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" The coefficient of the fourth term is the fum of all the products which can be made by multiplying together any three of the roots with their figns changed ; and fo of others. "
Elements of Algebra for the Use of Students in Universities: To which is ... - Page 185
by William Trail - 1796 - 311 pages
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A Treatise of Algebra, in Three Parts: Containing I. The Fundamental Rules ...

Colin MacLaurin - Algebra - 1756 - 432 pages
...all the produis that can be made by multiplying any two of the roots (a, b, ct d, e) by ont another. The coefficient of the fourth term is the fum of all the producís that can be made by multiplying into one another any three of the roots, with their ßgns...
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An Essay on Mathematical Language: Or, An Introduction to the Mathematical ...

Giovanni Alberto Baselli - Mathematics - 1787 - 440 pages
...of all the produite that can be made by multiplying any two of the roots together. That of the 4th is the fum of all the products which can be made by...roots with their figns changed ; and fo of others. The lad term is the product of all the roots, With their figns changed. 3. From induction it appears, that...
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A Treatise of Algebra: In Three Parts. Containing. The fundamental rules and ...

Colin MacLaurin - Algebra - 1796 - 504 pages
...all the produits that can be made by multiplying any two of the roots (a, bt c, d, e) by one another. The coefficient of the fourth term is the fum of all the producís that can be made by multiplying into one another any three of the roots, with their figns...
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A Treatise of Algebra,: In Three Parts. Containing I. The Fundamental Rules ...

Colin MacLaurin - Algebra - 1796 - 504 pages
...the frcdufls that can be made by multiplying any two of tbt roots (a, I, c, it, t) by tmi another. The coefficient of the fourth term is the fum of all the produEls that can be made by multiplying into one another any three of the roots, 'with their figns...
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Analytical Institutions in Four Books: Originally Written in ..., Volumes 1-2

Maria Gaetana Agnesi - Calculus - 1801
...co-efficient of the third term is the fum of all the products of all the pairs of roots which can be formed ; the co-efficient of the fourth term is the fum of all the products of all the ternaries or threes ; and fo on to the laft or conftant term, which is the product of all...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1814 - 303 pages
...co-efficients, in the third term, are ab, ac, be. In the fourth term, the co-efficient of x is the sum of all the products which can be made, by multiplying together any three of the roots, after their signs are changed. Thus the roots 6f the biquadratic equation are a, b, c, and d, and the...
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Encyclopaedia Perthensis; Or Universal Dictionary of the Arts ..., Volume 1

Encyclopedias and dictionaries - 1816
...can be made by multiplying any two of the roots together. The co-efficient of the fourth term is fhe fum of all the products, which can be made: by multiplying together any three of the roots with their li^ns changed ; and fo of others. The laft term is the product of all the roots, with their ligns changed....
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1820 - 332 pages
...Therefore In the third term of the original equation, B the co-efficient of x, is equal to the sum of all the products which can be made by multiplying together any two of the roots (Art. 500.) But each of these products will be excluded from too of the quotients...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1827 - 332 pages
...co-efficients, in the second term, are — a and — 6. In the third term, the co-efficient of x is the sum of all the products which can be made, by multiplying together any two of the roots. Thus, in the cubic equation, as the roots are a, 4, and c, the co-efficients, in...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1847 - 332 pages
...co-efficients, in the second term, are - a and - 6. In the third term, the co-efficient of x, is the sum of all the products which can be made, by multiplying together any two of the roots. Thus, in the cubic equation, as the roots are a, b, and c, the co-efficients, in...
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