An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 175
is a range ininvolution. 1.58 PROPERTIES OF CONJUGATE Ex. 5. Through a point 0 two conjugate lines are drawn, and any tangentmeets them in the points P and Q. Show that the other tangents from Pand Q to the circle intersect on the polar of 0. 258. Any two conjugate lines ivith respect to a circle,… … Let 0 be the pole of AB, and let AB intersect CD in H. Then, [OH, CD] is a harmonic range ; and therefore the pencil A [OB, CD] is harmonic. ^, ^ sin O^C sinO^D 1 heretore —.—rrm ~~—DTn• sua CAB sm BAD But the angle OAC is equal to the angle APC, and the angleCAB to the angle CPB. ^, , sin 04 C sin…
Geometry
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