newton enters trinity college, cambridge—origin of his propensity for mathematics—he studies the geometry of descartes unassisted—purchases a prism—revises dr. harrow’s optical lectures—dr. barrow’s opinion respecting colours—takes his degrees—is appointed a fellow of trinity college—succeeds dr. barrow in the lucasian chair of mathematics.

to a young mind thirsting for knowledge, and ambitious of the distinction which it brings, the transition from a village school to a university like that of cambridge,—from the absolute solitude of thought to the society of men imbued with all the literature and science of the age,—must be one of eventful interest. to newton it was a source of peculiar excitement. the history of science affords many examples where the young aspirant had been early initiated into her mysteries, and had even exercised his powers of invention and discovery before he was admitted within the walls of a college; but he who was to give philosophy her laws did not exhibit such early talent; no friendly counsel regulated his youthful studies, and no work of scientific eminence seems to have guided him in his course. in yielding to the impulse of his mechanical genius, his mind obeyed the laws of its own natural expansion, and, following the line of least resistance, it was thus drawn aside from the strongholds with which it was destined to grapple.

when newton, therefore, arrived at trinity college, he brought with him a more slender portion of science than falls to the lot of ordinary scholars; but this state of his acquirements was perhaps not unfavourable to the development of his powers. unexhausted by premature growth, and invigorated by healthful repose, his mind was the better fitted to27 make those vigorous and rapid shoots which soon covered with foliage and with fruit the genial soil to which it had been transferred.

cambridge was consequently the real birthplace of newton’s genius. her teachers fostered his earliest studies;—her institutions sustained his mightiest efforts;—and within her precincts were all his discoveries made and perfected. when he was called to higher official functions, his disciples kept up the pre-eminence of their master’s philosophy, and their successors have maintained this seat of learning in the fulness of its glory, and rendered it the most distinguished among the universities of europe.

it was on the 5th of june, 1660, in the 18th year of his age, that newton was admitted into trinity college, cambridge, during the same year that dr. barrow was elected professor of greek in the university. his attention was first turned to the study of mathematics by a desire to inquire into the truth of judicial astrology; and he is said to have discovered the folly of that study by erecting a figure with the aid of one or two of the problems of euclid. the propositions contained in this ancient system of geometry he regarded as self-evident truths; and without any preliminary study he made himself master of descartes’s geometry by his genius and patient application. this neglect of the elementary truths of geometry he afterward regarded as 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 deserved.7 dr. wallis’s arithmetic of infinites, saunderson’s logic, and the optics of kepler were among the books which he had studied with care. on these works he wrote comments during their perusal;28 and so great was his progress, that he is reported to have found himself more deeply versed in some branches of knowledge than the tutor who directed his studies.

neither history nor tradition has handed down to us any particular account of his progress during the first three years that he spent at cambridge. it appears from a statement of his expenses, that in 1664 he purchased a prism, for the purpose, as has been said, of examining descartes’s theory of colours; and it is stated by mr. conduit, that he soon established his own views on the subject, and detected the errors in those of the french philosopher. this, however, does not seem to have been the case. had he discovered the composition of light in 1664 or 1665, it is not likely that he would have withheld it, not only from the royal society, but from his own friends at cambridge till the year 1671. his friend and tutor, dr. barrow, was made lucasian professor of mathematics in 1663, and the optical lectures which he afterward delivered were published in 1669. in the preface of this work he acknowledges his obligations to his colleague, mr. isaac newton,8 for having revised the mss., and corrected several oversights, and made some important suggestions. in the twelfth lecture there are some observations on the nature and origin of colours, which newton could not have permitted his friend to publish had he been then in possession of their true theory. according to dr. barrow, white is that which discharges a copious light equally clear in every direction; black is that which does not emit light at all, or which does it very sparingly. red is that which emits a light more clear than usual, but interrupted by shady interstices. blue is that which discharges a rarified light, as in bodies which consist of white and black particles arranged29 alternately. green is nearly allied to blue. yellow is a mixture of much white and a little red; and purple consists of a great deal of blue mixed with a small portion of red. the blue colour of the sea arises from the whiteness of the salt which it contains, mixed with the blackness of the pure water in which the salt is dissolved; and the blueness of the shadows of bodies, seen at the same time by candle and daylight, arises from the whiteness of the paper mixed with the faint light or blackness of the twilight. these opinions savour so little of genuine philosophy that they must have attracted the observation of newton, and had he discovered at that time that white was a mixture of all the colours, and black a privation of them all, he could not have permitted the absurd speculations of his master to pass uncorrected.

that newton had not distinguished himself by any positive discovery so early as 1664 or 1665, may be inferred also from the circumstances which attended the competition for the law fellowship of trinity college. the candidates for this appointment were himself and mr. robert uvedale; and dr. barrow, then master of trinity, having found them perfectly equal in their attainments, conferred the fellowship on mr. uvedale as the senior candidate.

in the books of the university, newton is recorded as having been admitted sub-sizer in 1661. he became a scholar in 1664. in 1665 he took his degree of bachelor of arts, and in 1666, in consequence of the breaking out of the plague, he retired to woolsthorpe. in 1667 he was made junior fellow. in 1668 he took his degree of master of arts, and in the same year he was appointed to a senior fellowship. in 1669, when dr. barrow had resolved to devote his attention to theology, he resigned the lucasian professorship of mathematics in favour of newton, who may now be considered30 as having entered upon that brilliant career of discovery the history of which will form the subject of some of the following chapters.