 | Bourdon (M., Louis Pierre Marie) - 1831 - 446 σελίδες
...of sign, nor the number of negative roots greater than the number of PERMANENCES. 331 . Consequence. When the roots of an equation are all real, the number...number of variations, and the number of negative roots is equal to the number of permanences. For, let in denote the degree of the equation, n the number... | |
 | Charles Davies - 1835 - 378 σελίδες
...of sign, nor the number of negative roots greater than the number of PERMANENCES. 303. Consequence. When the roots of an equation are all real, the number of positive roots is equal to Hie number of variations, and the number of negative roots is equal to the number of permanences. For,... | |
 | John Radford Young - 1835 - 302 σελίδες
...necessarily, p=p' and r = t^ ; consequently, when the roots are all real, the number of positive roots will be equal to the number of variations, and the number of negative roots equal to the number of permanencies.' CHAPTER. II. ON THE TRANSFORMATION OF EQUATIONS. (19.) Algebraical... | |
 | 1838 - 372 σελίδες
...of sign, nor the number of negative roots greater than the number of PERMANENCES. 325. Consequence. When the roots of an equation are all real, the number...number of variations, and the number of negative roots is equal to the number of permanences. For, let m denote the degree of the equation, n the number of... | |
 | Andrew Bell (writer on mathematics.) - 1839 - 500 σελίδες
...lie discovered the important theorem, called " the rule of signs," that in an equation whose roots are all real, the number of positive roots is equal to the number of variations of the signs of its terms tяken in succession, and the number of the negative roots to that of the... | |
 | Charles Davies - 1842 - 368 σελίδες
...of sign, nor the number of negative roots greater than the number of PERMANENCES. 325. Consequence. When the roots of an equation are all real, the number...number of variations, and the number of negative roots is equal to the number of permanences. For, let m denote the degree of the equation, n the number of... | |
 | John Radford Young - 1842 - 276 σελίδες
...and » = »' Consequently, when the roots are all real, the number of positive roots will be exactly equal to the number of variations, and the number of negative roots to the number of permanencies. It must be borne in mind, however, that whether the roots are all real or not, the equation... | |
 | Charles Davies - 1845 - 382 σελίδες
...of signs, nor the number of negative roots greater than the number of PERMANENCES. Consequence. 328. When the roots of an equation are all real, the number...variations of the signs, p the number of permanences ; we shall have m = n + p. Moreover, let n' denote the number of positive roots, and p' the number... | |
 | 1847 - 408 σελίδες
...of signs, nor the number of negative roots greater than the number of PERMANENCES. Consequence. 328. When the roots of an equation are all real, the number...the number of variations, and the number of negative Toots to the number of permanences. For, let m denote the degree of the equation, n the number of variations... | |
 | 1848 - 394 σελίδες
...of signs, nor the number of negative roots greater than the number of PERMANENCES. Consequence. 328. When the roots of an equation are all real, the number of positive roots ii equal to Ike number of variations, and the number of negative roots to the number of permanences.... | |
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VARIATIONS of signs, nor the number of negative roots greater than the number of PERMANENCES. Consequence. 328. When the roots of an equation are all real, the number of positive roots is equal to the number of variations, and the number of negative roots... 
