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, an Italian lady of great learning, was born at Milan, March 16, 1718. Her inclinations from her earliest youth led her to the study of science, and at an age when young persons of her sex attend only to frivolous pursuits, she had made such astonishing progress in mathematics, that when in 1750 her father, professor in the university at Bologna, was unable to continue his lectures from infirm health, she obtained permission from the pope, Benedict XIV. to fill his chair. Before this, at the early age of nineteen, she had supported one hundred and ninety-one theses, which were published, in 1738, under the title “Propositiones Philosophicæ.” She was also mistress of Latin, Greek, Hebrew, French, German, and Spanish. At length she gave up her studies, and went into the monastery of the Blue Nuns, at Milan, where she died Jan. 9, 1799. In 1740 she published a discourse tending to prove “that the study of the liberal arts is not incompatible with the understandings of women,” This she had written when scarcely nine years old. Her “Instituzioni analitiche,” 1748, 2 vols. 4to, were translated in part by Antelmy, with the notes of M. Bossut, under the title of “Traites elementaires du Calcul differentiel et du Calcul integral,” 1775, 8vo: but more completely into English by that eminent judge of mathematical learning, the late rev. John Colson, M. A. F. R. S. and Lucasian professor of mathematics in the university of Cambridge. This learned and ingenious man, who had translated sir Isaac Newton’s Fluxions, with a comment, in 1736, and was well acquainted with what appeared on the same subject, in the course of fourteen years afterward, in the writings of Emerson, Maclaurin, and Simpson, found, after all, the analytical institutions of Agnesi to be so excellent, that he learned the Italian language, at an advanced age, for the sole purpose of translating that work into English, and at his death left the manuscript nearly prepared for the press. In this state it remained for some years, until Mr. Baron Maseres, with his usual liberal and active spirit, resolved to defray the whole expence of printing a handsome edition, 2 vols. 4to, 1801, which was superintended in the press by the rev. John Hellins, B. D. F. R. S. vicar of Potter’s-pury, in Northamptonshire. Her eloge was pronounced by Frisi, and translated into French by Boulard.

The third and best translation was made by Golius, professor of mathematics and Oriental languages at Leyden this work, which came out in 1669, 4to, after the death of Golius, is accompanied with the Arabic text, and many learned notes upon the first nine chapters, for this author did not live to carry them farther.

By what means he was educated is not certainly known, but he studied philosophy at Paris in the colUge of the cardinal ie Moine, and although naturallyof slow capacity, his uncommon diligence enabled him to accumulate a large stock of classical and general knowledge. Having taken the degree of master of arts at nineteen, he pursued his studies under the royal professors established by Francis I. viz. James Tusen, who explained the Greek poets; Peter Dones, professor of rhetoric; and Oronce Fine, professor of mathematics. He left Paris at the age of twenty-three, and went to Bourges with the sieur Colin, who had the abbey of St. Ambrose in that city. At the recommendation of this abbot, a secretary of state took Amyot into his house, to be tutor to his children. The great improvements they made under his direction induced the secretary to recommend him to the princess Margaret duchess of Berry, only sister of Francis I.; and by means of this recommendation Amyot was made public professor of Greek and Latin in the university of Bourges: he read two lectures a day for ten years; a Latin lecture in the morning, and a Greek one in the afternoon. It was during this time he translated into French the “Amours of Theagenes and Chariclea,” with which Francis I. was so pleased, that he conferred upon him the abbey of Bellosane. The death of this prince happening soon after, Amyot thought it would be better to try his fortune elsewhere, than to expect any preferment at the court of France; he therefore accompanied Morvillier to Venice, on his embassy from Henry II. to that republic. When Morvillier was recalled from his embassy, Amyot would not repass the Alps with him; choosing rather to go to Rome, where he was kindly received by the bishop of Mirepoix, at whose house he lived two years. It was here that, looking over the manuscripts of the Vatican, he discovered that Heliodorus, bishop of Tricca, was the author of the Amours of Theagenes; and finding also a manuscript more correct and complete than, that which he had translated, he was enabled to give a better edition of this work. His labours, however, in this way, did not engage him so as to divert him from improving his situation, and he insinuated himself so far into the favour of cardinal de Tournon, that his eminence recommended him to the king, to be preceptor to his two younger sons. While he was in this employment he finished his translation of “Plutarch’s Lives,” which he dedicated to the king; and afterwards undertook that of “Plutarch’s Morals,” which he finished in the reign of Charles IX. and dedicated to that prince. Charles conferred upon him the abbey of St. Cornelius de, Compeigne, although much against the inclination of the queen, who had another person in her eye; and he also made him grand almoner of France and bishop of Auxerre; and the place of grand almoner and that of curator of the university of Paris happening to be vacant at the same time, he was also invested in both these employments, of which Thuanus complains. Henry III. perhaps would have yielded to the pressing solicitations of the bishop of St. Flour, who had attended him on his journey into Poland, and made great interest for the post of grand almoner; but the duchess of Savoy, the king’s aunt, recommended Amyot so earnestly to him, when he passed through Turin, on his return from Poland, that he was not only continued in his employment, but a new honour was added to it for his sake: for when Henry III. named Amyot commander of the order oiF the Holy Ghost, he decreed at the same time, as a mark of respect to him, that all the grand almoners of France should be of course commanders of that order. Amyot did not neglect his studies in the midst of his honours, but revised all his translations with great care, compared them with the Greek text, and altered many passages: he designed to give a more complete edition of them, with the various readings of divers manuscripts, but died before he had finished that work. He died the 6th of February, 1593, in the 79th year of his age.

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

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

The first four books were badly translated by Joan. Baptista Memmius. But a better translation of these in Latin was made by Commandine, and published at Bononia in 1566. Vossius mentions an edition of the Conies in 1650; the fifth, sixth, and seventh books being recovered by Golius. Claude Richard, professor of mathematics in the imperial college of his order at Madrid, in the year 1632, explained, in his public lectures, the first four books of Apollonius, which were printed at Antwerp in 1655, in folio. And the grand duke Ferdinand the second, and his brother prince Leopold de Medicis, employed a professor of the Oriental languages at Rome to translate the fifth, sixth, and seventh books into Latin. These were published at Florence in 1661, by Borelli, with his own notes, who also maintains that these books are the genuine production of Apollonius, by many strong authorities, against Mydorgius and others, who suspected that these three books were not the real production of Apollonius.

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

, born in the province of Cosenza in the kingdom of Naples in 1651, was first a Carmelite, and afterwards professor of mathematics and natural philosophy. He died in 1702, leaving the following publications, 1. “A dissertation on the life of the Fcetus in utero” 1686. 2. “A translation of the Elements of Euclid,” 1691. 3. “A treatise on the power of the Holy See,” 1693. 4. “A translation of Apollonius on Conic Sections,” 1702, 4to.

, son of the preceding, and likewise a celebrated physician, was born at Copenhagen the 20th Oct. 1616. After some years education in his pwn country, he went to Leydcn in 1637, where he studied physic for three years. He travelled next to France; and resided two years at Paris and Montpellier, in order to improve himself under the famous physicians of these two universities. He went from thence to Italy, and continued three years at Padua, where he was treated with great honour and respect, and was made a member of the IncogiutL by John Francis Loredan. After having visited most parts of Italy, he went to Malta, from that to Padua, and then to Basil, where he received his doctor’s degree in physic, the 14th of Oct. 1645. The year following he returned to his native country, where he did not remain long without employment; for, upon the death of Christopher Longomontan us, professor of mathematics at Copenhagen, he was appointed his successor in 1647. In 1648 he was named to the anatomical chair; an employment more suited to his genius and inclination, which he discharged with great assiduity for thirteen years. His intense application having rendered his constitution very infirm, he resigned his chair in 1661, and the king of Denmark allowed him the title of honorary professor. He retired to a little estate he had purchased at Hagested, near Copenhagen, where he intended to spend the remainder of his days in peace and tranquillity. An unlucky accident, however, disturbed him in his retreat: his house took fire in 1670, and his library was destroyed, with all his books and manuscripts. In consideration of this loss, the king appointed him his physician, with a handsome salary, and exempted his land from all taxes. The university of Copenhagen, likewise, touched with his misfortune, appointed him their librarian; and in 1675 the king honoured him still farther, by giving him a seat in the grand council of Denmark. He died the 4th of Pec. 1680, leaving a family of five sons and three daughters. Gaspard, one of the sons, succeeded him in the anatomical chair; another was counsellor-secretary to the king, and professor of antiquities; John was professor of theology; Christopher, of mathematics; and Thomas, mentioned hereafter, professor of history. Margaret, one of the daughters of this learned family, acquired considerable fame for her poetical talents.

, a monk of the EcolesPies, or Pious Schools, was born at Mondovi, and died at Turin, May 22, 1781. He was professor of mathematics and philosophy, first at Palermo, then at Rome; and by his experiments and discoveries was so successful as to throw great light on natural knowledge, and especially on that of electricity. He was afterwards called to Turin to take upon him the professorship of experimental philosophy. Being appointed preceptor to the two princes, Benedict duke of Chablais, and Victor Amadscus duke of Ctirignan, neither the life of a court, nor the allurements of pleasure, were able to draw him aside from study. Loaded with benefits and honours, he spared nothing to augment his library, and to procure the instruments necessary for his philosophical pursuits. His dissertations on electricity would have been more useful, if he had been less strongly attached to some particular systems, and especially that of Mr. Franklin. He published, 1. “Experimenta quibus Electricitas Vindex late constituitur, &c.” Turin, 1771, 4to. 2. “Electricismo artificiale,” 1772, 4to, an English translation of which was published at Lond. 1776, 4to. We have also by him an “Essay on the cause of Storms and Tempests,” where we meet with nothing more satisfactory than what has appeared in other works on that subject; several pieces on the meridian of Turin, and other objects of astronomy and physics. Father Beccaria was no less respectable for his virtues than his knowledge.

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

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

In 1683, he went again to Leyden, to be present at the sale of Nicholas Heinsius’s library; where he purchased, at a great price, several of the classical authors, thut had been either collated with manuscripts, or illustrated with the original notes of Joseph Scaliger, Bonaventure Vulcanius, the two Heinsiuses, and other celebrated critics. Here he renewed his acquaintance with several persons of eminent learning, particularly Gruevius, Spanheim, Triglandius, Gronovius, Perizonius, Ryckius, Gallaeus, Rulaeus, and especially Nicholas Witsen, burgomaster of Amsterdam, who presented him with a Coptic dictionary, brought from Egypt by Theodore Petraeus of Holsatia; and afterwards transmitted to him in 1686, the Coptic and Ethiopic types made of iron, for the use of the printingpress at Oxford. With such civilities he was so much pleased, and especially with the opportunities he had of making improvements in Oriental learning, that he would have settled at Leyden, if he could have been chosen professor of the Oriental languages in that university, but not being able to compass this, he returned to Oxford. He began now to be tired of astronomy, and his health declining, he was desirous to resign but no other preferment offering, he was obliged to hold his professorship some years longer than he intended; in 1684 he took his degree of D. D. and in 1691, being presented to the rectory of Brightwell in Berkshire, he quitted his professorship, and was succeeded by David Gregory, professor of mathematics at Edinburgh. In 1692, he was employed in drawing up a catalogue of the manuscripts in Great Britain and Ireland, which was published at Oxford 1697, fol. Dr. Bernard’s share in this undertaking was the drawing up a most useful and complete alphabetical Index to which he prefixed this title, “Librorum manuscriptorum Magnae Britanniae et Hibernise, atque externarum aliquot Bibliothecarum Index secundum alphabetum Edwardus Bernardus construxit Oxonii.” In this Index he mentions a great number of valuable Greek manuscripts, which are to be found in several foreign libraries, as well as our own. Towards the latter end of his life, he was much afflicted with the stone, yet, notwithstanding this and other infirmities, he took a third voyage to Holland, to attend the sale of Golius’s manuscripts. After six or seven weeks absence, he returned to London, and from thence to Oxford. There he fell into a languishing consumption, which put an end to his life, Jan. 12, 1696, before he was quite fifty-nine years of age. Four days after, he was interred in St. John’s chapel, where a monument of white marble was soon erected for him by his widow, to whom he had been married only three years. In the middle of it there is the form of an Heart carved, circumscribed with these words, according to his own direction a little before he died, Habemus Cor Bernard!: and underneath E. B. S. T. P. Obiit Jan. 12, 1696. The same is also repeated on a small square marble, under which he was buried. As to this learned man’s character, Dr. Smith, who knew him well, gives him a very great one. “He was (says he) of a mild disposition, averse to wrangling and disputes and if by chance or otherwise he happened to be present where contests ran high, he would deliver his opinion with great candour and modesty, and in few words, but entirely to the purpose. He was a candid judge of other men’s performances; not too censorious even on trifling books, if they contained nothing contrary to good manners, virtue, or religion and to those which displayed wit, learning, or good sense, none gave more ready and more ample praise. Though he was a true son of the Church of England, yet he judged favourably and charitably of dissenters of all denominations. His piety and prudence never suffered him to be hurried away by an immoderate zeal, in declaiming against the errors of others. His piety was sincere and unaffected, and his devotions both in public and private very regular and exemplary. Of his great and extensive learning, the works he published, and the manuscripts he has left, are a sufficient evidence.” This character is supported by the concurring evidence of all his learned contemporaries. The works he published were 1. “Tables of the longitudes and latitudes of the fixed Stars.” 2. “The Obliquity of the Ecliptic from the observations of the ancients, in Latin.” 3. “A Latin letter to Mr. John Flamsteed, containing observations on the Eclipse of the Sun, July 2, 1684, at Oxford.” All these are in the Philosophical Transactions, 4, “A treatise of the ancient Weights and Measures,” printed first at the end of Dr. Edward Pocock’s Commentary on Hosea, Oxford, 1685, fol. and afterwards reprinted in Latin, with very great additions and alterations, under this title, “De mensuris & ponderibus antiquis, libri tres,” Oxon. 1688, 8vo. 5. “Private Devotions, with a brief explication of the Ten Commandments,” Oxford, 1689, 12mo. 6. “Orbis eruditi Literatura a charactere Samaritico deducta” printed at Oxford from a copper-plate, on one side of a broad sheet of paper: containing at one view, the different forms of letters used by the Phoenicians, Samaritans, Jews, Syrians, Arabs, Persians, Brachmans, and other Indian philosophers, Malabarians, Greeks, Cophts, Russians, Sclavonians, Ethiopians, Francs, Saxons, Goths, &c. all collected from ancient inscriptions, coins, and manuscripts together with the abbreviations used by the Greeks, physicians, mathematicians, and chymists. 7. “Etymologicum Britannicum, or derivations of the British and English words from the Russian, Sclavonian, Persian, and Armenian languages printed at the end of Dr. Hickes’s Grammatica Anglo- Saxonica & Moeso-Gotthica,” Oxon. 1689, 4to. 8. He edited Mr. William Guise’s “Misnoe pars prima, ordinis primi Zeraim tituli septem,” Oxon. 1690, 4to. 9. “Chronologiae Samaritanae Synopsis,” in two tables the first containing the most famous epochas, and remarkable events, from the beginning of the world the second a catalogue of the Samaritan High Priests from Aaron, published in the “Acta Eruditqrum Lipsiensia,” April 1691, p. 167, &c. He also was author of the following: 10. “Notse in fragmentum Seguierianum Stephani Byzantini” in the library of monsieur Seguier, chancellor of France part of which, relating to Dodone, were published by Gronovius, at the end' of his “Exercitationes de Dodone,” Leyden, 1681. 11. “Adnotationes in Epistolam S. Barnabce,” published in bishop Fell’s edition of that author, Oxon. 1685, 8vo. 12. “Short notes, in Greek and Latin, upon Cotelerius’s edition of the Apostolical Fathers, printed in the Amsterdam edition of them. 13.” Veterum testimonia de Versione LXXII interpretum," printed at the end of Aristeae Historia LXXII interpretum, published by Pr. Henry Aldrich, Oxon. 1692, 8vo. 14. He translated into Latin, the letters of the Samaritans, which Dr. R. Huntington procured them to write to their brethren, the Jews in England, in 1673|­while he was at Sichem. Dr. Smith having obtained a copy of this translation, gave it to the learned Job LudoL fus, when he was in England, who published it in the collection of Samaritan Epistles, written to himself and other learned men. Besides these works, he also assisted several learned men in their editions of books, and collated manuscripts for them and left behind him in manuscript many books of his own composition, with very large collections which, together with the books enriched in the margin with the notes of the most learned men, and collected by him in France and Holland, were purchased by the curators of the Bodleian library, for the sum of two hundred pounds. They likewise bought a considerable number of curious and valuable books out of his library, which were wanting in the Bodleian, for which they paid one hundred and forty pounds. The rest of his books were sold by auction, all men of letters striving to purchase those which had any observations of Dr. Bernard’s own hand.

