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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 134

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 134
d at P. If A QB be the circle on AB as diameter, PQM an ordi-nate perpendicular to AB, the tangent at P will be parallel tothe chord QA. 102. To find the length of the arc of a cycloid. Let RPS be the position of the generating circle corre-sponding to the point P in the cycloid, PR being the… … of Pp due to the rotation, and pP = i^ parallel to the basedue to the translation of the centre of the circle; and PPwill ultimately coincide with PR. Draw pn perpendicular toPPi^ then, since Pp = P>, PP= 2Pn = 2 [PP- Bp) ultimately.Hence the arc of the cycloid measured from the vertex…

Mechanics · Celestial mechanics

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