An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 290
rsect in the point 0. If the points 0, B, Che coUinear, showthat the locus of the point P will be a straight line. Involution. 426. If \AA, BB, CC] be a range in involution the ranges{AA, BC\, [AA, BC] are equicross and conversely. Let 0 be the centre of the involution, then by definition (§ 66)we… … Let E be one of the double points, and let P be any point onthe circle whose centre is 0 and radius OE. The circle which cutsthis circle orthogonally and passes through A will pass through A,since OA .OA= OE=OF. It is evident therefore that thecircles PAA, PBE, FCC will touch each other at P. Hence…
Geometry
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