The principles of the differential and integral calculus simplified |
Termos e frases comuns
1+x² a+bx AN=x angle asymptote base binomial theorem calculus centre circle cone contrary flexure convex cubical parabola curve cycloid d³y day dx2 df(x differential calculus differential coefficient dividing dx dx dx dx dy dy dx ellipse equal equation EXAMPLES expression find the value formula of reduction fraction function given h approaches h incr hence increased increment h integral inverse function Let y=log limiting ratio limiting value loge maximum minus moment of inertia multiplying nearer NP=y ordinate parabola perpendicular point of contrary quantity radius radius of gyration rectangle reducing Required the limiting Rule side slant height solidity substituting these values subtangent surface takes the increment tangent PT Taylor's Theorem triangle value of incr variable velocity versin x²+1 x2dx
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Página 247 - PRINCIPLES of GEOMETRY, MENSURATION, TRIGONOMETRY, LAND-SURVEYING, and LEVELLING: Containing familiar Demonstrations and Illustrations of the most important Propositions in Euclid's Elements ; Proofs of all the useful Rules and...
Página 129 - It was also shown in the same article, that the differential of the sum of any number of functions is equal to the sum of...
Página 33 - Since the areas of circles are to one another as the squares of their radii...
Página 200 - X.) : hence the surface of the sphere is equal to the convex surface of the circumscribed cylinder. But the surface of the sphere is equal to four great circles...
Página 40 - x". It is not "dy" divided by "dx" or "d" multiplied by "y" divided by "d" multiplied by "x." In precise mathematical terms a derivative of a function is the limit of the ratio of the increment of the function to the increment of the independent variable when the latter increment varies and approaches zero as a limit.
Página 34 - The convex surface of a cylinder is equal to the circumference of the base, multiplied by the altitude.
Página 118 - ... the tangent of the angle which the line makes with the axis of abscissae), was lately employed by M. Crova* for the discussion of experiments relating to the degree of constancy possessed by so-called
Página 51 - ... the differential of the denominator multiplied by the numerator, and divide the whole by the square of the denominator.
Página 82 - Naperian logarithm of a quantity is equal to the differential of the quantity divided by the quantity itself.