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 EducationJ. and J.J. Deighton, 1838 - 172 pages |
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abscissa angle of contact angular velocity asymptotes axiom axis body moves Book CD² centre of force chord of curvature circle circular projection conic section conjugate conjugate hyperbola cos² cotan curve curvilinear cylinder d³y diameter differential coefficient Doctrine of Limits drawn dx dx dy dx ellipse equal angles equation equiangular spiral Euclid figure finite force tending function Hence hyperbola increment indefinitely infinitely latus rectum Lemma magnitude motion ordinate parabola parallel parallelograms perpendicular polygon portions Prop proportional propositions quantity radius ratio rectangle right angle Scholium similar triangles sin² space described straight line subtense tan² tangent U₁ ultimately equal ultimately vanishes whence Y₁
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Page 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...
Page 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.
Page 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.