Newcomb, Simon, 1835-1909 · New York, H. Holt and company · leaf 126
li-tude of the other pair. Proof. Let the circles P and P touch the circles 0 and0 at the points M, N, M and N. The point of meeting, S, of the lines iVif and NM willbe a centre of similitude of 0 and 0 (§91). Hence we have SM. SN = SM. SN. (§ 93) But SM. >SiVis equal to the square of the… … It is shown in the same way that a centre of similitude ofP and P is on the radical axis of 0 and 0\ Q. E. D. Cor. 1. If each of three circles is a tangent of the samenature to two other circles, then, by this theorem, one of thecentres of similitude of each two out of the three circles mustlie on…
Geometry, Analytic
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