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)
hyperbola and the tangents atthe vertices of the hyperbola. LEMMA V. 43 LEMMA V. All the homologous sides of similar figures are proportional^whether curvilinear or rectilinear, and tlieir areas are in- the duplicate ratio of the homologous sides. [[Similar curvilinear figures are figures whose… … Then AB.al.: BA similarly, BC-.lc iiAB CD.cd..BC sa^, ah :: SA : sa-^ be :: SA : sa. therefore, componendo,AB 4- BC ^- CD + ... :ah j^ Ic -^ cd-{- : SA : sa.r Now this, being true for all similar polygons, will betrue in the limit, when the number of the sides AB,BC, ... and ah, be, ... is…
Mechanics · Celestial mechanics
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