Smart, Edward Howard · London : Macmillian and Co. · leaf 142
onal pair of con-jugate diameters. Hence the result follows by § 7, Chap. IV. II. If any straight line cut the hyperbola and its asym-ptotes, the intercepts between the curve and the asymptotesare equal. Take any chord QQ (Fig. 57) and join its middle point Vto the centre C. Then QQ is parallel to… … Fig. 57. But if QQ cut the asymptotes in q and g-, by the previousprop. 00 ^Vg is a harmonic range, and therefore ^V = V^. ButQV = VQ. /, ^Q = 5Q. Q.E.D. Cor. The portion of a tangent intercepted between theasymptotes is bisected at the point of contact. For let the chord move parallel to itself…
Geometry, Projective
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