Examples of the Processes of the Differential and Integral Calculus |
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Page vi
... volume too much , I have not done this to as great an extent as I wished , but these digressions short as they are may serve to relieve the dryness of a mere collection of Examples . TRINITY COLLEGE , October , 1841 . EDITOR'S NOTICE ...
... volume too much , I have not done this to as great an extent as I wished , but these digressions short as they are may serve to relieve the dryness of a mere collection of Examples . TRINITY COLLEGE , October , 1841 . EDITOR'S NOTICE ...
Page 41
... for the volume of any solid referred to rectangular co - ordinates : and it becomes fffr2 dr sine de dp when referred to polar co - ordinates . ( 10 ) Having given a function of x and CHANGE OF THE INDEPENDENT VARIABLE . 41.
... for the volume of any solid referred to rectangular co - ordinates : and it becomes fffr2 dr sine de dp when referred to polar co - ordinates . ( 10 ) Having given a function of x and CHANGE OF THE INDEPENDENT VARIABLE . 41.
Page 104
... volume . π Let a be the given volume , æ the radius of the cylinder , y its base . Then y = a determines the cylinder of least surface . a = ( 29 ) The content of a cone being given , find its form when the surface is a maximum . Let πα ...
... volume . π Let a be the given volume , æ the radius of the cylinder , y its base . Then y = a determines the cylinder of least surface . a = ( 29 ) The content of a cone being given , find its form when the surface is a maximum . Let πα ...
Page 117
... volume under the least surface . If x , y , z be the edges of the parallelopiped , and if a3 be the volume of a cube to which it is equal , then by the condition of the minimum we easily find x = y = x = a , so that the surface equals ...
... volume under the least surface . If x , y , z be the edges of the parallelopiped , and if a3 be the volume of a cube to which it is equal , then by the condition of the minimum we easily find x = y = x = a , so that the surface equals ...
Page 121
... ( 17 ) tion is Tabc ( a2 l2 + b2 m2 + c2n2 ) § ' To find the volume of the ellipsoid whose equa- ax2 + a'y2 + a ′′ x2 + 2 by z + 2 b ′ x z + 2b ′′ xy = c . As in the preceding examples we have first to find MAXIMA AND MINIMA . 121.
... ( 17 ) tion is Tabc ( a2 l2 + b2 m2 + c2n2 ) § ' To find the volume of the ellipsoid whose equa- ax2 + a'y2 + a ′′ x2 + 2 by z + 2 b ′ x z + 2b ′′ xy = c . As in the preceding examples we have first to find MAXIMA AND MINIMA . 121.
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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