The Doctrine of Limits with Its Applications: Namely, Conic Sections, the First Three Sections of Newton, the Differential Calculus. A Portion of a Course of University Education

J. and J.J. Deighton, 1838 - 172 páginas

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Página 28 - III, the former figure is to the former sum, and the latter figure to the latter sum in a ratio of equality.] QED Cor. Hence, if two quantities of any kind whatever, be divided into any, the same, number of parts; and those parts, when their number is increased, and magnitude diminished indefinitely, assume the same given ratio each to each, viz. the first to the first, the second to the second, and so on in order, the whole quantities will be to one another in the same given ratio. For, if, in the...
Página 64 - A cone is a solid figure described by the revolution of a right-angled triangle about one of the sides containing the right angle, which side remains fixed.
Página 78 - When bodies describe different circles with uniform motions, the forces tend to the centres of the circles, and are as the squares of the velocities divided by the radii of the circles. By Art.

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