 | Colin MacLaurin - 1756 - 538 sider
..." when all the roots of an equation are negative^ it is plain there will be no changes in the figns of the terms' of that equation" § 19. In general,...as many pofitive roots in any equation as there are changesin the figns of the terms from -\- to — , or from — to -f- -, and the remaining roots are... | |
 | Colin MacLaurin - 1756 - 480 sider
...the roots of an equation are negative, it is plain there will be no changes in the Jigns of the iermt of that equation" § 19. In general, " there are as...roots in any equation as there are changes in the figns of the terms from + to — , or from • — to 4- '* and the remaining roots are negative."... | |
 | Colin MacLaurin - 1771 - 484 sider
...roots of an equation are negative, it is plain there will be no changes in the figns of the terms cf that equation" § 19. In general, " there are as many...roots in any equation as there are changes in the figns of the terms from + to — , or from — to + ; and the remaining roots are negative." negative."... | |
 | John Bonnycastle - 1782 - 272 sider
...there can bе по changes in the ßgns of the terms ofthat equation. And, in general, there will be as many pofitive roots in any equation, as there are changes in the Л. figns of the terms of that equation, from + to —, or from — to + ; and all the reft of the... | |
 | John Mole - 1788 - 346 sider
...and оде front the third to the fourth Term, which ihew that there are two affirmative Roots ; for there are as many pofitive Roots in any Equation as there are Changes of the Signs of the Terms from + to — , and from — to + ; the two like Signs — and — which... | |
 | Dublin city, univ - 1875 - 386 sider
...biquadratic from that of the reducing cubic. 12. Show that there will be as many pairs of imaginary roots in any equation as there are changes in the signs of the leading terms of Sturm's auxiliary functions when none of them are wanting. If some of them be wanting,... | |
 | William Davis, John Hampshire - 1809 - 582 sider
...there muft be one pofitive root more in the equation (D) than Ihere is in (E). Defcartes' rule is, that there are as many pofitive roots in any equation as there are changes in the figns of the terms from + to — , 01 from — to +> ar"l that the remaining roots are negative. From... | |
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Xx + bXx+cxx + d, &c. = o, will exprefs the equation to be produced ; all whofe terms will plainly be pofitive ; fo that " -when all the roots of an equation are negative, it is plain there will be no changes in the Jigns of the iermt of that equation 