber, in which Cassini and he were employed for some time, though nothing was entirely executed.

In 1664, he had the honour of a pension from LouisXIV. a prince to whom he was not subject, nor could be useful. In consequence, he resolved to finish his Divination upon Aristeus, with a view to dedicate it to that prince; but he was interrupted in this task again by public works, and some negotiations which his master entrusted to him. In 1666, he was honoured by the grand duke with the title of his first mathematician. He resolved three problems, which had been proposed to all the mathematicians of Europe, and dedicated the work to the memory of Mr. Chapelain, under the title of “Enodatio Problematum,” c. He proposed the problem of the quadrable arc, of which Leibnitz and l'Hospital gave solutions by the Calculus Differentialis. In 1669, he was chosen to fill, in the Royal Academy of Sciences, a place among the eight foreign associates. This new favour reanimated his zeal; and he published three books of his Divination upon Aristeus, at Florence in 1701, which he dedicated to the king of France. It is a thin folio, entitled “De Locis Solidis secunda Divinatio Geometrica,” &c. This was a second edition enlarged; the first having been printed at Florence in 1673. Viviani laid out the fortune which he had raised by the bounties of his prince, in building a magnificent house at Florence; in which he placed a bust of Galileo, with several inscriptions in honour of that great man; and died in 1703, at eighty-one years of age.

, a mathematician and astronomer of great talents, was born about 1734, and rose from a low situation, little connected with learning, to some of the first ranks in literary pursuits. His early labours contributed to the “Ladies Diary,” a useful little work which has formed many eminent mathematicians. In 1761) he was deemed a fit person to be sent to Hudson’s Bay to observe the transit of Venus over the sun; and the manner hi which he discharged that trust did honour to his talents.

, an able mathematician, was born about 1735 at Newcastle upon Tyne, and descended from a family of considerable antiquity. He received the rudiments of his education at the grammar-school of Newcastle under the care of the rev. Dr. Moises, a clergyman of the church of England. At the age of ten he was removed from Newcastle to Durham, that he might be under the immediate direction of his uncle, a dissenting minister; and having decided in favour of the ministry among the dissenters, he was in 1749 sent to one of their academies at Kendal. In 1751 he studied mathematics at Edinburgh under the tuition of Dr. Matthew Stewart, and made a very great progress in that science. In 1752 he studied theology for two years at Glasgow. Returning home, he began to preach, and in 1757 was ordained minister of a congregation of dissenters at Durham. While here he was a frequent contributor to the “Ladies’ Diary,” in which, as we have recently had occasion to notice, most of the mathematicians of the last and present age, tried their skill; and here also he finished his valuable work on the sphere, which was not, however, published until 1775, when it appeared under the title of the “Doctrine of the Sphere,” in 4to. In the end of 1761, or the beginning of 1762, he accepted of an invitation to become pastor at Great Yarmouth, where he carried on his mathematical pursuits, and having contributed some valuable papers to the Royal Society, he was in 1771 elected a fellow of that learned body. In the same year he accepted an invitation from a congregation at Birmingham, but was induced to recede from this engagement, and accept the office of mathematical tutor to the dissenting academy at Warrington, from which he again removed in 1774 to Nottingham, being chosen one of the ministers of a congregation in that town. Here he entered with great zeal into all the political disputes of the times, and always against the measures of government. After a residence of twenty-four years at Nottingham, Mr. Walker went to Manchester, where he undertook the office of theological tutor in the dissenting academy of that town, to which the duties of mathematical and classical tutor being likewise added, he was soon obliged to resign the whole, in consideration of his age and infirmities. He continued after this to reside for nearly two years in the neighbourhood of Manchester, and was for some time president of the Literary and Philosophical Society of that town, a society which has published several volumes of valuable memoirs, some contributed by Mr. Walker. He then removed to the village of Wavertree near Liverpool, and, in the spring of 1S07, died in London, at the age of seventythree. He was a man of very considerable talents, which appeared to most advantage in the departments of philosophy and the belles lettres, as may be seen in his “Essays on Various Subjects,” published in 1809, 2 vols. 8vo, to which a copious life is prefixed. Some volumes of his “Sermons” have also been published, which probably were suited to the congregations over which he presided, but contain but a very small portion of doctrinal matter, and that chiefly of what is called the liberal and rational kind.

