## The Analyst: A Monthly Journal of Pure and Applied Mathematics, Volumes 3-4Pierson & Blair, 1876 |

### From inside the book

Results 1-5 of 42

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**integral**being taken between the limits xg , and x = h ; to which correspond the terminal ordinates . Since it is always possible to change the limits of integration to 0 and 1 by putting x = g + ( h — g ) t , so that Sydx = ( h — 9 ) ... Page 3

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**integrals**and ob- serving that Ayo + Ay1 + ... + Ayn - 1 = Y1 - Yo + Y2 - Y1 + ... + Yn - Ym1 = Ya - Yo Byo + By + ... + Syn - 1 = Ay , Ay 。 + & c . , — we have for the value of the**integral**between the extreme ordinates , after some ... Page 4

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**integral**ST m dt =。Mm A m and then shall have S'yelt = 0 Aoyo + A131 + A2Y2 + ... + Anym the values of A , A1 , A2 , & c . , serving for all cases . The values of the ratio TM are 0 Mo T 1 = 1 ) ( nt — 2 ) ( nt — 3 ) . . . . ( nt — n ) ... Page 5

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**integral**by this method we have only to multiply the known value of the ordinate by the corresponding value of A and take the sum of the products . It will be noticed that we always have An - m = Am . ( 6 ) . The preceding formulæ are ... Page 6

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**integrals**Ja , + 12 + 1dx , & c . In 1814 Gauss published a memoir on approximate quad- rature , probably having been led to consider the subject from its use in computing the perturbations of the minor planets . The title of this ...### Other editions - View all

### Common terms and phrases

5th degree a₁ algebraic ANALYST angle ARTEMAS MARTIN assumed axis b₁ C₁ circular coefficients common logarithms constant curve denote determine differential distance E. B. SEITZ ellipse Elliptic Functions equal equation expression factor formula function given circle gives hence hyperbola integral intersection inverse Lagrange's Theorem locus logarithms method multiply observations orbital orbital force ORSON PRATT oxen parabola parallel perpendicular plane points at infinity position probable error quadrics quadrilateral radius ratio reduce represent result roots sides SOLUTION BY PROF SOLUTIONS of problems sphere square substitution surface tangent Taylor's Theorem Theorem tion triangle UNION SPRINGS unknown quantities values velocity whence zero