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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)

Newton, Isaac, Sir, 1642-1727, Frost, Percival, 1817-1898 · London, Macmillan · leaf 258

An illustration from 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, leaf 258
In this case, with >S and H as foci, and SP + PRasmajor axis, describe an ellipse, then PUh half thechord of curvature at P through S. III. If P?7 be greater than 2SP lSGP is less thanlSPG, and angles SGP, HPG are together less than PROP. XVIT. PROBLEM IX. 239 two right angles, therefore GS… … In this case, with >S and H as foci, and HP - SP astransverse axis, describe an hyperbola, then P 27 ishalf the chord of curvature at P through S. In all these cases, a body may be supposed to revolvein the conic section described, under the action of theforce tending to >S, Art. 164, and the…

Mechanics · Celestial mechanics

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