# A Short Comment on Sir I. Newton's Principia; Containing Notes Upon Some Difficult Places of That Excellent Book

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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. 1770 edition. Excerpt: ... CP-z, r-radius TC. PK = y, TK = -, Fig. / = tan. PTC. Then A =-yxy and A l s6' r Fl: yx = area CPK. But TPC expresses the mean motion, and therefore TPK is the equation, which is as TK x PK or uy. But by the nature of the circle, z--rr rr+tt and since / is in a given ratio to /, (or as.3123 to.. rrt t 6a, ) therefore z is as-.--or--7-X TK rr+tt s/rr+tt oryx TK, or as uy. Therefore decreasing the tangent in the sub-duplicate ratio of 11073 to j0973, or in the simple ratio of 6a to 68, 6877; accelerates the area in proportion of PK1, as it ought to do. ib.--in a proportion compounded of the duplicate, &c for y cor. 16. pr. 66. L. I.) all angular errors are as the square of the time of the moon's revolution, directly, and the square of the time of the earth's revolution inverfly; that is (by pr. 15. L. I.) as the square of the time of the moon's revolution directly, and the cube of the earth's distance from the sun inversly. Pr. 30. And this force by prop. 25, is, &c."j The force 3PK: force ML:: 3IT: PT (for these are the fame) and force ML: centripetal force by', which the moon revolves, &c.:: 1: 17844 (by pr. 25. therefore ex equo, force 3PK: centripetal force the moon revolves with:: 3 IT x: PT X; 7844. Or as IT: rad. x 59,575 ib. the half of which the moon it should be, which the moon, by the action of the faid force, as it is in the first edition. ib. And the angle PTM is equal to the angle, 5J. &c.j for in this cale LM is perpendicular to iViP. Let PR be a tangent to the point P; then the tri Fig. angle RPT is a right one; and angle RPM = 57. angle PTM. And angle LPM: (RPM = ) PTM (when the radius is PM):: LM: RM:: force producing LM: force producing RM:: 1: 59575 Pr. 3t. cor. and the decrement is to the...show more

## Product details

• Paperback | 38 pages
• 189 x 246 x 2mm | 86g
• Miami Fl, United States
• English
• black & white illustrations
• 1236568265
• 9781236568267