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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 150

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 150
perpendicular to PU, is equal to AG, PU will be the tangentat P. 135. If a rectangular hyperhola he described, having centreG and semi-transverse axis GA, the ordinate of the hyperholawill he equal to the arc of the catenary. For, let AR be the hyperbola, thereforeEN = GN - GA = PM -UM = PW, .: BN=… … Since QRS is a triangle of the forces acting upon PQ^ tension at P : weight of PQ :: B8: QJR, .: PM: PQ:: BS: QR:: ^PQ : QR, ultimately; therefore 2PM is the vertical chord of curvature, and PG^ thepart of the normal Intercepted between the point P and thedirectrix is equal to the radius of…

Mechanics · Celestial mechanics

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