Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Сторінка 95
... considered is that involving dxn - 1 d " u dx all the others vanish when a is put equal to a , so that is reduced to one term . dx " The investigation of the maximum and minimum values of u is sometimes facilitated by the following ...
... considered is that involving dxn - 1 d " u dx all the others vanish when a is put equal to a , so that is reduced to one term . dx " The investigation of the maximum and minimum values of u is sometimes facilitated by the following ...
Сторінка 110
... considered to be a value greater than any other , and conversely for a minimum . This remark of Français is of more importance geometrically than analytically ; and I may add , that in geometry the failure Annales de Gergonne , Vol . 11 ...
... considered to be a value greater than any other , and conversely for a minimum . This remark of Français is of more importance geometrically than analytically ; and I may add , that in geometry the failure Annales de Gergonne , Vol . 11 ...
Сторінка 161
... considered as an asymptotic circle the radius of which is zero , as the curve makes an infinite number of revolutions before it reaches it . The same remark applies to the logarithmic spiral , and many other curves for which r is zero ...
... considered as an asymptotic circle the radius of which is zero , as the curve makes an infinite number of revolutions before it reaches it . The same remark applies to the logarithmic spiral , and many other curves for which r is zero ...
Сторінка 176
... considered to be completely traced unless the negative , as well as the positive , values of the variables be taken into account . This however is merely a matter of convention , and we might , if it were thought proper , restrict ...
... considered to be completely traced unless the negative , as well as the positive , values of the variables be taken into account . This however is merely a matter of convention , and we might , if it were thought proper , restrict ...
Сторінка 224
... considered the general theory of questions of this kind , so well adapted for exemplifying the utility of his Cal- culus ; and in two memoirs in the Acta Eruditorum , he gave a general process for the solution of all problems which ...
... considered the general theory of questions of this kind , so well adapted for exemplifying the utility of his Cal- culus ; and in two memoirs in the Acta Eruditorum , he gave a general process for the solution of all problems which ...
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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