Principles of modern geometry, with numerious applications to plane and spherical figures; and an appendix, containing questions for exercise. Intended chiefly for the use of junior students (1862)
Mulcahy, John, 1810?-1853 · Dublin Hodges, Smith · leaf 81
quired to prove that threeright lines, AP, BQ, CR, drawnfrom A,B,C to the middle pointsof the corresponding sides of thelatter triangle, meet in a point. B In order to prove this theorem, let us suppose AP and BQto meet in V; let VX, VY, VZ be drawn perpendicular to thesides of the triangle ABC,… … ADDITIONAL EXAMPLES ON TRANSVERSALS. 71 BA-AC VY _ , ,. , Q T n AB/ BC/ = y^- But (Art. 9, Lemma 1) It follows that VYVX CB; CA = 1 • AB • CA that is, VY . CB = VX • CA, and therefore (joining CV) the triangle CVB= the triangle CVA.Hence it appears, ex absurdo, that the joining line C V must…
Geometry -- Problems, exercises, etc · Geometry
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