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 145
r-ence between di/^ and dy2, is by definition d^y.Bat when a curve is concave upward it lies aboveits tangent. Hence dy2 >> dy-, and dyz — %i =-\- d-y. On the other hand, when the curve is con-vex upward, as in Fig. 119, it lies below its tangentand dy2 <idi/-[. Whence dy.j. — dyi = — d-y.… … Fig. 118. principle be established. Finally, the sign of d^dx^ is the same as that of dy, since dx- being a squareis always positive. 170, Cor. 1.—By a course of reasoning en-tirely similar^ taking y as the independent vari- 77 . 7 , 7 ^^ able, it may be shown that -f t/ Y P ; R E /* [ 3 [ 3 C ) X…
Geometry, Analytic · Calculus
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