John Bernoulli had the degree of doctor of physic at Basil, and two years afterward was named professor of mathematics in the university of Groningen. It was here that he discovered the mercurial phosphorus or luminous barometer; and where he resolved the problem proposed by his brother concerning Isoperimetricals. On the death of his brother James, the professor at Basil, our author returned to his native country, against the pressing invitations of the magistrates of Utrecht to come to that city, and of the university of Groningen, who wished to retain him. The academic senate of Basil soon appointed him to succeed his brother, without assembling competitors, and contrary to the established practice: an appointment which he held during his whole life.

, a celebrated physician and philosopher, and son of John Bernoulli last mentioned, was born at Groningen Eeb. the 9th, 1700, where his father was then professor of mathematics. He was intended by his father for trade, but his genius led him to other pursuits. He passed some time in Italy; and at twenty -four years of age he declined the honour offered Rim of becoming president of an academy intended to have been established at Genoa. He spent several years with great credit at Petersburgh; and in 1733 returned to Basil, where his father was then professor of mathematics and here our author successively filled the chair of physic, of natural and of speculative philosophy. In his work “Exercitationes Mathematics?,” 1724, he took the only title he then had, viz, “Son of John Bernoulli,” and never would suffer any other to be added to it. This work was published in Italy, while he was there on his travels and it classed him in the rank of inventors. In his work, “Hydrodyriamica,” published in 4to at Strasbourg, in 1738, to the same title was also added that of Med. Prof. Basil.

, cosmographer and historiographer to Louis XIII. of France, and regius professor, of mathematics, was born at Beveren in Flanders, on the confines of the dioceses of Bruges and Ypres, Nov. 14, 1565. He was brought into England when but three months old, by his parents, who dreaded the persecution of the protestants which then prevailed in the Netherlands. He received the rudiments of his education in the suburbs of London, under Christian Rychius, and his learned daughter-in-law, Petronia Lansberg. He afterwards completed his education at Leyden, whither his father, then become protestant minister at Rotterdam, removed him in his twelfth year. In 1582, when only seventeen years of age, he began the employment of teaching, which he carried on at Dunkirk, Ostend, Middleburgh, Goes, and Strasburgh but a desire for increasing his own stock of learning induced him to travel into Germany with Lipsius, and the same object led him afterwards into Bohemia, Silesia, Poland, Russia, and Prussia. On his return to Leyden he was appointed to a professor’s chair, and to the care of the library, of which, after arranging it properly, he published a' catalogue. In 1606, he was appointed regent of the college, but afterwards, having taken part with the disciples of Arminius, and published several works against those of Gomarus, he was dismissed from all his employments, and deprived of every means of subsistence, with a numerous family. In March 1620, he presented a petition to the states of Holland for a pension, which was refused. Two years before, Louis XIII. had honoured him with the title of his cosmographer, and now constrained by poverty and the distress of his family, he went to France and embraced the popish religion, a change which gave great uneasiness to the protestants. Some time after he was appointed professor of rhetoric in the college of Boncourt, then historiographer to the king, and lastly assistant to the regius professor of mathematics. He died Oct. 3, 1629. A veryline engraving of him occurs at the back of the dedication to Louis XIII. of his “Theatrum Geographise veteris,” but (the collectors will be glad to hear) only in some copies of that work, which are supposed to have been presents from the author.

, a Swedish astronomer, was born about the middle of the seventeenth century. He became professor of mathematics at Upsal in 1679, but his zeal for the Cartesian system made him be considered as a dangerous innovator, and he might have been a serious sufferer from the prejudices raised against him, if he had not met with a kind protector in Charles XL This prince having travelled to Torneo, was so struck with the phenomena of the sun at the spring solstice, that he sent Biilberg and Spola to make observations on it, in the frontiers of Lapland, and their observations were confirmed by those of the French mathematicians sent thither by Louis XV. Under king Charles’s protection, Biilberg received considerable promotion, and having studied divinity, was at last made bishop of Strengnes. 'He died in 1717, leaving, 1. “Tractatus de Cometis,” Stockholm, 1682. 2. “Elementa Geometrices,” Upsal, 1687. 3. “Tractatus de refractione solis inoccidui,” Stockholm, 1696. 4. “Tractatus de reformatione Calendarii Juliani et Gregoriani,” Stockholm, 1699, and many other philosophical and theological dissertations.

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

, privy- counsellor of the landgrave of Hesse, and professor of mathematics and philosophy at Giessen, was born at Darmstadt, Nov. 17, 1720, and died July 6, 1790. As a philosopher, he adhered to the principles of Wolf, who had been his master, but in mathematics he followed and added to the improvement of the age, by many useful and experimental treatises. His “Magazine for engineers and artillery-men,” 1777 85, 12 vols. 8vo, procured him very considerable reputation. He also wrote, 1. “Logica, ordine scientifico in usum. auditorum conscripta,” Francfort, 1749 62 69, 8vo. 2. “Metaphysica,” Giessen, 1673, 8vo, and an improved edition, 1767, 8vo. He had a considerable hand in the “Francfort Encyclopaedia” and, along with F. K. Schleicher, wrote the “New Military Library,” Marbourg, 1789 90, 4 vols.

After this he removed from the noviciate to the Roman college, in order to study philosophy, which he did for three years, and as geometry made part of that course, he soon discovered that his mind was particularly turned to this science, which he cultivated with such rapid success, as to excel all his condisciples, and had already begun to give private lessons in mathematics. According to the ordinary course followed by the Jesuits, their young men, after studying philosophy, were employed in teaching Latin and the belles lettres for the space of five years, as a step to the study of theology and the priesthood at a riper age; but as Boscovich had discovered extraordinary talents for geometrical studies, his superiors dispensed with the teaching of the schools , and commanded him to commence the study of divinity, which he did for four years, but without neglecting geometry and physics, and before that space was ended, he was appointed professor of mathematics, an office to which he brought ardent zeal and h'rst-rate talents. Besides having seen all the best modern productions on mathematical subjects, he studied diligently the antient geometricians, and from them learned that exact method of reasoning which is to be observed in all his works. Although he himself easily perceived the concatenation of mathematical truths, and could follow them into their most abstruse recesses, yet he accommodated himself with a fatherly condescension to the weaker capacities of his scholars, and made every demonstration clearly intelligible to thm. When he perceived that any of his disciples were capable of advancing faster than the rest, he himself would propose his giving them private lessons, that so they might not lose their time; or he would propose to them proper books, with directions how to study by themselves, being always ready to solve difficulties that might occur to them. He composed also new elements of arithmetic, algebra, plain and solid geometry, &c. and although these subjects had been well treated by a great many authors, yet Boscovich’s work will always be esteemed by good judges as a masterly performance, well adapted to the purpose for which ii was intended. To this be afterwards added a new exposition of Conic Sections, the only part of his works which lias appeared in English, It was within these few years translated, abridged, and somewhat altered, by the rev. Mr, Newton of Cambridge.

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

It was upon the 30th of November 1680, that the royal society, as a proof of the just sense of his great worth, and of the constant and particular services which through a course of many years he had done them, made choice of him for their president; but he being extremely, and, as he says, peculiarly tender in point of oaths, declined the honour done him, by a letter addressed to his much respected friend Mr. Robert Hooke, professor of mathematics at Gresham college. About this time, Dr. Burnet being empioyed in compiling his admirable History of the Reformation, Mr. Boyle contributed very largely to the ex pence of publishing it; as is acknowledged by the doctor in his preface to the second volume. It was probably about the beginning of the year 1681, that he was engaged in promoting the preaching and propagating of the gospel among the“Indians; since the letter, which he wrote upon that subject, was in answer to one from Mr. John Elliot of New England, dated Nov. 4, 1680. This letter of Mr. Boyle is preserved by his historian; and it shews, that he had a great di-Hke to persecution on account of opinions in religion. He published in 1633, nothing but a short letter to Dr. Beal, in relation to the making of fresh water out of salt; but in 1684 he printed two very considerable works; 29.” Memoirs for the natural history of human blood, especially the spirit of that liquor,“8vo. 30.” Experiments and considerations about the porosity of bodies," 8vo.

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

, a celebrated French writer, was born at Rouen, Aug. 26, 1688, and commenced his noviciate among the Jesuits of Paris, Sept. 8, 1704. In 1706, he began his philosophical course in the royal college, and in 1708 was sent to Caen to complete his studies that he might take orders. Some of his pieces are dated from that city in 1710 and 1712, and one from Bourges in 1719. He appears indeed to have passed several years in the country, where he taught rhetoric. In 1713, he returned to Paris to study theology, and in 1722 he was again at Paris, where he took the vows in the society of Jesuits, and was intrusted with the education of the prince of Talmont. About the same time he assisted in the “Memoirs of the Arts and Sciences,” and continued his labours in that journal until 1729, when he was obliged to leave Paris for some time for having assisted in publishing father Margat’s History of Tamerlane, which it appears had g=ven offence. His absence, however, was not long, and on his return, or soon after, he was employed in continuing the “History of the Gallican church,” of which six volumes had been published by fathers Longueval and Fontenay. In 1725, he was appointed professor of mathematics, and filled that chair for six years with much reputation. It was probably in this situation that he read his lecture, on the “use of mathematical knowledge in polite literature,” now printed in the second volume of his works, nor did his various public employments prevent his publishing many other works, which were well received by the public. In 1722 he published, but without his name, his “Morale Chretienne,” Paris, a small volume, of which four editions were soon bought up. In 1723, he also published the first of his three letters, entitled “Examen du poema (de M. Racine) sur la grace,” 8vo, and in 1724, “La vie de Timperatrice Eleonore,” taken from that by father Ceva; the same year, “Abreg des vertus de soeur Jeanne Silenie de la Motte des Goutes,” Moulins, 12mo; and a new edition of father Mourgues “Traite de la Poesie Francoise,” with many additions, 12mo. But the work which contributed most to his reputation was his “Greek Theatre,” entitled “Theatre des Grecs, contenant des traductions ct analyses des tragedies Grecques, des discours et des remarques concernant la theatre Grec, &c.” 1730, 3 vols. 4to, and often reprinted in 12mo, in France and Holland. This useful work, not now in such high reputation as formerly, is yet well known in this country by the translation published by Mrs. Charlotte Lennox in 1760, 3 vols. 4to; to which the earl of Corke and Orrery contributed a general preface, and translated the three preliminary discourses: Dr. Sharpe, Dr. Grainger, and Mr. Bourryau translated some other parts, and Dr. Johnson contributed a dissertation on the Greek comedy, and the general conclusion of the work, which, in this translation, is certainly highly polished and improved. “Brumoy,” says Dr. Warton, “has displayed the excellencies of the Greek tragedy in a judicious and comprehensive manner. His jtranslations are faithful and elegant; and the analysis of those plays, which on account of some circumstances in ancient manners would shock the readers of this age, and would not therefore bear an entire version, is perspicuous and full. Of all the French critics, he and the judicious Fenelon have had the justice to confess, or perhaps the penetration to perceive, in what instances Corneille and Racine have falsified and modernized the characters, and overloaded with unnecessary intrigues the simple plots of the ancients.”

