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)
ss than any assignablevolume, hence the conditions that the two series may have thesame limit are satisfied, and hence also the volume of revolution,which is greater than one sum and less than the other, isultimately in a ratio of equality to either sum. The same argument applies when the… … LEMMA II.j III. 21 Thus, let SABCFhe a sectorial area, and let the angle ASFbe divided into equal portions A8B^ BSC, ... and the circulararcs Ab\ aBc\ hCd\ ... be drawn with centre S, then, sincethe difference of the two series of circular sectois is the sumof the areas ah\ bo, ..., it is equal to…
Mechanics · Celestial mechanics
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