, an eminent English mathematician, was born Nov. 2S, 1616, at Ashford in Kent, of which place his father of the same names was then minister, but did not survive the birth of this his eldest son above six years. He was now left to the care of his mother, who purchased a house at Ashford for the sake of the education of her children, and placed him at school there, until the plague, which broke out in 1625, obliged her to remove him to Ley Green, in the parish of Tenterden, under the tuition of one James Movat or Mouat, a native of Scotland, who instructed him in grammar. Mr. Movat, says Dr. Wallis, “was a very good schoolmaster, and his scholar I continued for divers years, and was by him well grounded in the technical part of grammar, so as to understand the rules and the grounds and reasons of such rules, with the use of them in such authors, as are usually read in grammar schools: for it was always my affectation even from a child, in all parts of learning or knowledge, not merely to learn by rote, which is soon forgotten, but to know the grounds or reasons of what I learn, to inform my judgment as well as furnish my memory, and thereby make a better impression on both.” In 1630 he lost this instructor, who was engaged to attend two young gentlemen on their travels, and would gladly have taken his pupil Wallis with them; but his mother not consenting on account of his youth, he was sent to Felsted school in Essex, of which the learned Mr. Martin Holbeach was then master. During the Christmas holidays in 1631, he went home to his mother at Ashford, where finding that one of his brothers had been learning to cypher, he was inquisitive to know what that meant, and applying diligently was enabled to go through all the rules with success, and prosecuted this study at spare hours on his return to Felsted, where also he was instructed in the Latin, Greek, and Hebrew tongues, and in the rudiments of logic, music, and the French language.

Notwithstanding this opposition to the ruling powers, he was in June following appointed by the parliamentary visitors, Savilian professor of geometry at Oxford, in room of Dr. Peter Turner, who was ejected; and now quitting his church, he went to that university, entered of Exeter college, and was incorporated master of arts. Acceptable as this preferment was, he was not an inattentive observer of the theological disputes of the time; and when Baxter published his “Aphorisms of Justification and the Covenant,” our author published some animadversions on them, which Baxter acknowledged were very judicious and moderate. Before the end of this year, Wallis, in perusing the mathematical works of Torricelli, was particularly struck with what. he found there of Cavalleri’s method of indivisibles, this being the first time he had heard or seen any thing of that method, and conceived hopes of attaining by it some assistance in the problem concerning the quadrature of the circle. He accordingly spent a very considerable time in studying it, but found some insuperable difficulties, which, with what he had accomplished, he communicated to Mr. Seth Ward, then Savilian professor of astronomy, Rook, professor of astronomy at Gresham college, and Christopher Wren, then fellow of All Souls, and several other eminent mathematicians at that time in Oxford, but not meeting with the assistance he wished, he desisted from the farther pursuit. In 1653, he published a grammar of the English tongue, for the use of foreigners in Latin, under this title: “Grammatica Linguse Anglicanae, cum Tractatu de Loquela seu Sonorum Formatione,” in 8vo. In the piece “De Loquela,” &c. he tells us, that “he has philosophically considered the formation of all sounds used in articulate speech, as well of our own as of any other language that he knew; by what organs, and in what position, each sound was formed; with the nice distinctions of each, which in some letters of the same organ are very subtle: so that by such organs, in such position, the breath issuing from the lungs will form such sounds, whether the person do or do not hear himself speak.” This we shall find he afterwards endeavoured to turn to an important practical use. In 1654, he was admitted to the degree of D.D. after performing the regular exercise, which he printed afterwards, and in August of that year, made some observations on the solar eclipse, which happened about that time. About Easter, 1655, the proposition in his “Arithmetica Infinitorum,” containing the quadrature of the circle, being printed, he sent it to Mr. Oughtred; and soon after, in the same year, he published that treatise in 4to, dedicated to the same eminent mathematician. To this he prefixed a treatise on conic sections, which he sdtin a new light, considering them as absolute planes, constituted of an infinite number of parallelograms, without any relation to the cone, and demonstrated their properties from his new method of infinites.

