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 239
Fig. 2. and M meet in C the pole of PA. Take L the harmonic conjugateto P with respect to M and K\ then LD is the polar of P (237,Cor.), but (238) C lies on the polar of P, therefore LD producedpasses through C. Lastly (Fig. 3), let both C and D lie without the circle, and letPA and PB cut the… … Fig. 3- tangents at these points meet in C and D (238, a). By (238) 0and D both lie on the polar of P, therefore CD is the polar of P.In all cases the converse is obvious. Q. e. d. Cor. Hence, (a) if any number of straight lines pass through apoint, their poles all lie on the polar of that point…
Geometry
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