CHAPTER II.

NEWTON ENTERS TRINITY COLLEGE, CAMBRIDGE—ORIGIN OF HIS LOve of MATHEMATICS—STUDIES DESCARTES' GEOMETRY, AND THE WRITINGS OF SCHOOTEN AND WALLIS-IS DRIVEN FROM CAMBRIDGE BY THE PLAGUE-OBSERVES LUNAR HALOS IN 1664-TAKES HIS DEGREE OF B.A. IN 1665-DISCOVERS FLUXIONS IN THE SAME YEAR-HIS FIRST SPECULATIONS ON GRAVITY-PURCHASES A PRISM TO STUDY COLOURS -REVISES BARROW'S OPTICAL LECTURES-BUT DOES NOT CORRECT HIS ERRONEOUS OPINIONS ABOUT COLOURS-IS ELECTED A MINOR FELLOW OF TRINITY IN 1667—AND A MAJOR FELLOW IN 1668-TAKES HIS DEGREE OF M.A. HIS NOTE-BOOK, WITH HIS EXPENSES FROM 1666 TO 1669-MAKES A SMALL REFLECTING TELESCOPE-HIS LETTER OF ADVICE TO FRANCIS ASTON, WHEN GOING UPON HIS TRAVELS -HIS CHEMICAL STUDIES-HIS TASTE FOR ALCHEMY—HIS PAPER ON FLUXIONS SENT TO BARROW AND COLLINS IN 1669.

To a young mind thirsting for knowledge, and ambitious of the distinction which it brings, the transition from a provincial school to a university like that of Cambridge, from intellectual solitude to the society of men imbued with all the literature and science of the age, must be an event of the deepest 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 a scientific character 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 in the line of least resistance, it was thus drawn aside from the precipitous path which it was fitted to climb, and the unbarred strongholds which it was destined to explore.

When Newton, therefore, entered Trinity College, he brought with him a more slender portion of science than at his age 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 to 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 birth-place 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.

With letters of introduction from his uncle, the Rev. James Ayscough, to his friends in Cambridge, Sir Isaac left Woolsthorpe in June 1661, and was admitted Subsizar at Trinity College on the 5th of that month, and matriculated Sizar1 on the 8th of July. Neither history

1 "This class of students," says Mr. Edleston, were required to perform various menial services, which now seem to be considered degrading to a young man who is endeavouring, by the force of his intellect, to raise himself to his proper position in society. The following extract from the Conclusion Book of Trinity College,

nor tradition has handed down to us any distinct account. of the studies which Newton pursued at Cambridge during the first three or four years of his residence in that University. In Conduit's Memoirs of Newton, transmitted to Fontenelle,1 we find very little information on this point, and even that little is by no means correct. Before Newton left Woolsthorpe, his uncle had given him a copy of Sanderson's Logic, which he seems to have studied so thoroughly, that when he afterwards attended the lectures on that work, he found that he knew more of it than his tutor. Finding him so far advanced, his tutor intimated to him that he was about to read Kepler's Optics to some Gentlemen Commoners, and that he might attend the Readings if he pleased. Newton immediately studied the book at home, and when his tutor gave him notice that his Lectures upon it were to commence, he was surprised to learn that it had been already mastered by his pupil.

About the same time probably he bought a book on Judicial Astrology at Stourbridge fair, 2 and in the course of perusing it he came to a figure of the Heavens, which he could not understand without a previous knowledge of trigonometry. He therefore purchased an English Euclid,

while it affords an example of one of their duties, will also serve to illustrate the rampant buoyancy of the academic youth at the time of the Restoration."

" Jan. 16, 1660-1. Ordered also that no Bachelor, of what condition soever, nor any Undergraduate, come into the upper butteries, save only a Sizar that is sent to see his tutor's quantum, and then to stay no longer than is requisite for that purpose, under penalty of 6d. for every time; but if any shall leap over the hatch, or strike a butler or his servant upon this account of being hindered to come into the butteries, he shall undergo the censure of the Masters and Seniors."-Edleston's Correspondence of Sir Isaac Newton and Professor Cotes, Lond. 1850, p. xli.