In 1656 he published a work on the angle of contact, in which he exposes the opinion of Peletarius. In the foU lowing year, having completed his plan of lectures, he published the whole, in two parts, under the title of “Mathesis Universalis, sive Opus Arithmeticum.” While this was in the press, he' received a challenge from Mr. Fermat of Toulouse, which engaged him in an epistolary dispute with that gentleman, as well as- with Mr. Frenicle of Paris. The problem was “Invenire cubum, qui additis omnibus suis partibus aliquotis confieiat quadratum.” This challenge had been sent by Fermat to Frenicle, Schooten, and Huygens. Dr. Wallis sent a solution of it before the end of March, which being objected to both by Frenicle and Fermat, occasioned a dispute which was carried on this year and part of the next, after which both these gentlemen acknowledged the sufficiency of Wallis’ s solution, with the encomium of being the greatest mathematician in Europe. Wallis, however, having heard that Frenicle was about to publish the correspondence, and being, from some circumstances in his conduct, a little suspicious of misrepresentation, requested sir Kenelm Digby, then at Paris, through whose hands the whole had passed, to give his consent to the publication of it by the doctor himself, which being readily granted, it appeared in 1658, under the title of “Commercium Epistolicum.”

The civil war breaking out, Ward was involved not a little in the consequences of it. His good master and patron, Dr. Samuel Ward, was in 1643 imprisoned in St> John’s college, which was then made a gaol by the parliament-forces; and Ward, thinking that gratitude obliged him to attend him, continued with him to his death, which happened soon after. He was also himself ejected from his fellowship for refusing the covenant; against which he soon after joined with Mr. Peter Gunning, Mr. John Barwick, Mr. Isaac Barrow, afterwards bishop of St. Asaph, and others in drawing up a treatise, which was afterwards printed. Being now obliged to leave Cambridge, he resided some time with Dr, Ward’s relations in and about London, and at other times with the mathematician Oughtred, at Albury, in Surrey, with whom he had cultivated an acquaintance, and under whom he prosecuted his mathematical studies. He was invited likewise by the earl of Carlisle and other persons of quality, to reside in their families, with offers of large pensions, but preferred the house of his friend Ralph Freeman, at Aspenden in Hertfordshire, esq. whose sons he instructed, and with whom he continued for the most part till 1649, and then he resided some months with lord Wen man, of Thame Park in Oxfordshire.

Dr. Smith, the learned editor of sir Peter Warwick’s “Discourse of Government,” says, “That the author was a gentleman of sincere piety, of strict morals, of a great and vast understanding, and of a very solid judgment; and that, after his retiring into the country, he addicted himself to reading, study, and meditation; and, being very assiduous in his contemplations, he wrote a great deal on various subjects, his genius not being confined to any one particular study and learning.” What we have, however, of his in print is, “A Discourse of Government, as examined by reason, scripture, and the law of the land, written in 1678,” and published by Dr. Thomas Smith in 1694, with a preface, which, being displeasing to the then administration, was suffered to remain but in very few copies *. His principal work was, Memoirs of the Reign of King Charles I. with a Continuation to the Restoration;“adorned with a head of the author after Lely, engraved by White, and taken at a later period of his life than that which appeared in the” Gentleman’s Magazine“for Sept. 1790. The Memoirs were published in 1701, 8vo; and to which is not unfrequently added his” Discourse on Government,“before mentioned. This History, with several others of the time of Charles I. have this peculiar merit, that the authors of them were both actors and sufferers in the interesting scenes which they describe. Our author is justly allowed to be exceeded by none of them in candour and integrity. There is likewise ascribed to our author” A Letter to Mr. Lenthal, shewing that Peace is better than War,“small 8vo, of 10 pages, published anonymously, 1646; and in the British Museum some recommendatory letters from him in favour of Mr. Colfins the mathematician which are published in Birch’s” 'History of the Royal Society;“and in the Life of Collins, in the newedition of the” Biographia Britannica."

, a gallant officer and able engineer, was the son of a grazier, who lived at Holbeach, in Lincolnshire, where he was born about 1737, and educated at Gosberton school. Here his genius for the mathematics soon discovered itself, and in 1753 he was a frequent contributor to the “Ladies Diary.” About this time his abilities became known to Mr. Whichcot, of HarpsweJJ, then one of the members of parliament for Lincolnshire, who introduced him to the royal academy at Woolwich; and he soon after obtained a commission in the corps of engineers. Under the celebrated mathematician, Thomas Simpson, Watson prosecuted his studies at Woolwich, and continued to write for the “Ladies Diary,” of which Simpson was at that time the editor. Such was Simpson’s opinion of Watson’s abilities, that at his decease he left him his unfinished mathematical papers, with a request that he would revise them, and make what alterations and additions he might think necessary; but of this privilege it seems to be doubted whether he made the best use. (See Simpson, p. 20.)

