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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 54

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 54
on that of the tangentat P, which is deduclble from the idea of a tangent being in thedirection of the curve at the point of contact. Let AB^ BC be the diameter and ordinate; ^i>the tangentat A ; CD parallel to AB-^ P, Q points near each other;PJ/, QN and Pm, Qn parallel respectively to AD and… … T jL M ,_JW M the parallelogram Pn^ and the complements PJV, PU are equal;therefore the parallelograms PN^ Pn are ultimately in the ratio2 ; L Hence, in the eurvillnear areas ABC^ ACD two gets ofparallelograms can be inscribed which are ultimately in the ratio2:1, each to each; therefore area ABC…

Mechanics · Celestial mechanics

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