Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Сторінка 43
... 20 ( dx ) dy 2 dy -y + m = 0 . dx ( 4 ) Eliminate a and b from the equation y - ax2 - bx = 0 ; the result is d2y 2 dy dx9 x dx + 2y = 0 . ( 5 ) Eliminate the constants m and a from IV Elimination of Constants and Functions PAGE 1.
... 20 ( dx ) dy 2 dy -y + m = 0 . dx ( 4 ) Eliminate a and b from the equation y - ax2 - bx = 0 ; the result is d2y 2 dy dx9 x dx + 2y = 0 . ( 5 ) Eliminate the constants m and a from IV Elimination of Constants and Functions PAGE 1.
Сторінка 44
... eliminating , dy x - 2y + y = 0 . da ( 8 ) Eliminate a and ẞ from the equation . ( x − a ) 2 + ( y − - ß ) 2 = r2 ... ELIMINATION OF CONSTANTS AND FUNCTIONS .
... eliminating , dy x - 2y + y = 0 . da ( 8 ) Eliminate a and ẞ from the equation . ( x − a ) 2 + ( y − - ß ) 2 = r2 ... ELIMINATION OF CONSTANTS AND FUNCTIONS .
Сторінка 45
... Eliminating b , we have d3y and = b dx3 da3 dz d'y d'z d3y = 0 . dx3 dx2 dx2 da3 This is the condition that a curve ... ELIMINATION OF CONSTANTS AND FUNCTIONS . 45 9.
... Eliminating b , we have d3y and = b dx3 da3 dz d'y d'z d3y = 0 . dx3 dx2 dx2 da3 This is the condition that a curve ... ELIMINATION OF CONSTANTS AND FUNCTIONS . 45 9.
Сторінка 46
... eliminating cot na by the last equation , we have d'y da2 - dy 2 m + ( n2 + m2 ) y = 0 . dx ( 15 ) Eliminate the ... ELIMINATION OF CONSTANTS AND FUNCTIONS .
... eliminating cot na by the last equation , we have d'y da2 - dy 2 m + ( n2 + m2 ) y = 0 . dx ( 15 ) Eliminate the ... ELIMINATION OF CONSTANTS AND FUNCTIONS .
Сторінка 47
... 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 from the equation and y ≈ = y " ( 1 ) + y * ↓ ( ~ ) . Differentiating with ...
... 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 from the equation and y ≈ = y " ( 1 ) + y * ↓ ( ~ ) . Differentiating with ...
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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