The Mathematical Principles of Natural Philosophy (1729)/Appendix

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Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/453 Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/454 Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/455 ii APPENDIX. And'E°2, ° = (Anza = 374'-'.§ 'E'=»-fdd-~zdx—xx:)—au--zdx—xx. Also?2 -:fill--f I;z "': zafx—ld.-xx--xxz) gl; PE ' x -aa: Th. P Z e T 7; q z7x . Therefore

- #12 . h H,

2-nv#-1-J- 'dF' z of xr” '/ - da-P. x ls” the flu- xion of the attractive force of the sphere on the body P, or the ordinate of a curve whose area represents that force. But the fluent of .Q is x;/ and the fluent of X3 “+d” ""7"f '- / '“ r zdx IS sdd 4/ Aa- zdx (by Tak. 1. Fmnq.. Caja.. Quad:-.of Curv.) U Therefore x-f-°i?'?;f, /-aa-|-zdxtis thege. nerai expression of the area of the curve. Now let xza, then area: (4- ' 'f1£f."/-“, , d¢ 1- - Q: - O

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3 I ii' -1-r 3 dd A Alsolet x- -;¢, then area = (¢- '/-¢¢, ..-gd; r)d' ""°f' ' B 3 = T 1 0 the force whereby the sphere attracts the body 3 P Q5 as (A-B or as:-.)3-éS'. .-4- . M 54 %PS* az, z.. The Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/457 Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/458 Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/459 Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/460