An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 158
and therefore the angles X^KX,, X3KX1,X1KX2 are constant. That is, the angles SJiISs, S3KS1, SiKS^ areconstant; and therefore the point K must lie on the circle SiS^Ss. 225. Since three corresponding lines form a triangle in per-spective with the triangle of similitude, so that the centre of… … Let Xi, X.2, X3 be any three corresponding lines which areconcurrent, and let K be the point of intersection. Then wehave *^1 2 ^^1^3 ^~ 2 ■ ^S • Hence S^K divides the angle between x^ and x^ into partswhose sines are in a constant ratio. Let Xj, X2, X3 cut the circle of similitude in the points…
Geometry
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