had obtained his degree in August 1665, the University closed down as a precaution against the Great Plague of London. Although he had been undistinguished as a Cambridge student, Newton's private studies at his home in Woolsthorpe over the next two years saw the development of his theories on calculus, optics and the law of gravitation. In 1667 he returned to Cambridge as a fellow of Trinity. Newton had stated that when he had purchased a book on astrology at Stourbridge fair, near Cambridge, he was unable, on account of his ignorance of trigonometry, to understand a figure of the heavens which was drawn in the book. He, therefore, bought an English edition of Euclid's Elements which included an index of propositions, and, having turned to two or three which he thought might be helpful, found them so obvious that he dismissed it "as a trifling book", and applied himself to the study of René Descartes' Geometry. It is reported that in his examination for a scholarship at Trinity, to which he was elected on 28 April 1664, he was examined in Euclid by Dr Isaac Barrow, who was disappointed in Newton's lack of knowledge of the subject. Newton was convinced to read the Elements again with care, and formed a more favourable opinion of Euclid's merit. Newton's study of Descartes' Geometry seems to have inspired him with a love of the subject, and introduced him to higher mathematics. In a small commonplace book, dated January 1664, 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 François Viète and Frans van Schooten, annotations out of John Wallis's Arithmetic of Infinities, 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". In this same book the following entry made by Newton himself, many years afterward, gives a further account of the nature of his work during the period when he was an undergraduate: That Newton must have begun early to make careful observations of natural phenomena is shown by the following remarks about halos, which appear in his Optics, book ii. part iv. obs. 13: He formulated the three laws of motion: Every object in a