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

### From inside the book

Results 1-5 of 32

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**factors**2 + 1 and ( x — 1 ) " + 1 , and inversely every function which has the**factor**+1 . ( x - 1 ) +1 , and be- sides only constant**factors**, fulfils the condition . Since y ( x ) is of the ( n + 1 ) th order , Пlx = +1 ( x ) dx , is ... Page 19

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**factor**. This appears from the fact that every constituent of the Determinant contains one and but one element from ...**factors**multiplying a1 , a , & c . , or a1 , b1 & c . , are recognised as the minors obtained from the given ... Page 20

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**factors**, the De- terminant vanishes . For it is the sum of other Determinants which are separately evanescent . E. g . 1 | kb1 + le1 , b1 , C1 kb2 + lc2 , b2 , C2 kbz + lcg , bз , C3 \ and these latter vanish by 5 ° . = \ kb 1 , kb 2 ... Page 21

... value if written la + b + c , b , c , 1 , b , c , 1 , c , a , c + a + b , a , b , = ( a + b + c ) 1 , a , b , b + c + a , c , a , it is evident that a + b + c is a

... value if written la + b + c , b , c , 1 , b , c , 1 , c , a , c + a + b , a , b , = ( a + b + c ) 1 , a , b , b + c + a , c , a , it is evident that a + b + c is a

**factor**of a + b + c3abc . α b 88 d 8 . с b a 6880 -21- Page 22

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**factor**of this Determinant . 10 , c , b , 9 . 0 , a , b , a , 0 , · c ( 0 — ab ) + b ( ac — 0 ) — 2abc . = § 7. Applications of Determinants . If we write the Determinant a 1 b1 .... a2 ba an ba n1 N2 nn in the form given in 6o , § 5 ...### 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