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 164
reshall be harmonic. Because the three straight lines AD, BE, CF pass through thesame point 0, therefore (168) *> ■ *> -■ {X; & and because the transversal FL cuts the sides of the triangle ABC,therefore (167) BL ■ LG ■■ iBF FA\BL • LC - \AE : EC) 169.] AND IN MODERN GEOMETRY. 135… … In the same manner it can be proved, that every other fourpoints on the same straight line or four lines passing through thesame point are harmonic ranges or pencils. Again, join LA. Then L. AECM is an harmonic pencil.Therefore if ML, LC, LE, and LA be produced to meet anytransversal, they will cut…
Geometry
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