 | Charles de Neuvéglise - Mathematics - 1700 - 1254 pages
...; for from the algebraical Expreffions of the Quantities and the binomial Theorem, it appears that the Coefficient of the third Term is the Sum of the Products of the Roots, taken two by iwo ; whence its Square is equal to the Sum of the Squares of the Produâs of two by two, more the... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | Thomas Leybourn - Mathematics - 1830 - 630 pages
...second term of an equation with its proper sign, is the sum of the roots with their signs changed ; the coefficient of the third term is the sum of the products of every two roots with their signs changed ; the coefficient of the fourth term is the sum of the products... | |
 | Bourdon (M., Louis Pierre Marie) - Algebra - 1831 - 446 pages
...the roots themselves, is equal to the coefficient of the second term taken with a contrary sign. 2d. The sum of the products of the roots taken two and two with their respective signs, is equal to the coefficient of the third term. 3d. The sum of the products of the... | |
 | Peter Nicholson - Algebra - 1831 - 326 pages
...term, are the second terms or parts of the binomial factors, of •which the equation is the product ; the coefficient of the third term is the sum of the products of every two of these second parts, the coefficient of the fourth term is the sum of the products of every... | |
| |
... the coefficient of the fourth term is the sum of the products of the... 
