Examples of the Processes of the Differential and Integral Calculus |
From inside the book
Results 1-5 of 30
Page ix
... Asymptotes to Curves ...... 144 Singular Points in Curves 162 XI . On the Tracing of Curves from their Equations 175 XII . On the Curvature of Curved Lines ......... 188 XIII . Application of the Differential Calculus to Geometry of ...
... Asymptotes to Curves ...... 144 Singular Points in Curves 162 XI . On the Tracing of Curves from their Equations 175 XII . On the Curvature of Curved Lines ......... 188 XIII . Application of the Differential Calculus to Geometry of ...
Page 129
... asymptote . included between the curve and the asymptote is three times the area of the generating circle . The application of this curve to the solution of the 9 On the Generation of Curves and the Investigation of their Equations from ...
... asymptote . included between the curve and the asymptote is three times the area of the generating circle . The application of this curve to the solution of the 9 On the Generation of Curves and the Investigation of their Equations from ...
Page 131
... asymptote to both branches . When a > b there is a loop in the inferior conchoid at O as in the figure ; when ab the loop degenerates into a cusp ; and when a < b there are two points of contrary flexure , one on each side of the line ...
... asymptote to both branches . When a > b there is a loop in the inferior conchoid at O as in the figure ; when ab the loop degenerates into a cusp ; and when a < b there are two points of contrary flexure , one on each side of the line ...
Page 132
... asymptote to the curve , which has two points of contrary flexure corresponding to a = ( 4 ) The Lemniscate of Bernoulli . 3 a 2 If a point be taken such that the product of the lines . drawn from it to two fixed points is constant , it ...
... asymptote to the curve , which has two points of contrary flexure corresponding to a = ( 4 ) The Lemniscate of Bernoulli . 3 a 2 If a point be taken such that the product of the lines . drawn from it to two fixed points is constant , it ...
Page 133
... asymptote . The whole area included between the curve , the axis of and any ordinate is equal to twice the triangle formed by the ordinate , the tangent at its extremity and the axis of x ; and the solid formed by the revolution of the ...
... asymptote . The whole area included between the curve , the axis of and any ordinate is equal to twice the triangle formed by the ordinate , the tangent at its extremity and the axis of x ; and the solid formed by the revolution of the ...
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