The principles of the differential and integral calculus simplified

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Página 247 - Fund. 12mo. 5s. cloth. TATE. -EXERCISES ON MECHANICS AND NATURAL PHILOSOPHY; or, an Easy Introduction to Engineering. Containing various Applications of the Principle of Work : the Theory of the Steam- Engine, with Simple Machines Theorems and Problems on Accumulated Work, &c. New Edition. 12mo. 2s. cloth. TATE.— KEY TO TATE'S EXERCISES ON MECHANICS AND NATURAL PHILOSOPHY.
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.

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