The colonel’s genius was formed for great undertakings. He was judicious in planning, cool and intrepid in action, and undismayed in danger. He studied mankind, and was a good politician. Few, perhaps, better understood the interests of the several nations of Europe and the East. He was humane, benevolent, and the friend of indigent genius. When Mr. Rollinson, a man of great abilities as a mathematician, conducted the Ladies Diary, after the death of Mr. Simpson, and was barely existing on the pittance allowed him by the proprietors, the colonel sought and found him in an obscure lodging, and generously relieved his necessities, though a stranger to his person. This the old man related while the tears of gratitude stole down his cheeks. He survived the colonel’s bounty but a short time.

, an eminent puritan divine, was born at Banbury in Oxfordshire, in May 1583, where his father, Thomas Whately, was justice of the peace, and had been several times mayor. He was educated at Christ’scollege, Cambridge, under the tuition of Mr. Potman, a man of learning and piety, and was a constant hearer of Dr. Chaderton, Perkins, and other preachers of the Puritan-stamp. It does not appear that he was originally destined for the church, as it was not until after his marriage with the daughter of the Rev. George Hunt that he was persuaded to study for that purpose, at Edmund -hall, Oxford. Here he was incorporated bachelor of arts, and, according to Wood, with the foundation of logic, philosophy, and oratory, that he had brought with him from Cambridge, he became a noted disputant and a ready orator. In 1604, he took his degree of M. A. as a member of Edmund-hall, “being then esteemed a good philosopher and a tolerable mathematician.” He afterwards entered into holy orders, and was chosen lecturer of Banbury, his native place. In 1610, he was presented by king James to the vicarage of Banbury, which he enjoyed until his death. He also, with some of his brethren, delivered a lecture, alternately at Stratford-upon-Avon. In his whole conduct, Mr. Leigh says, he “was blameless, sober, just, holy, temperate, of good behaviour, given to hospitality”,&c. Fuller calls him “a good linguist, philosopher, mathematician, and divine;” and adds, that he “was free from faction?' Wood, who allows that he possessed excellent parts, was a noted disputant, an excellent preacher, a good orator, and well versed in the original text, both Greek and Hebrew, objects, nevertheless, that,” being a zealous Calvinist, a noted puritan, and much frequented by the precise party, for his too frequent preaching, he laid such a foundation of faction at Banbury, as will not easily be removed.“Granger, who seems to have considered all these characters with some attention, says, that” his piety was of a very extraordinary strain; and his reputation as a preacher so great, that numbers of different persuasions went from Oxford, and other distant places, to hear him. As he ever appeared to speak from his heart, his sermons were felt as well as heard, and were attended with suitable effects.“In the life of Mede, we have aa anecdote of him, which gives a very favourable idea of his character. Having, in a sermon, warmly recommended his hearers to put in a purse by itself a certain portion from every pound of the profits of their worldly trades, for works of piety, he observed, that instead of secret grudging, when objects of charity were presented, they would look out for them, and rejoice to find them. A neighbouring clergyman hearing him, and being deeply affected with what he so forcibly recommended, consulted him as to what proportion of his income he ought to give.” As to that,“said Whately,” lam not to prescribe to others; but I will tell you what hath been my own practice. You know, sir, some years ago, I was often beholden to you for the loan of ten pounds at a time; the truth is, I could not bring the year about, though my receipts were not despicable, and I was not at all conscious of any unnecessary expenses. At length, I inquired of my family what relief was given to the poor; and not being satisfied, I instantly resolved to lay aside every tenth shilling of all my receipts for charitable uses; and the Lord has made me so to thrive since I adopted this method, that now, if you have occasion, I can lend you ten times as much as I have formerly been forced to borrow."

, Camdenian professor of history at Oxford, was born at Jacobstow, in Cornwall, 1573, and admitted of Broadgate-hall in that university. He took the degrees in arts, that of master being completed in 1600; and, two years after, was elected fellow of Exeter-college. Leaving that house in 1608, he travelled beyond the seas into several countries; and at his return found a patron in lord Chandois. Upon the death of this nobleman, he retired with his wife to Gloucester-hall in Oxford, where, by the care and friendship of the principal, he was accommodated with lodgings; and there contracted an intimacy with the celebrated mathematician, Thomas Allen, by whose interest Camden made him the first reader of that lecture which he had founded in the university. It was thought no small honour that on this occasion he was preferred to Bryan Twyne, whom Camden named as his successor, if he survived him, but Twyne died first. Soon after, he was made principal of that hall; and this place, with his lecture, he held to the time of -his death, which happened Aug. 1, 1647. He was buried in the chapel of Exetercollege. Wood tells us, that he was esteemed by some a learned and genteel man, and by others suspected to be a Calyinist. He adds, that he left also behind him a widow and children, who soon after became poor.

