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)
cubical parabola PM^ oc OM^; .-. QR-PM: PAP :: ON^- OM : OliP, but QN+PM=2PM, and ON^-i ON.OM+ OM = ZOM\ ultimately; .-. QN- PM: ^PM:: ON- OM: ^Oilf ultimately, and QN-PM: PM:: ON- OM = MT; therefore 3IT is two-thirds of OM. 56 NEWTON. (3) To find tlie inclination of the tangent at any point ofa… … ^ 71^ ut €r JL Making the same construction as before, irt Art. 35, BTV SP:: QR : SP- SQ ultimately.Let SQ meet the circle in q^ and draw qn perpendicularto BC, then QE : pq :: SP: Sp ultimately,also pq : mn r: Sp :pm ............^ .•. QR\mn:xSP:pm ; but mn = Bm — Bn = SP— SQ; .-. QR : SP- SQ :r…
Mechanics · Celestial mechanics
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