An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 298
, P {ABC...], be any two homogi-aphic pencils.Let a circle be described passing through P and cutting the raysof the pencils in the points A, B, G...; and A, B, G,...; respec-tively. Then, if X, Y, Z be the points of intersection of the pairs of DOUBLK BAYS OF HOMOGRAPHIC PENCILS. 281 lines BC, BG;… … Let XYZ cut the circle in /S and S. Then we shall haveP {AB, CS} = A [AB, CS} = A [AZ, YS}= A [AZ, YS} = A [AB, OS} = P {AB, CS}.Therefore PS will be one double ray of the pencils P {ABG...},P {ABC...}; and similarly PS will be the other double ray. 439. Ex. 1. Show that, if S, S be the double…
Geometry
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