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 138
- e. d. Ex. 1. Find the value of the subtangent to the spiral of Archim-edes. Solution.—The equation is r = ^7- ; whence — = 27r.dr 27r = 7-7 X 27r = —. Subt = ^^-=r Xdr iLii.—The annexed figure furnishes an il-lustration. PT is subtangent for point Sand = the square of the numerical value of6… … Fig. 111. ASYMPTOTES TO POLAR CURVES. 109 Hence PT = 27t, or somewhat more than I4 times the circumference (247r)?_81 of the measuring circle. If B is the point of tangency, 0 =t 27t, and subt PT =27t, or the circumference of the measuring circle. In this spiral the subtangentvaries as the square…
Geometry, Analytic · Calculus
Internet Archive · Boston College Libraries · Public Domain Mark 1.0. Free to use for anything.
