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Algebra Analytical Geometry asymptotes axis of abscissas becomes binomial chord circle circumference College conjugate diameters conjugate hyperbola corresponding cuts the axis cycloid distance draw drawn ellipse equal to zero exponent Find the integral find the point focus Formula function Geom Geometry given point Hence hyperbola I.—Theorem inch per second increase uniformly increment inscribed Integrate the expression intersects the axis logarithmic logarithmic spiral Loomis major axis maximum minimum minor axis multiplied negative obtain parabola parallel parameter perpendicular point of contact point of inflection polar curve Prof Professor of Mathematics Prop Proposition I.—Theorem Proposition II.—Theorem radius vector ratio rectangle rectangular axes represent Required the differential required to find Scholium secant secant line second differential coefficient side solidity spiral square straight line Substituting this value subtangent suppose tang tangent line Taylor's theorem theorem Trigonometry unity vertex whence
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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'.