, an ingenious mathematician, was born in Nottinghamshire, and educated at the Blue Coat school of Nottingham. Of his early history we have little information, but it appears that he kept an academy at Bingham, in the above county, for some years, and afterwards was preferred to the living of Sulney, where he died at an advanced age, Oct. 30, 1802. In his latter days he had a remarkably strong and retentive memory, as a proof of which, he told a friend that he made a common practice of solving the most abstruse questions in the mathematics without ever committing a single figure, &c. to paper till finished and, upon its being observed how much pen and paper might assist him!" he replied, “I have to thank God for a most retentive memory and so long as it is enabled to exercise its functions, it shall not have any assistance from art.” When is mind was occupied in close study, he always walked to and fro in an obscure part of his garden, where he could neither see nor be seen of any one, and frequently paced, in this manner, several miles in a day.

, an ingenious and learned English bishop, was the son of Mr. Walter Wilkins, citizen and goldsmith of Oxford, and was born in 1614, at Fawsley, near Daventry, in Northanvptonshire, in the house of his mother’s father, the celebrated dissenter Mr. John Dod. He was taught Latin and Greek by Edward Sylvester, a teacher of much reputation, who kept a private school in the parish of All-Saints in Oxford and his proficiency was such, that at thirteen he entered a student of New-innhall, in 1627. He made no long stay there, but was removed to Magdalen-hall, under the tuition of Mr. John Tombes, and there took the degrees in arts. He afterwards entered into orders; and was first chaplain to William lord Say, and then to Charles count Palatine of the Khine, and prince elector of the empire, with whom he continued some time. To this last patron, his skill in the mathematics was a very great recommendation. Upon the breaking out of the civil war, he joined with the parliament, and took the solemn league and covenant. He was afterwards made warden of Wadham-college by the committee of parliament, appointed for reforming the university; and, being created bachelor of divinity the 12th of April, 1648, was the day following put into possession of his wardenship. Next year he was created D. D. and about that time took the engagement then enjoined by the powers in being. In 1656, he married Robina, the widow of Peter French, formerly canon of Christ-church, and sister to Oliver Cromwell, then lord-protector of England: which marriage being contrary to the statutes of Wadham-college, because they prohibit the warden from marrying, he procured a dispensation from Oliver, to retain the wardenship notwithstanding. In 1659, he was by Richard Cromwell made master of Trinity-college in Cambridge; but ejected thence the year following upon the restoration. Then he became preacher to the honourable society of Gray’s-inn, and rector of St. Lawrence-Jewry, London, upon the promotion Dr. Seth Ward to the bishopric of Exeter. About this time, he became a member of the Royal Society, was chosen of their council, and proved one of their most eminent members. Soon after this, he was made dean of Rippon; and, in 1668, bishop of Chester, Dr. Tillotson, who had married his daughter-in-law, preaching his consecration sermon. Wood and Burnet both inform us, that he obtained this bishopric by the interest of Villiers duke of Buckingham; and the latter adds, that it was no stnall prejudice against him to be raised by so bad a man. Dr. Walter Pope observes, that Wilkins, for some time after the restoration, was out of favour both at Whitehall and Lambeth, on account of his marriage with Oliver Cromwell’s sister; and that archbishop Sheldon, who then disposed of almost all ecclesiastical preferments, opposed his promotion; that, however, when bishop Ward introduced him afterwards to the archbishop, he was very obligingly received, and treated kindly by him ever after. He did not enjoy his preferment long; for he died of a suppression of urine, which was mistaken for the stone, at Dr. Tiilotson’s house, in Chancery-lane, London, Nov. 19, 1672. He was buried in the chancel of the church of St. Lawrence Jewry; and his funeral sermon was preached by Dr. William Lloyd, then dean of Bangor, who, although Wilkins had been abused and vilified perhaps beyond any man of his time, thought it no shame to say every thing that was good of him. Wood also, different as his complexion and principles were from those of Wilkins, has been candid enough to give him the following character “He was,” says he, “a person endowed with rare gifts he was a noted theologist and preacher, a curious critic in several matters, an excellent mathematician and experimentist, and one as well seen in mechanisms and new philosophy, of which he was 3 great promoter, as any man of his time. He also highly advanced the study and perfecting, of astronomy, both at Oxford while he was warden of Wadham-college, and at London while he was fellow of the Royal Society; and I cannot say that there was any thing deficient in him, but a constant mind and settled principles.”

