Elements of Analytical Geometry and of the Differential and Integral CalculusHarper & Brothers, 1851 - 278 páginas |
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Términos y frases comunes
a²-x² a²+x² algebraic altitude angle asymptotes axes axis of abscissas becomes binomial theorem chord circle circumference conjugate diameters conjugate hyperbola convex corresponding cosine cycloid described divided draw drawn dx dx dx² ellipse equal to zero exponent Find the integral formula gent Geom given point Hence hyperbola hyperbolic spiral inch per second increase uniformly increment inscribed Integrate the expression logarithmic logarithmic spiral major axis maximum minimum multiplied negative obtain ordinate parabola parallel parenthesis perpendicular polar curve Prop PROPOSITION II.-THEOREM radius of curvature radius vector ratio rectangle rectangular represent Required the differential required to determine required to find revolution SCHOLIUM secant line second differential coefficient side solidity spiral square straight line Substituting this value subtangent suppose surface tang tangent line Taylor's theorem theorem transverse axis unity versed sine vertex whence
Pasajes populares
Página 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.
Página 259 - The convex surface of a cone is equal to the circumference of the base multiplied by half the slant height.
Página 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.
Página 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.
Página 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...
Página 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.
Página 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.
Página 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.
Página 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.