Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 100
Сторінка 47
... differential equation to cylindrical surfaces . ( 17 ) If y Ꮗ a = - by the elimination of the function we find da dz ( x − a ) - + ( y - dx b ) = ≈ - C . dy This is the differential equation to conical surfaces . ( 18 ) Eliminate ...
... differential equation to cylindrical surfaces . ( 17 ) If y Ꮗ a = - by the elimination of the function we find da dz ( x − a ) - + ( y - dx b ) = ≈ - C . dy This is the differential equation to conical surfaces . ( 18 ) Eliminate ...
Сторінка 50
... differential coefficients of f , p , Y. Differentiating ( 1 ) with respect to a , { x ƒ ' ( a ) + y p ' ( a ) + ... equation there results dx ( ) ( ) d2 z 2 - = 0 . dx dy This is the differential equation to developable surfaces ...
... differential coefficients of f , p , Y. Differentiating ( 1 ) with respect to a , { x ƒ ' ( a ) + y p ' ( a ) + ... equation there results dx ( ) ( ) d2 z 2 - = 0 . dx dy This is the differential equation to developable surfaces ...
Сторінка 195
... equation to the evolute - - 81aß2 = 16 { 2a ( a2 − 6a a ) } } 2 { ± ( a2 — 6a a ) 3 — a } . - ( 5 ) In the hypocycloid , the equation to which is x3 + y3 = a3 , a = x + 3x1y3 , B = y + 3x1ys . Adding these a + B = x + y + 3 ( xy ) 3 ...
... equation to the evolute - - 81aß2 = 16 { 2a ( a2 − 6a a ) } } 2 { ± ( a2 — 6a a ) 3 — a } . - ( 5 ) In the hypocycloid , the equation to which is x3 + y3 = a3 , a = x + 3x1y3 , B = y + 3x1ys . Adding these a + B = x + y + 3 ( xy ) 3 ...
Сторінка 196
... equation differential equation in a or B , tion to the evolute . ( 6 ) In the cycloid dy dx 1+ dy dx y 2 2a = whence yẞ = 2y , or y - = = - Substituting this value in d ( - B ) da = dß dx - da dy " and we have a which is the differential ...
... equation differential equation in a or B , tion to the evolute . ( 6 ) In the cycloid dy dx 1+ dy dx y 2 2a = whence yẞ = 2y , or y - = = - Substituting this value in d ( - B ) da = dß dx - da dy " and we have a which is the differential ...
Сторінка 197
... differential equation to the evolute . ( 9 ) The equation to the logarithmic curve is y = aca ; - a2 + y2 y a2 " or y ' -2y + 2 = 0 B ± ( B2 - 8 a2 ) $ ; whence y - B = From this y da and 4a dß + B ± ( ß3 − 8 a2 ) * = 0 - 0 . is the ...
... differential equation to the evolute . ( 9 ) The equation to the logarithmic curve is y = aca ; - a2 + y2 y a2 " or y ' -2y + 2 = 0 B ± ( B2 - 8 a2 ) $ ; whence y - B = From this y da and 4a dß + B ± ( ß3 − 8 a2 ) * = 0 - 0 . is the ...
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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