Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 44
Сторінка 29
... radius of curvature when a is the independent variable is dy + dx - d2y dx2 When y is made the independent variable , it becomes da d { 1 + ( - / - ) " } d2x dy ( 3 ) Transform d2y ' dy dy 3 -x CHANGE OF THE INDEPENDENT VARIABLE . 29.
... radius of curvature when a is the independent variable is dy + dx - d2y dx2 When y is made the independent variable , it becomes da d { 1 + ( - / - ) " } d2x dy ( 3 ) Transform d2y ' dy dy 3 -x CHANGE OF THE INDEPENDENT VARIABLE . 29.
Сторінка 44
... , 2 dx dy d2y da dx Substituting these values of yẞ and a -a , we have 3 + ( d ) } * 2 = dy in which a and ẞ no longer appear . 12 , This is the expression for the square of the radius dx2 44 ELIMINATION OF CONSTANTS AND FUNCTIONS .
... , 2 dx dy d2y da dx Substituting these values of yẞ and a -a , we have 3 + ( d ) } * 2 = dy in which a and ẞ no longer appear . 12 , This is the expression for the square of the radius dx2 44 ELIMINATION OF CONSTANTS AND FUNCTIONS .
Сторінка 45
Duncan Farquharson Gregory William Walton. This is the expression for the square of the radius of curvature of any curve . ( 9 ) Eliminate m from the equation ( a + mẞ ) ( x2 - my3 ) = my2 ; the result is dy axy + ( Bx2 — ay2 — y3 ) ...
Duncan Farquharson Gregory William Walton. This is the expression for the square of the radius of curvature of any curve . ( 9 ) Eliminate m from the equation ( a + mẞ ) ( x2 - my3 ) = my2 ; the result is dy axy + ( Bx2 — ay2 — y3 ) ...
Сторінка 103
... radius of the a circle ; then is the half - angle of the segment . - If u be the segment , u = ax - x2 sin Whence COS a 818 a 818 a COS is a maximum . x a cos a 2 - x sin = 0 . 20 If cos a - = 0 , or x a maximum . a - If 00 = tan a ...
... radius of the a circle ; then is the half - angle of the segment . - If u be the segment , u = ax - x2 sin Whence COS a 818 a 818 a COS is a maximum . x a cos a 2 - x sin = 0 . 20 If cos a - = 0 , or x a maximum . a - If 00 = tan a ...
Сторінка 104
... radius of the cylinder , y its base . Then a = y = a determines the cylinder of least surface . ( 29 ) The content of a cone being given , find its form when the surface is a maximum . Let πα 3 be the given content , a the radius of the ...
... radius of the cylinder , y its base . Then a = y = a determines the cylinder of least surface . ( 29 ) The content of a cone being given , find its form when the surface is a maximum . Let πα 3 be the given content , a the radius of the ...
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Загальні терміни та фрази
a² b2 a²x² angle arbitrary constant asymptote becomes C₁ c²x² Cambridge circle co-ordinates condition Crelle's Journal curvature curve cycloid determine differential coefficients differential equation dx dx dx dy 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 plane of reference radius SECT singular solution spiral Substituting subtangent surface tangent plane theorem triangle vanish whence x²)³