1 Collections for the History of the Town and Soke of Grantham, &c. By EDMUND TURNOR, F.R.S., F.S.A. Lond. 1806, pp. 159, 160. Conduit's MSS. were written subsequently to the Memoirs above referred to.

• Demoivre says, that the Book on Astrology was bought at Stourbridge, the seat of the Cambridge fair, close to the town.

with an index of all the problems at the end of it, and having turned to two or three which he thought likely to remove his difficulties, he found the truths which they enunciated so self-evident, that he expressed his astonishment that any person should have taken the trouble of writing a demonstration of them. He therefore threw aside Euclid" as a trifling book," and set himself to the study of Descartes' Geometry, where problems not so simple seem to have baffled his ingenuity. Even after reading a few pages, he got beyond his depth, and laid aside the work; and he is said to have resumed it again and again, alternately retreating and advancing till he was master of the whole, without having received any assistance.2 The neglect which he had shown of the elementary truths of geometry he afterwards regarded as a mistake in his mathematical studies; and on a future occasion 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."3

The study of Descartes' geometry seems to have inspired Newton with a love of the subject, and to have introduced him to the higher mathematics. In a small commonplace book, bearing on the 7th page the date of Jan. 1663-4, there are several articles on angular sections, and the squaring of curves and "crooked lines that may be squared," several calculations about musical notes ;— geometrical propositions from Francis Vieta and Schoo

1 Newton's copy of Descartes' Geometry I have seen among the family papers. It is marked in many places with his own hand, Error, Error, non est Geom. 2 This statement is different from that of Conduit in his Memoirs, but I give it on his own authority, as founded on later inquiries.

3

Pemberton's View of Sir Isaac Newton's Philosophy. PREF.

ten ;-annotations out of Wallis's Arithmetic of Infinites, together with observations on Refraction,-on the grinding of "spherical optic glasses," on the errors of lenses, and the method of rectifying them, and on the extraction of all kinds of roots, particularly those "in affected powers."1

This commonplace book is particularly interesting from its containing the following important entry by Newton himself, after the lapse of thirty-five years, and when he had completed all his discoveries.

July 4, 1699.—By consulting an account of my expenses at Cambridge,2 in the years 1663 and 1664, I find that in the year 1664, a little before Christmas, I, being then Senior Sophister, bought Schooten's Miscellanies and Cartes' Geometry, (having read this Geometry and Oughtred's Clavis3 clean over half a year before,) and borrowed Wallis's works, and by consequence made these annotations out of Schooten and Wallis, in winter between the years 1664 and 1665. At such time I found the method of Infinite Series; and in summer 1665, being forced from Cambridge by the plague, I computed the

In this commonplace book we find the date November 1665, so that its contents were written in 1664 and 1665.

In the commonplace book which contains the "annotations out of Schooten and Wallis," no expenses are entered, so that there must be another note-book which I have not found, in which the purchase of Schooten's Miscellanies and Descartes' Geometry is recorded. It is not likely that the second note-book of 1659, mentioned by Conduit, contained expenses incurred in 1663 and 1664.

3 Conduit remarks that in reading this work he did not entirely understand it, especially what "relates to Quadratic and Cubic Equations."-MSS. A translation of the Clavis was published and recommended by Halley in 1694.

4 The plague commenced in Westminster about the end of 1664. It raged during the hotter months of 1665, and had so far abated before the end of the year, that the inhabitants returned to their homes in December. The date of Newton's quitting Cambridge, viz., 1665, as written under his own hand in his commonplace book, coincides with these facts, and is on this account probably the correct one; but Peniberton makes the date 1666, which is adopted by Professor Rigaud, and seems to