 | Abraham de Moivre - 1756 - 376 σελίδες
...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... | |
 | Charles Hutton - 1811 - 404 σελίδες
...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... | |
 | Charles Hutton - 1812 - 624 σελίδες
...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... | |
 | Adrien Marie Legendre - 1819 - 574 σελίδες
...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... | |
 | Charles Hutton - 1822 - 680 σελίδες
...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... | |
 | Silvestre François Lacroix - 1825 - 324 σελίδες
...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... | |
 | Charles Davies - 1835 - 378 σελίδες
...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... | |
 | 1838 - 372 σελίδες
...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... | |
 | 1839 - 368 σελίδες
...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... | |
 | Francis Henney Smith - 1841 - 46 σελίδες
...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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... is equal to the sum of the products of the roots taken three and three ; and so on. 
