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 176
two triangles be co-polar, they shall also be co-axial ; and conversely, if two triangles be co-axial they shallalso be co-polar. First, let ABC, ABC be the two co-polar triangles, 0 beingthe pole, so that A and A, B and B, C and C are the corre-sponding vertices, and the sides BG and BC, CA and… … vertex 0, therefore [LCL>B]= [LCEB], and therefore {A.LCDB\ = {A\LCEB}. Therefore the pencils A.LCBB and Af .LCEB have acommon ray A A and the same anharmonic ratio, therefore (165)the intersections of the corresponding rays, AL and AL, AC andAC, AB and ABr lie on the same straight line, that…
Geometry
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