 | Charles Davies - 1835 - 378 páginas
...reciprocal of this proposition is evident. Descartes' Rule. 302. An equation of any degree whatever cannot have a greater number of positive roots than there are variations in the signs ofitt terms, nor a greater number of negative roots than there are permanences of these signs.... | |
 | Benjamin Peirce - 1837 - 300 páginas
...even; and if this last term is negative, the number of these roots must be uneven. 197. Theorem. An equation cannot have a greater number of positive roots than there are VARIATIONS in the signs of its terms, nor a greater number of negative roots than there are PERMANENCES of these Demonstration.... | |
 | 1838 - 372 páginas
...reciprocal of this proposition is evident. t Descartes't Rule. 324. An equation of any degree whatever cannot have a greater number of positive roots than there are variations in the signs of Us terms, nor a greater number of negative roots than there are permanences of these signs.... | |
 | Bourdon (M., Louis Pierre Marie) - 1839 - 368 páginas
...of this proposition is evident. Descartes' Rule. 324. An equation of any degree whatever cannot hone a greater number of positive roots than there are variations in the signs of Us terms, nor a greater number of negative roots than there are permanences of these signs.... | |
 | Charles Davies - 1842 - 368 páginas
...reciprocal of this proposition is evident. Descartes' ' Rule. 324. An equation of any degree whatever cannot have a greater number of positive roots than there are variations in the signs of Us terms, nor a greater number of negative roots than there are permanences of these signs.... | |
 | John Radford Young - 1842 - 276 páginas
...surpass. The rule is enunciated as in the following proposition. PROPOSITION XI. THEOREM. (28.) An equation cannot have a greater number of positive roots than there are change* of sign from + to — , and from — to -)- in the series of terms forming its first member.... | |
 | Charles Davies - 1845 - 382 páginas
...reciprocal of this proposition is evident. Descartes' Rule. 327. An equation of any degree whatever, cannot have a greater number of positive roots than there are variations in the signs of its terms, nor a greater number of negative roots than there are permanences of these signs.... | |
 | Samuel Alsop - 1846 - 300 páginas
...But, by this change of sign, the signs of all the roots are changed. (Art. 1:19.) Hence, since this equation cannot have a greater number of positive roots than there are variations of signs ; it follows that the original equation cannot have a greater number of negative roots than... | |
 | Samuel Alsop - 1848 - 336 páginas
...degree, the last term of which is negative, has at least two real roots, with contrary signs. 142. An equation cannot have a greater number of positive roots than .there are variations of signs, in successive terms, nor can it have a greater number of negative roots than there are continuations... | |
 | Benjamin Peirce - 1851 - 294 páginas
...multiplied by every different power of x from the highest to unity, and also a constant term, such as I. 296. Descartes' Theorem. A complete equation cannot...row of signs of its terms, nor a greater number of pf&i'iiv* roots than there are permanences in this row of signs. Proof. If the equation is that of... | |
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An equation of any degree whatever cannot have a greater number of positive roots than there are variations in the signs of Us terms, nor a greater number of negative roots than there are permanences of these signs. 
