Smart, Edward Howard · London : Macmillian and Co. · leaf 80
n, we could construct the image of the other Xin any straight line passing through the homothetic centre.Calling this image X we could not, by any rotation in theirown plane, bring X and X into coincidence.X and X are then called inversely similar. COAXAL CIRCLES. § 14. Prop. The locus of points… … Fig. 24. Draw TX perpendicular to CC, and let O be the middlepoint of CC Then CT^ - CT2 = Cp2 + PT^ - CP^ - Pr. But PT = PT ; .. CT2 - CT2 = CP2 - CP2 = constant for all positions of T. COAXAL CIRCLES 63 But CT2 - CT^ = (CX- + XT-) - (CX2 + XT^) = CX^-CX2 = 2CC.OX. But CC is constant; .. OX is…
Geometry, Projective
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