LEADER 03757nam 22005055a 450 001 9910153614803321 005 20110329234510.0 010 $a3-03719-592-4 024 70$a10.4171/092 035 $a(CKB)3710000000962493 035 $a(CH-001817-3)127-110329 035 $a(PPN)178155896 035 $a(EXLCZ)993710000000962493 100 $a20110329j20110329 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFrom Cardano's great art to Lagrange's reflections: filling a gap in the history of algebra$b[electronic resource] /$fJacqueline Stedall 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2011 215 $a1 online resource (236 pages) 225 0 $aHeritage of European Mathematics (HEM) ;$x2523-5214 330 $aThis book is an exploration of a claim made by Lagrange in the autumn of 1771 as he embarked upon his lengthy 'Re?flexions sur la re?solution alge?brique des e?quations': that there had been few advances in the algebraic solution of equations since the time of Cardano in the mid sixteenth century. That opinion has been shared by many later historians. The present study attempts to redress that view and to examine the intertwined developments in the theory of equations from Cardano to Lagrange. A similar historical exploration led Lagrange himself to insights that were to transform the entire nature and scope of algebra. Progress was not confined to any one country: at different times mathematicians in Italy, France, the Netherlands, England, Scotland, Russia, and Germany contributed to the discussion and to a gradual deepening of understanding. In particular, the national Academies of Berlin, St Petersburg, and Paris in the eighteenth century were crucial in supporting informed mathematical communities and encouraging the wider dissemination of key ideas. This study therefore truly highlights the existence of a European mathematical heritage. The book is written in three parts. Part I offers an overview of the period from Cardano to Newton (from 1545 to 1707) and is arranged chronologically. Part II covers the period from Newton to Lagrange (from 1707 to 1770) and treats the material according to key themes. Part III is a brief account of the aftermath of the discoveries made in the 1770s. The book attempts throughout to capture the reality of mathematical discovery by inviting the reader to follow in the footsteps of the authors themselves, with as few changes as possible to the original notation and style of presentation. 517 $aFrom Cardano's Great Art to Lagrange's Reflections 517 $aFrom Cardano's Great Art to Lagrange's Reflections 517 $aFrom Cardano's Great Art to Lagrange's Reflections 517 $aFrom Cardano's Great Art to Lagrange's Reflections 517 $aFrom Cardano's Great Art to Lagrange's Reflections 517 $aFrom Cardano's Great Art to Lagrange's Reflections 517 $aFrom Cardano's Great Art to Lagrange's Reflections 517 $aFrom Cardano's Great Art to Lagrange's Reflections 517 $aFrom Cardano's Great Art to Lagrange's Reflections 517 $aFrom Cardano?s Great Art to Lagrange?s Reflections 606 $aHistory of mathematics$2bicssc 606 $aHistory and biography$2msc 615 07$aHistory of mathematics 615 07$aHistory and biography 686 $a01-xx$2msc 700 $aStedall$b Jacqueline$0471736 801 0$bch0018173 906 $aBOOK 912 $a9910153614803321 996 $aFrom Cardano's great art to Lagrange's reflections: filling a gap in the history of algebra$92565454 997 $aUNINA