An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 105
passes through X, and that uz, xfzintersect in the point X. 88 INVOLUTION PROPERTY Hence, X and X are two of the centres of the tetrastigm yi/z^ ; andtherefore by § 141, the segment ytf is divided harmonically by z^ and XX,and likewise the segment zz is divided harmonically by yy and XX. Similarly… … It follows that the lines xx, yy\ zi are concurrent, and that if 0 be thepoint in which they intersect, each segment such as xx is divided harmonicallyin the point 0 and the point where it cuts the line XX. Ex. Deduce the theorem given in § 140, Ex. 1, by considering the lineXX to be the line at…
Geometry
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