The Mathematical Principles of Natural Philosophy Volume 2

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1729 edition. Excerpt: ... The mathematical principles of natural philosophy Sir Isaac Newton MOTION O F BODIES. BOOK IlT SECTION I. Of the Motion of Bodies that are re* fijled in the ratio of the Velocity. Proposition I. Theorem I. If a body is resisted in the ratio of its velocity* the motion lost by resistance is as the space gone over in its motion. O R since the motion lost in each equal DEGREESparticle of time is as the velocity, that is, as the particle of space gone over; thesis by composition, the motion loft in the whole time will be as the whole space gone over. QE. T>, ■Yo L. II. B Co*. Cor. Therefore if the body, destitute of all gravity, move by its innate force only in free spaces, and there be given both its whole motion at the beginning, and also the motion remaining after some part of the way is gone over; there will be given also the whole space which the body can describe in an infinite time. For that space will be to the space now described, as the whole motion at the beginning is to the part lost of that motion. Lemma I. Quantities proportional to their differences are continually proportional. Let A be to A-- B as B to C and C to C--Z>, &c. and, by conversion, A will be to B as B to C and Cto A &c.