An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 277
on the line OP.That is to say the reciprocal of any point P on the circle T is thediameter of this circle which is perpendicular to OP. 409. To find the reciprocal of a given circle. Let P be any point on a given circle X, and let P be theinverse point with respect to S, the circle of… … Since the circle X passes through the point P (so that thepower (ZP) is zero) which is a limiting point of the system(p, S, P, P), it follows by § 329, that (Xp):iXS) = PC:PO. But (§ 407) GP:PO = p:k, where p, k denote the radii of the circles p, T. Hence, if r denote the radius of X, and 6 the…
Geometry
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