Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Сторінка v
... tion which is implied in the old notation ; and if it were at any time necessary to consider integration merely as the inverse of differentiation , I should pre- fer to employ such a symbol as d which expresses the required idea better ...
... tion which is implied in the old notation ; and if it were at any time necessary to consider integration merely as the inverse of differentiation , I should pre- fer to employ such a symbol as d which expresses the required idea better ...
Сторінка 121
... tion is Tabc ( a2 l2 + b2 m2 + c2n2 ) § ' To find the volume of the ellipsoid whose equa- ax2 + a'y2 + a ′′ x2 + 2 by z + 2 b ′ x z + 2b ′′ xy = c . As in the preceding examples we have first to find MAXIMA AND MINIMA . 121.
... tion is Tabc ( a2 l2 + b2 m2 + c2n2 ) § ' To find the volume of the ellipsoid whose equa- ax2 + a'y2 + a ′′ x2 + 2 by z + 2 b ′ x z + 2b ′′ xy = c . As in the preceding examples we have first to find MAXIMA AND MINIMA . 121.
Сторінка 130
... tion of the cube , but it is more readily applicable to an- other problem not less celebrated among the ancients , that of the trisection of an angle . The curve is gencrated in the following manner : take the indefinite straight line ...
... tion of the cube , but it is more readily applicable to an- other problem not less celebrated among the ancients , that of the trisection of an angle . The curve is gencrated in the following manner : take the indefinite straight line ...
Сторінка 133
D. F. Gregory. portional to the logarithm of the ordinate . Hence its equa- tion is y = bet , or , as it is generally written , y = a * . The subtangent is constant , and the axis of a is an asymptote . The whole area included between ...
D. F. Gregory. portional to the logarithm of the ordinate . Hence its equa- tion is y = bet , or , as it is generally written , y = a * . The subtangent is constant , and the axis of a is an asymptote . The whole area included between ...
Сторінка 141
... tion let AOP = 0 , OP = r , and when 2 let r = a . = α a Then = Ꮎ or = Ꮎ , - 27 2π which is the equation to the curve . * Principia , I. Prop . 49 . The following are its principal properties . The area of GENERATION OF CURVES . 141.
... tion let AOP = 0 , OP = r , and when 2 let r = a . = α a Then = Ꮎ or = Ꮎ , - 27 2π which is the equation to the curve . * Principia , I. Prop . 49 . The following are its principal properties . The area of GENERATION OF CURVES . 141.
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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