, an eminent French Inathematician and astronomer, was born at Rumigiiy in the diocese of Rheims on March 15, 1713. His father having quitted the army, in which he had served, amused himself in his retirement with studying mathematics and mechanics, in which he proved the author of several inventions of considerable use to the public. From this example of his father, our author “almost in his infancy took a fancy to mechanics, which proved of signal service to him in his maturer years. At school he discovered early tokens of genius. He came to Paris in 1729; where he studied the classics, philosophy, and mathematics, and afterwards divinity in the college de Navarre, with a view to the church, but he never entered into priest’s orders, apprehending that his astronomical studies, to which he had become much devoted, might too much interfere with his religious duties. His turn for astronomy soon connected him with the celebrated Cassini, who procured him an apartment in the observatory; where, assisted by the counsels of this master, he soon acquired a name among the astronomers, in 1739 he was joined with M. Cassini de Thury, son to M. Cassini, in verifying the meridian through the whole extent of France; and in the same year he was, named professor of mathematics in the college of Mazarine. In 1741 or author was admitted into the academy of sciences as an adjoint member for astronomy and had many excellent papers inserted in their memoirs; beside which he published several useful treatises, viz. Elements of Geometry, Astronomy, Mechanics, and Optics. He also carefully computed all the eclipses of the sun and moon that had happened since the Christian sera, which were printed in the work entitled” L'Art de verifier les dates,“&c. Paris, 1750, 4to. He also compiled a volume of astronomical ephemerides for the years 1745 to 1755; another for the years 1755 to 1765 and a third for the years 1765 to 1775 as also the most correct solar tables of any; and an excellent work entitled” Astronomic fundamenta novissimis solis et stellarum observationibus stabilita."

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

, a learned Jesuit, of a distinguished family in Placentia, was born there in 1617, and became professor of mathematics and theology at Rome. He was one of the two ecclesiastics who contributed to convert Christina, queen of Sweden, to the popish faith. She had desired that two Jesuits might be sent to confer with her on the subject. In 1652 he returned to Italy, and, as he had considerable political talents, was appointed superior to several houses belonging to the society of Jesuits: and he presided over the university of Parma for thirty years, and acted as confessor to two successive duchesses of Parma. Amidst all these occupations he had leisure for his mathematical studies and publications. He died at Parma, Dec. 22, 1707. His principal works are, 1. “Vacuum proscriptum,” Genoa, 1649. 2. “Terra machinis mota,” Rome, 1668, 4to. 3. “Mechanicorum libri octo,” 1684, 4to. 4. “De igne dissertationes,” 1686 and 1695. 5. “De angelis disputatio theologica,” Placentia, 1703. 6. “Hydrostaticse dissertationes,” Parma, 1695* 7. “Opticae disputationes,” Parma, 1705. What is somewhat extraordinary is, that he composed this treatise on optics at the age of eighty-eight, when he was already blind. His works on physics abound with good experiments and just notions.

After some education in his father’s house he was sent to study philosophy at the Mazarine college, where the celebrated Varignon was then professor of mathematics; from whose assistance young Cassini profited so well, that at fifteen years of age he supported a mathematical thesis with great honour. At the age of seventeen he was admitted a member of the academy of sciences; and the same year he accompanied his father in his journey to Italy, where he assisted him in the verification of the meridian at Bologna, and other measurement* On his return he made other similar operations in a journey into Holland, where he discovered some errors in the measure of the earth by Snell, the result of which was communicated to the academy in 1702. He made also a visit to England in 1696, where he was made r a member of the royal society. In 1712 he succeeded his father as astronomer royal at the observatory. In 17 17 he gave to the academy his researches on the distance of the fixed stars, in which he shewed that the whole annual orbit, of near 200 million of miles diameter, is but as a point in comparison of that distance. The same year he communicated also his discoveries concerning the inclination of the orbits of the satellites in general, and especially of those of Saturn’s satellites and ring. In 1723 he undertook to determine the cause of the moon’s libration, by which she shews sometimes a little towards one side, and sometimes a little on the other, of that half which is commonly behind or hid from our view.

In 1652 she first proposed to resign in favour of her successor, but the remonstrances of the States delayed this measure until 1654, when she solemnly abdicated the crown, that she might be at perfect liberty to execute a plan of life which vanity and folly seem to have presented to her imagination, as a life of true happiness, the royal cum dignitatc. Some time before this step, Anthony Macedo, a Jesuit, was chosen by John IV. king of Portugal, to accompany the ambassador he sent into Sweden to queen Christina; and this Jesuit pleased this princess so highly, that she secretly opened to him the design she had of changing her religion. She sent him to Rome with letters to the general of the Jesuits; in which she desired that two of their society might be dispatched to her, Italians by nation, and learned men, who should take another habit that she might confer with them at more ease upon matters of religion. The request was granted; and two Jesuits were immediately sent to her, viz. Francis Malines, divinity professor at Turin, and Paul Casati, professor of mathematics at Rome, who easily effected what Macedo, the first confidant of her design, had begun. Having made her abjuration of the Lutheran religion, at which the Roman catholics triumphed, and the protestants were discontented, both without much reason, she began her capricious travels: from Brussels, or as some say, Inspruck, at which she played the farce of abjuration, she went to Rome, where she intended to fix her abode, and where she actually remained two years, and met with such a reception as suited her vanity. But some disgust came at last, and she determined to visit France, where Louis XIV. received her with respect, but the ladies of the court were shocked at her masculine appearance, and more at her licentious conversation. Here she courted the learned, and appointed Menage her master of ceremonies, but at last excited general horror by an action, for which, in perhaps any other country, she would have been punished by death. This was the murder of an Italian, Moualdeschi, her master of the horse, who had betrayed some secret entrusted to him. He was summoned into a gallery in the palace, letters were then shewn to him, at the sight of which he turned pale, and intreated for mercy, but he was instantly stabbed by two of her own domestics in an apartment adjoining that in which she herself was. The French court was justly offended at this atrocious deed, yet it met with vindicators, among whom was Leibnitz, whose name was disgraced by the cause which he attempted to justify. Christina was sensible that she was now regarded with horror in France, and would gladly have visited England, but she received no encouragement for that purpose from Cromwell: she therefore, in 1658, returned to Rome, and resumed her amusements in the arts and sciences. But Rome had no permanent charms, and in 1660, on the death of Gustavus, she took a journey to Sweden for the purpose of recovering her crown and dignity. She found, however, her ancient subjects much indisposed against her and her new religion. They refused to confirm her revenues, caused her chapel to be pulled down, banished all her Italian chaplains, and, in short, rejected her claims. She submitted to a second renunciation of the throne, after which she returned to Rome, and pretended to interest herself warmly, first in behalf of the island of Candia, then besieged by the Turks, and afterwards to procure supplies of men and money for the Venetians. Some differences with the pope made her resolve, in 1662, once more to return to Sweden; but the conditions annexed by the senate to her residence there, were now so mortifying, that she proceeded no farther than Hamburgh, and from Hamburgh again to Rome, where she died in 1689, leaving a character in which there is little that is amiable. Vanity, caprice, and irresolution deformed her best actions, and Sweden had reason to rejoice at the abdication of a woman who could play the tyrant with so little feeling when she had given up the power. She left some maxims, and thoughts and reflections on the life of Alexander the Great, which were translated and published in England in 1753; but several letters attributed to her are said to be spurious.

Vol. IX, purely primitive. This he thought to be the only means of making the minds of sincere Christians easy and quiet. This he believed would make men much more charitable to one another: and make the governors of the church and state transact their important affairs with greater ease and freedom from disturbances.“Upon the whole, bishop Hoadly makes no scruple to declare, that” by Dr. Clarke’s death, the world was deprived of as bright a light, and masterly a teacher of truth and virtue, as ever yet appeared amongst us and,“says he in the conclusion of his account,” as his works must last as long as any language remains to convey them to future times, perhaps I may flatter myself that this faint and imperfect account of him may be transmitted down with them. And I hope it will be thought a pardonable piece of ambition and self-interestedness, if, being fearful lest every thing else should prove too weak to keep the remembrance of myself in being, I lay hold on his fame to prop and support my own. I am sure, as I have little reason to expect that any thing of mine, without such an assistance, can live, I shall think myself greatly recompensed for the want of any other memorial, if my name may go down to posterity thus closely joined with his; and I myself be thought of, and spoke of, in ages to come, under the character of The Friend of Dr. Clarke.“' On the other hand, Whiston, who wrote his Life, and held him in as high estimation as either Dr. Hare or Dr. Hoadly, candidly mentions those failings, some of which, perhaps, may occur to the reader in perusing the preceding pages, and considerably lessen our opinion of his consistency. In the lirst place, he blames Clarke for subscribing the articles, at a time when he could not, with perfect truth and sincerity, assent to the Athanasian parts of them; namely, at his taking the degree of doctor in divinity. Mr. Whiston, then professor of mathematics at Cambridge, endeavoured to dissuade him from it; and, when he could not prevail on that head, he earnestly pressed him to declare openly, and in writing, in what sense he subscribed the suspected articles: but he could not prevail on this head neither. Upon this occasion, professor James, who suspected Dr. Clarke of an inclination to heretical pravity, said to him, upon his subscribing the articles,” he hoped he would not go from his subscription.“The doctor replied,” He could promise nothing as to futurity, and eould only answer as to his present sentiments*“However, Mr.Whiston acknowledges, that Dr. Clarke, for many years before he died, perpetually refused all, even the greatest preferments, which required subscription, and never encouraged those who consulted him to subscribe. In the next place, he objects to Dr. Clarke his not acting sincerely, boldly, and openly, in the declaration of his true opinions, and his over-cautious and over-timorous way of speaking, writing, and acting, in points of the highest consequence. When Mr. Whiston gave him frequent and vehement admonitions upon this head, his general answer, he tells us, was, who are those that act better than I do” Very few of which,“says he,” I could ever name to him though I did not think that a sufficient excuse.“Lastly, Mr. Whiston is greatly displeased with Dr. Clarke’s conduct in relation to the affair of the convocation, and concludes the account of that affair with these words” Thus ended this unhappy affair unhappy to Dr. Clarke’s own conscience unhappy to his best friends and above all unhappy as to its consequences, in relation to the opinion unbelievers were hereupon willing to entertain of him, as if he had prevaricated all along in his former writings for Christianity."

, an eminent astronomer, was born at Thorn in Prussia, January 19, 1473. His father was a stranger, but from what part of Europe is unknown. He settled here as a merchant, and the archives of the city prove that he obtained the freedom of Thorn in 1462. It seems clear that he must have been in opulent circumstances, and of consideration, not only from the liberal education which he bestowed upon his son, but from the rank of his wife, the sister of Luca Watzelrode, bishop of Ermeland, a prelate descended from one of the most illustrious families of Polish Prussia. Nicholas was instructed in the Latin and Greek languages at home; and afterward sent to Cracow, where he studied philosophy, mathematics, and medicine: though his genius was naturally turned to mathematics, which he chiefly studied, and pursued through all its various branches. He set out for Italy at twenty-three years of age; stopping at Bologna, that he might converse with the celebrated astronomer of that place, Dominic Maria, whom he assisted for some time in making his observations. From hence he passed to Rome, where he was presently considered as not inferior to the famous Regiomontanus. Here he soon acquired so great a reputation, that he was chosen professor of mathematics, which he taught there for a long time with the greatest applause and here also he made some astronomical observations about the year 1500.

When Dr. Plume’s professorship for astronomy and experimental philosophy was contended for, Mr. Whiston was one of the electors. Besides Mr. Cotes, there was another candidate, who had been a scholar of Dr. Harris’s. As Mr. Whiston was the only professor of mathematics who was directly concerned in the choice, the rest of the electors naturally paid a great regard to his judgment. At the time of election, Mr. Whiston said, that he pretended himself to be not much inferior to the other candidate’s master, Dr. Harris; but he confessed “that he was but a child to Mr. Cotes.” The votes were unanimous for Mr. Cotes, who was then onJy in the twenty-fourth year of his age.

, an excellent French geometrician, a member of the old academy of sciences, and more recently of the conservative senate, and the national institute of France, was horn at Paris, Jan. 28, 1739, and was early distinguished for literary industry, and habits of study and reflection, which were confined at last to the pursuit of mathematical knowledge and natural philosophy. In 1766 he was appointed professor of the latter in the college of France, as coadjutor of Le Monnier, which situation he filled for thirty-two years with great reputation. 3u 1769 he was appointed professor of mathematics in the military school in 1772 he was admitted into the academy of sciences as adjoint-geometer, and in 1777 he published the first edition of his lessons on the “Calcul differentiel, et Calcul integral,” 2 vols. 12mo, reprinted in 1796 and 1797, in 2 vols. 4to, a work which manifests the depth and precision of his geometrical knowledge. In 1787 he published his “Introduction a l‘etude de l’Astronomie physique,” 8v; and in 1798, “Elemens d'Algebre,” 8vo. There are also various essays by him in the Memoirs of the Academy of Sciences. In 1791 he was appointed municipal officer of the commune of Paris, and his office being to provide the metropolis with provisions at that distracted period, he must have executed its duties with no common prudence and skill to have given satisfaction. In 1796 he resumed his professor’s chair in the college of France, and in 1799 was chosen a member of the conservative senate. His conduct in political life we are unacquainted with. He died at Paris December 30, 1808.

