Newton's principia, first book sections I, II, III, with notes and illustrations and a collection of problems, principally intended as examples of Newton's methods (1900)
ncesof ^from C, C from A, and A from B respectively, they willdescribe similar equiangular spirals with a common pole. 204 NEWTON. PEOP. X, PROBLEM V. If a hody he revoUing in an ellipse, to find the law ofcentripetal force tending to the centre of the ellipse. Let GA, CB be the semiaxes of the… … Then F= 2U QR ultimately. CP QTBut, by similar triangles QTU, PFO, QT^ _PF^ , _qU _ CDQU~ CP PI QT PF\CD TQ CPAC\BC pu.ua CP CP Ua = 2CP ultimately, and PU=QRQT AC\BC 2QR~ CP 2K\QR ,. jP=limit of ultimately; h\CPAC\BC-^ CP\QT therefore the force is proportional to the distancefrom the centre.…
Mechanics · Celestial mechanics
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