Examples of the Processes of the Differential and Integral Calculus |
From inside the book
Results 1-5 of 69
Page x
... Surfaces , Rectification of Curves , and Cubature of Solids 412 X. Geometrical Problems Involving the Solution of Differential Equations 440 XI . Evaluation of Definite Integrals 464 XII . Comparison of Transcendents 506 DIFFERENTIAL ...
... Surfaces , Rectification of Curves , and Cubature of Solids 412 X. Geometrical Problems Involving the Solution of Differential Equations 440 XI . Evaluation of Definite Integrals 464 XII . Comparison of Transcendents 506 DIFFERENTIAL ...
Page 47
... 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 from the equation and y ≈ = y " ( 1 ) + ...
... 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 from the equation and y ≈ = y " ( 1 ) + ...
Page 50
... this equation there results dx ( ) ( ) d2 z 2 - = 0 . dx dy This is the differential equation to developable surfaces . ( 24 ) Eliminate the arbitrary function from the equation 50 ELIMINATION OF CONSTANTS AND FUNCTIONS .
... this equation there results dx ( ) ( ) d2 z 2 - = 0 . dx dy This is the differential equation to developable surfaces . ( 24 ) Eliminate the arbitrary function from the equation 50 ELIMINATION OF CONSTANTS AND FUNCTIONS .
Page 99
... of the problem , To find the height at which a light should be placed so that a small plane surface at a given horizontal distance shall receive the greatest illumination from it . ( 11 ) W = X ( a + x 7-2 MAXIMA AND MINIMA . 99.
... of the problem , To find the height at which a light should be placed so that a small plane surface at a given horizontal distance shall receive the greatest illumination from it . ( 11 ) W = X ( a + x 7-2 MAXIMA AND MINIMA . 99.
Page 104
... surface . a = ( 29 ) The content of a cone being given , find its form when the surface is a maximum . Let πα 3 be the given content , the radius of the base , y the height of the cone . the cone of greatest surface . a Then x = • y ...
... surface . a = ( 29 ) The content of a cone being given , find its form when the surface is a maximum . Let πα 3 be the given content , the radius of the base , y the height of the cone . the cone of greatest surface . a Then x = • y ...
Other editions - View all
Common terms and phrases
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