Calculus, with applications; an introduction to the mathematical treatment of science (1900)
Hayes, Ellen, 1851- · Boston, Allyn and Bacon · leaf 126
stead of X, I7, since they do not occur in connectionwith the old coordinates and therefore cannot be con-fused with them. For example, x2 + y2 = r2 being the equation to a circlewith its center at the origin, (x — a)2 + (y — b)2 = r2 is ANALYTIC GEOMETRY, 115 the same circle with its center at (a,… … Fig. 11 NowOB1 cosa = 0C=0B + BC=x + BC=z + PBf sin «. Therefore x = OB cos a — PBf sin « that is, x — X cos a — Y sin a. Similarly, ^ = Xsin a -f-1 cos a, 116 CALCULUS. Hence, if in any equation F(x, y)=0 we writex cos a — y sin a for x and # sin a + y cos a for y, thegeometric result is the…
Calculus · Geometry, Analytic
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