Beman, Wooster Woodruff, 1850-1922, Smith, David Eugene, 1860-1944 · Boston, Ginn & company · leaf 192
he external division, if the ratiois unity, is impossible, it is often said that the point of division, P, is atinfinity. In the case of internal division, the ratios AP : PB and AC : CD areevidently positive; but in the case of external division each ratio isevidently negative because PB and CD… … Given the triangle ABC, and DE so drawn that AD : DC= BE: EC. To prove that DE II AB. Proof. 1. Suppose DE not ii AB, but that DX II AB. Then BX: XC = AD : D C. Prop. X, cor. 1 2. But this is impossible, for the division of BC in theratio AD : DC is unique. Prop. XI, cor. 3. .. DX must be identical…
Geometry
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