Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Сторінка iii
... Theorems given in Elementary Treatises on the subject , but I have also introduced demonstrations of propositions which , although important and interesting , do not usually find a place in works devoted to the exposition of the ...
... Theorems given in Elementary Treatises on the subject , but I have also introduced demonstrations of propositions which , although important and interesting , do not usually find a place in works devoted to the exposition of the ...
Сторінка ix
... of the Differential Calculus to Geometry of Three Dimensions 200 XIV . Envelops to Lines and Surfaces XV . General Theorems in the Differential Calculus ......... 224 237 PART II . INTEGRAL CALCULUS . CHAPTER PAGE I. Integration.
... of the Differential Calculus to Geometry of Three Dimensions 200 XIV . Envelops to Lines and Surfaces XV . General Theorems in the Differential Calculus ......... 224 237 PART II . INTEGRAL CALCULUS . CHAPTER PAGE I. Integration.
Сторінка 1
... theorem du = du dy dx dy dx ' y being some function of x , and u some function of y . This theorem may be extended to any number of functions , so that du du dv ds dy = dx da dv ds dy Ex . ( 1 ) Let u = ( a + bx " ) " . Then y = a + bx ...
... theorem du = du dy dx dy dx ' y being some function of x , and u some function of y . This theorem may be extended to any number of functions , so that du du dv ds dy = dx da dv ds dy Ex . ( 1 ) Let u = ( a + bx " ) " . Then y = a + bx ...
Сторінка 9
... Theorem which bears his name . He also conceived the existence of differentials with fractional or irrational indices , but he made no steps towards the calculation of such functions in any cases . In recent years that branch of the ...
... Theorem which bears his name . He also conceived the existence of differentials with fractional or irrational indices , but he made no steps towards the calculation of such functions in any cases . In recent years that branch of the ...
Сторінка 12
... Theorem of Leib- nitz , the enunciation of which is as follows . If u , v be two functions of x , then ď ( uv ) d'u = v dx dx + r dv dr - lu r ( r− 1 ) ď2 v dr - 2 u + da dar - 1 1.2 dx2 dx - 2 + & c . Commer . Epis . Leib . et Bern ...
... Theorem of Leib- nitz , the enunciation of which is as follows . If u , v be two functions of x , then ď ( uv ) d'u = v dx dx + r dv dr - lu r ( r− 1 ) ď2 v dr - 2 u + da dar - 1 1.2 dx2 dx - 2 + & c . Commer . Epis . Leib . et Bern ...
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a² b2 a²x² angle arbitrary constant assume asymptote becomes branches C₁ Cambridge circle co-ordinates condition Crelle's Journal curvature curve cycloid determine differential coefficients differential equation dx dx dx dy dx dx² dy dx dy dy dy dy dz dz dz eliminate ellipse equal Euler factor formula fraction function Geometry gives Hence hypocycloid infinite intersection John Bernoulli Let the equation lines of curvature locus logarithmic logarithmic spiral Multiply negative origin parabola perpendicular radius SECT singular points singular solution spiral Substituting subtangent surface tangent plane theorem triangle University of Cambridge vanish whence x²)³