Elements of the Differential and Integral Calculus: By a New Method, Founded on the True System of Sir Isaac Newton, Without the Use of Infinitesimals Or LimitsS.C. Griggs, 1875 - 343 páginas |
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Términos y frases comunes
actual change actual increment algebraic angle asymptote axes axis of abscissas becomes zero circumference cone consider convex coordinates corresponding cosine cube cycloid d2 u dx2 decreasing differential calculus diminishing direction divided dx dx2 dx² dy dx ellipse equa equal to zero equation evolute exponent expression ferential find the differential finite formula found Art function hyperbola infinite infinity integral lemma logarithm logarithmic spiral maximum or minimum minus multiplied negative obtain ordinate origin osculatory circle parabola parallel point of tangency polar curve positive PROPOSITION radius of curvature radius vector rate of change rate of increase ratio rectangle reduce represent the rate second differential coefficient side Substituting these values subtangent suppose suppositive increments surface symbol tangent line tends to move tion triangle uniform change uniform rate velocity whence
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Página 121 - 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.
Página 301 - Ttie area of a circle is equal to the square of the radius multiplied by тт.
Página xi - And in like manner, by the ultimate ratio of evanescent quantities is to be understood the ratio of the quantities not before they vanish, nor afterwards, but with which they vanish.
Página 4 - QUANTITIES, AND THE RATIOS OF QUANTITIES, WHICH IN ANY FINITE TIME CONVERGE CONTINUALLY TO EQUALITY, AND BEFORE THE END OF THAT TIME APPROACH NEARER THE ONE TO THE OTHER THAN BY ANY GIVEN DIFFERENCE, BECOME ULTIMATELY EQUAL.
Página xi - Perhaps it may be objected, that there is no ultimate proportion of evanescent quantities; because the proportion, before the quantities have vanished, is not the ultimate, and when they are vanished, is none. But by the same argument it may be alleged that a body arriving at a certain place, and there stopping, has no ultimate velocity; because the velocity, before the body comes to the place, is not its ultimate velocity; when it has arrived, there is none.
Página 215 - The cycloid is the curve described by a point in the circumference of a circle, as it rolls along a straight line. Let OX be the straight line. As the circle NPT, with radius a, rolls along this line, the point P describes the cycloid OBO'.
Página 57 - NUMERATOR AND DENOMINATOR IS THE DIFFERENTIAL OF THE NUMERATOR MULTIPLIED BY THE DENOMINATOR, MINUS THE DIFFERENTIAL OF THE DENOMINATOR MULTIPLIED BY THE NUMERATOR, DIVIDED BY THE SQUARE OF THE DENOMINATOR.
Página 151 - ... the differential of a surface of revolution is equal to the circumference of a circle perpendicular to the axis, into the differential of the arc of the meridian curve.
Página 125 - Then du = da? — a"ladx , that is, the differential of a constant raised to a power denoted by a variable exponent, is equal to the power, multiplied by the Naperian logarithm of the root into the differential of the exponent. 37. Resuming the expressions it = a* — ax = a"la , regarding « as the independent variable and x as the function, we have, Art.
Página xxii - The moment of any genitum is equal to the moments of each of the generating sides drawn into the indices of the powers of those sides, and into their coefficients continually.