The _Principia_, as I have said, is a classic. Like other books to which that compliment is paid, it is rarely read: indeed, I doubt whether there are a dozen men in Cambridge who have glanced all through it, even in a cursory manner. When I was an undergraduate the course for the Tripos involved five sections (1, 2, 3, 9, and 11) of the first book, but now, probably with good reason, even this slight acquaintance with the work is no longer required, and to-day the character of these investigations is unfamiliar to most mathematicians, while the fact that it is written in Latin tends to diminish the number of its readers. I will, then, with your permission, describe briefly its frame-work. First, however, let me remark on how different was the knowledge of mathematics, even among experts, at the time it was written from that current to-day. In the geometry of the circle and conics mathematicians were familiar with the methods of Greek science, and in their application Newton was unrivalled among his contemporaries, but outside geometry methods of investigation were far to seek. Analysis had been but little developed; algebraic notation had only recently taken definite form; trigonometry was still used mainly as an adjunct to astronomy; analytical geometry had been invented by Descartes, but no text-books on it of modern type were available; while nothing about the calculus had been published. Mechanics, however, had recently been treated as a science--statics by Stevinus and dynamics by Galileo--and this paved the way for Newton's investigations. In particular, Galileo had established principles which foreshadowed the first two laws of motion, and had deduced formulae in linear motion like _v² = 2fs_, _s = ½ft²_, and in circular motion like _f = v²/r_. Newton prefaced the _Principia_ by explaining that the earliest problems in natural philosophy which attract attention are connected with the phenomena of motion, and it was with motion that the book dealt. To discuss motion effectively, it was necessary to give precision to the language used, and accordingly he propounded definitions of mass, momentum, inertia, and so on, which have settled the language of the subject. He next enunciated his three well-known laws of motion, and described the experiments on which he based them. He followed this up by deducing rules for the composition and resolution of forces, and discussed relative motion. This preliminary matter is followed by the first book, concerned with the motion of bodies in an unresisting medium. It is divided into fourteen sections containing ninety-eight propositions with various interpolated lemmas, corollaries, and scholia.