An Elementary Treatise on the Differential and Integral Calculus, Volume 25 (Google eBook)

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J. Smith, 1816 - Calculus - 720 pages
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Page 583 - 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.
Page 33 - 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.
Page 122 - 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.
Page iii - 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 of the Integral Calculus, was executed by Mr. G. Peacock, of Trinity College, and by Mr. Herschel, of St. John's College, in nearly equal proportions.
Page 582 - 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.
Page 497 - It was also shown in the same article, that the differential of the sum of any number of functions is equal to the sum of their...
Page 309 - x". It is not "dy" divided by "dx" or "d" multiplied by "y" divided by "d" multiplied by "x." In precise mathematical terms a derivative of a function is the limit of the ratio of the increment of the function to the increment of the independent variable when the latter increment varies and approaches zero as a limit.
Page 588 - Geométrica censetur; malui demonstrationes rerum sequentium ad ultimas quantitatum evanesceutium summas et rationes, primasque nascentium, id est ad limites summarum et rationum deducere; et propterea limitum illorum demonstrationes qua potui brevitate praemittere. His enim idem praestatur quod per methodum Indivisibilium ; et principiis demonstratis jam tutius utemur.
Page 581 - ... less than any assigned area, however small ; and since the circle is necessarily less than the first, and greater than the second, it must differ from either of them by a quantity less than that by which they differ from each other...
Page 251 - B sin A cos B = £{sin (A + B) + sin (A - B)}. cos A sin B = £{sin (A + B) - sin (A - B)}. cos A cos B = i{cos (A + B) + cos (A - B)}.

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