03256nam a22004335i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001700153072001600170072002300186072001500209100007600224245014000300250001800440264006900458300004200527336002600569337002600595338003600621347002400657490006800681505033000749520138301079650002202462650001702484650001302501650002402514650003802538710003402576773002602610776003602636776003602672830006802708856004602776978-3-031-48158-1DE-He21320251030112656.0cr nn 008mamaa240729s2024    sz |    s    |||| 0|eng d  a97830314815817 a10.1007/978-3-031-48158-12doi 4aQ124.6-127.2 7aPDX2bicssc 7aSCI0340002bisacsh 7aPDX2thema1 aHøyrup, Jens.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aExplorations and False Trailsh[electronic resource] :bThe Innovative Techniques That Brought About Modern Algebra /cby Jens Høyrup.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aX, 143 p. 15 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aSpringerBriefs in History of Science and Technology,x2211-45720 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. .  aThis book provides a unique perspective on the history of European algebra up to the advent of Viète 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-Khwārizmī, 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 Viète'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 Viète 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. 0aSciencexHistory. 0aMathematics. 0aHistory.14aHistory of Science.24aHistory of Mathematical Sciences.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303148157408iPrinted edition:z9783031481598 0aSpringerBriefs in History of Science and Technology,x2211-457240uhttps://doi.org/10.1007/978-3-031-48158-1