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)
on of the diameter^ areeach equal to four times the focal distance of that point. Let AP be a parabola, P any point, BQ a. subtense parallelto the diameter PMx, QM the ordinate at Q^ S the focus.Then, by a property of the parabola, Q]\P = 4:SP.PM; there-fore 4:SP is a third proportional to P3I and… … And, since P8^ PM are equally inclined to the tangent at P,the chords in those directions are equal; therefore the chord ofcurvature through S is four times the focal distance SP. 78. One-fourth of tlie diameter of curvature at any pointof a parahola is a third proportional to the perpendicular…
Mechanics · Celestial mechanics
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