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 68
oftheir chords, A Qq, APp any straight lines meeting the curves inQ, q and P, p respectively ; .-. AQ : Aq :: AP : Ap\hence, AP, Ap are similar portions of the curve; therefore, by Lemma Y,arc AP : arc Ap :: AP : Ap :: AB : Ab-,therefore arcs AP, Ap vanish simultaneously, or, when AP assumes its… … NEWT. 50 NEWTON. Let S be the intersection of two common tangents to thecircles which intersect in the produced line Cc joining theircenters, and let CQ, cq be radii at the points of contact. Draw SpP through S cutting the circles in p, P, Cq is parallel to CQ,and OP : cp :: CQ : cq :: CS : cS-,..…
Mechanics · Celestial mechanics
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