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 166
0 = 90°, positivefrom S = 900 to 0 = 150°, etc.Whence we see that r begins at0 when 0 = 0°, increases tOl0 = 30°, diminishes as 6 passesfrom 30° to 60°, becomes 0° for6 = 60°, continues to dimin-ish (becoming negative) as 0passes to 90^, becomes —a, at90°, etc, [The pupil should trace r through an… … The equation in terms of the perpendicular upon the pole is p = ■f.2 (9a-—Sr^)^ , dp 18a r — Srwhence —- = and the curve is always concave toward the pole. dr {9a^ — 8rO« RATE OF CURVATURE. 137 Ex. 3. Construct the locus whose equation is x^by first passing to the polar equation. Solution.—The…
Geometry, Analytic · Calculus
Internet Archive · Boston College Libraries · Public Domain Mark 1.0. Free to use for anything.
