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" ... is equal to the sum of the products of the roots taken three and three ; and so on. "
Elements of Algebra: Tr. from the French of M. Bourdon, for the Use of the ... - Page 237
by Bourdon (M., Louis Pierre Marie) - 1831 - 389 pages
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The Doctrine of Chances: Or, a Method of Calculating the Probabilities of ...

Abraham de Moivre - Electronic books - 1756 - 376 pages
...Unity ; 2°, the laft but one by the Sum of the Roots wanting the firft ; 3°, the laft but two, by the Sum of the Products of the Roots taken two and two, excluding that product wherein the firft Root is concerned ; 4°, the laft but three, by the Sum of...
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A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton - Mathematics - 1811 - 404 pages
...second term if b — a + 2c = 0, or a — b = 2c. Cor. 3. An equation will want its third term, if the sum -of the products of the roots taken two and two, is partly positive, partly negative, and these mutually destroy each other. Remark. An incomplete equation...
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A Course of Mathematics: For the Use of Academies as Well as ..., Volume 2

Charles Hutton - Mathematics - 1812 - 624 pages
...the second term if b — a + 2c = 0, or a—b =. 2c. Cor. 3. An equation will want its third term, if the sum of the products of the roots taken two and two, is partly positive, partly negative, and these mutually destroy each other. Remark. An incowfilefe...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 574 pages
...taken with the contrary sign* will be the sum of the roots ; The coefficient of the third term will be the sum of the products of the roots, taken two and two ; The coefficient of the fourth term, ta],en with the contrary sign, will be the sum of the products...
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A Course of Mathematics for the Use of Academies, as Well as Private Tuition

Charles Hutton - Mathematics - 1822 - 680 pages
...second term if b — a -f 2c = 0, or arb ••= 2c. Cor. 3. An equation will want its third term, if the sum of the products of the roots taken two and two, is partly positive, partly negative * and these mutually destroy each other. Remark* --.Ant incomplete...
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Elements of Algebra

Silvestre François Lacroix - Algebra - 1825 - 324 pages
...taken with the contrary sign, will be the sum of the roots ; The coefficient of the third term will be the sum of the products of the roots, taken two and two ; The coefficient of the fourth term, taken with the contrary sign, will be the sum of the products...
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Elements of Algebra: Tr. from the French of M. Bourdon. Revised and Adapted ...

Charles Davies - Algebra - 1835 - 378 pages
...The algebraic sum of the roots, taken with contrary signs, is equal to the co-efficient of the se<ond term ; or, the algebraic sum of the roots themselves,...signs, is equal to the co-efficient of the third term. The sum of the products of the roots taken three and three with their signs changed, is equal to the...
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Elements of Algebra

Algebra - 1838 - 372 pages
...The double sign has been placed in the last relation, because the product —ax—bx—c. . . X— I will be plus or minus according as the degree of the...signs, is equal to the co-efficient of the third term. The sum of the products of the roots taken three and three with their signs changed, is equal to the...
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Elements of Algebra

Algebra - 1839 - 368 pages
...has been placed in the last relation, because the product — ax— *x— c. . . x—l will be phis or minus according as the degree of the equation is...signs, is equal to the co-efficient of the third term. The sum pf the products of the roots taken three and three with their signs changed, is equal to the...
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Lecture on the History of Mathematics

Francis Henney Smith - Mathematics - 1841 - 46 pages
...successive formation of the co-efficients of an equation, from the comInflation of the sum of its roots, the sum of the products of the roots, taken two and two, three and three, &c. He appears to have been the first who understood the use of negative roots, and...
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