Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Сторінка 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.
Сторінка 105
... solid angle formed by planes each passing through two angles of the prism ; find the inclination of these planes to the axis of the prism in order that for a given content the total surface may be the least possible . = Let ABC abc ...
... solid angle formed by planes each passing through two angles of the prism ; find the inclination of these planes to the axis of the prism in order that for a given content the total surface may be the least possible . = Let ABC abc ...
Сторінка 106
... solid angle , and he found them to be 109. 28 ' and 70. 32 " respectively . It occurred to Réaumur that this might be the form , which , for the same . solid content , gives the minimum of surface , and he requested Koenig to examine ...
... solid angle , and he found them to be 109. 28 ' and 70. 32 " respectively . It occurred to Réaumur that this might be the form , which , for the same . solid content , gives the minimum of surface , and he requested Koenig to examine ...
Сторінка 133
... solid formed by the revolution of the curve round . its asymptote is equal to a cylinder , the radius of whose base is the bounding ordinate , and whose height is the tangent at its extremity . This curve was invented by James Gregorie ...
... solid formed by the revolution of the curve round . its asymptote is equal to a cylinder , the radius of whose base is the bounding ordinate , and whose height is the tangent at its extremity . This curve was invented by James Gregorie ...
Сторінка 208
... Vol . I. p . 137. The reader is referred also to Gregory's Solid Geometry , where the same equation is presented under a more simple and elegant form . 2 2 u = 0 , ช W = - 208 APPLICATION TO GEOMETRY OF THREE DIMENSIONS .
... Vol . I. p . 137. The reader is referred also to Gregory's Solid Geometry , where the same equation is presented under a more simple and elegant form . 2 2 u = 0 , ช W = - 208 APPLICATION TO GEOMETRY OF THREE DIMENSIONS .
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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