LEADER 03531nam 22005655 450 001 9910878055703321 005 20241205221029.0 010 $a9783031481581$b(electronic bk.) 010 $z9783031481574 024 7 $a10.1007/978-3-031-48158-1 035 $a(MiAaPQ)EBC31572223 035 $a(Au-PeEL)EBL31572223 035 $a(CKB)33566327300041 035 $a(DE-He213)978-3-031-48158-1 035 $a(EXLCZ)9933566327300041 100 $a20240729h20242024 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aExplorations and false trails $ethe innovative techniques that brought about modern algebra /$fJens Hřyrup 210 1$aCham :$cSpringer,$d2024. 215 $a1 online resource (x, 143 pages) $cillustrations 225 1 $aSpringerBriefs in history of science and technology,$x2211-4572 311 08$aPrint version: Hřyrup, Jens Explorations and False Trails Cham : Springer,c2024 9783031481574 320 $aIncludes bibliographical references and index. 327 $aPreface -- Introduction -- Chapter 1. Geometric proofs -- Chapter 2. Powers of the unknown -- Chapter 3. Abbreviations, glyphs, symbols and symbolic calculation -- Chapter 4. Embedding and parenthesis function -- Chapter 5. Several unknowns -- Chapter 6. The transition to incipient modern algebra -- Bibliography -- Index. . 330 $aThis book provides a unique perspective on the history of European algebra up to the advent of Vičte and Descartes. The standard version of this history is written on the basis of a narrow and misleading source basis: the Latin translations of al-Khw?rizm?, Fibonacci's Liber abbaci, Luca Pacioli's Summa, Cardano's Ars magna?with neither Fibonacci nor Pacioli being read in detail. The existence of the Italian abacus and German cossic algebra is at most taken note of but they are not read, leading to the idea that Vičte's and Descartes' use of genuine symbolism (not only abbreviations), many unknowns, and abstract coefficients seem to be miraculous leaps. This book traces the meandering development of all these techniques along with the mostly ignored but very important parenthesis function, by means of detailed readings of all pertinent sources, including the abacus and cossic algebra and French algebra from Chuquet to Gosselin. It argues for a necessary distinction between abbreviating glyphs and genuine symbols serving within a symbolic syntax, which allows it to trace the emergence of symbolic calculation. Characterization of the mathematical practice of the environment within which Vičte and Descartes moved allows for an explanation of how these two figures did not even need to invent abstract coefficients but rather received them as a gift. 410 0$aSpringerBriefs in history of science and technology.$x2211-4572 606 $aAlgebra$xHistory 606 $aScience$xHistory 606 $aMathematics 606 $aHistory 606 $aHistory of Science 606 $aHistory of Mathematical Sciences 615 0$aAlgebra$xHistory. 615 0$aScience$xHistory. 615 0$aMathematics. 615 0$aHistory. 615 14$aHistory of Science. 615 24$aHistory of Mathematical Sciences. 676 $a509 700 $aHřyrup$b Jens$0390350 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910878055703321 996 $aExplorations and False Trails$94201766 997 $aUNINA