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)
tangents AD. But, even in this case, the angle between the chord andthat tangent which belongs to the portion of the curve con-gidered continually diminishes and ultimately vanishes. The Suhtangenf. 32. Def, The part of the line of abscissse intercepted be-tween the tangent at any point and the… … a curve, and let <Q be a point near P, OiY, NQ its abscissaand ordinate. 54 NEWTON. Let QPU meet OX the line of abscissae in Z7; then, if PRparallel to OM meet QN in i2, PM: MU:-. QR : PR.. QN- PM : ON- OM. Now as Q approaches to P, the limiting position of QPU isthat of the tangent at P, viz.…
Mechanics · Celestial mechanics
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