Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Сторінка 222
... 1 ' = -- " s = 0 , t = = • a a a The reader is referred to Gregory's Solid Geometry for a symmetrical method of determining Umbilici . Hence we have 4xy a2 + 4x2 a a ' 222 APPLICATION TO GEOMETRY OF THREE DIMENSIONS .
... 1 ' = -- " s = 0 , t = = • a a a The reader is referred to Gregory's Solid Geometry for a symmetrical method of determining Umbilici . Hence we have 4xy a2 + 4x2 a a ' 222 APPLICATION TO GEOMETRY OF THREE DIMENSIONS .
Сторінка 355
... solid . Fourier , Traité de la Chaleur , p . 471 and p . 509 . ( 5 ) Let Whence dz d2 % dx2 = α dt d or + b dt -bt € - n a d2 - bz ; d2 dx2 2 f ( x ) . ≈ = 0 . This is the equation for determining the motion of heat in a ring . Fourier ...
... solid . Fourier , Traité de la Chaleur , p . 471 and p . 509 . ( 5 ) Let Whence dz d2 % dx2 = α dt d or + b dt -bt € - n a d2 - bz ; d2 dx2 2 f ( x ) . ≈ = 0 . This is the equation for determining the motion of heat in a ring . Fourier ...
Сторінка 424
... solid be referred to rectangular co - ordinates its volume ( V ) is found by integrating the triple integral fffdx dydz . If we integrate first with respect to , and suppose the integral to begin when ≈ = 0 , is the volume , V = ffzdx ...
... solid be referred to rectangular co - ordinates its volume ( V ) is found by integrating the triple integral fffdx dydz . If we integrate first with respect to , and suppose the integral to begin when ≈ = 0 , is the volume , V = ffzdx ...
Сторінка 425
... solid terminated laterally by a cylinder perpendicular to the plane of xy , having for its base any curve as LL'NN ' ( fig . 54 ) , we take the integral with respect to y from y = MN to y = MN ' , which are given in terms of a by the ...
... solid terminated laterally by a cylinder perpendicular to the plane of xy , having for its base any curve as LL'NN ' ( fig . 54 ) , we take the integral with respect to y from y = MN to y = MN ' , which are given in terms of a by the ...
Сторінка 427
... solid common to both . Taking the intersection of the axes of the cylinders as the origin , and their axes as the axes of y and x , their equations are x2 + z2 = a2 , x2 + y2 = a2 , = ffdx dyz = ffdx dy ( a2 – x2 ) 3 . Integrating with ...
... solid common to both . Taking the intersection of the axes of the cylinders as the origin , and their axes as the axes of y and x , their equations are x2 + z2 = a2 , x2 + y2 = a2 , = ffdx dyz = ffdx dy ( a2 – x2 ) 3 . Integrating with ...
Інші видання - Показати все
Загальні терміни та фрази
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