Smart, Edward Howard · London : Macmillian and Co. · leaf 72
point on it is a straight line. Let O be the point, k the radius of inversion (Fig. 16). Take P any point on the given circle. On OP take P sothat OP. OP = F. AVe want the locus of P. Let A be the other end of the diameter through O, andtake X on this diameter so that OA. OX = U-. X is then a fixed… … Fig. 16. OA therefore meets OA at a fixed point; i.e. the locus of Pis a straight line perpendicular to OA and passing through theinverse of A. § 6. Prop. The inverse of a circle with respect to anypoint is a circle. Let O and k be as before. Let 0 (Fig. 17) be the centre of the circle to…
Geometry, Projective
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