An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 50
is harmonic. Hence it follows as above thatOP must pass through Q. 61. This theorem furnishes an easy construction for obtainingthe harmonic conjugate of a point with respect to a given pair ofpoints. Let .4, JS be any given points on a straight line, and supposethat we require the harmonic… … L. 34 PROPERTY OF TWO PENCILS. Let A and B be joined to any point 0, and let a straight linebe drawn through P cutting OA, OB in C and I) respectively.Join AD, BC, and let them intersect in 0. By the last article, the line joining the harmonic conjugatesof P with respect to A, B; and C, D; must…
Geometry
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