Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 54
Сторінка 102
... origin . Let OP = x , and let the co - ordinates of A and B be a , b , a1 , b1 . Then u = AP + BP = { b2 + ( x − a ) 3 } } + { b‚2 + ( a ̧ − x ) 2 } 3 = minimum . Whence 00 -α = 2 - a1 < -00 { b2 + ( x − a ) 2 } } = { b‚2 + ( a ̧ ...
... origin . Let OP = x , and let the co - ordinates of A and B be a , b , a1 , b1 . Then u = AP + BP = { b2 + ( x − a ) 3 } } + { b‚2 + ( a ̧ − x ) 2 } 3 = minimum . Whence 00 -α = 2 - a1 < -00 { b2 + ( x − a ) 2 } } = { b‚2 + ( a ̧ ...
Сторінка 123
... origin , CA , CB as the axes of x and y . AC = a , BC = b , ACB = 0 . The general equation to an ellipse is Ax2 + Bxy + Cy2 + Dx + Ey + 1 = 0 , which involves five arbitrary constants ; three of these may be determined by the conditions ...
... origin , CA , CB as the axes of x and y . AC = a , BC = b , ACB = 0 . The general equation to an ellipse is Ax2 + Bxy + Cy2 + Dx + Ey + 1 = 0 , which involves five arbitrary constants ; three of these may be determined by the conditions ...
Сторінка 124
... origin gives A a2 + 2 Baß + Cß2 + 1 = 0 . ( 1 ) The condition that the curve shall pass through the point a = a , y = 0 , gives - - Subtracting ( 1 ) from ( 2 ) we have A ( a − a ) 2 - 2 B ( a − a ) ẞ + C ẞ2 + 1 = 0 . ( 2 ) A ( 2a - a ) ...
... origin gives A a2 + 2 Baß + Cß2 + 1 = 0 . ( 1 ) The condition that the curve shall pass through the point a = a , y = 0 , gives - - Subtracting ( 1 ) from ( 2 ) we have A ( a − a ) 2 - 2 B ( a − a ) ẞ + C ẞ2 + 1 = 0 . ( 2 ) A ( 2a - a ) ...
Сторінка 132
... origin be taken at the middle point between them , the equation to the curve is { y2 + ( a + x ) 2 } { y2 + ( a − x ) 2 } = c1 . When c = a , the equation is reduced to ( x2 + y2 ) 2 = 2 a2 ( x2 — y2 ) . - This was the curve used by ...
... origin be taken at the middle point between them , the equation to the curve is { y2 + ( a + x ) 2 } { y2 + ( a − x ) 2 } = c1 . When c = a , the equation is reduced to ( x2 + y2 ) 2 = 2 a2 ( x2 — y2 ) . - This was the curve used by ...
Сторінка 135
... origin . The farther these points are removed from the origin the more nearly is the curve perpendicular to the axis of x , the value of dy da π at the intersection being ± ( 2n − 1 ) — - 2 " 2na being the abscissa of the point where ...
... origin . The farther these points are removed from the origin the more nearly is the curve perpendicular to the axis of x , the value of dy da π at the intersection being ± ( 2n − 1 ) — - 2 " 2na being the abscissa of the point where ...
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