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 Bust in CAREFULLY REVISED AND CORRECTED BY W. DAVIS, Author of the "Treatise on Land Surveying," the "Use of the Globes," IN THREE VOLUMES. VOL. III. London: PRINTED FOR H. D. SYMONDS, NO. 20, PATERNOSTER ROW. 1803. Printed by Knight & Compton, Middle Street, Cloth Fair. The effects of centripetal forces.. The certainty of the argument.. What follows from the supposed diurnal motion of the stars... The incongruous confequences of this fuppofition... That there is a centripetal force really directed to the centre of That those centripetal forces decrease in the duplicate proportion of the distances from the centre of every planet That the fuperior planets are revolved about the fun, and by That the circumfolar force throughout all the regions of the planets decreaseth in the duplicate proportion of the distances That the circum-terrestrial force decreases in the duplicate propor- 8 10 ibid The fame proved in the hypothefis of the earth's motion... The decrement of the forces in the duplicate proportion of the. diftances from the earth and planets, proved from the eccentri- city of the planets, and the very flow motion of their apfes..... 13 The quantity of the forces tending towards the feveral planets: Why the density is greater in some of the planets and less in others; but the forces in all are as their quantities of matter.... Another analogy between the forces and bodies, proved in the 14 |