His works are, 1. “The use of the proportional Rules in Arithmetic and Geometry; also the use of Logarithms of numbers, with those of sines and tangents;” printed ill French, at Paris, 1624, 8vo, and at London, in English^ 1626, 1645, and 1658. In this book, Mr. Wingate speaks of having been the first who carried the logarithms tqf France; but an edition of Napier’s “Description and construction of Logarithms” was printed at Lyons in 1620, four years earlier than Wingate’s publication. 2. “Of Natural, and Artificial Arithmetic, or Arithmetic made easy,” Lond. 1630, 8vo, which has gone through numerous editions; the best is that by Mr. Doclson. 3. 4 Tables of Logarithms of the signs and tangents of all the degrees and minutes of the Quadrant; with the use and application of the same,“ibid. 1633, 8vo. 4.” The Construction and use of Logarithms, with the resolution of Triangles, &c.“5.” Ludus Mathematicus: or an Explanation of the description, construction, and use of the numerical table of proportion,“ibid. 1654, 8vo. 6.” Tacto-metria, seu Tetagne-nqme-t tria, or the Geometry of regulars, &c.“ 8vo. 7.” The exact Surveyor of Land, &c.“8vo. 8.” An exact abridgment of all the statutes in force and use from the Magna Charta to 1641,“1655, 8vo, reprinted and continued to 1663, 1680, 1681, and 1684. 9.” The body of the common law of England,“1655, &c. 8vo. 10.” Maxims of reason, or the Reason of the Common Law of England,“1658, fol. 11.” Statuta Pacis; or, the Table of all the Statutes which any way concern the office of a justice of peace, &c." 12mo. 12. An edition of Britton, 1640, 12mo. He was supposed to be the editor of some other law books, which show equal judgment and industry, but he is now remembered only as a mathematician.

, a good astronomer and mathematician, was born in 1728. He was maternally descended from the celebrated clock and watchmaker, Daniel Quare, in which business he was himself brotignt up, and was educated in the principles of the Quakers, all his progenitors for many generations having been of that community, whose simplicity of manners he practised through life. It appears that he cultivated the study of astronomy at a very early age, as he had a communication on that subject in the “Gentleman’s Diary” for 1741, which must have been written when he was thirteen years of age. Soon after this he became a frequent writer both in the Diaries and in the Gentleman’s Magazine, sometimes under his own name, but oftener with the initials G. W. only. In 1764 he published a map, exhibiting the passage of the moon’s shadow over England in the great solar eclipse of April 1, that year; the exact correspondence of which to the observations gained him great reputation. In the following year he presented to the commissioners of longitude a plan for calculating the effects of refraction and parallax, on the, moon’s distance from the sun or a star, to facilitate the discovery of the longitude at sea. Having taught mathematics in London for many years with much reputation, he was in 1767 elected F. R. S. and appointed head master of the royal naval academy at Portsmouth, where he died of a paralytic stroke in 1785, aged fiftyseven.

, a learned and illustrious English architect and mathematician, was nephew to bishop Wren, and the son of Dr. Christopher Wren, who was fellow of St. John’s college, Oxford, afterwards chaplain to Charles I. and rector of Knoyle in Wiltshire; made dean of Windsor in 1635, and presented to the rectory of Hasely in Oxfordshire in 1638; and died at Blechindon, in the same county, 1658, at the house of Mr. William Holder, rector of that parish, who had married his daughter. He was a man well skilled in all the branches of the mathematics, and had a great hand in forming the genius of his only son Christopher.' In the state papers of Edward, earl of Clarendon, vol.1, p. 270, is an estimate of a building to be erected for her majesty by dean Wren. He did another important service to his country. After the chapel of St. George and the treasury belonging to it had been plundered by the republicans, he sedulously exerted himself in recovering as many of the records as could be procured, and was so successful as to redeem the three registers distinguished by the names of the Black, Blue, and lied, which were carefully preserved by him till his death. They were afterwards committed to the custody of his son, who, soon after the restoration, delivered them to Dr. Bruno Ryves, dean of Windsor.

