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abscissas Algebra algebraic quantities altitude angle apply asymptote auxiliaries employed auxiliary quantities Binomial Theorem body called centre of gravity co-ordinates constant convex cusp cycloid cylinder derived determine Differential Calculus differential equation distance divided eliminate equa equal evident example exponent expression find the area find the differential Find the integral find the value finite force formula given infinitesimal intersects the axis logarithmic manner maxima and minima maximum or minimum method multiplied negative obtain ordinate osculatory circle parabola plane curve point of inflexion polar curves preceding primitives proposed radius of curvature reducing regarded required to find revolution right line second differential coefficient simple solid solid of revolution solution sought spiral square subtangent subtracting suppose surface Taking the integral Taylor's Theorem theorem tion variable quantity vary velocity vertex whence by substitution
Page 226 - The squares of the periods of revolution of any two planets are proportional to the cubes of their mean distances from the sun.
Page 94 - ... the tangent of the angle which the line makes with the axis of abscissae), was lately employed by M. Crova* for the discussion of experiments relating to the degree of constancy possessed by so-called
Page 75 - F(x±y), the differential coefficient will be the same if we suppose x to vary and y to remain constant, as when we suppose y to vary and x to remain constant, For, make x ± y — a/ : we shall then have M = F(a/) , du and — =p.
Page 172 - Curve is ono whose equation contains transcendental functions. Many of the higher plane curves possess historical interest, from the labor bestowed on them by ancient mathematicians. We shall consider only a few of them. THE CISSOID OF DIOCLES. 148. This curve was invented by Diocles, a Greek geometer who lived about the sixth century of the Christian era; the purpose of its invention was the solution of the problem of finding two mean proportionals. It may be defined as follows : If pairs of equal...
Page 233 - A magnitude is said to be ultimately equal to its Limit; and the two are said to be ultimately in a ratio of equality. 4. A line or figure ultimately coincides with the line or figure which is its Limit.
Page 40 - To divide a number a into two parts such that the sum of the squares of the parts shall be the least possible.
Page 176 - Ex. 2. The axes of two equal right circular cylinders intersect at right angles. Required the volume common to the cylinders. Let OA and OB (fig.
Page 238 - This curve is traced by a point in the circumference of a circle which rolls upon a straight line as a directrix, as the curve oa2as (Fig.