THE MATHEMATICAL PRINCIPLES OF NATURAL PHILOSOPHY. BY SIR ISAAC NEWTON. Translated into English BY ANDREW MOTTE. TO WHICH ARE added, Newton's Syftem of the World; A SHORT Comment on, and Defence of, the Principia, BY W. EMERSON. WITH THE LAWS OF THE MOON'S MOTION According to Gravity. BY JOHN MACHIN, Astron., Prof. at Gresh., and Sec. to the Roy. Soc. A new Edition, (With the LIFE of the AUTHOR; and a PORTRAIT, taken from the Buft in CAREFULLY REVISED AND CORRECTED BY W. DAVIS, Author of the "Treatise on Land Surveying," the "Use of the Globes," IN THREE VOLUMES. VOL. II. London: PRINTED FOR H. D. SYMONDS, NO. 20, PATERNOSTER ROW. 1803. Printed by Knight & Compton, Middle Street, Cloth Fair. Of the motion of bodies that are refifted in the ratio of the velocity. PROPOSITION I. THEOREM I. If a body is refifted in the ratio of its velocity, the motion loft by refiftance is as the Space gone over in its motion. FOR fince the motion loft in each equal particle of time is as the velocity, that is, as the particle of space gone over, then, by compofition, the motion loft in the whole time will be as the whole space gone over. Q.E.D. COR. Therefore if the body, deftitute of all gravity, move by its innate force only in free spaces, and there be given both its whole motion at the beginning, and alfo the motion remaining after fome 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 loft of that motion. |