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 π a = cos n ( 2r + 1 ) • To find a ,, make ∞ = ( 2r + 1 ) — in the second equation , when we obtain sin n ( 2r + 1 ) π π a1 DEVELOPMENT OF FUNCTIONS . 73.
... Every term on the second side vanishes except the first , and there remains π a = cos n ( 2r + 1 ) • To find a ,, make ∞ = ( 2r + 1 ) — in the second equation , when we obtain sin n ( 2r + 1 ) π π a1 DEVELOPMENT OF FUNCTIONS . 73.
Сторінка 105
... side of the hexagon , = a , AP , the height of the prism , b , OSN = 0. Then = ON = NM = 1α , and SN = The surface of ABPQ = a cosec 0 , and QM = a cot 0 . 1a ( 2b – - a cot 0 ) . 3a2 The surface of PQRS PR . SN = 2 Whence the total ...
... side of the hexagon , = a , AP , the height of the prism , b , OSN = 0. Then = ON = NM = 1α , and SN = The surface of ABPQ = a cosec 0 , and QM = a cot 0 . 1a ( 2b – - a cot 0 ) . 3a2 The surface of PQRS PR . SN = 2 Whence the total ...
Сторінка 118
... sides , A , B , C the angles , and DEF , being the inscribed triangle , let CD = x , AE = y , BF = % . Then if u be ... sides , each intersecting pair makes equal angles with the side in which they meet ; consequently the triangle formed ...
... sides , A , B , C the angles , and DEF , being the inscribed triangle , let CD = x , AE = y , BF = % . Then if u be ... sides , each intersecting pair makes equal angles with the side in which they meet ; consequently the triangle formed ...
Сторінка 125
... its centre coincides with the centre of gravity of the triangle ; and that the points of contact bisect the sides of the triangle . Bérard , Ib . p . 284 . ( 20 ) To find a point within a triangle MAXIMA AND MINIMA , 125.
... its centre coincides with the centre of gravity of the triangle ; and that the points of contact bisect the sides of the triangle . Bérard , Ib . p . 284 . ( 20 ) To find a point within a triangle MAXIMA AND MINIMA , 125.
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Загальні терміни та фрази
a₁ a² b2 a²x² angle arbitrary constant assume asymptote becomes branches C₁ c²x² circle co-ordinates condition Crelle's Journal curvature curve cycloid determine differential coefficients differential equation dx dx dx dy dx² dy dy dy dz dy² dz dz eliminate ellipse equal Euler factor formula fraction function gives Hence hypocycloid infinite Integrating with respect intersection John Bernoulli Let the equation lines of curvature locus logarithmic logarithmic spiral Mémoires multiplying negative origin parabola perpendicular radius SECT singular points singular solution spiral Substituting subtangent surface tangent plane theorem triangle vanish whence x²)³
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