, a noted English mathematician, who flourished in the latter part of the sixteenth century and beginning of the seventeenth, is thus characterised in a Latin paper in the library of Gonvile and Caius college, Cambridge: “This year (1615) died at London, Edward Wright, of Garveston, in Norfolk, formerly a fellow of this college; a man respected by all for the integrity and simplicity of his manners, and also famous for his skill in the mathematical sciences; so that he was not undeservedly styled a most excellent mathematician by Richard Hackluyt, the author of an original treatise of our English navigations. What knowledge he had acquired in the science of mechanics, and how usefully he employed that knowledge to ths public as well as to private advantage, abundantly appear both from the writings he published, and from the many mechanical operations still extant, which are standing monuments of his great industry and ingenuity. He was the first undertaker of that difficult but useful work, by which a little river is brought from the town of Ware in apew canal, to supply the city of London with water but by the tricks of others he was hindered from completing the work he had begun. He was excellent both in contrivance and execution, nor was he inferior to the most ingenious mechanic in the making of instruments, either of brass or any other matter. To his invention is owing whatever advantage Hondius’s geographical charts have above others; for it was Wright who taught Jodocus Horn dius the method of constructing them, which wa.s till then unknown; but the ungrateful Hondius concealed the name of the true author, and arrogated the glory of the invention to hjmself. Of this fraudulent practice the good man could nqt help complaining, and justly enough, in the preface to his treati.se of the” Correction of Errors in the art of Navigation;“which he composed with excellent judgment and after long experience, to the great advancement of naval affairsi For the improvement of this art he was appointed mathematical lecturer by the East India company, and read lectures in the house of that worthy knight sir Thomas Smith, for which he had a yearly salary of fifty pounds, This office he discharged with great reputation, and much to the satisfaction of his hearers. He published in English a book on the doctrine of the sphere, and another concerning the construction of sun-dials. He also prefixed an ingenious preface to the learned Gilbert’s book on the loadstone. By these and other his writings, he has transmitted his fame to latest posterity. While he was yet a fellow of this college, he could not be concealed in his private study, but was called forth to the public business of the nation by the queen, about 1593. He was ordered to attend the earl of Cumberland in some maritime expeditions. One of these he has given a faithful account of, in the manner of a journal or ephemeris, to which he has prefixed an elegant hydrographical chart of his own contrivance. A little before his death he employed himself about an English translation of the book of logarithms, then lately discovered by lord Napier, a Scotchman, who had a great affection for him. This posthumous work of his- was published soon after by his only son Samuel Wright, who was also a scholar of this college. He had formed many other useful designs, but was hindered by death from bringing them to perfection. Of him it may truly be said, that he studied more to serve the public than himself; and though he was rich in fame, and in the promises of the great, yet he died poor, to tfie scandal of an ungrateful age.” So far the memoir; other particulars concerning him are as follow:

, an eminent Italian mathematician, was born at Bologna in January 1692, and was educated among the Jesuits. His first pursuit was the law, which he soon exchanged for philosophy, and particularly mathematics. In philosophy he was at first a Cartesian, but when sir Isaac Newtbn’s discoveries were divulged, he was among the first to acknowledge his great superiority, particularly in optics and astronomy. He was made librarian and secretary to the academy of Bologna, and wrote a Latin history of its transactions continued down to 1766, and he also contributed many mathematical papers of great importance. But his talents were not confined to philosophy and mathematics: he was also a distinguished poet both in the Tuscan and Latin languages, and in the latter, was thought a successful imitator of Catullus, Tibullus, Ovid, and Virgil. After a life honourably spent in those various pursuits, which procured him great fame, he died Dec. 25, 1777. He published a great many works, both in Italian and Latin, which are enumerated by Fabroni.

, a learned philosopher, mathematician, and divine, of the sixteenth century, was born at Landshut, in Bavaria. He taught at Vienna for a considerable time, and resided afterwards near the bishop of Passau in Bavaria, where he died in 1549, leaving several works; which are different in their spirit, according as they were written before or after he quitted the Romish church. Among these, his notes on some select passages of the Holy Scriptures, Basil, 151?, folio, and his “Description of the Holy Land,” Strasburg, 1536, folio, are particularly esteemed. There is an excellent life of Ziegler in Scbelhorn’s “Amoenitates.”