An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 160
h are collinear,and let Ii, I2, I3 be the invariable points. Since Jj, P, are points FIGURES DIRECTLY SIMILAR. 143 of ^1 and /o, P, the corresponding points of F«, it follows that thetriangles S3I1I.2, S^PiP, are directly similar. Therefore, the angle/S3P1P2 is equal to the angle /SsZi/j, and… … Hence, the angle SiP^O is equal to the angle S^SM, and there-fore to the angle SsP^P^. Therefore the line PiP-Ps must passthrough the point 0. 230. It is evident from the last article that when threecorresponding points Pi, Pj, P, are collinear, each of them lies ona fixed circle. That is, Pj lies…
Geometry
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