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

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

This new principle being now established, he was soon able to construct object-glasses, in which the different refrangibility of the rays of light was corrected, and the name of achromatic was given to them by the late Dr. Bevis, on account of their being free from the prismatic colours, and not by Lalande, as some have said. As usually happens on such occasions, no sooner was the achromatic telescope made public, than the rivalship of foreigners, and the jealousy of philosophers at home, led them to doubt of its reality and Euler himself, in his paper read before the academy of sciences at Berlin in 1764, says, “I am not ashamed frankly to avow that the first accounts which were published of it appeared so suspicious, and even so contrary to the best established principles, that I could not prevail upon myself to give credit to them;” and he adds, *' I should never have submitted to the proofs which Mr. Dollond produced to support this strange phenomenon, if M. Clairaut, who must at first have been equally surprized at it, had not most positively assured me that Dpllond’s experiments were but too well founded.“And when the fact could be no longer disputed, they endeavoured to find a prior inventor, to whom it might be ascribed; and several conjecturers were honoured with the title of discoverers. But Mr. Peter Dollond in the paper we have just mentioned, has stated and vindicated, in the most unexceptionable and convincing manner, his father’s right to the first discovery of this improvement in refracting telescopes, as well as of the principle on which it was founded. In so doing he has corrected the mistakes of M. de la Lande in his account of this subject; those of M. N. Fuss, professor of mathematics at St. Petersburg, in his” Eulogy on Euler,“written and published in 1783; and those of count Cassini, in his” Extracts of the Observations made at the Royal Observatory at Paris in the year 1787;" and it must appear to every impartial and candid examiner, that Mr. Dollond was the sole discoverer of the principle which led to the improvement of refracting telescopes.

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

The concluding period of Erigena’s life is involved in some degree of uncertainty. According to Cave and Tanner, he removed from France to England in the year 877, and was employed by king Alfred in the restoration of learning at the university of Oxford, but this proceeds upon the tradition that Alfred did restore learning at Oxford, which has no foundation whatever. It is said by Tanner, that in the year 879 he was appointed professor of mathematics and astronomy at Oxford, which is likewise very doubtful, although it may not be improbable that he read lectures in Little University hall,- now part of Brazennose college, without the rank of professor. Here he is reported to have continued three years, when, upon account of some differences which arose among the gownsmen, he retired to the abbey of Mahnesbury, where he opened a school. Behaving, however, with harshness and severity to his scholars, they were so irritated, that they are reported to have murdered him with the iron bodkins which were then used in writing. According to others, the scholars were instigated to this atrocious act by the monks, who had conceived a hatred against Scotus, as well for his learning as his heterodoxy. Such is Leland’s account, who expressly says that it was the Scotus who translated Dionysius. The time of his death js differently stated, but is generally referred to the year 883. Some, however, place it in either the year 884 or 886. Such is the state of facts, as given by most of the English writers; but other authors suppose that our historians have con.­founded John Scotus Erigena with another John Scot, who was an Englishman, and who taught at Oxford. Accordr ing to Mackenzie, Erigena retired to England in the year 864, and died there about the year 874. As a proof of the last circumstance, he refers to a letter of Anastasius the librarian to Charles the Bald, written in the year 875, which speaks of Scotns as of a dead man. Dr. Henry thinks it most probable that he ended his days in France. Anastasius had so high an opinion of Erigena, that he ascribed his translation of the works of Dionysius to the especial influence of the spirit of God. He was undoubtedly a very extraordinary man for the period in which he lived. During a long time he had a place in the list of the saints of the church of Rome; but at length, on account of its being discovered that he was heterodox with regard to the doctrine of transubstantiation, Baronius struck his name out of the calendar. A catalogue of Scotus’s works in general may be seen in Cave. Bale has added to the number, but probably without sufficient reason. The following are all that have been printed: 1. “De divisione Nature,” Oxon. by Gale, 1681, fol. 2. “De pncdestinatione Dei, contra Goteschalcum,” edited by Gilb. Maguin in his “Vindiciac praedestinationis et gratiæ,” vol. I. p. 103. 3. “Excerpta de differentiis et societatibus Graeci Latinique verbi,” in Macrobius’s works. 4. “De corpore et sanguine Domini,” 1558, 1560, 1653; Lend. 1686, 8vo. 5. “Ambigtia S. Maximi, seu scholia ejus in difh'ciles locos S. Gregorii Nazianzeni, Latino versa,” along with the “Divisio Nature,” Oxford, 1681, folio. 6. “Opera S. Dionysii quatuor in Latinam linguam conversa,” in the edition of Dionysius, Colon. 1536. Many of his Mss. are preserved in various libraries.

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

, inventor of the first method of resolving biquadratic equations, was born at Bologna about 1520. He studied mathematics under the celebrated Cardan, who, having had a problem given him lor solution, gave it his pupil as an exercise of his ingenuity; and this led to the discovery of a new method of analysis, which is precisely that of biquadratics. Cardan published this method, and assigned the invention to its real author, who, had it not been for this liberal conduct of the master, would have been unknown to posterity. At the age of eighteen he was appointed a tutor in arithmetic, and was equal to the task of disputing with the most distinguished mathematicians of his own age. He was afterwards appointed professor of mathematics at Bologna, where he died in 1565. Ferrari, although, like many other learned men of his age, addicted to astrology, was an excellent classical scholar, a good geographer, and well versed in the principles of architecture.

, in French Finé, professor of mathematics in the Royal college at Paris, was the son of a physician, and born at Briungon, in Dauphine, in 1494. He went young to Paris, where his friends procured him a place in the college of Navarre. He there applied himself to polite literature and philosophy; yet devoted himself more particularly to mathematics, for which he had a strong natural inclination, and made a considerable progress, though without the assistance of a master. He acquired likewise much skill in mechanics; and having both a genius to invent instruments, and a skilful hand to make them, he gained high reputation by the specimens he gave of his ingenuity. He first made hinaself known by correcting and publishing Siliceus’s “Arithmetic,” and the “Margareta Philosopiiica.” He afterwards read private lectures in mathematics, and then taught that science publicly in the college of Gervais; by which he became so famous, that he was recommended to Francis I. as the fittest person to teach mathematics in the new college which that prince had founded at Paris. He omitted nothing to support the glory of his profession; and though he instructed his scholars with great assiduity, yet he found time to publish a great many books upon almost every part of the mathematics. A remarkable proof of his skill in mechanics is exhibited in the clock which he invented in 1553, and of which there is a description in the Journal of Amsterdam for March 29, 1694. Yet his genius, his labours, his inventions, and the esteem which an infinite number of persons shewed him, could not secure him from that fate which so often befalls men of letters. He was obliged to struggle all his life with poverty; and, when he died, left a wite and six children, and many debts. His children, however, found patrons, who for their father’s sake assisted his family. He died in 1555, aged sixty-one. Like all the other mathematicians and astronomers of those times, he was greatly addicted to astrology; and had the misfortune to be a long time imprisoned, because he had foretold some things which were not acceptable to the court of France. He was one of those who vainly boasted of having found out the quadrature of the circle. His works were collected in 3 vols. folio, in 1535, 1542, and 1556, and there is an Italian edition in 4to, Venice, 1587.

, an eminent physician of Montpellier, the son of Nicholas Fizes, professor of mathematics in that university, was born in 1690, and at first educated by his father, who hoped that he would succeed him in the mathematical chair; but his disposition being more to the study of medicine, his father sent him to complete his medical education at Paris, under the tuition of Du Verney, Lemery, and the two messrs. De Jussieu. On his return to Montpellier, he employed himself in observing diseases in the hospital de la Charite, and in public teaching. On the death of his father, he was appointed joint professor of mathematics with M. de Clapiers, and soon became his sole successor. In 1732, the medical professorship in the university being vacant by the resignation of M. Deidier, Fizes was elected his successor. He fulfilled the duties of this chair with great propriety, but was more highly distinguished as a practitioner. He appreciated at once the character of the most complicated disease; and was above all admired for the accuracy of his prognostics. These qualifications placed him at the head of his profession at Montpellier; his fame extended to the metropolis, and he was invited to the office of physician to the duke of Orleans. His age was now, however, advanced; and the fear of the jealousy which this high appointment might produce among his brethren, led him to make some efforts to be permitted to decline this honour. He removed to Paris, nevertheless; but, unused to the intrigues and railJeries and cabals of a court, he was unhappy in his situation; his health began to fail, and he was induced to request permission to resign his office, and returned to Montpellier, after residing fourteen months at Paris, honoured with the protection of the prince, and the friendship of M. Senac, Astruc, Bordeu, &c. He was accused of a little misanthropy on this occasion; but he was an enemy to adulation and selfishness, and seemed to revolt from very species of artificial politeness. He resumed the functions of his professorship at Montpellier but for a short period; for he was carried off by a malignant fever in the course of three days, and died on August 14, 1765, aged about seventy-five years. His works were principally essays on different points of theory and practice. 1. “De Hominis Liene sano,” Montpellier^ 1716; 2. “De naturali Secretione Bilis in Jecore,” ibid.' 1719 3. “Specimen de Suppuratione in Partibus mollibus,” ibid. 1722 4. “Partium Corporis himiani Solidarum Conspectus Anatomico-Mechanicus,” ibid. 1729; 5. “De Cataracta” 6. “Universae Physiologiae Conspectus,” ibid. 1737; 7. “De Tumoribus in Genere,” ibid. 1738; 8. “Tractatus de Febribus,” ibid. 1749. The greater part of the writings of Fizes were collected in one 4to volume, and were published at Montpellier in 1742.

His ingenious friend, Dr. Robert Smith, then Plumian professor of mathematics in Cambridge, and afterwards master of Trinity college there, being engaged in composing “A complete system of Optics,” Mr. Folkes furnished him with several curious remarks, for vhich. he received the acknowledgments of the professor in the preface to that work, published in 1738, 4to. As he had not seen France in his travels to Italy, he made a tour to Paris in May 1739, chiefly with a view of seeing the academies there, and conversing with the learned men who do honour to that city and the republic of letters, and by whom he was received with all the testimonies of reciprocal regard. Sir Huns Sloane having, on account of his advanced age and growing infirmities, resigned the office of president of the royal society, at tlje annual election in 1741, Mr, Folkes was unanimously chosen to fill that honourable post, which he did with the highest reputation to the society and himself, and soon after his election he presented the society with 100l. The following year he was chosen to succeed Dr. Halley, as a memher of the royal academy of sciences at Paris. The university of Oxford also, being desirous of having a gentleman of his eminence in the learned world a member of their body, conferred on him in the year 1746, the degree of LL. D. upon receiving whick be returned them a compliment in a Latin speech, admired for its propriety and elegance. He was afterwards admitted to the same degree at Cambridge.

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

, a person memorable in English history for having been privy to the celebrated conspiracy called “The Gunpowder Plot,” was born in Nottinghamshire in 1555, and bred at Winchester school; whence he went to Rome, and took the Jesuit’s habit in 1575. After studying under Bellarmin, Saurez, and Christopher Clavius, he was for some time professor of philosophy and Hebrew in the Italian college at Rome; and when Clavius, professor of mathematics, was disabled by old age, he supplied his place in the schools. He returned to England in 1586, as provincial of his order; although it was made treason the year before, for any Romish priest to come into the queen’s dominions. Here, under pretence of establishing the catholic faith, he laboured incessantly to raise some disturbance, in order to bring about a revolution; and with this view held a secret correspondence with the king of Spain, whom hs solicited to project n expedition against his country. This not proceeding so fast as he would have it, he availed himself of the zeal of some papists, who applied to him, as head of their order, to resolve this case of conscience; namely, “Whether, for the sake of promoting the catholic religion, it might be permitted, should necessity so require, to involve the innocent in the same destruction with the guilty?” to which this casuist replied without hesitating, that, “if the guilty should constitute the greater number, it might.” This impious determination gave the first motion to that horrible conspiracy, which was to have destroyed at one stroke the king, the royal family, and both houses of parliament; but the plot being providentially discovered, Garnet was sent to the Tower, and was afterwards tried, condemned to be hanged for high-treason, and executed at the west end of St. Paul’s, May 3, 1606. He declared just before his execution, that he was privy to the gunpowder plot; but, as it was revealed to him in confession, thought it his duty to conceal it. But besides this miserable subterfuge, it was proved that he knew something of it, out of confession. He has been placed by the Jesuits among their noble army of martyrs. He was pyobably an enthusiast, and certainly behaved at his execution in a manner that would have done credit to a better cause. It is said, however, upon other authority, that he declined the honour of martyrdom, exclaiming, “Me niartyretn O quale martyrem” “I a martyr! O what a martyr!” Dodd’s account of his execution is rather interesting. He published some works, among which are enumerated, i. “A treatise of Christian Renovation or Birth,” London, 1616, 8vo. 2. “Canisius’s Catechism, translated from the Latin,” ibid. 1590, 8vo, and St. Omers, 1622. Several works were published in defence of the measures taken against, him.

Gassendi had from his infancy a turn to astronomy, which grew up with his years; and, in 1618, he had begun to make observations upon the stars, and to digest them into a method. His reputation daily increasing, he became so eminent in that science, that in 1645 he was appointed royal professor of mathematics at Paris, by the interest of Alphonse du Plessis, cardinal of Lyons, and brother to car/dinal Richelieu. This institution being chiefly designed for astronomy, Gassendi not only employed himself very diligently in observations, but read lectures with great applause to a crowded audience. He did not, however, hold this place long; for, contracting a cold, which brought on a dangerous cough, and an inflammation of his lungs, he found himself under a necessity of quitting Paris; and being advised by the physicians to return to Digue for the benefit of his native air, he went there in 1647. This advice had the desired success; which was also effected the sooner by the kindness of Louis Valois, earl of Alais, and viceroy of Provence, who, observing the philosopher’s circumstances, invited him to his house; where Gassendi’s conversation upon points of learning gave him so high an idea of his talents, that he frequently made use of him as a friend and counsellor in political affairs. After enjoying this honourable ease until this nobleman was called to court, Gassendi returned to Digne, where he began to write the Ij^e of his patron, the famous Nicolas Peiresc, a task which had been enjoined him by the earl of Alais.

, a learned French physician, professor of mathematics, and a member of several learned societies, was born at Paris March 7, 1722. His first public services in the literary world were the arrangement and preparation for the press of M. la Condamiue’s memoir on the measure of the first three degrees of the meridian in the Southern hemisphere. In the Encyclopaedia he was chosen for the department of the mechanic arts, and his numerous articles are remarkable for accuracy and perspicuity. He had a great turn for mechanics, and invented several machines still employed in agriculture and chemistry, c. in France. In connexion with the unfortunate baron de Marivetz, he published a learned and elaborate work entitled “Physique du monde,” five volumes of which he published during the life of his colleague, and afterwards three others. The whole was to have been comprized in 14 vols. 4to, but of these eight only have appeared. In 1779 he published “Prospectus d'un traite de geometric physique particuliere du royaume de France,” 4to. He died at Paris in 1800.

