 | Abraham de Moivre - 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 - 1812 - 634 pages
...its roots partly real, partly imaginary, will want the second term if b — a + 2c = 0, or a—b =. 2c. Cor. 3. An equation will want its third term,...and these mutually destroy each other. Remark. An incowfilefe equation may be thrown imo the form of com/ilete equations, by introducing, with the coefficient... | |
 | Charles Hutton - 1816 - 618 pages
...article, which has its roots partly real, partly imaginary, will want the second term if b — a -f. 2c = 0, or a — b = 2c. Cor. 3. An equation will want its third term, if the sum of the products ot the roots taken two and two, is partly positive, partly negative, and these mutually destroy each... | |
 | Charles Hutton - 1818 - 652 pages
...second term if b — a -f- 2e = 0, or e — 6 = Se. Cor. 3. An equation will want its third term, if Ihe sum of the products of the roots taken two and two,...partly negative, and these mutually destroy each other. Rtmnrk. An incomplete equation may be thrown into the form of complete equations, by introducing, with... | |
 | Adrien Marie Legendre - 1819 - 576 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 - 1822 - 680 pages
...roots partly real, partly imaginary, will want the second term if b — a -f 2c = 0, or arb ••= 2c. Cor. 3. An equation will want its third term,...negative * and these mutually destroy each other. Remark* --.Ant incomplete equation may be thrown into the form ;of complete equations, by introducing, with... | |
 | Charles Hutton - 1826 - 680 pages
...roots partly real, partly imaginary, will want the second term if 6 — a +£«=(), or a — 6=2c. Cor. 3. An equation will want its third term, if the...Remark An incomplete equation may be thrown into the form of complete equations, by introducing, with the co-efficient a cypher, the absent powers of the... | |
 | Silvestre François Lacroix - 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... | |
 | Charles Hutton - 1831 - 656 pages
...its roots partly real, partly imaginary, will want the second term if b — a + 2c = 0, or a — 6 = 2c. Cor. 3. An equation will want its third term,...Remark. An incomplete equation may be thrown into the form of complete equations, by introducing, with the coefficient a cypher, the absent powers of the... | |
 | Charles Hutton - 1831 - 654 pages
...its roots partly real, partly imaginary, will want the second term if b — a -j2c = 0, or a — 6 = 2c. Cor. 3. An equation will want its third term, if the sum of the produces of the roots taken two and two, is partly positive, partly negative, and these mutually destroy... | |
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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. 
