An Elementary Treatise on the Differential and Integral CalculusJ. Smith, 1816 - 720 lappuses |
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abscissæ algebraical apply arbitrary constant axis becomes Calculus circle co-ordinates consequently considered const corresponding cycloid deduce denominator denote determine differen Differential Calculus differential coefficients differential equation dx dx dx dy dx² dy dx dy dy dy² elimination equa example exponent expression factor ferential follows formula fraction func given gives infinite Integral Calculus limits logarithms maxima and minima obtain ordinate osculating circle parabola partial fraction particular solution preceding primitive equation proposed curve proposed equation proposed function quantity radius radius of curvature ratio reduce represent result right line second order substitute suppose tangent tial tion Trig U₁ vanish variables whence whole number x d x
Populāri fragmenti
583. lappuse - Proposition 14. The surface of any isosceles cone excluding the base is equal to a circle whose radius is a mean proportional between the side of the cone [a generator] and the radius of the circle which is the base of the cone.
588. lappuse - Sed quoniam durior est hypothesis indivisibilium, et propterea methodus illa minus geométrica censetur, maliu demostrationes rerum sequentium ad ultimas quantitatum evanescentium summas et rationes, primasque nascentium, id est, ad limites summarum et rationum deducere; et propterea limitum illorum demostrationes, qua potui brevitate, praemittere.
33. lappuse - The part 2az, which is independent of h, is therefore the limit of the ratio of the increment of the function to that of the variable.
122. lappuse - It is the curve described by a point in the circumference of a circle, while the circle itself rolls in a straight line along a plane.
iii. lappuse - It may be considered as an abridgement of his great work on the Differential and Integral Calculus, although in the demonstration of the first principles, he has substituted the method of limits of D'Alembert, in the place of the more correct and natural method of Lagrange, which was adopted in the former.! The first part of this Treatise, which is devoted to the exposition of the principles of the Differential Calculus, was translated by Mr. Babbage. The translation of the second part, which treats...
582. lappuse - DO, do, of the inscribed circles. The surfaces of these polygons are to each other as the squares of the homologous sides AB, ab (B.
118. lappuse - R is equal to the cube of the normal divided by the square of the semiparameter, R= _ ___ ?, since N = 2/w sec w.
581. lappuse - ... supposing that the change, which the variable quantity undergoes, is one of continued increase, or continued diminution. Such, for example, is the area of a circle, with regard to the areas of the circumscribed and inscribed polygons ; for, by increasing the number of sides of these figures, their difference may be made 01 ar less than any assigned area, however small: and...
142. lappuse - For as any primitive equation between x and y enables us theoretically to determine either y as a function of x, or x as a function of y, it is indifferent which of the two variables we suppose independent. It is usual...
612. lappuse - Our notion, indeed, of a ratio, whose terms are evanescent, is necessarily obscure, however rigorously its existence and magnitude may be demonstrated ; and its introduction into all our reasonings in the establishment of this Calculus, is calculated to throw a mystery over all its operations, which can only be removed by our knowledge of its more simple and natural origin.