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

, the first of an eminent family of learned men in Scotland, was the son of the Rev. Mr. John Gregory, minister of Drumoak in the county of Aberdeen, and was born at Aberdeen in November 1638. His mother was a daughter of Mr. David Anderson of Finzaugh, or Finshaugh, a gentleman who possessed a singular turn for mathematical and mechanical knowledge. This mathematical genius was hereditary in the family of the Andersons, and from them it seems to have been transmitted to their descendants of the names of Gregory, Reid, &c. Alexander Anderson, cousin -german of the said David, was professor of mathematics at Paris in the beginning of the seventeenth century, and published there several valuable and ingenious works; as may be seen in our vol. II. The mother of James Gregory inherited the genius of her family; and observing in her son, while yet a child, a itrong propensity to mathematics, she instructed him herself in the elements of that science. His education in the languages he received at the grammar-school of Aberdeen, and went through the usual course of academical studies at Marischal college, but was chiefly delighted with philosophical researches, into which a new door had been lately opened by the key of the mathematics. Galileo, Kepler, and Des Cartes were the great masters of this new method; their works, therefore, Gregory made his principal study, and began early to make improvements upon their discoveries in optics. The first of these improvements was the invention of the reflecting telescope, which still bears his name; and which was so happy a thought, that it has given occasion to the most considerable improvements made in optics, since the invention of the telescope. He published the construction of this instrument in his “Optica promota,” 1663, at the age of twenty-four. This discovery soon attracted the attention of the mathematicians, both of our own and foreign countries, who immediately perceived its great importance to the sciences. But the manner of placing the two specula upon the same axis appearing to Newton to be attended with the disadvantage of losing the central rays of the larger speculum, he proposed an improvement on the instrument, by giving an oblique position to the smaller speculum, and placing the eye-glass in the side of the tube. It is observable, however, that the Newtonian construction of that instrument was long abandoned for the original or Gregorian, which is now always used when the instrument is of a moderate size; though Herschel has preferred the Newtonian form for the construction of those immense telescopes which he has of late so successfully employed in observing the heavens.

In 1668 our author published at London another work, entitled “Exercitationes Geometricae,” which contributed still much farther to extend his reputation. About this time he was elected professor of mathematics in the university of St. Andrew’s, an office which he held for six years. During his residence there he married, in 1669, Mary, the daughter of George Jameson, the celebrated painter, whom Mr, Walpole has termed the Vandyke of Scotland, and who was fellow disciple with that great artist in the school of Rubens at Antwerp. His fame placed him in so great esteem with the royal academy at Paris, that, in the beginning of 1671, it was resolved by that aca^ demy to recommend him to their grand monarch for a pension; and the design was approved even by Mr. Huygens, though he said he had reason to think himself improperly treated by Mr. Gregory, on account of the controversy between them. Accordingly, several members of that academy wrote to Mr. Oldenburg, desiring him to acquaint the council of the royal society with their proposal; informing him likewise, that the king of France was willing to allow pensions to one or two learned Englishman, whom they should recommend. But no answer was ever made to that proposal; and our author, with respect to this particular, looked upon it as nothing more than a compliment.

We are assured, that at his death he was in pursuit of a general method of quadrature, by infinite series, like that of sir Isaac. This appeared by his papers, which came into the hands of his nephew, Dr. David Gregory, who published several of them; and he himself assured Mr. Collins, he had found out the method of making sir Isaac’s series; who thereupon concluded he must have written a treatise upon it. This encouraged Mr. Stewart, professor of mathematics in Aberdeen, to take the trouble of examining his papers, then in the hands of Dr. David Gregory, the late dean of Christ church, Oxford; but no such treatise could be found, nor any traces of it, and the same had been declared before by Dr. David Gregory; whence it happens, that it is still unknown what his method was of making those serieses. However, Mr. Stewart affirms, that, in turning over his papers, he saw several curious upon particular subjects, not yet printed. On the contrary, some letters which he saw confirmed Dr. David Gregory’s remark, and made it evident, that our author had never compiled any treatise, containing the foundations of this general method, a very short time before his death; so that all that can be known about his method can only be collected from his letters, published in the short history of his “Mathematical Discoveries,” compiled by Mr. Collins, and his letters to that gentleman in the “Commercium Epistolicum.” From these it appears, that, in the beginning of 1670, when Mr. Collins sent him sir Isaac Newton’s series for squaring the circular zone, it was then so much above every thing he comprehended in this way, that after having endeavoured in vain, by comparing it with several of his own, and combining them together, to discover the method of it, he concluded it to be no legitimate series; till, being assured of his mistake by his friend, he went again to work, and after almost a whole year’s indefatigable pains, as he acknowledges, he discovered, at last, that it might be deduced from one of his own, upon the subject of die logarithms, in which he had given a method for finding the power to any given logarithm, or of turning the root of any pure power into an infinite series; and in the same manner, viz. by comparing and combining his own series together, or else by deduction therefrom, he fell upon several more of sir Isaac’s, as well as others like them, in which he became daily more ready by continual practice; and this seems to have been the utmost he ever actually attained to, in the progress towards the discovering any universal method for those series.

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

, professor of chemistry and of the practice of medicine in the university of Jena, was born in that city, December 21, 1697, his father being professor of mathematics in the same university. From his earliest years he had evinced a disposition to the study of anatomy, and was accustomed to steal from his parents, whf> destined him for the church, to attend the lectures of Slevoight on that subject. After the death of his father he relinquished even the study of the mathematics, to which he had applied himself during several years, and gave up his attention exclusively to medical pursuits. In 1721 he took the degree of M. D. and in 1726 was appointed professor; and he held the chair of the practice of medicine at the time of his death, which occurred June 22, 1755.

, a learned astronomer, and member of most of the learned societies of Europe, was born in 1720, at Chemnitz, in Hungary, and first educated at Neusol. Having in 1738 entered the society of the Jesuits, he was sent by them to the college of Vienna, where, during his philosophical studies, he displayed a genius for mechanics, and employed his leisure hours in constructing water-clocks, terrestrial and celestial globes, and other machines. In 1744 and 1745 he studied mathematics, now become his favourite pursuit, under the celebrated Froelich, and not only assisted Franz, the astronomer of the Jesuits’ observatory, in his labours, but also in arranging the museum for experimental philosophy. At the same time he published a new edition of Crevellius’s “Arithmetica numeralis et literalis,” as a text-book. In 1746 and 1747 he taught Greek and Latin in the catholic school of Leutschau, in Hungary, and returning to Vienna in the latter year, was employed as the instructor in the mathematics, and the art of assaying, of several young men destined for offices in the Hungarian mines. In 1750 he published, “Adjumentum memoriae manuale Chronologicogenealogico-historicum,” which has since been translated into various languages, and of which an enlarged edition appeared in 1774. In 1751 and 1752 he obtained the priesthood, completed his academical degrees, and was appointed professor of mathematics at Clausenburg. Here he published his “Elementa Arithmetical 1 for the use of his pupils, and had prepared other works, when he was, in Sept. 175”2, invited to Vienna, and appointed astronomer and director of the new observatory, in the building of which he assisted, and made it one of the first in Europe, both as to construction and apparatus. From 1757 to 1767 he devoted himself entirely to astronomical observations and calculations for the “Ephemerides,” each volume of which, published annually, contained evident proofs of his assiduity. About the same time he published a small work, entitled “An Introduction towards the useful employment of Artificial Magnets.”

, or Hemsterhusius, one of the most famous critics of his country, the son of Francis Hemsterhuis, a physician, was born at Groningen, Feb. 1, 1635. After obtaining the rudiments of literature from proper masters, and from his father, he became a member of his native university in his fourteenth year, 1698. He there studied for some years, and then removed to Leyden, for the sake of attending the lectures of the famous James Perizonius on ancient history. He was here so much noticed by the governors of the university, that it was expected he would succeed James Gronovius as professor of Greek. Havercamp, however, on the vacancy, was appointed, through the intrigues, as Ruhnkenius asserts, of some who feared they might be eclipsed by young Hemsterhuis; who in 1705, at the age of nineteen, was called to Amsterdam, and appointed professor of mathematics and philosophy. In the former of these branches he had been a favourite scholar of the famous John Bernouilli. In 1717, he removed to Franeker, on being chosen to succeed Lambert Bos as professor of Greek; to which place, in 1738, was added the professorship of history. In 1740 he removed to Leyden to accept the same two professorships in that university. It appears that he was married, because his father-in-law, J. Wild, is mentioned; he died April 7, 1766, having enjoyed to the last the use of all his faculties. He published, 1. “The three last books of Julius Pollux’s Onomasticon,” to complete the edition of which, seven books had been finished by Lederlin. This was published at Amsterdam in 1706. On the appearance of this work, he received a letter from Bentley, highly praising him for the service he had there rendered to his author. But this very letter was nearly the cause of driving him entirely from the study of Greek criticism: for in it Bentley transmitted his own conjectures on the true readings of the passages cited by Pollux from comic writers, with particular view to the restoration of the metre. Hemsterhuis had himself attempted the same, but, when he read the criticisms of Bentley, and saw their astonishing justness and acuteness, he was so hurt at the inferiority of his own, that he resolved, for the time, never again to open a Greek book. In a month or two this timidity went off, and he returned to these studies with redoubled vigour, determined to take Bentley for his model, and to' qualify himself, if possible, to rival one whom he so greatly admired. 2. “Select Colloquies of Lucian, and his Timon,” Amst. 1708. 3. “The Plutus of Aristophanes, with the Scholia,” various readings and notes, Harlingen, 1744, 8vo. 4. “Part of an edition of Lucian,” as far as the 521st page of the first volume; it appeared in 1743 in four volumes quarto, the remaining parts being edited by J. M. Gesner and Reitzius. The extreme slowness of his proceeding is much complained of by Gesner and others, and was the reason why he made no further progress. 5. % “Notes and emendations on Xenophon Ephesius,” inserted in the 36 volumes of the te Miscellanea Critica“of Amsterdam, with the signature T. S. H. S. 6.” Some observations upon Chrysostom’s Homily on the Epistle to Philemon,“subjoined to Raphelius’s Annotations on the New Testament. 7.” Inaugural Speeches on various occasions.“8. There are also letters from him to J. Matth. Gesner and others; and he gave considerable aid to J. St. Bernard, in publishing the ' Eclogae Thomae Magistri,” at Leyden, in 1757. His “Philosophical Works” were published at Paris in 1792, 2 vols. 8vo, but he was a better critic -than philosopher. Ruhnkenius holds up Hemsterhusius as a model of a perfect critic, and indeed, according to his account, the extent and variety of his knowledge, and the acuteness of his judgment, were very extraordinary.

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

, or Halifax, or Sacrobosco, was, according to Leland, Bale, and Pits, born at Halifax in Yorkshire, which Mr. Watson thinks very improbable; according to Stainhurst, at Holywood near Dublin; and according to Dempster and Mackenzie, in Nithsdale in Scotland. There may perhaps have been more than one of the name to occasion this difference of opinion. Mackenzie informs us, that having finished his studies, he entered into orders, and became a canon regular of the order of St. Augustin in the famous monastery of Holywood in Nithsdale. The English biographers, on the contrary, tell us that he was educated at Oxford. They all agree however in asserting, that he spent most of his life at Paris; where, says Mackenzie, he was admitted a member of the university, June 5, 1221, under the syndics of the Scotch nation; and soon after was elected professor of mathematics, which he taught with applause for many years. According to the same author, he died in 1256, as appears from the inscription on his monument in the cloisters of the convent of St. Maturine at Paris.

, a celebrated Danish astronomer, and professor of that science at Copenhagen, was born at Laegsted, in Jutland, in 1679. He studied at Aalburg under very unfavourable circumstances, beingobliged, at the same period, to submit to various kinds of labour. In 1714, he was appointed professor of mathematics at Copenhagen, and in 1725 he was elected a member of the Danish academy of sciences. He died in 1764. He was author of many works connected with his favourite pursuits, among which were “Copernicus Trinmphans, sive de Parallaxi Orbis Annui;” in which he shews himself an enthusiast for the system of Copernicus; the “Elements of Astronomy;” and “the Elements of Mathematics;” but he is best known in this country by his “Natural History of Iceland,” fol. 1758. His mathematical works were published in four vols, 4to, Copenhagen, 1735, &c.

, born May 19, 1652, at Pont-de-Vesle, entered among the Jesuits in 1669, and acquired great skill in mathematics; accompanied the marechals d'Estrées and de Tourville, during twelve years, in all their naval expeditions, and gained their esteem. He was appointed king’s professor of mathematics at Toulon, and died there February 23, 1700, leaving, “Recueil des Traités de Mathematiques les plus necessaires a, un officier,” 3 volsi 12mo; “L'Art des armies navtrles, ou Traite” des evolutions navales,“Lyons, 1697, and more completely in 1727, folio. This work is not less historical than scientific, and contains an account of the most considerable naval events of the fifty preceding years. He presented it to Louis XIV. who received it graciously, and rewarded the author with 100 pistoles, and a pension of 600 livres a treatise on the construction of ships, which he wrote in consequence of some conversation with marechal de Tourville, is printed at the end of the preceding. In 1762, lieutenant O'Bryen published in 4to,” Naval Evolutions, or a System of Sea-discipline,“extracted from father L'Hoste’s” L'Art des armees navales."

