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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abscissa Algebra angle of contact angular velocity asymptotes Axiom axis becomes bisects body moves Book central force centre of force chord of curvature circular projection conic section conical surfaces conjugate conjugate hyperbola constant cotan curve cylinder diameter differential coefficient Doctrine of Limits drawn ellipse equal angles equation equiangular spiral Euclid figure force tending function Hence hyperbola increment infinitely integral latus rectum Lemma manner meet motion ordinate parabola parallel parallelograms perpendicular polygon portions Prop proportional propositions quadratic factors quantity rectangle right angle sides similar triangles space described straight line subtense surface tangent ultimately equal ultimately vanishes values whence
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...