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 233
se = 2jrAC. BC \ AC.K* and = BC*BC Therefore, in different ellipses described about the samecenter of force, the squares of the periodic time vary as the cubesof the major axes. 214 NEWTON. 179. To find the time from an apse to any point of an ellipticorbit described under the action of a force… … <* S C 2V JC A Time in AP : periodic time :: area ASP : 7rAC.SC and area ASQ = sector ACQ + triangle SCQ therefore, if u be the circular measure of ^ ACQ, and e theeccentricity of the ellipse, area ASQ = \A C* (u + e sin u) -.,. z and time in AP : - 1 — :: u + esin u : 2?r, i. e. the time from…
Mechanics · Celestial mechanics
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