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

His first separate publication appeared in 1767, under the title of “An Essay on the English Government;” and his second, after a long interval, in 1780, without his name, “Hymns to the Supreme Being, in imitation of the Eastern Songs.” Of this pleasing publication two editions were printed. In 1784 he circulated, also without his name, “Proposals for establishing, at sea, a Marine School, or seminary for seamen, as a means of improving the plan of the Marine Society,” &c. His object was to fit up a man of war as a marine school. In 1788 he published a large 4to volume, entitled “Morsels of Criticism, tending to illustrate some few passages in the Holy Scriptures upon philosophical principles and an enlarged view of things.” The fate of this work was somewhat singular. The author received sixty copies for presents; and the greater part of the remaining impression, being little called for, was converted into waste paper. Some time after, however, the notice taken of it in that popular poem, “The Pursuits of Literature,” brought it again into notice; a second edition appeared in 8vo, and a second volume of the 4to in 1801. This works abounds in singular opinions: among others, the author attempts to prove that John the Baptist was an angel from heaven, and the same who formerly appeared in the person of Elijah: that there will be a second appearance of Christ upon earth (something like this, however, is held by other writers): that this globe is a kind of comet, which is continually tending towards the sun, and will at length approach so near as to be ignited by the solar rays upon the elementary fluid of fire: and that the place of punishment allotted for wicked men is the centre of the earth, which is the bottomless pit, &c, &c. It is unnecessary to add, that these reveries did not procure Mr. King much reputation as a philosophical commentator on the Scriptures. His next publications indicated the variety of his meditations and pursuits. In 1793 he produced “An Imitation of the Prayer of Abel,” and “Considerations on the Utility of the National Debt.” In 1796 he amused himself and the public with “Remarks concerning Stones said to have fallen from the Clouds, both in these days and in ancient times;” the foundation of which was the surprizing shower of stones said, on the testimony of several persons, to have fallen in Tuscany, June 16, 1796, and investigated in an extraordinary and full detail by the abbate Soldani, professor of mathematics in the university of Sienna. This subject has since employed other pens, but no decisive conclusions have been agreed upon. Mr. King’s next publication, however, belonged to the province in which he was best able to put forth his powers of research “Vestiges of Oxford Castle or, a small fragment of a work intended to be published speedily, on the history of ancient castles, and on the progress of architecture,” 1796, a thin folio. This interesting memoir was accordingly followed by a large history of ancient castles, entitled “Munimenta Antiqua,” of which 3 vols. folio have appeared, and part of a fourth. These volumes, although he maintains some theories which are not much approved, undoubtedly entitle him to the reputation of a learned, able, and industrious antiquary. It was his misfortune, however, to be perpetually deviating into speculations which he was less qualified to establish, yet adhered to them with a pertinacity which involved him in angry controversies. In 1798 he published a pamphlet called “Remarks on the Signs of the Times;” about which other ingenious men were at that time inquiring, and very desirous to trace the history and progress of the French Revolution and war to the records of sacred antiquity; but Mr. King ventured here to assert the genuineness of the second book of Esdras in the Apocrypha. Mr. Gough criticised this work with much freedom and justice in the Gentleman’s Magazine, and Mr. King thought himself insulted. On his adding “A Supplement to his Remarks” in 1799, he met with a more powerful antagonist in bishop Horsley, who published “Critical Disquisitions on Isaiah xviii, in a Letter to Mr. King.” While preparing a fourth volume of his “Mummenta,” Mr. King died, April 16, 1807, and wa buried in the church -yard at Beckenham, where his country-seat was. Mr. King was a man of extensive reading, and considerable learning, and prided himself particularly on intense thinking, which, however, was not always under the regulation of judgment.

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

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

, professor of mathematics, and of medicine, in the university of Helmstadt, the son of John Liddel, a reputable citizen of Aberdeen, was born there in 1561, and educated in the languages and philosophy at the schools and university of Aberdeen. In 1579, having a great desire to visit foreign countries, he went from Scotland to Dantzic, and thence through Poland to Francfort on the Oder, where John Craig, afterwards first physician to James VI. king of Scotland, then taught logic and mathematics. By his liberal assistance Mr. Liddei was enabled to continue at the university of Francfort for three years, during which he applied himself very diligently to mathematics and philosophy under Craig and the other professors, and also entered upon the study of physic. In 1582, Dr. Craig being about to return to Scotland, sent Liddel to prosecute his studies at Wratislow, or Breslaw, in Silesia, recommending him to the care of that celebrated statesman, Andreas Dudithius; and during his residence at Breslaw, Liddel made uncommon progress in his favourite study of mathematics, under Paul Wittichius, an eminent professor.

, a celebrated astronomer of Germany, whose name deserves to be preserved, was born about 1542, in the dutchy of Wirtemberg, and spent his youth in Italy, where he made a public speech in favour of Copernicus, which served to wean Galileo from Aristotle and Ptolemy, to whom he had been hitherto entirely devoted. He returned afterwards to Germany, and became professor of mathematics at Tubingen; where he had among his scholars the great Kepler. Tycho Brahe, though he did not assent to Maestlin, has yet allowed him to be an extraordinary person, and well acquainted with the science of astronomy. Kepler has praised several ingenious inventions of Mæstlin’s, in his “Astronomia Optica.” He died in 1590, after having published many works in mathematics and astronomy, among which were his treatises “De Stella nova Cassiopeia;” “Ephemerides,” according to the Prutenic Tables, which were first published by Erasmus Reinoldus in 1551. He published Iikew4se “Thesis de Eclipsibus” and an “Epitome of Astronomy,” &c.

, or Maginus, professor of mathematics in the university of Bologna, was born at Padua in 1536. He was remarkable for his great assiduity in acquiring and improving the knowledge of the mathematical sciences, with several new inventions for these purposes, and for the extraordinary favour he obtained from most princes of his time. This doubtless arose partly from the celebrity he had in matters of astrology, to which he was greatly addicted, making horoscopes, and foretelling events both relating to persons and things. He was invited by the emperor Rodolphus to come to Vienna, where he promised him a professor’s chair, about 1597; but not being able to prevail on him to settle there, he nevertheless gave him a handsome pension. It is said, he was so much addicted to astrological predictions, that he not only foretold many good and evil events relative to others with success, bat even foretold his own death, which came to pass the same year: all which he represented as under the influence of the stars. Tomasini says, that Magini, being advanced to his 61st year, was struck with an apoplexy, which ended his days; and that a long while before, he had told him and others, that he was afraid of that year. And Roffeni, his pupil, says, that Magini died under an aspect of the planets, which, according to his own prediction, would prove fatal to him; and he mentious Riccioli as affirming that he said, the figure of his nativity, and his climacteric year, doomed him to die abouf that time; which happened in 1618, in the 62d year of his age.

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

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

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

, brother to the preceding, was born at Bologna, March 25, 1681, and having devoted himself to mathematical studies acquired the reputation of the best algebraist in Italy. At the age of twenty he composed a work on the equations of the first degree, which obtained the praises of the learned world. In 1708, the senate of Bologna appointed him one of their secretaries; and in 1720 he was made professor of mathematics in the university of that city, of which, in 1726, he became chancellor. He was much employed in hydrostatic labours, and with great success: nor did he shew less skill in the science of geography. He died in 1761. He published “De constructione aequationum differentialium primi gradus,” Bonon. 1707. This procured him a letter of congratulation from the celebrated Leibnitz. His other works are principally among the memoirs of the institute of Bologna.

, 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.

When he had obtained deacon’s orders, he applied for the place of head-master of the grammar-school at Hull, and having obtained it, was soon after chosen afternoon, lecturer in the principal church in that town. Under his auspices, the school, which had decayed through the negligence of his immediate predecessors, soon acquired and retained very considerable celebrity, and as the master’s salary rose in proportion to the increase of scholars, his income now, on the whole, amounted to upwards of 200L a year. The first use he made of this great change of circumstances was to discharge those duties that arose from the situation of his father’s family. His pious affection instantly led him to invite his mother (then living at Leeds in poverty) to Hull, where she became the manager of his house. He also sent for two indigent orphans, the children of his eldest brother, and took effectual care of their education. At this time his youngest brother, Isaac, whose prospects of advancement in learning were ruined by his father’s death, was now humbly employed in the woollen manufactory at Leeds. From this situation his brother Joseph instantly removed him, and employed him as his assistant in teaching the lower boys of his crowded school at Hull. By his brother’s means also, he was sent to Queen’s college, Cambridge, in 1770, of which he is now master, professor of mathematics, and dean of Carlisle. Of the affection between those brothers, the survivor thus speaks, “Perhaps no two brothers were ever more closely bound to each other. Isaac, in particular, remembers no earthly 7 thing without being able to connect it, in some way, tenderly with his brother Joseph. During all his life” he has constantly aimed at enjoying his company as much as circumstances permitted. The dissolution of such a connection could not take place without being severely felt by the survivor. No separation was ever more bitter and afflicting; with a constitution long shattered by disease, he never expects to recover from That wound."

, an able mathematical and medical writer, was born at Rheims about 1536, of a family which possessed jthe estate of Monantheuil in the Vermandois, in Picardy. He was educated at Paris in the college de Presles, under Kamus, to whose philosophical opinions he constantly adhered. Having an equal inclination and made equal progress in mathematics and medicine, he was first chosen professor of medicine, and dean of that faculty, and afterwards royal professor of mathematics. While holding the latter office he had the celebrated De Thou and Peter Lamoignon among the number of his scholars. During the troubles of the League, he remained faithful to his king, and even endangered his personal safety by holding meetings in his house, under pretence of scientific conversations, but really to concert measures for restoring Paris to Henry IV. He died in 1606, in the seventieth year of his age. His works are, 1 “Oratio pro mathematicis artibus,” Paris, 1574, 4to. 2. “Admonitio ad Jacobum Peletarium de angulo contactus,” ibid. 1581, 4to. 3. “Oratio pro suo in Regiam cathedram ritu,” ibid. 1585, 8vo. 4. “Panegyricus dictus Henrico IV. statim a felicissima et auspicatissima urbis restitutione,” &c. ibid. 1594, translated into French in 1596. 5. “Oratio qua ostenditur quale esse debeat collegium professorum regiorum,” &c. ibid. 15&6, 8vo. 6.“Commentarius in librum Aristotelis Tt^I Tuv /x>i%avjv,” Gr. and Lat. ibid. 1599, 4to. 7. “Ludus latromathematicus,” &c. ibid. 1597, 8vo, and 1700. 8. “De puncto primo Geometriae principio liber, 7 ' Leyden, 1600, 4to. This was at one time improperly attributed to his son, Thierry. 9.” Problematis omnium quse & 1200 annis inventa sunt nobilissimi demonstratio," Paris, 1600. He left some other works, both ms. and printed, of less consequence.

, physician and regius professor of mathematics at Paris, was born at Villefranche in Beaujolois, Feb. 23, 1583. After studying philosophy at Aix in Provence, and physic at Avignon, of which he commenced doctor in 1613, he went to Paris, and lived with Claude Dormi, bishop of Boulogne, who sent him to examine the nature of metals in the mines of Hungary. This gave occasion to his “Mundi sublunaris Anatomia,” which was his first production, published in 1619. Upon his return to his patron the bishop, he took a fancy to judicial astrology, and began to inquire, by the rules of that art, into the events of 1617. Among these he found, that the bishop of Boulogne was threatened with the loss of either liberty or life, of which he forewarned him. The bishop laughed at Morin’s prediction; but, engaging in state-intrigues, and taking the unfortunate side, he was treated as a rebel, and actually imprisoned that very year. After the fall of his prelate, he lived with the abbe de la Bretonniere, in quality of his physician, for four years; and, in 1621, was taken into the family of the duke of Luxemburg, where he lived eight years more, Jn 1630, he was chosen professor royal of mathematics.

, 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 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,”

, professor of civil law at Geneva, about 1724, was created a citizen of Geneva in 1726, and died there in 1760. He published “Four letters on Ecclesiastical Discipline,” Utrecht, 1740;“A description of the Government” of the Germanic Body,“Geneva, 1742, 8vo, and a few other professional tracts. His eldest son, Louis Necker, a pupil of D'Alembert’s, became professor of mathematics at Geneva in 1757, but quitted that city for Paris, where he entered into partnership with the bankers Girardot and Haller, the son of the celebrated physician; and in 1762 settled at Marseilles, whence in 1791 he returned to Geneva. In 1747 he published” Theses de Electricitate,“4to, and wrote in the French Encyclopaedia, the articles of Forces and Friction. There is also a solution of an algebraical problem by him in the” Memoirs des savans etrangers," in the collection of the Memoirs of the Academy of Sciences. He died about the end of the last century.

, a Dutch author, was the son of a carpenter at Dimmermeer, near Amsterdam, and was born in 1764. In his childhood he evinced extraordinary proofs of genius, and at the age of ten years produced some excellent pieces of poetry, and was, even then, able to solve problems in mathematics without having had any instruction from a master. The Batavian government appointed him one of the commissioners of longitude, and he was successively professor of mathematics and philosophy at Utrecht and Amsterdam. He died in 1794. He was author of several works, among which may be mentioned the following: 1. Poems in the Dutch language; 2. A tract on the means of enlightening a People; 3. On the general utility of the Mathematics; 4. Of the System of Lavoisier; and 5. A treatise on Navigation. To these may be added treatises on the form of the globe on the course of comets, and the uncertainty of their return and on the method of ascertaining the latitude at sea.

In 1701 he made Mr. Whiston his deputy professor of mathematics at Cambridge; and gave him all the salary from that time, though he did not absolutely resign the professorship till 1703, in which year he was chosen president of the royal society, and continued to fill that honourable situation till the time of his death. On April 16, 1705, he was knighted by queen Anne, at Trinity college lodge, Cambridge.

