Newton's Principia, sections I, II, III, with notes and illustrations. Also a collection of problems (1863)
Newton, Isaac, Sir, 1642-1727, Frost, Percival, 1817-1898 · Cambridge, London, Macmillan and Co · leaf 106
ty destroyed in time AK : space described:: aAKk : aAKk :: Aa : Aa :: resistance : the velocity, hence, since the resistance varies as the velocity, the velocitydestroyed varies as the space described. 6. A particle slides down the smooth arc of a cycloid,whose axis is vertical, and vertex… … Let v = velocity at P, and T= time in falling from B to A ;therefore v9 = 2g . EM, and 2AB = gT. (1) . But, by the properties of the cycloid, (see Appendix n.) .-. AL* - AP* = ±AB . EM. (2). Take Al, Ap, Aq, on the tangent at A respectively equalto AL, AP, AQ, and letjrt, gu perpendicular to Al be…
Mechanics · Celestial mechanics
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