An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 289
be two ranges on different lines, show that thepoints of intersection of the pairs of lines BC, BC; CA, CA ; AB, AB;will be coUinear. (§ 157.) … Let BC, BC intersect in X; CA, CA in Y; and AB, AB in Z. JoinTX, YZ, YB. Then it is easy to see that, Y{AA, BZs =A {CA, BB},since these pencils have the common transversal AB.Similarly, Y {CC, BX} = C {CA, BB}. But it is evident that A {CA, BB] = C{CA, BB}.Hence, Y {AA, BZ} = Y{CC, BX}. Therefore…
Geometry
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