colleague, John Kepler, a German, born in 1571, at Wiel, in the dutchy of Wittemburg, and educated at Tubingen. His early and uncommon proficiency in mathematical learning recommended him to the attention of the univer ́sity of Gratz, in Stiria, as a proper person to occupy the mathematical chair. From this time astronomy became the chief object of his attention; and, in 1595, he published Mysterium Cosmographicum, "The Mystery of Cosmography;" in which he undertook to demonstrate, upon geometrical principles, the admirable proportions of the. celestial orbs, and to explain the reasons of their number, magnitudes, and periodical revolutions; a work abounding with clear and accurate mathematical reasoning. At Prague, whither he was driven, about the year 1600, by the troubles and persecutions of his own country, Kepler, with his family, notwithstanding his personal abilities and merit, and his connexion with Tycho Brahe, was reduced to poverty. At length, through the indulgence of the emperor, he was recalled to his native country, and taught mathematics, first at Lints, and afterwards at Sagan, in Silesia. He died in the year 1631.

For the particulars of Kepler's great discoveries and improvements in astronomy, we must refer the reader to his works. We cannot, however, omit to remark, that this penetrating philosopher suggested hints in natural science which Des Cartes afterwards assumed as his own, and discovered truths, which served as a firm foundation for subsequent improvements in the great edifice of mathematical astronomy. Kepler found, that every primary planet describes an elliptic orbit, in one focus of which is the sun; that, in equal times, equal areas are described by a line drawn from the sun to the planet; and that the squares of the periodical times of the planets are as the cubes of their distances from the sun. He was also acquainted with the principle of gravitation, and knew that revolving bodies endeavour to fly from their orbit in a tangent. But, not knowing how to apply the principle of gravitation to the explanation of the laws of the celestial motions which he had discovered, he ascribed them to the influence of a distinct animating principle, or soul, which he supposed to reside in each planet.

Gassend. t. v. p. 451. 471. Bayle. Weidler. 1. e. e. 15. p. 414.

Contemporary with Kepler was Galileo Galilei,a1 ́ a native of Florence, whose astronomical inventions and discoveries have immortalized his name. Destined by his father for the medical profession, he was educated in the schools of Pisa: but he soon discovered so strong a predilection, and such uncommon talents, for astronomical studies, that he was permitted to follow the natural bias of his mind without any professional restraint. Having been well instructed in the Greek tongue, he read Euclid, Archimedes, and other ancient mathematicians in the original. His reputation as a mathematician became so great, that the Duke of Tuscany appointed him, before he was twenty-six years of age, to the mathematical chair in the university of Pisa. Afterwards, in the year 1592, at the invitation of the republic of Venice, he removed to Padua.

With the study of mathematics, Galileo united that of physics, particularly the doctrines of mechanics and optics. Being informed, in the year 1609, that Jansen, a Dutchman, had invented a glass, by means of which distant objects appeared as if they were near, he turned his attention to the subject; and, after several attempts to apply his ideas on the doctrine of refraction to practice, he invented and constructed an optical instrument, by means of which, as he himself says, objects appeared magnified a thousand times. Turning his Telescope towards the heavens, he discovered unheard-of wonders. On the surface of the moon he saw lofty mountains and deep vallies. The milky way he discovered to be a crowded assemblage of fixed stars, invisible to the naked eye. Venus he found to vary in its phases like the moon. The figure of Saturn he observed to be oblong, consisting of three distinct parts. Jupiter he saw surrounded with four moons, which he named Medicean stars. And on the sun's disk he perceived spots, from the motion of which he inferred, that the sun revolves about its axis. The book in which these wonderful discoveries were recorded, Galileo dedicated to the Duke of Tuscany, who was so delighted with his countryman's ingenuity and success, that he wrote him a congratulatory letter, and gave him the title of the Philosopher and Mathematician of Tuscany. The whole astronomical world ap

"Viviani Vit. Gal. Act. Phil. v. iii. p. 261. 400.

plauded his attempts, although not a few were secretly inclined to suspect, that his supposed discoveries were only the amusing dreams of a brilliant imagination.

Galileo now began to inquire to what useful purposes his new discoveries might be applied, and soon perceived, that, by means of observations which he was now able to make upon the satellites of Jupiter, geographical longitudes might be found. He engaged the Duke of Tuscany to apprize the King of Spain of the great benefits which navigation might derive from this discovery; but no regard was paid to the suggestion.

