Elements of the Differential Calculus: With Examples and ApplicationsGinn Company, 1898 - 258 стор. |
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Загальні терміни та фрази
4x approaches 4x limit abscissa actual velocity algebraic angle approaches zero axis called circle constant coördinates corresponding increments cscx curvature cycloid D₂ D₂log D₂u D₂x D₂y D₂y)² Day)² decreasing definite value differentiate distance fallen equal equation evolute EXAMPLES expression formulas fraction function fx-fa given curve given point hence hyperbola increases indefinitely independent variable Indeterminate Forms infinitesimal instant integration length limit approached loga logx maxima and minima maximum mean curvature method minimum values negative normal number of sides obtained ordinate Osculating Circle parabola point x,y polygon positive quantity radius radius of curvature ratio secant line sin² sinx subtangent Suppose tangent tanx Taylor's Theorem Theorem true value variable increases vertex whole number x+4x Δα Δη Уо
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Сторінка iii - Its peculiarities are the rigorous use of the Doctrine of Limits, as a foundation of the subject, and as preliminary to the adoption of the more direct and practically convenient infinitesimal notation and nomenclature ; the early introduction of a few simple formulas and methods for integrating ; a rather elaborate treatment of the use of infinitesimals in pure geometry ; and the attempt to excite and keep up the interest of the student by bringing in throughout the whole book, and not merely at...
Сторінка 164 - P'S = P'F, from the definition of a parabola ; PB=PF—QF; .-. P'N=P'Q. = limit rcoBPP'fr]= limit (~P^ P=P [cos />/>'£ J P' = p [_ jP'j cos rPF cos T'PR _ Art. 162; .-. T'PR=T'PF, and the tangent at any point of a parabola bisects the angle between the focal radius and the diameter through the given point.
Сторінка 190 - The Centre of Gravity of a body is a point so situated that the force of gravity produces no tendency in the body to rotate about any axis passing through this point. The subject of centres of gravity belongs to Mechanics, and...
Сторінка 81 - As the curvature of a circle has been found to be the reciprocal of its radius, a circle may be drawn which shall have any curvature required. A circle tangent to a curve at any point, and having the same curvature as the curve at that point, is called the osculating circle of the curve at the point in question. Its...