Newcomb, Simon, 1835-1909 · New York, H. Holt and company · leaf 343
theorem is proved. 281*. Theorem II. The continued product of the dis-tance-ratios in which any transversal cuts the sides of a tri-angle is equal to unity. Proof Let a transversalcut the sides of the triangleabc in the points x, y and z. Through any vertex, as^b, draw a line parallel to… … ex while cy cy ^ c/y_ay ay 318 MODERN GEOMETRY. The continued product of these equations gives ££.*?.. oy. ^ 1. Q. E. D.Dz ex ay Remaek. Since the demonstration takes no account ofalgebraic signs, we have not yet shown whether the productis + 1 or — 1. It is evident that the transversal must…
Geometry, Analytic
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