Smart, Edward Howard · London : Macmillian and Co. · leaf 162
Fig. 69. The diagonals of this rectangle (which of course intersect atthe centre) are the asymptotes. We shall speak of BC as the length of the (pseudo-) conjugateaxis of the hyperbola, though B is not a point on the curve. Def. The hyperbola which has the same asymptotes, butBCB as transverse and… … But FN AN . NA ac^ PN2 Pig. 70.and AN. NA = AC2-CN2, BC^ „ sec^ a= tan-^ a — s— CN - AC2 AC^ cosec- a .. CN^ sec^ a - FN^ cosec^ a = AC^ sec^ aand CL. CL = AC^ sec^ a = constant. But the angle LCL is constant. .*. the triangle LCL is of constant area. Second Proof. Let LPL, MQM be tangents at two…
Geometry, Projective
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