Osgood, William F. (William Fogg), 1864-1943, Graustein, William Caspar, 1888-1941, joint author · New York, The Macmillan company · leaf 187
slope A «o(i). To prove the theorem, let a point P, starting from the vertexA, trace the upper half of the right-hand branch of (1). Then the tangent, T, at P, starting fromthe vertical position at A, turnscontinuously in one direction, and,as Precedes indefinitely, approachesthe asymptote S as its… … Fig. 7 a * The geometrical evidence of this is convincing, but not conclusive.To clinch it, we give the following analytical proof: If the coordinatesof P are (x, y), the slope \ of T is, by (11), § 2, According to Ch. VIH, § 4, eq. (3), V b Vt-S Hence x=*. J °a/i-- When P traces the upper half of…
Geometry, Analytic
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