A general geometry and calculus : including book I. of the general geometry, treating of loci in a plane; and an elementary course in the differential and integral calculus (1881)
Olney, Edward, 1827-1887 · New York : Sheldon and Co. · leaf 132
value of the subtangent of 3/2 = 2^ at a: = 2 ? 5 S Ex. 4. If upon the same transverse axis different ellipses be drawn,prove that the corresponding subtangents are equal. Sugs. —The general value is SuU. ■■A^B^ — B^x-^ A^ — £C2 ■ BX , , , a result which B^x X does not depend upon B. This truth is… … Fig. 104. Ex. 5. Find the subtangent to the hyperbola referred to obliqueasymptotes. Result, Subt = x. ScH.—In Fig. 100, P being the point of tangency {x, y), DT = Subt. =X = AD. Now since PD is parallel to AO, PT = OP ; i. e., The inter-cepts of a tangent to a hyperbola between the point of…
Geometry, Analytic · Calculus
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