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 165
63,KB.) 170. Given three consecutive rays of an harmonic pencilor three consecutive points of an harmonic range; find thefourth harmonic. More generally, given any three rays of ananharmonic pencil or any three points of an anharmonic rangeand the anharmonic ratio; find the remaining ray or… … in F, 0 and E, A. Join AC, EF, and let these lines meet in D.Join OD. OD is the required fourth harmonic. This is evidentfrom (169), since the three straight lines AF, CE and OB drawnthrough the angles of the triangle A OC meet in the same point P. If three points A, B, C of an harmonic range be…
Geometry
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