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Exercises on Euclid and in modern geometry for the use of schools, private students, and junior university students (1881)

McDowell, James L · Cambridge, Deighton, Bell, and Co. · leaf 212

An illustration from Exercises on Euclid and in modern geometry for the use of schools, private students, and junior university students, 1881, leaf 212 — G and (7 are conjugate pairs of points ininvolution (208). N.B. If the transversal pass through 0, the intersection ofthe diagonals, 0 is a focus of the system, since the two conjugatepoints G and G then coincide at 0. 213. Any straight line meeting a circle and the sides ofany inscribed… … sides in A, A and C, C. Then shall these three pairs of points bein involution. For {P. ABGB} = {P. QBSB} = {i?. QBSB} = {P. CfBA B} = {£. ABCB], since {#. GBAB} = CB. BAf: C-B. ^, and {7?. ABCB} = AB. BC: ^^. <7£, which two ratios are identical, or if the rays RC\ PB be producedthe pencil will…

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