An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 103
C^-iAB.BC. CD.DA cos a,where a> is the difference of the angles BAD, BCD. Ex. 4. If any straight line cut the connectors AB, BC, CD, DA in thepoints X, Y, X, Y respectively, show that AX BY Cr DYXB • YC ■ XD • YAEx. 5. Show that the bisectors of the angles of a triangle are the sixconnectors of… … = 1. = 1. A F B Let A BCD be the tetrastigm, EFG its central triangle; andlet GE meet AB in F. Since A G, BD, GE are concurrent, we have (§ 94) AF BC GDFBCGDA Also since FCD is a transversal of the triangle GAB (§ 104), AF BG GDBF-GCAD Therefore AF:FB = AF:BF; that is, {FF, AB] is a harmonic range.…
Geometry
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