LEADER 03500nam 2200661Ia 450 001 9910813589903321 005 20200520144314.0 010 $a1-282-93542-9 010 $a9786612935428 010 $a1-4008-2696-9 024 7 $a10.1515/9781400826964 035 $a(CKB)2670000000059261 035 $a(EBL)617545 035 $a(OCoLC)697174426 035 $a(SSID)ssj0000469500 035 $a(PQKBManifestationID)11299156 035 $a(PQKBTitleCode)TC0000469500 035 $a(PQKBWorkID)10531564 035 $a(PQKB)11410623 035 $a(DE-B1597)446440 035 $a(OCoLC)979576704 035 $a(DE-B1597)9781400826964 035 $a(Au-PeEL)EBL617545 035 $a(CaPaEBR)ebr10435959 035 $a(CaONFJC)MIL293542 035 $a(PPN)170235769 035 $a(FR-PaCSA)45003567 035 $a(MiAaPQ)EBC617545 035 $a(EXLCZ)992670000000059261 100 $a20050930d2006 uy 0 101 0 $aeng 135 $aurnn#---|u||u 181 $ctxt 182 $cc 183 $acr 200 10$aGeneral theory of algebraic equations /$fEtienne Bezout ; translated by Eric Feron 205 $aCore Textbook 210 $aPrinceton $cPrinceton University Press$dc2006 215 $a1 online resource (362 p.) 300 $aDescription based upon print version of record. 311 $a0-691-11432-3 327 $tFront matter --$tContents --$tTranslator's Foreword --$tDedication from the 1779 edition --$tPreface to the 1779 edition --$tIntroduction --$tBook One --$tBook Two 330 $aThis book provides the first English translation of Bezout's masterpiece, the General Theory of Algebraic Equations. It follows, by almost two hundred years, the English translation of his famous mathematics textbooks. Here, Bézout presents his approach to solving systems of polynomial equations in several variables and in great detail. He introduces the revolutionary notion of the "polynomial multiplier," which greatly simplifies the problem of variable elimination by reducing it to a system of linear equations. The major result presented in this work, now known as "Bézout's theorem," is stated as follows: "The degree of the final equation resulting from an arbitrary number of complete equations containing the same number of unknowns and with arbitrary degrees is equal to the product of the exponents of the degrees of these equations." The book offers large numbers of results and insights about conditions for polynomials to share a common factor, or to share a common root. It also provides a state-of-the-art analysis of the theories of integration and differentiation of functions in the late eighteenth century, as well as one of the first uses of determinants to solve systems of linear equations. Polynomial multiplier methods have become, today, one of the most promising approaches to solving complex systems of polynomial equations or inequalities, and this translation offers a valuable historic perspective on this active research field. 606 $aEquations, Theory of 606 $aMathematics 615 0$aEquations, Theory of. 615 0$aMathematics. 676 $a512.9/4 686 $aSK 230$qBSZ$2rvk 700 $aBezout$b Etienne$f1730-1783.$0331688 701 $aFeron$b Eric$f1967-$01706029 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910813589903321 996 $aGeneral theory of algebraic equations$94093183 997 $aUNINA