An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 58
any one range, are har-monically conjugate with the double points of the other two ranges. Let A, B, C, Dhe the four given points. Then we shall have a range inwhich A, B and C, D are conjugate couples; a range in which A, C and B, Dare conjugate couples; and a range in which ^1, D and B, C are… … Let the circles described on HH and FF as diameters meet in P. Thenby § 48, Ex. 2, PH bisects the angles BPC, APD. Hence the angles APB,CPD are equal. But PF bisects the angle APB, and PF the angle CPD;therefore the angle FPB is equal to the angle CPF. Hence the angle FPEis equal to the angle HPF.…
Geometry
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