An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 55
C. LM= 0, where P is any point on the same line. 38 CONSTRUCTION OF A RANGE By § 27, Ex. 5, the expression on the left-hand side must be equal toOA . OA. Jm+ OB. OB .JVL+OC. OC. Lif,where 0 is the centre of the involution ; and this expression= 0A.0A. {MN+ NL + LiPf=0. Ex. 4. Show also that Z.12.… … Let A, A; B, B; be two pairs of points on a straight line.Through A and B draw any two lines AP, BP intersecting in P ;and through A, B draw AQ, BQ parallel to BP, AP respectively,meeting in Q. Let PQ meet .45 in 0. Then since AP is parallel to BQ, and BP parallel to AQ,we have OA : OB =OP:OQ=OB:…
Geometry
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