An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 78
rse theorems of those in examples 1—5. POLAR WITH RESPKCT TO A TRIANGLE. 61 Ex. 7. If XYZ, XYZ be any two transversals of the triangle ADC,and if YZ, YZ meet in P ; ZX, ZX in Q ; and XY, XY in R ; show thatAP, BQ, Cli cut the sides BC, CA, AB in three collinear points. Pole and Polar with respect… … Let YZ, ZX, XY meet BC, CA, AB respectively in the pointsX, 1, Z. Since X, Y, Z are collinear we have by § 104, BJC GY AZCX- AY- BZ~ But since AX, BY, GZ are concurrent, we have by § 94,BX GY AZ_XG • YA ■ ZB~ Therefore BX-.XC^BXiGX. Similarly, we shall have GY:YA = CY:AY, and AZ:ZB = AZ:BZ:…
Geometry
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