Elements of Analytic Geometry and of the Differential and Integral Calculus

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Harper & Bros., 1859 - Calculus - 277 pages
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Page 36 - A circle is a plane figure bounded by a curved line, every point of which is equally distant from a point within called the center.
Page 259 - The convex surface of a cone is equal to the circumference of the base multiplied by half the slant height.
Page 25 - Y below it, then both a and b will be negative, so that the equation becomes y=—ax—b. If we suppose the straight line to pass through the origin A, then b will be equal to zero, and the general equation becomes y—ax, which is the equation of a straight line passing through the origin. Ex. 1. Let it be required to draw the line whose equation is...
Page 187 - The value of the ratio of the increment of the function to that of the variable is composed of two parts, 2ax and ah.
Page 126 - This new value of the function will be frequently referred to hereafter under the form '=tt+AA+BA'. (2) PROPOSITION VIII. — THEOREM. (179.) The differential of the sum or difference of any number of functions dependent on the same variable, is equal to the sum or difference of their differentials taken separately. Let us suppose the function u to be composed of several variable terms, as, for example, u=y+z — v, where y, z, and v are functions of x.
Page 23 - In this equation n is the tangent of the angle which the line makes with the axis of abscissas, and B is the intercept on this axis from the origin.
Page 191 - CURVES. (259.) An asymptote of a curve is a line which continually approaches the curve, and becomes tangent to it at an infinite distance from the origin of co-ordinates.
Page 129 - The differential of a fraction is equal to the denominator into the differential of the numerator, minus the numerator into the differential of the denominator, divided by the square of the denominator.
Page 127 - PROPOSITION IX. — THEOREM. (180.) The differential of the product of two functions dependent on the same variable, is equal to the sum of the products obtained by multiplying each by the differential of the other. Let us designate two functions by u and v, and suppose them to depend on the same variable x ; then, when x is increased so as to become x+h, the new functions may be written, Art. 178, u'=u+Kh +BA", v'=v+A.'h+B'h'.
Page 36 - A radius of a circle is a straight line drawn from the centre to the circumference.

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