calculus, therefore, was not so much an individual discovery as the grand result of a succession of discoveries by different minds. Indeed, no great discovery ever flashed upon the mind at once, and though those of Newton will
influence mankind to the end of the world, yet it must be admitted that Pope's lines are only a "poetic fancy":–-
" God said, `Let Newton be,' and all was light."
" Nature and Nature's laws lay hid in night; " [][c]God said, `Let Newton be,' and all was light."
Isaac Newton (1642-1727) was born at Woolsthorpe, in
Lincolnshire, the same year in which Galileo died. At his birth he was so small and weak that his life was despaired of. His mother sent him at an early age to a village school, and in his twelfth year to the public school at Grantham. At first he seems to have been very inattentive to his studies and very low in the school; but when, one day, the little Isaac received a severe kick upon his stomach from a boy who was above him, he laboured hard till he ranked higher in school than his antagonist. From that time he continued to rise until he was the head boy.33 At Grantham, Isaac showed a decided taste for mechanical inventions. He constructed a water-clock, a wind-mill, a carriage moved by the person who sat in it, and other toys. When he had attained his fifteenth year his mother took him home to assist her in the management of the farm, but his great dislike for farm-work and his irresistible passion for study, induced her to send him back to Grantham, where he remained till his eighteenth year, when he entered Trinity College, Cambridge (1660). Cambridge was the real birthplace of Newton's genius. Some idea of his strong intuitive powers may be drawn from the fact that he regarded the theorems of ancient geometry as self-evident truths, and that, without any preliminary study, he made himself master of Descartes' Geometry. He afterwards regarded this neglect of elementary geometry a mistake in his mathematical studies, and he expressed to Dr. Pemberton his regret that "he had applied himself to the
works of Descartes and other algebraic writers before he had
considered the Elements of Euclid with that attention which so excellent a writer deserves." Besides Descartes' Geometry, he studied Oughtred's Clavis, Kepler's Optics, the works of
Vieta, Schooten's Miscellanies, Barrow's Lectures, and the
works of Wallis. He was particularly delighted with Wallis'
Arithmetic of Infinites, a treatise fraught with rich and varied suggestions. Newton had the good fortune of having for a teacher and fast friend the celebrated Dr. Barrow, who had been elected professor of Greek in 1660, and was made Lucasian professor of mathematics in 1663. The mathematics of Barrow and of Wallis were the starting-points from which Newton, with a higher power than his masters', moved onward into wider fields. Wallis had effected the quadrature of curves whose ordinates are expressed by any
integral and positive power of ( 1 − x 2 ) . We have seen how Wallis attempted but failed to interpolate between the areas thus calculated, the areas of other curves, such as that of the circle; how Newton attacked the problem, effected the interpolation, and discovered the Binomial Theorem, which afforded a much easier