Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Сторінка 133
... subtangent is constant , and the axis of a is an 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 a ...
... subtangent is constant , and the axis of a is an 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 a ...
Сторінка 142
... subtangent will be equal to the circumference of the circle whose radius is a . If at the extremity of the arc formed by two revolutions , it will be double of the circumference , and so on . This curve was invented by Conon , but its ...
... subtangent will be equal to the circumference of the circle whose radius is a . If at the extremity of the arc formed by two revolutions , it will be double of the circumference , and so on . This curve was invented by Conon , but its ...
Сторінка 143
... subtangent , and the area is one half of the triangle contained by the bounding radius , the tangent at its extremity , and the subtangent . But the most remarkable properties of this curve were discovered by James Bernoulli , who ...
... subtangent , and the area is one half of the triangle contained by the bounding radius , the tangent at its extremity , and the subtangent . But the most remarkable properties of this curve were discovered by James Bernoulli , who ...
Сторінка 144
... equations to the normal are y ' - y du or dx = ( y ' - y ) dx dy - = nc . -- ( x ' − x ) ; du - ( x ' − x ) = 0 . dy The length of the subtangent is y The length of On the Tangents, Normals, and Asymptotes to Curves.
... equations to the normal are y ' - y du or dx = ( y ' - y ) dx dy - = nc . -- ( x ' − x ) ; du - ( x ' − x ) = 0 . dy The length of the subtangent is y The length of On the Tangents, Normals, and Asymptotes to Curves.
Сторінка 145
Duncan Farquharson Gregory William Walton. The length of the subtangent is y The length of the subnormal is y dx dy dy dx dx • { + ( 1 ) } ' The length of the tangent is y The length of the normal is ༧ { 1 + dy ' dy dx The perpendicular ...
Duncan Farquharson Gregory William Walton. The length of the subtangent is y The length of the subnormal is y dx dy dy dx dx • { + ( 1 ) } ' The length of the tangent is y The length of the normal is ༧ { 1 + dy ' dy dx The perpendicular ...
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a² b2 a²x² angle arbitrary constant asymptote becomes C₁ c²x² Cambridge circle co-ordinates condition Crelle's Journal curvature curve cycloid determine differential coefficients differential equation dx dx dx dy 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 plane of reference radius SECT singular solution spiral Substituting subtangent surface tangent plane theorem triangle vanish whence x²)³