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Exercises on Euclid and in modern geometry for the use of schools, private students, and junior university students (1881)

McDowell, James L · Cambridge, Deighton, Bell, and Co. · leaf 179

An illustration from Exercises on Euclid and in modern geometry for the use of schools, private students, and junior university students, 1881, leaf 179 — quired triangle are topass. Omitting the third point, find the point P through whichthe base always passes. Join P with the omitted point, and letthe joining line meet OA, OB in the points A, B. AB is the baseof the required triangle. Join AL and BM meeting in G. ABOis the required triangle. 150… … Let LM, LN be the two fixed straight lines, 0, P, Q the threefixed poinds. Take two positions of the triangle, ABC, ABC,and join BO, LP, LQ. [MAAL] = [NBBL], since each is the anharmonic ratio of thepencil with vertex 0. ^p Therefore {P. MAAL\ = {Q . NBBL}. . Therefore the pencils P. MAAL and Q .…

Geometry

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