Examples of the Processes of the Differential and Integral CalculusJ and J. J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 18
Сторінка 129
... finding two mean proportionals . The curve is generated in the follow- ing manner : In the diameter ACB ( fig . 12 ) of the circle . ADBE take BM AN , erect the ordinates QM , RN and join AQ ; the locus of the point P where the line AQ ...
... finding two mean proportionals . The curve is generated in the follow- ing manner : In the diameter ACB ( fig . 12 ) of the circle . ADBE take BM AN , erect the ordinates QM , RN and join AQ ; the locus of the point P where the line AQ ...
Сторінка 130
... finding two mean proportionals , or the duplica- 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 . angle . The curve is generated in ...
... finding two mean proportionals , or the duplica- 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 . angle . The curve is generated in ...
Сторінка 137
... finding the area and the centre of gravity of any segment of the curve as well as the content and surface of the solids formed by the revolution of the segment round the axis of the curve , and the base of the segment , and to the ...
... finding the area and the centre of gravity of any segment of the curve as well as the content and surface of the solids formed by the revolution of the segment round the axis of the curve , and the base of the segment , and to the ...
Сторінка 158
... finding what value of makes infinite ; and if the same value of de make either finite or equal to zero , a line drawn through dr the extremity of the subtangent parallel to r is an asymptote to the curve . Spirals may have asymptotic ...
... finding what value of makes infinite ; and if the same value of de make either finite or equal to zero , a line drawn through dr the extremity of the subtangent parallel to r is an asymptote to the curve . Spirals may have asymptotic ...
Сторінка 163
... finding what differential coefficient vanishes , it is generally more d2y convenient to try whether change sign on substituting dx2 in it values of x a little greater and a little less than that which makes it vanish . If it do change ...
... finding what differential coefficient vanishes , it is generally more d2y convenient to try whether change sign on substituting dx2 in it values of x a little greater and a little less than that which makes it vanish . If it do change ...
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Загальні терміни та фрази
a² b2 a²x² angle arbitrary constant asymptote axis becomes C₁ c²x² Cambridge circle co-ordinates condition curvature curve cycloid cylinder determine differential coefficients differential equation dx dx dx dy dx dx² dy dx dy dy dy dy dz eliminate ellipse equal Euler find the value formula function Geometry gives Hence hypocycloid infinite Integrating with respect intersection John Bernoulli Let the equation lines of curvature locus logarithmic logarithmic spiral maximum minimum Multiply negative origin parabola perpendicular radius radius of curvature singular solution spiral Substituting subtangent surface tangent plane theorem tractory triangle vanish whence x²)³