An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 226
L = PR : PL=QR : QL^QR : QL.Let PQ cut PQ in T, then it is evident thatPR + PR = PT+PT,QR + QR = QT+QT.But, since the triangles TPP, TQQ are equiangular,PP : QQ = PT+PT : TQ + TQ.Hence PP : QQ = PL + PL : QL + QL. Poncelets theorem. 334. If a tetrastigm be inscribed in a circle of a given… … Let A, B,C, Dhe any four points on a circle, and let AC, BDtouch another circle at the points P, P. Let PP cut AB, CD inQ and Q; and AD, BC in R and R. The triangles AQP, DQF ai-e obviously similar; therefore AQ:AP=DQ:DPAgain, AP:AQ = smAQP:s,inAPQ, and BP :BQ=sm BQP: sin BFQ. But the angles APQ,…
Geometry
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