Elements of the Differential and Integral Calculus

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Sanborn & Carter, 1859 - Calculus - 240 pages
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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 207 - ... base; the one of the air of the external atmosphere, and the other column of the air in the chimney, of the same height when hot, but reduced by cooling to the temperature of the atmosphere. Now, according...
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(xy), 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.
Page 190 - To find the equations of motion of a body, moving in a plane and acted upon by any forces in that plane.

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