Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Сторінка vi
D. F. Gregory. The sources from which the Examples have been taken are indicated by the references which will be found in the body of the work . For although I have not thought it necessary to cite an authority for every example , I have ...
D. F. Gregory. The sources from which the Examples have been taken are indicated by the references which will be found in the body of the work . For although I have not thought it necessary to cite an authority for every example , I have ...
Сторінка 17
... example , but the following method gives it under a form which is more convenient in practice ; 1 a2 + x 2 1 = 2a ( - ) x + a ( - ) x - a - Differentiating r times , 1 d − ( − ) ' + 1 ̧ † ( r − 1 ) ... ..2 . - { = ( ~ ) " + 1 " T 1 ...
... example , but the following method gives it under a form which is more convenient in practice ; 1 a2 + x 2 1 = 2a ( - ) x + a ( - ) x - a - Differentiating r times , 1 d − ( − ) ' + 1 ̧ † ( r − 1 ) ... ..2 . - { = ( ~ ) " + 1 " T 1 ...
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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