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 64
e generated by the arc PPf about the directrix isequal to 2ir x area MQQM. LEMMA V. 45 LEMMA V. All the homologous sides of similar figures are proportionalivhether curvilinear or rectilinear, and their areas are inthe duplicate ratio of the homologous sides. [Similar curvilinear figures are… … Then,Similarly, AB : ab :: SA : sa. BO : be :: AB : ab :: SA : sa CD : cd :: BC : be :: SA : sa, Therefore, componendo,AB + BC+CD+ ... SA : sa, Now this, being true for all similar polygons, will be truein the limit, when the number of the sides AB, BC, ...and ab, be, ... is increased, and their…
Mechanics · Celestial mechanics
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