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 129
OP is the radius of curvature, and 2/SP is thechord of curvature through the pole. If a be the angle of the spiral, OP = SP cosec a. 91. The following is an illustration of Art. 88.Since SY : SY :: SP : SP, SY : SP :: 8Y-SY : SP-SP, :: 2SY: chord of curvature at P, by Art. 88;therefore the chord of… … By the triangle of forces QSE (see Appendix II).Tension at P : weight of PQ :: SE : QE-, LEMMA XI. Ill .-. PM : PQ :: SB : QB, :: \PQ : QB ultimately; therefore 2PM is the limit of the third proportional to QB andPQ, and is, therefore, the vertical chord of curvature. Hence, the normal PG is equal…
Mechanics · Celestial mechanics
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