Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Сторінка 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 ...
Сторінка 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 ...
Сторінка 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 ...
Сторінка 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 ...
Сторінка 152
... asymptote is a line which , intersecting the axes at a finite distance from the origin , is a tangent to the curve at an infinite distance , it appears that if a , or y remain finite when or y are infinite , their values will determine ...
... asymptote is a line which , intersecting the axes at a finite distance from the origin , is a tangent to the curve at an infinite distance , it appears that if a , or y remain finite when or y are infinite , their values will determine ...
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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