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 124
t to the curve makes with the axis of abscissas. 94 PROPERTIES OF PLANE LOCL Dem.—Let MN, Fig. 96, be any planecurve whose equation is y =^f{x). Let P andP be consecutive points, and PD and P Dconsecutive ordinates. Then is RS, drawnthrough P and P, a tangent. Draw PEparallel to XX. Since P and P… … Fig. 96. tan a = tan P P E = PE dx Q. E. D. Ex. 1. What angle does a tangent to the curve y = x^ — ^2 +1, atthe point a: = 2, make with the axis of ^ ? Solution. -^ = dx-^ — 2x, which, for a = 2 becomes dx -^ = 8, using (ccj y) to designate the particular point CLtC in distinction from the general…
Geometry, Analytic · Calculus
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