A comet appearing in the year 1618, Galileo, in order to correct the prevailing errors of philosophers upon the subject of celestial phænomena, wrote a treatise which he called, Systema Cosmicum, "The System of the World," in which he shewed the perfect agreement of the Copernican system with the appearances of nature. The publication of this treatise, though preceded by another, in which it was proved, from the authority of the fathers, and other orthodox divines, that the language of Scripture is not to be strictly followed on questions merely physical, raised a general alarm among the bigots of the Romish church. This incomparable philosopher was, in 1615, cited before the Court of Inquisition, accused of heresy, and thrown into prison. Well-knowing that any justification of himself, or explanation of his doctrine, would be fruitless, Galileo retracted the obnoxious tenet, that the sun stands still; and, after five months' confinement, was released. His work was censured and prohibited.

In 1636, this ingenious and industrious philosopher resumed his design of measuring geographical distances in longitude, and communicated his plan to the States-General of the United Provinces. By their order, the plan was examined, and the necessary calculations were made for drawing the tables. But a misfortune, which at this time happened to Galileo, interrupted the laudable design. After the astronomical labours of twenty-seven years, this useful philosopher lost his sight. The papers which he had drawn up were sent to Holland; and it was still hoped that he might furnish further instructions towards completing the design; but, about the beginning of the year 1642, a slow

fever, occasioned by the pain which he suffered in his eyes and limbs, released him from envy and persecution. The light which Galileo cast upon natural philosophy by his astronomical inventions and improvements, which are doubtless in a great measure to be ascribed to his knowledge of mathematics, entitle him to a place in the first class of mathematical philosophers. He discovered, that in the descent of falling bodies, the spaces described are as the squares of the times; and that the motion of projectiles is in the curve of a parabola.

From the time of Galileo, the practice of applying mathematics to the improvement of physical knowledge became general; and many excellent geometricians arose, who subjected the phænomena of nature to mathematical calculation. Gregory de St. Vincent, who enlarged the boundaries of the higher geometry, applied the properties of the hyperbola to astronomy. Des Cartes, Wallis, Huygens, and others, pursued a similar track. Since the sublime inventions of the Differential Calculus by Leibnitz, and of the Method of Fluxions by Newton, natural philosophy has received continual improvement by the labours of Leibnitz, L'Hospital, Varignon, the Bernouillis, Cotes, Saunderson, Maclaurin, and other eminent mathematicians. But the first luminary in this bright constellation, by the universal consent of philosophers, is the immortal Newton.

ISAAC NEWTON 85 was born at Woolstrope, in Lincolnshire, in the year 1642. He received his first instruction at the grammar school at Grantham. He gave early indications of that sublime genius, which afterwards performed such wonders, in his insatiable thirst after knowledge, and the almost intuitive facility with which he first conceived the theorems of Euclid. Though not inattentive to classical studies, he directed the chief exertions of his penetrating and exalted understanding towards mathematical science, in which, not contented with a perfect comprehension of whatever had been already done by others, he was wonderfully assiduous and successful in investigating new truths.

The university of Cambridge boasts the honour of haying educated Newton. His first preceptor was the cele

Eloge par Fontenelle. Pemberton's Review, præf. Hist. of the Royal Society. Life of Newton, Lond. 1728. Biog. Brit. Gen. Dict.

brated geometrician, Isaac Barrow. In 1667, Newton took his degree of Master of Arts, and was soon after admitted Fellow of Trinity College, and appointed Lucasian Professor of Mathematics. In 1688, he was chosen representative in the convention parliament for the university, and continued to adorn this high station till the dissolution of this parliament in the year 1701; he was also appointed Master of the Mint, and in this post rendered signal service to the public. In the year 1703, he was elected President of the Royal Society, and remained in that office as long as he lived.

Whilst Newton gave many proofs of his astonishing capacity for mathematical researches, he shewed himself possessed of a mind equally capable of extending the knowledge of nature, by the reports which he made to the Royal Society of many curious and important experiments in natural philosophy. In the year 1671, his papers on the properties of light were read to that Society, from which it appeared that colour, which had hitherto been explained by ingenious but unsupported hypotheses, was in fact owing to a property in the rays of light hitherto unobserved, their different degrees of refrangibility. These papers were afterwards completed; and, in the year 1704, the whole was published in three books, under the general title of "Optics; or, a Treatise of the Reflections, Refractions, Inflections, and Colours of Light."

The result of this great philosopher's successful endeavours to subject the phænomena of nature to the laws of mathematics, was first communicated to the public in the year 1687, in the immortal work entitled, Philosophiæ naturalis Principia mathematica, "Mathematical Principles of Natural Philosophy:" this was succeeded by several treatises purely mathematical, in which the wonderful genius of this great geometrician is further displayed. His Method of Fluxions was first published in 1704.

In the midst of his philosophical and mathematical labours, Newton found leisure to attend to critical inquiries. He wrote a treatise "On the Chronology of ancient Kingdoms," in which, from a diligent comparison of various notes of time in ancient writers with each other, and with astronomical phænomena, he concludes, that, in former