| Nicolas Vilant - 1798 - 196 pages
...all degrees to be produced by a multiplication of binomial factors. Every affefted equation will have **as many roots as there are units in the exponent of the** higheft power of the variable quantity ; and, if the terms of the equation are alternately affirmative... | |
| Charles Hutton - 1812 - 624 pages
...that which characterizes these roots is, that on substituting each of them successively instead of x+ **the aggregate of the terms of the equation vanishes...exponent of the highest power of the unknown quantity,** und that each root has the properly of rendering, by its substitution in place of the unknown quantity,... | |
| 1823 - 876 pages
...degree may be considered as proekiced by the multiplication of аз many simple equations ns there arc **units in the exponent of the highest power of the unknown quantity.** From this he deduced the relation which exists bctw en the roots of an equation, and the coefficients... | |
| Charles Hutton - 1826 - 682 pages
...that which characterizes these roots is, that on substituting eacb of them successively instead of r, **the aggregate of the terms of the equation vanishes...of the highest power of the unknown quantity, and** thnt each root h;is the property of rendering, by its substitution in place of the unknown quantity,... | |
| Charles Hutton - 1831 - 662 pages
...aggregate of the terms of the equation vanishes, by the opposition of the signs + and — . ' 1 he **preceding equation is only of the fourth power or...quantity, the aggregate of all the terms of the equation** equul to nothing. It must be observed that we cannot have all at once x = a, x = b, x = c, &c. for... | |
| Charles Hutton - 1831 - 656 pages
...is only of the fourth power or degree ; but it is manifest that the above remark applies i<equations **of higher or lower dimensions : viz. that in general...rendering, by its substitution in place of the unknown** quantify, the aggregate of all Ihe terms of the equation equal to nothing. It must be observed that... | |
| Charles Davies - 1835 - 374 pages
...law should be remembered. Second Property. 264. Every equation involving but one unknown quantity, **has as many roots as there are units in the exponent of** its degree, and no more. Let the proposed equation be if+Par-i+Q«" 3+ • • . +Tx+\J=0. Since every... | |
| 1838 - 372 pages
...law should be remembered. Second Property. 281. Every equation involving but one unknown quantity, **has as many roots as there are units in the exponent of** its degree, and no more. Let the proposed equation be xn+Pxm~l+Q.xm-2+ . . . +Ta;+U=0. Since every... | |
| John Radford Young - 1842 - 276 pages
...all arranged on one side, the polynomial we thus get is composed of as many simple binomial factors **as there are units in the exponent of the highest power of the unknown quantity.** The discovery of these factors would he the discovery of the roots of the equation, since these are... | |
| Ormsby MacKnight Mitchel - 1845 - 308 pages
...on of the divisors of all degrees. 234. As an exemplification of the principle, that every equation **has as many roots as there are units in the exponent of the highest power of the unknown quantity,** we propose to examine the equation xm—! =0. Let us commence by making m=2, and we have x2 — 1=0By... | |
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