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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)

Newton, Isaac, Sir, 1642-1727, Frost, Percival, 1817-1898 · London, Macmillan · leaf 39

An illustration from 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, leaf 39
tion, 16. In a manner exactly similar to Lemma IT. it may beshewn that, if Aa be perpendicular to AE., and the wholefigure revolve round AE as an axis, the ultimate ratios, whichthe sums of the volumes of the cylinders, generated respectivelyby the rectangles Ah^ Be, ... and aB, hC, ... and the… … Thus the difference of the cylinders generated by Ah andoB is the annulus generated by the rectangle «5, and thedifference of the two series of cylinders, which have all equalheights AB^ BG^ ... is the sum of such annuli, and is easilyseen to be the cylinder generated by aB^ which, since the…

Mechanics · Celestial mechanics

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