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

### From inside the book

Results 1-5 of 57

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**multiplying**by the common base , 4 imate value Sydt = = 1 n 4. ( yo + y1 + Y2 + .... + Yn − 1 + Yn ) . This method is obvious and must be very ancient . It is a correct principle of approximation and when n is infinite gives the exact ... Page 2

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**Multiply**by dx and integrate from 0 to 1. Then Syda 1 1 1 = yo + - 2 12 1230 + 244yo- 19 720 Ayo + 3 160 45yo & c . , - which will be the area comprised between the ordinates yo and y1 . In the same way the area comprised between y ... Page 3

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**multiply**the preceding general value of y by dx and inte- grate between the limits 0 and n , where n denotes the number of intervals , we have 0 Syda n2 = nyo + Ayo + n3 2 6 12 ) Fyo + n4 n3 + 24 6 n2 ) . Byo n5 n4 11n3 n6 + + ηδ + 720 ... Page 4

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**multiply**the whole sum by three tenths of the common interval . ( 5 ) . The following elegant method was given by Roger Cotes in his Harmonia Mensurarum , published in 1722 , and is an elaboration of the method indicated by Newton . In ... Page 5

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**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 in such form that it is not necessary to ...### 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