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 189
ichhas the same length as the curve. 238, I^rop,—The formula for the rectification of plane curves is dz = Vdx.^ + dy2; in which z represents the length of the curve, and x and j the general co-ordinates. Dem.—Let M N be any plane curve, AD= X, and P D =: y ^® ^^1 co-ordinates, andlet D D represent… … have at once dz = \/dx^ -\- dy^. q. e. d. Fig. 172. 239, ScH.—To apply this formula to any particular curve, we havesimply to find dv or dy from the equation of the proposed curve, substituteit in the formula, and then integrate between proper limits. Ex. 1. Rectify the semi-cubical parabola whose…
Geometry, Analytic · Calculus
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