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Common terms and phrasesalgebraic altitude angle Anthon's asymptotes axis of abscissas becomes binomial chord circle circumference conjugate diameters conjugate hyperbola corresponding cosine cubical parabola cuts the axis cycloid described distance divided draw ellipse equal to zero exponent Find the integral Formula function Geom given point Hence hyperbola I.—Theorem II.—Theorem inch per second increase uniformly increment inscribed Integrate the expression intersects the axis logarithmic logarithmic spiral major axis maximum minimum minor axis multiplied negative obtain ordinate parabola parallel parenthesis perpendicular point of inflection polar curve Prop Proposition I.—Theorem Proposition II.—Theorem radius of curvature radius vector ratio rectangle represent Required the differential required to determine required to find Scholium secant line second differential coefficient Sheep extra side solidity spiral square straight line Substituting this value subtangent suppose surface tang tangent line Taylor's theorem theorem transverse axis unity value in equation vertex whence Popular passagesPage 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 211 - ... the tangent of the angle which the tangent makes with the axis of abscissas, this coefficient must have as many values as there are intersecting branches. Page 123 - 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 205 - O = slope of the indifference curve on A or B = —— It is thus clear from above that if we have to find out the MRS^ at a point on the indifference curve we can do so by drawing tangent at the point on the indifference curve and then measuring the slope by estimating the value of the tangent of the angle which the tangent line makes with the X-axis. Principle of Diminishing Marginal Rate of Substitution An important principle of economic theory is that marginal rate of substitution of X for Y... Page 281 - Grammar of the Greek Language. For the use of Schools and Colleges. 12mo, Sheep extra, 75 cents. Page 191 - By differentiating, we have dy" _ m + ~~ 2y" ' hence, the equation of the tangent to a line of the second order is ,, yy'= and the equation of the normal Of Asymptotes of Curves. 125. 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. Let AX and AY be the co-ordinate axes, and the equation of any tangent line, as TP. 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 10 - In a right angled triangle, the perpendicular is equal to the square of the sum of the hypothenuse and perpendicular, diminished by the square of the base, and divided by twice the sum of the hypothenuse and perpendicular. Page 197 - Hence, the radius of curvature at any point of a conic section, is equal to the cube of the normal divided by the square of half the y parameter, and the radii at different points are to each other as the cubes of the corresponding normals. References to this bookFrom Google ScholarThe Lengthening Shadow: The Story of Related RatesBill Austin, Don Barry, David Berman - 2000 - Mathematics Magazine References from web pagesNietz Collection li_shanlan (print-only) Historia Mathematica : The first Chinese translation of the last ... Collection of Early American Mathematics Books Bibliographic information
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