A first course in projective geometry . where PPj, PP/; QQj,QQj are drawn parallel to the asymptotes Cx, Coo. P/C^_Q/co_ P^oo. QjCP/oo. QjC ~ PjCTq^oo ? 216 PROJECTIVE GEOMETRY whence ihe result required easily Fig. 109. III. As illustrating theorem (b) of § 2, we may deduce auseful property of tangents to a parabola. Since the parabola touches the line at infinity, we may takethis line as one of the fixed tangents. If any variable tangentcuts three other fixed tangents at H, K, L, then {HKLoo} is HK constant, — is Applying this to Fig. 110, in which the tangents at

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A first course in projective geometry . where PPj, PP/; QQj,QQj are drawn parallel to the asymptotes Cx, Coo. P/C^_Q/co_ P^oo. QjCP/oo. QjC ~ PjCTq^oo ? 216 PROJECTIVE GEOMETRY whence ihe result required easily Fig. 109. III. As illustrating theorem (b) of § 2, we may deduce auseful property of tangents to a parabola. Since the parabola touches the line at infinity, we may takethis line as one of the fixed tangents. If any variable tangentcuts three other fixed tangents at H, K, L, then {HKLoo} is HK constant, — is Applying this to Fig. 110, in which the tangents at P,Q, R cut one another at points P, Q, R, let the variabletangent be brought to ultimate coincidence with the tangentat P. The point of intersection of these two is then P, and PROPERTIES OF THE CONIC 217 PRaccordingly we have {PRQx} = -— = const, for all positions of QRthe variable tangent.

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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometryprojective