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 Limits
S.C. Griggs, 1875 - 343 עמודים
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actual angle apply arising asymptote axes axis of abscissas base becomes binomial calculus called circle circumference cone consider constant contain convex coordinates corresponding curvature curve cycloid decreasing denominator depend described determine developed difference diminishing direction distance divided ellipse entire equal equation estimate EXAMPLES exponent expression extremity factors formula fraction function given gives hence increase increment indicates infinite integral length less limits logarithm maximum means measuring method move multiplied negative normal obtain origin parabola parallel parenthesis passing positive principles PROPOSITION quantity radius vector rate of change ratio reduce referred represent result rule shows side sine square Substituting Substituting these values successive suppose surface symbol taken tangent tangent line tion triangle true uniform unit variable volume whence zero
עמוד 133 - 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.
עמוד xxiii - But the answer is easy; for by the ultimate velocity is meant that with which the body is moved, neither before it arrives at its last place and the motion ceases, nor after, but at the very instant it arrives; that is, that velocity with which the body arrives at its last place, and with which the motion ceases.
עמוד 315 - Ttie area of a circle is equal to the square of the radius multiplied by тт.
עמוד xxxiii - So far that letter. And these last words relate to a treatise I composed on that subject in the year 1671. The foundation of that general method is contained in the preceding Lemma.
עמוד xxiii - 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.
עמוד 229 - 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'.
עמוד xxiii - 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, is none.
עמוד 69 - 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.