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)
inge at B and B for ever. M 82 NEWTON, LEMMA XL The vanishing siiltenses of the angle of contact, in all curveswhich have finite curvature at the point of contact, areultimately in the duplicate ratio of the chords of the con-terminous arcs. Case 1. Let AB be the arc of a curve, AD its tangent atA,… … the points D, B, G move towards the points d, h, g,and let / be the point of ultimate intersection of thelines BG, AG, when the points B, D move up to ^1. It is evident that the distance GI may be made lessthan any assigned distance by diminishing AB. But, since the angles ABD and GAB are equal,…
Mechanics · Celestial mechanics
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