Smart, Edward Howard · London : Macmillian and Co. · leaf 211
is 4SP. Let TQQ be parallel to PP, the focal chord (Fig. 98). Lettpt be the tangent parallel to PP, and let it be cut at t and /by the tangents at P and P which intersect at right angles ath on the directrix (§ 9). Now the triangles ^pt, StP being similar (§ 8 (3)), tptP Spsi S[SP /P2 SpSP TANGENT… … Fig. 98. But PP = 2tt = 4.tp (§11, Chap. VIII.)= Apk, since tkt is a right angle,= 48^... chord of curvature through S = 4SP.From this expressions for the diameter of curvature may beobtained. Note. It will be subsequently proved that a circle cannotcut a conic in more than four points. Three of…
Geometry, Projective
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