, professor of mathematics and natural philosophy at Leyden, was born at Diemermeer, a village near Amsterdam, Nov. 5, 1764. His father, by trade a carpenter, having a great fondness for books, and being tolerably well versed in the mathematics, instructed his son himself till he attained his eleventh year, who appears to have exhibited very extraordinary proofs of genius long before that time. When only three years old, his mother put into his hand some prints, which had fifty verses at the bottom of them by way of explanation. These verses she read aloud, without any intention that her son should learn them, but was much surprized some time after to hear him repeat the whole from memory, with the utmost correctness, on being only shown the prints. Before he was seven years old he had read more than fifty different books, and in such a manner that he could frequently repeat passages from them both in prose and in verse. When about the age of eight, Mr. Aenese of Amsterdam, one of the greatest calculators of the age, asked him if he could tell the solid contents of a wooden statue of Mercury which stood upon a piece of clock-work. “Yes,” replied young Nieuwland, “provided you give me a bit of the same wood of which the statue was made for I will cut a cubic inch out of it, and then compare it with the statue.” Poems which (says his eulogist) display the utmost liveliness of imagination, and which he composed in his tenth year, while walking or amusing himself near his father’s house, were received with admiration, and inserted in different poetical collections. Such an uncommon genius must soon burst through those obstacles which confine it. Bernardus and Jeronirao de Bosch, two opulent gentlemen of Amsterdam, became young Nieuwland’s patrons, and he was taken into the house of the former in his eleventh year, and received daily instruction from the latter for the space of four years. While in this situation he made considerable progress in the Latin and Greek languages, and studied philosophy and the mathematics under Wyttenbach. In 1733 he translated the two dissertations of his celebrated instructors Wyttenbach and de Bosch, on the opinions which the ancients entertained of the state of the soul after death, which had gained the prize of the Teylerian theological society. From September 1784 to 1785 he studied at Leyden, and afterwards applied with great diligence at Amsterdam to natural philosophy, and every branch of the mathematics, under the direction of professor Van Swinden. He had scarcely begun to turn his attention to chemistry, when he made himself master of Lavoisier’s theory, and could apply it to every phenomenon.

, 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.

, a very ingenious but visionary man, was by birth a Norman, of a small hamlet called Dolerie where he was born in 1510. Never did genius struggle with more vigour against the extremes of indigence. At eight years old, he was deprived of both his parents by the plague when only fourteen, unable to subsist in his native place, he removed to another near Pontoise, and undertook to keep a school. Having thus obtained a little money, he went to Paris, to continue his studies but there was plundered and suffered so much from cold, that he languished for two years in an hospital. When he recovered, he again collected a little money by gleaning irv the country, and returned to Paris, where he subsisted by waiting on some of the students in the college of St. Barbe; but made, at the same time, so rapid a progress in knowledge, that he became almost an universal scholar. His acquirements were so extraordinary, that they became known to the king, Francis I. who, touched with so much merit, under such singular disadvantages, sent him to the East to collect manuscripts. This commission he executed so well, that on his return, he was appointed royal professor of mathematics and languages, with a considerable salary. Thus he might appear to be settled for life; but this was not his destiny. He was, unfortunately for himself, attached to the chancellor Poyet, who fell under the displeasure of the queen of Navarre and Postel, for no other fault, was deprived of his appointments, and obliged to quit France. He now became a wanderer, and a visionary. From Vienna, from Rome, from the order of Jesuits, into which he had entered, he was successively banished for strange and singular opinions; for which also he was imprisoned at Rome and at Venice. Being released, as a madman, he returned 10 Paris, whence the same causes again drove him into Germany. At Vienna he was once more received, and obtained a professorship; but, having made his peace at home, was again recalled to Paris, and re-established in his places. He had previously recanted his errors, but relapsing into them, was banished to a monastery, where he performed acts of penitence, and died Sept. 6, 1581, at the age of seventy-one. Postel pretended to be much older than he was, and maintained that he had died and risen again which farce he supported by many tricks, such as- colouring his beard and hair, and even painting his face. For the same reason, in most of his works, he styles himself, “Postellus restitntus.” Notwithstanding his strange extravagances, he was one of the greatest geniuses of his time; had a surprising quickness and memory, with so extensive a knowledge of languages, that he boasted he could travel round the world without an interpreter. Francis I. regarded him as the wonder of his age Charles IX. called him his philosopher; and when he lectured at Paris, the crowd of auditors was sometimes so great, that they could only assemble in the open court of the college, while he taught them from a window. But by applying himself very earnestly to the study of the Rabbins, and of the stars, he turned his head, and gave way to the most extravagant chimeras. Among these, were the notions that women at a certain period are to have universal dominion over men that all the mysteries of Christianity are demonstrable by reason that the soul of Adam had entered into his body that the angel Raziel had revealed to him the secrets of heaven and that his writings were dictated by Jesus Christ himself. His notion of the universal dominion of women, arose from his attachment to an old maid at Venice, in consequence of which he published a strange and now very rare and high-priced book, entitled “Les tres-marveilieuseS victoires des Femmes du Nouveau Monde, et comme elles doivent par raison a tout le monde commander, et me' me a; eeux qui auront la monarchic du Monde viel,” Paris, 1553, 16mo. At the same time, he maintained, that the extraordinary age to which he pretended ttf have lived, was occasioned hy his total abstinence from all commerce with that sex. His works are as numerous as, they are strange and some of them are very scarce, hut very little deserve to be collected. One of the most important is entitled “De orbis concordia,” Bale, 1544, folio. In this the author endeavours to bring all the world to the Christian faith under two masters, the pope, in spiritual affairs, and the king of France in temporal. It is divided into four books; in the first of which he gives the proofs of Christianity; the second contains a refutation of the Koran; the third treats of the origin of idolatry, and all false religions and the fourth, on the mode of converting Pagans, Jews, and Mahometans, Of his other works, amounting to twenty-six articles, which are enumerated in the “Dictionnaire Historique,” and most of them by Brunet as rarities with the French collectors, many display in their very titles the extravagance of their contents; such as, “Clavis absconditorum a, constitutione ixmndi,” Paris, 1547, 16mo; “De Ultimo judicio;” “Proto-evangelium,” &c. Some are on subjects of more real utility. But the fullest account of the whole may be found in a book published at Liege in 1773, entitled “Nouveaux eclaircissemens sur 3a Vie et les ouvrages de Guillaume Postel,” by father des Billons. The infamous book, “De tribus impostoribus,” has been very unjustly attributed to Postel, for, notwithstanding all his wildness, he was a believer.

Ramus was bred up in the catholic religion, but afterwards deserted it, and began to discover his new principles in 1552, by removing the images from the chapel of his college. This naturally increased the number as well as bigotry of his enemies, who now succeeded in compelling him to leave the university. He still appears to have had a friend in the king, who gave him leave to retire to Fontainbleau; where, by the help of books in the royal library, he pursued geometrical and astronomical studies. As soon as his enemies knew where he was, he found himself nowhere safe; so that he was forced to go and conceal himself in several other places. During this interval the excellent and curious collection of books he had left in the college was plundered; but, after a peace was concluded in 1563, between Charles IX. and the protestauts, he again took possession of his employment, maintained himself in it with vigour, and was particularly zealous in promoting the study of the mathematics. This lasted till the second civil war in 1567, when he was forced to leave Paris and shelter himself among the protestants, in whose army he was at the battle of St. Denys. Peace having been concluded some months after, he was restored to his professorship; but, foreseeing that the war would soon break out again, he obtained the king’s leave to visit the universities of Germany. He accordingly undertook this journey in 1568, and received much respect and great honours wherever he came. He returned to France after the third war in 1571; and lost his life miserably, in the massacre of St. Bartholomew’s day, 1572. Charpentaire, a professor of mathematics, who had been eclipsed by the superior talents of Ramus, seized the opportunity of being revenged upon his rival, and employed assassins to murder him. Ramus gave them money in order to procure his escape, but in vain; for, after wounding him in many places, they threw him out of a window; and, his bowels gushing out in the fall, some Aristotelian scholars, encouraged by their masters, spread them about the streets; then dragged his body in a most ignominious manner, and threw it into the Seine.

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.

, 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.

After the death of Copernicus, Rheticus returned to Wittemberg, viz. in 1541 or 1542, and was again admitted to his office of professor of mathematics. The same year, by the recommendation of Melancthon, he went to Norimberg, where he found certain manuscripts of Werner and Regiomontanus. He afterwards taught mathematics at Leipsic. From Saxony he departed a second time, for what reason is not known, and went to Poland; and from thence to Cassovia in Hungary, where he died December 4, 1576, near sixty-three years of age.

, a very learned divine, was born in Dublin, Oct. 16, 1705. His father was a native of Scotland, who carried on the linen-manufacture there; and his mother, Diana Allen, was of a very reputable family in the bishopric of Durham, and married to his father in England. From his childhood he was of a very tender and delicate constitution, with great weakness in his eyes till he was twelve years of age, at which period he was sent to school. He had his grammar-education under the celebrated Dr. Francis Hutcheson, who then taught in Dublin, but was afterwards professor of philosophy in the university of Glasgow. He went from Dr. Hutcheson to that university in 1722, where he remained till 1725, and took the degree of M. A. He had for his tutor Mr. John Lowdon, professor of philosophy; and attended the lectures of Mr Ross, professor of humanity; of Mr. Dunlop, professor of Greek; of Mr. Morthland, professor of the Oriental languages; of Mr. Simpson, professor of mathematics; and of Dr. John Simpson, professor of divinity. In the last-mentioned year, a dispute was revived, which had been often agitated before, between Mr. John Sterling the principal, and the students, about a right to chuse a rector, whose office and power is somewhat like that of the vice-chancellor of Oxford or Cambridge. Mr. Robertson took part with his fellow- students, and was appointed by them, together with William Campbell, esq. son of Campbell of Mamore, whose family has since succeeded to the estates and titles of Argyle, to wait upon the principal with a petition signed by more than threescore matriculated students, praying that he would, on the 1st day of March, according to the statutes, summon an university-meeting for the election of a rector; which petition he rejected with contempt. On this Mr. Campbell, in his own name and in the name of all the petitioners, protested against the principal’s refusal, and all the petitioners went to the house of Hugh Montgomery, esq. the unlawful rector, where Mr. Robertson read aloud the protest against him and his- authority. Mr. Robertson, by these proceedings, became the immediate and indeed the only object of prosecution. He was cited before the faculty, i. e. the principal and the professors of the university, of wbotn the principal was sure of a majority, and, after a trial which lasted several clays, had the sentence of expulsion pronounced against him; of which sentence he demanded a copy, and was so fully persuaded of the justice of his cause, and the propriety of his proceedings, that he openly and strenuously acknowledged and adhered to what he had done. Upon this, Mr. Lowdon, his tutor, and Mr. Dunlop, professor of Greek, wrote letters to Mr. Robertson’s father, acquainting him of what had happened, and assuring him that his son had been expelled, not for any crime or immorality, but for appearing very zealous in a dispute about a matter of right between the principal and the students. These letters Mr. Robertson sent inclosed hi 'one from himself, relating his proceedings and suffer! ngs in the cause of what he thought justice and right. Upon this his father desired him to take every step he might think proper, to assert and maintain his own and his fellowstudents claims; and accordingly Mr. Robertson went up to London, and presented a memorial to John duke of Argyle, containing the claims of the students of the university of Glasgow, their proceedings in the vindication of them, and his own particular sufferings in the cause. The duke received him very graciously, but said, that “he was little acquainted with things of this sort;” and advised him “to apply to his brother Archibald earl of Hay, who was better versed in such matters than he.” He then waited on lord Hay, who, upon reading the representation of the case, said “he would consider of it.” And, upon consideration of it, he was so affected, that he applied to the king for a commission to visit the university of Glasgow, with full power to examine into and rectify all abuses therein. In the summer of 1726, the earl of Hay with the other visitors repaired to Glasgow, and, upon a full examination into the several injuries and abuses complained of, they restored to the students the right of electing their rector; recovered the right of the university to send two gentlemen, upon plentiful exhibitions, to Baliol college in Oxford; took off the expulsion of Mr. Robertson, and ordered that particularly to be recorded in the proceedings of the commission; annulled the election uf the rector who had been named by the principal; and assembled the students, who immediately chose the master of Ross, son of lord Ross, to be their rector, &c. These things so affected Mr* Sterling, that he died soon after; but the university revived, and has since continued in a most flourishing condition.

, 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.

, professor of mathematics at Leyden about the middle of the seventeenth century, was a very acute proficient in that science. He published, in 1649, an edition of Descartes’s geometry, with learned and elaborate annotations on that work, as also those of Beaume, Hudde, and Van Heauralt. Schooten published also two very useful and learned works of his own composition; “Principia Matheseos universalis,” 1651, 4to; and “Exercitationes Mathematics,” 1657, 4to.

, a learned member of the royal society, and of the board of longitude, was the eldest son of Mr. Scott, of Bristow, in Scotland, who married Miss Stewart, daughter of sir James Stewart, lord advocate of Scotland in the reigns of William III. and queen Anne. That lady was also his cousin-german, their mothers being sisters, and both daughters of Mr. Robert Trail, one of the ministers of Edinburgh, of the same family as the rev. Dr. William Trail, the learned author of the “Life of Dr. Robert Simson, professor of mathematics at Glasgow.”

, professor of mathematics in the king’s academy at Woolwich, fellow of the Royal Society, and member of the royal academy at Stockholm, was born at Market-Bosworth, in Leicestershire, Aug. 20, 1710. His father was a stuff-weaver in that town: and, though in tolerable circumstances, yet, intending to bring up his son to his own business, he took so little care of his education, that he was only taught English. But nature had furnished him with talents and a genius for far other pursuits, which led him afterwards to tut: highest rank in the mathematical and philosophical sciences.

professor of mathematics in the uni- our author wa* professor of geometry

Through the interest and solicitations of William Jones, esq. he was, in 1743, appointed professor of mathematics, then vacant by the death of Mr. Derham, in the Royal academy at Woolwich; his warrant bearing date August 25th. And in 1745 he was admitted a fellow of the Royal Society, having been proposed as a candidate by Martin Folkes, esq. president, William Jones, esq. Mr. George Graham, and Mr. John Machiu, secretary; all very eminent mathematicians. The president and council, in consideration of his very moderate circumstances, were pleased to excuse his admission fees, and likewise his giving bond for the settled future payments.

When the vacancy in the professorship of mathematics at Glasgow did occur, in the following year, by the resignation of Dr. Robert Sinclair, or Sinclare (a descendant or other relative probably of Mr. George Sinclare, who died in that office in 1696), the university, while Mr. Simson was still in London, appointed him to fill it; and the minute of election, which is dated March 11, 1711, concluded with this very proper condition, “That they will admit the said Mr. Robert Simson, providing always, that he give satisfactory proof of his skill in mathematics, previous to his admission.” He returned to Glasgow before the ensuing session of the college, and having gone through the form of a trial, by resolving a geometrical problem proposed to him, and also by giving “a satisfactory specimen of his skill in mathematics, and dexterity in reaching geometry and algebra;” having produced also respectable certificates of his knowledge of the science, from Mr. Caswell and others, he was duly admitted professor of mathematics, on the 20th of November of that year.

Mr. Simson, immediately after his admission, entered on the duties of his office; and his first occupation necessarily was the arrangement of a proper course of instruction for the students who attended his lectures, in two distinct classes. Accordingly he prepared elementary sketches of some branches on which there were not suitable treatises in general use. Both from a sense of duty and from inclination, he now directed the whole of his attention to the study of mathematics; and though he had a decided preference for geometry, which continued through life, yet he did not devote himself to it to the exclusion of the other branches of mathematical science, in most of which there is sufficient evidence of his being well skilled. From 1711, he continued near fifty years to teach mathematics to two separate classes, at different hours, five days in the week, during a continued session of seven months. His manner of teaching was uncommonly clear and successful; and among his scholars, several rose to distinction as mathematicians; among which may be mentioned the celebrated names of Dr. Matthew Stewart, professor of mathematics at Edinburgh; the two Rev. Dr. Williamsons, one of whom succeeded Dr. Simson at Glasgow; the Rev. Dr. Trail, formerly professor of mathematics at Aberdeen; Dr. James Moor, Greek professor at Glasgow: and professor Robison, of Edinburgh, with many others of distinguished merit. In 17.58, Dr. Simson, being then seventy-one years of age, found it necessary to employ an assistant in teaching; and in 1761, on his recommendation, the Rev. Dr. Williamson was appointed his assistant and successor.

He published, 1. “Tyrocinia mathematica,” Glas. 1661, 12nto. 2. “Ars Nova et Magna Gravitatis et Levitatis,” Rotterd. 1669, 4to. 3. “Hydrostatics,” Eclin. 1672, 4to. 4. “Hydrostatical Experiments, with a Discourse on Coal,” Edin. 1680, 8vo. 5. “Principles of Astronomy and Navigation,” Edin. 1688, 12mo. Mr. Sinclare’s writings, in the opinion of a very able judge, are not destitute of ingenuity and research, though they may contain some erroneous and eccentric views. His work on Hydrostatics, and his “Ars Nova et Magna,” and perhaps also his political principles, provoked the indignation of some persons; on which occasion Mr. James Gregory, then professor of mathematics at St. Andrew’s, animadverted on him rather severely in a treatise entitled, “The great and new art of weighing Vanity,” &c. (See Gregory, vol. XVI. p. 278). Besides the works above mentioned, a publication in defence of witchcraft, entitled “Satan’s Invisible World,” has been ascribed to him: it bears the initials G. S. of his name; and witchcraft was a standard article of belief in Scotland at that time. He also translated and published under the same initials Dickson’s “Truth’s Victory over Error,” suppressing the author’s name (see David Dickson), for which he is censured by Wodrow, the ecclesiastical historian and biographer of professor Dickson, while he allows him the merit of some good intention.

, 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.

Mr. Stewart’s views made it necessary for him to attend the lectures in the university of Edinburgh in 1741; and that his mathematical studies might suffer no interruption, he was introduced by Dr. Simson to Mr. Maclaurin, who was then teaching with so much success both the geometry and the philosophy of Newton, and under whom Mr. Stewart made that proficiency which was to be expected from the abilities of such a pupil, directed by those of so great a master. Eut the modern analysis, even when thus powerfully recommended, was not able to withdraw his attention, from the relish of the ancient geometry, which he had imbibed under Dr. Simson. He still kept up a regular correspondence with this gentleman, giving him an account of his progress, and of his discoveries in geometry, which were now both numerous and important, and receiving in return many curious communications with respect to the Loci Plani, and the Porisms of Euclid. Mr. Stewart pursued this latter subject in a different, and new direction, and was led to the discovery of those curious and interesting propositions, which were published, under the title of “General Theorems,” in 1746, which, although given without the demonstrations, placed their discoverer at once among the geometricians of the first rank. They are, for the most part, Porisms, though Mr. Stewart, careful not to anticipate the discoveries of his friend, gave them only the name of Theorems. While engaged in them, Mr. Stewart had entered into the church, and become minister of Roseneath. It was in that retired and romantic situation, that he discovered the greater part of those theorems. In the summer of 1746, the mathematical chair in the university of Edinburgh became vacant, by the death of Mr. Maclaurin. The “General Theorems” had not yet appeared; Mr. Stewart was known only to his friends; and the eyes of the public were naturally turned on Mr. Stirling, who then resided at Leadhills, and who was well known in the mathematical world. He however declined appearing as a candidate for the vacant chair; and several others were named, among whom was Mr. Stewart. Upon this occasion he printed his “Theorems,” which gave him a decided superiority above all the other candidates. He was accordingly elected professor of mathematics in the university of Edinburgh, in September 1747. The duties of this office gave a turn somewhat different to his mathematical pursuits, and led him to think of the most simple and elegant means of explaining those difficult propositions, which were bit erto only accessible to men deeply versed in the modern analysis. In doing this, he was pursuing the object which, of all others, he most ardently wished to obtain, viz. the application of geometry to such problems as the algebraic calculus alone had been thought able to resolve. His solution of Kepler’s problem was the first specimen of this kind which he gave to the world, and which, unlike all former attempts, was at once direct in its method and simple in its principles. This appeared in vol. II. of the “Essays of the Philosophical Society of Edinburgh,” for 1756; and in the first volume of the same collection are some other propositions by him, which are an extension of a curious theorem in the fourth book of Pappus.

In the meantime, while this work was going on, Sturmius filled the office of professor of mathematics at Wolfenbuttel, and it was there he published his “Sciagraphia Templi Hierosolymitani,” in fol. In 1697 he obtained permission of the duke of Wolfenbuttel to travel, and went into the Netherlands and into France: the result of his observations, chiefly on subjects of architecture, he published in 1719, folio, with numerous plates, from his own designs. This work shows great skill in architecture, but, as his eulogist is disposed to allow, a taste somewhat fastidious, and a wish to estimate all merit in the art by certain preconceived opinions of his own. In 1702 he was appointed professor of mathematics in the university of Francfort on the Oder. The king of France having promised a reward to the inventor of a sixth order of architecture, Sturmius, among others, made an attempt, which he called the German order, and which he intended to hold a middle rank between the Ionic and the Corinthian. It is unnecessary to add that no attempt of this kind has succeeded.

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.

, 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.

, marechal of France, commissioner-general of fortifications, and the greatest engineer which France has produced, was the son of Urban le Prestre, seigneur de Vauban, a descendant of an ancient and noble family of Nivernois. He was born May 1, 1633, and was in the army at the early age of seventeen, where his uncommon talents and genius for fortification soon became known, and were eminently displayed at the sieges of St. Menehould, 1652 and 1653, of Stenay 1654, and of several other places in the following years. He consequently rose to the highest military ranks by his merit and services: and was made governor of the citadel of Lisle in 1668, and commissioner-general of fortifications in 1678. He took Luxemburg in 1684, and, being appointed lieutenant-general in 1688, was present, the same year, at the siege and capture of Philipsburg, Manheim, and Frankendal, under the dauphin. This prince, as a reward for his services, gave him four pieces of cannon, which he was permitted to chuse from the arsenals of these three towns, and place in his castle at Bazoche; an honour afterwards granted to the famous marechal Saxe. M. de Vauban commanded on the coast of Flanders in 1689, and was made marechal of France, Jan. 14, 1703. His dignity was expensive to him, but the king would not permit him to serve as an inferior officer, though he offered it in a very handsome manner. He died at Paris, March 30, 1707, aged seventy-four. He was a man of high and independent spirit, of great humanity, and entirely devoted to the good of his country. As an engineer, he carried the art of fortifying, attacking, and defending towns, to a degree of perfection unknown before his time. He fortified above 300 ancient citadels, erected thirty- three new ones, and had the principal management and direction of fifty-three sieges, and was present at one hundred and forty engagements. But his countrymen tell us that it was unnecessary for him to exert his skill in defending a fort; for the enemies of France never attacked those in which he was stationed. His works are, a treatise entitled “La Dixme Roïale,” 1707, 4to and 12mo, which displays some patriotic principles, but the plan is considered as impracticable. A vast collection of Mss. in 12 vols. which he calls his “Oisivetés,” contain his ideas, reflections, and projects, for the advantage of France. The three following works are also attributed to him, but whether he wrote them, or whether they have been compiled from his Memoirs, and adapted to his ideas, is uncertain: “Maniere de fortifier,” 8vo and 12mo, printed also at Paris by Michalet, 8vo, under the title of “L'Ingéieur François.” M. Hebert, professor of mathematics, and the abbe“du Fay, have written notes on this treatise, which is esteemed, and is said to have been revised by the chevalier de Cambrai, and reprinted at Amsterdam, 1702 and 1727, 2 vols. 4to; 2.” Nouveau Traite de l'Attaque et de la Défense des Places, suivant le Systeme de M. de Vauban, par M. Desprez de Saint Savin,“1736, 8vo, much esteemed; 3.” Essais sur la Fortification, par M. de Vauban,“1740, 12mo. As to the” Political Testament" ascribed to him, it was written by Peter le Pesant, sieur de Boïs Guillebert, lieutenant-general of the bailiwic of Rouen, who died 1714. M. de Vauban’s second cousin, Anthony de Prestre, known by the name of Puy Vauban, was also a very eminent engineer. He died lieutenant-general of the king’s forces, and governor of Bethune, April 10, 1731, aged seventy-seven.

In 1647, he happened to meet with Oughtred’s “Clavis,” of which he made himself master in a few weeks, and discovered a new method of resolving cubic equations, which he communicated to Mr. Smith, professor of mathematics at Cambridge, with whom he held a literary correspondence upon mathematical subjects for some years. The Independents having now acquired the superiority, our author joined with some other ministers of London, in subscribing a paper, entitled “A testimony to the truth of Jesus Christ, and to the solemn league and covenant: as also against the errors, heresies, and blasphemies of these times, and the toleration of them.” Not long after this, he exchanged St. Gabriel Fenchurch-.street, for St. Martin’s Ironmonger-lane; and in 1648, subscribed, as minister of that church, to the remonstrance against putting the king to death; and to a paper entitled “A curious and faithful representation of the judgments of ministers of the Gospel within the province of London, in a letter from them to the General and his Council of War.” Dated Jan. 17, 1648.

, Lucasian professor of mathematics in the university of Cambridge, was descended from an ancient family at Mitton, in the parish of Fittes, Shropshire, being the eldest son of John Waring of that place. He was born in 1734, and after being educated at the free school at Shrewsbury, under Mr. Kotchkis, was sent on one of Millington’s exhibitions to Magdalen college, Cambridge, where he applied himself with such assiduity to the study of mathematics, that in 1757, when he proceeded bachelor of arts, he was the senior wrangler, or most distinguished graduate of the year. This honour, for the securing of which he probably postponed his first degree to the late period of his twenty-third year, led to his election, only two years afterwards, to the office of Lucasian professor. The appointment of a young man, scarcely twenty-five years of age, and still only a bachelor of arts, to a chair which had been honoured by the names of Newton, Saunderson, and Barrow, gave great offence to the senior members of the university, by whom the talents and pretensions of the new professor were severely arraigned. The first chapter of his “Miscellanea Analytica,” which Mr. Waring circulated in vindication of his scientific character, gave rise to a controversy of some duration. Dr. Powell, master of St. John’s, commenced the attack by a pamphlet of “Observations” upon this specimen of the professor’s qualifications for his office. Wariug was defended in a very able reply, for which he was indebted to Mr. Wilson, then an under-graduate of Peter House, afterwards sir John Wilson, a judge of the common pleas, and a magistrate justly beloved and revered for his amiable temper, learning, honesty, and independent spirit. In 1760, Dr. Powell wrote a defence of his “Observations,” and here the controversy ended. Mr. Waring’s deficiency of academical honours was supplied in the same year by the degree of M. A. conferred upon him by royal mandate, and he remained in the undisturbed possession of his office. Two years afterwards, his work, a part of which had excited so warm a dispute, was published from the university press, in quarto, under the title of “Miscellanea Analytica de Æquationibus Algebraicis et Curvarum Proprietatibus,” with a dedication to the duke of Newcastle. It appears from the title-page, that Waring was by this time elected a fellow of his college. The book itself, so intricate and abstruse are its subjects, is understood to have been little studied even by expert mathematicians. Indeed, speaking of this and his other works, in a subsequent publication, he says himself, “I never could hear of any reader in England out of Cambridge, who took the pains to read and understand what I have written.”

At seven years of age young Mr. Windham was placed at Eton, where he remained until he was about sixteen, distinguishing himself by the vivacity and brilliancy of his talents. On leaving Eton in 1766, he went to the university of Glasgow, where he resided for about a year in the house of Dr. Anderson, professor of natural philosophy, and diligently attended his lectures and those of Dr. Robert Simson, professor of mathematics. For this study Mr. Windham had an early predilection, and left behind him three treatises on mathematical subjects. In Sept. 1767 he was entered a gentleman commoner of University-college, Oxford, Mr. (afterwards sir Robert) Chambers being his tutor. While here he took so little interest in public affairs, that it became the standing joke of one of his contemporaries, that “Windham would never know who was prime minister.” This disinclination to a political life, added to a modest diffidence in his own talents, led him about this period, to reject an offer which, by a youth not more than twenty years of age, might have been considered as a splendid one, that of being named secretary to his father’s friend, lord Townshend, who had been appointed lord-lieutenant of Ireland.