Examples of the Processes of the Differential and Integral Calculus |
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Page iv
... satisfy themselves of the logical validity of the process . The principles of the method are so simple that I think the short sketch which I have given of them in Chap . xv . will be sufficient to make its application readily understood ...
... satisfy themselves of the logical validity of the process . The principles of the method are so simple that I think the short sketch which I have given of them in Chap . xv . will be sufficient to make its application readily understood ...
Page v
... satisfy himself by attempting to use it in transforming a multiple Integral from one system of independent variables to another , a problem which is of frequent occurrence , but which I have not seen solved analyti- cally in any work in ...
... satisfy himself by attempting to use it in transforming a multiple Integral from one system of independent variables to another , a problem which is of frequent occurrence , but which I have not seen solved analyti- cally in any work in ...
Page 112
... satisfy the n + r equations , M1 = 0 , M1 = 0 ... M1 = 0 , L1 = 0 ... L , = 0 . As it is indifferent which of the variables we eliminate in order to determine A , ... A , the most general way of stating the result is , that we have the ...
... satisfy the n + r equations , M1 = 0 , M1 = 0 ... M1 = 0 , L1 = 0 ... L , = 0 . As it is indifferent which of the variables we eliminate in order to determine A , ... A , the most general way of stating the result is , that we have the ...
Page 167
... satisfy both the equation to the ellipse and that to the asymptote , it appears that the ellipse touches all the three sides of the triangle in their middle points , which by Chap . VII . Ex . 19 , is the property of the maximum ellipse ...
... satisfy both the equation to the ellipse and that to the asymptote , it appears that the ellipse touches all the three sides of the triangle in their middle points , which by Chap . VII . Ex . 19 , is the property of the maximum ellipse ...
Page 170
... satisfy the equations " = 0 , dx - du 0 , = 0 , and proceding dy in the same way , we may ascertain the positions and the plu- rality of all the multiple points of the curve . ( 1 ) Let the equation to the curve be Here , when ∞ = du ...
... satisfy the equations " = 0 , dx - du 0 , = 0 , and proceding dy in the same way , we may ascertain the positions and the plu- rality of all the multiple points of the curve . ( 1 ) Let the equation to the curve be Here , when ∞ = du ...
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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