Newcomb, Simon, 1835-1909 · New York, H. Holt and company · leaf 367
sectors of the angles, and thethree points P will be the centres of the escribed circles. HARMONIC POINTS AND LINES. 337 308. Correlative Theorem. If three points on a linehe taken 07i the sides of a triangle, and the fourth harmonicsto two of them be constructed, these fourth harmonics loill heon… … Because x, y and z are fourth harmonics, 7 ^ az hx^^ cy iP) az _ hz~ hx _ ex ~ cy _ ay ~ ayBecause x, y and z are on a right line,az hx cy _bz ex ay~ By substituting for any two of these factors their valuesfrom {b), we prove the theorem, by § 288. EXERCISES. 1. Any two orthogonal circles cut the…
Geometry, Analytic
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