Examples of the Processes of the Differential and Integral Calculus |
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Page iii
... respect it will be seen to agree with Professor Peacock's Collection of Examples ; and indeed if a second edition of that excellent work had been published I should not have undertaken the task of making this compilation . But as ...
... respect it will be seen to agree with Professor Peacock's Collection of Examples ; and indeed if a second edition of that excellent work had been published I should not have undertaken the task of making this compilation . But as ...
Page 28
... respect to a are transformed into those of a with respect to y by means of the formulæ , dy dx = dx dy " ď y d.r2 = dy2 da d 39 d'y dx3 3 ( d ) dy 2 dx dx 5 dy dy dx dy and similarly for higher orders . The reader will find the ...
... respect to a are transformed into those of a with respect to y by means of the formulæ , dy dx = dx dy " ď y d.r2 = dy2 da d 39 d'y dx3 3 ( d ) dy 2 dx dx 5 dy dy dx dy and similarly for higher orders . The reader will find the ...
Page 45
... respect to x , d % dey b = dx2 dx Eliminating b , we have d3y and = b dx3 da3 dz d'y d'z d3y = 0 . dx3 dx2 dx2 da3 This is the condition that a curve in three dimensions should be a plane curve . ( 11 ) Eliminate the exponentials from ...
... respect to x , d % dey b = dx2 dx Eliminating b , we have d3y and = b dx3 da3 dz d'y d'z d3y = 0 . dx3 dx2 dx2 da3 This is the condition that a curve in three dimensions should be a plane curve . ( 11 ) Eliminate the exponentials from ...
Page 46
... respect to a only , dz dx = y ( y ) ; and therefore c ( 16 ) Eliminate the function dz = 0 . dx from the equation - y N≈ = - $ ( x − mx ) . Differentiating with respect to a only , - n dz dx = ( 1 - m 15 ) . p ' ( x − mz ) ( - dx ...
... respect to a only , dz dx = y ( y ) ; and therefore c ( 16 ) Eliminate the function dz = 0 . dx from the equation - y N≈ = - $ ( x − mx ) . Differentiating with respect to a only , - n dz dx = ( 1 - m 15 ) . p ' ( x − mz ) ( - dx ...
Page 47
... respect to x , ( 1 ) dx dx = - yx " -2 ' X %% + 1 کلا کی Differentiating with respect to y , xr - 1 ( 2 ) d = ' ' ( ) + " y ' ( ) + 2 + ( ) · dy | + ny2 - 1 Multiply ( 1 ) by a , ( 2 ) by y and add , - then dz dz + y = NX . dx dy This ...
... respect to x , ( 1 ) dx dx = - yx " -2 ' X %% + 1 کلا کی Differentiating with respect to y , xr - 1 ( 2 ) d = ' ' ( ) + " y ' ( ) + 2 + ( ) · dy | + ny2 - 1 Multiply ( 1 ) by a , ( 2 ) by y and add , - then dz dz + y = NX . dx dy This ...
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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