| 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 - 624 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 - 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 - 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 - 682 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 - 662 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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