Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Сторінка 21
... side of ( 1 ) , and as this last consists of a finite number of terms having positive indices , the terms in the product of ( 2 ) and ( 3 ) which contain negative indices must disappear of themselves . Hence taking the terms with ...
... side of ( 1 ) , and as this last consists of a finite number of terms having positive indices , the terms in the product of ( 2 ) and ( 3 ) which contain negative indices must disappear of themselves . Hence taking the terms with ...
Сторінка 73
... Every term on the second side vanishes except the first , and there remains a = cos n ( 2r + 1 ) — · To find a1 , make x = ( 2r + 1 ) — in the second equation , when we obtain 2 π sin n ( 2 + 1 ) 2 π DEVELOPMENT OF FUNCTIONS . 73.
... Every term on the second side vanishes except the first , and there remains a = cos n ( 2r + 1 ) — · To find a1 , make x = ( 2r + 1 ) — in the second equation , when we obtain 2 π sin n ( 2 + 1 ) 2 π DEVELOPMENT OF FUNCTIONS . 73.
Сторінка 105
... side of the hexagon , AP , the height of the prism , b , OSN = 0 . = = a , Then and QM = a cot 0 . ON = NM = a , and SN = a cosec 0 , The surface of ABPQ = ļa ( 2b - a cot 0 ) . 3a2 The surface of PQRS PR . SN = cosec 0 . 2 Whence the ...
... side of the hexagon , AP , the height of the prism , b , OSN = 0 . = = a , Then and QM = a cot 0 . ON = NM = a , and SN = a cosec 0 , The surface of ABPQ = ļa ( 2b - a cot 0 ) . 3a2 The surface of PQRS PR . SN = cosec 0 . 2 Whence the ...
Сторінка 118
... side in which they meet ; consequently the triangle formed by these lines is the triangle of least perimeter which can be inscribed in the given triangle . See Cambridge Mathematical Journal , Vol . 1. p . 157 . ( 14 ) To find the least ...
... side in which they meet ; consequently the triangle formed by these lines is the triangle of least perimeter which can be inscribed in the given triangle . See Cambridge Mathematical Journal , Vol . 1. p . 157 . ( 14 ) To find the least ...
Сторінка 129
... side of AB ; the two branches meet in a cusp at the point A , and have the line HK as a common asymptote . included between the curve and the asymptote is three times the area of the generating circle . The application of this curve to ...
... side of AB ; the two branches meet in a cusp at the point A , and have the line HK as a common asymptote . included between the curve and the asymptote is three times the area of the generating circle . The application of this curve to ...
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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