Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Сторінка 36
D. F. Gregory. rentials in terms of the new variables , because one is supposed to vary while the others are constant . To introduce this condition we proceed as follows . Let for example there be a double integral ffVda dy , and let x ...
D. F. Gregory. rentials in terms of the new variables , because one is supposed to vary while the others are constant . To introduce this condition we proceed as follows . Let for example there be a double integral ffVda dy , and let x ...
Сторінка 50
... supposed to be a function of the other , and we may write dz dx dz = F Eliminating the function F from this equation there results dx ( ) ( ) d2 z 2 - = 0 . dx dy This is the differential equation to developable surfaces . ( 24 ) ...
... supposed to be a function of the other , and we may write dz dx dz = F Eliminating the function F from this equation there results dx ( ) ( ) d2 z 2 - = 0 . dx dy This is the differential equation to developable surfaces . ( 24 ) ...
Сторінка 129
... supposed to have lived about the sixth century of our era , was invented by him for the purpose of constructing the solution of the problem of finding two mean proportionals . The curve is generated in the follow- ing manner : In the ...
... supposed to have lived about the sixth century of our era , was invented by him for the purpose of constructing the solution of the problem of finding two mean proportionals . The curve is generated in the follow- ing manner : In the ...
Сторінка 176
... supposed to remain ก m n perpendicular to each other , this angle must be taken in a plane perpendicular to that of the original axes . Hence , if there be a series of values of y all affected by the same m quantity ( + ) " , they will ...
... supposed to remain ก m n perpendicular to each other , this angle must be taken in a plane perpendicular to that of the original axes . Hence , if there be a series of values of y all affected by the same m quantity ( + ) " , they will ...
Сторінка 219
... ( w ) = 0 , ( u ' ) = 0 , w = 6 % , w ' = = 0 , ( v ) = 0 , ( w ' ) = 0 . the locus of the tangent lines becomes a x2 + by2 = 0 , x . which , a and b being supposed to APPLICATION TO GEOMETRY OF THREE DIMENSIONS . 219.
... ( w ) = 0 , ( u ' ) = 0 , w = 6 % , w ' = = 0 , ( v ) = 0 , ( w ' ) = 0 . the locus of the tangent lines becomes a x2 + by2 = 0 , x . which , a and b being supposed to APPLICATION TO GEOMETRY OF THREE DIMENSIONS . 219.
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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