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absolute value angle approaches a limit approaches zero axes axis becomes infinite bounded center of curvature circle coefficients constant continuous function contour convergent series coordinates corresponding defined definite integral denote determine developable surface differential diverges double integral double points double series envelope equal evident example expression finite follows formula function f(x given curve given series Hence increases indefinitely independent variables infinite number infinitesimal intersection interval less Let us consider Let us suppose lies line integral lines of curvature necessary and sufficient negative obtained osculating plane parallel parameter partial derivatives plane curve point M0 polynomial positive number power series preceding radius of curvature ratio rational function region replaced respect roots satisfy the equation sequence series converges skew curve straight line tangent plane theorem tion transformation unity upper limit vanish whence written xy plane
Page 382 - of a given series of positive terms is greater than or equal to the corresponding term of a known divergent series of positive
Page 363 - Differentiating the first of these equations with respect to y and the second with respect to x,
Page 538 - which have contact of the second order with a given curve at a fixed point is a circle.
Page 65 - It is required to express the successive derivatives of y with respect to x in terms of
Page 449 - denotes the sum of the products of the first n natural numbers taken
Page 2 - the value of the other, they are said to be functions of each other.
Page 74 - =f(x, y) be a function, of the two independent variables x and y, and let