dc.date.accessioned 2006-04-04T10:12:57Z dc.date.available 2006-04-04T10:12:57Z dc.date.issued 2005 dc.identifier.uri urn:nbn:de:hebis:34-200604048979 dc.identifier.uri http://hdl.handle.net/123456789/200604048979 dc.format.extent 4587692 bytes dc.format.mimetype application/pdf dc.language.iso ger dc.publisher Universität Kassel, FB 17, Mathematik/Informatik ger dc.subject Historia ger dc.subject Mathematik / Geschichte ger dc.subject Gericke, Helmuth ger dc.subject Diophantus ger dc.subject Negative Zahlen ger dc.subject Geschichte der Zahlen ger dc.subject Bashmakowa, Isabella ger dc.subject Schappacher, Norbert ger dc.subject.ddc 510 dc.title Negative Größen bei Diophant? ger dc.type Preprint dcterms.abstract In this paper we champion Diophantus of Alexandria and Isabella Basmakova against Norbert Schappacher. In two publications ([46] and [47]) he puts forward inter alia two propositions: Questioning Diophantus' originality he considers affirmatively the possibility, that the Arithmetica are the joint work of a team of authors like Bourbaki. And he calls Basmakova's claim (in [5]), that Diophantus uses negative numbers, a "nonsense", reproaching her for her "thoughtlessness". First, we disprove Schappacher's Bourbaki thesis. Second, we investigate the semantic meaning and historical significance of Diophantus' keywords leipsis and mparxis. Next, we discuss Schappacher's epistemology of the history of mathematics and defend Basmakova's methods. Furthermore, we give 33 places where Diophantus uses negative quantities as intermediate results; they appear as differences a - b of positive rational numbers, the subtrahend b being bigger than the minuend a; they each represent the (negative) basis (pleyra) of a square number (tetragonos), which is afterwards computed by the formula (a - b)^2 = a^2 + b^2 - 2ab. Finally, we report how the topic "Diophantus and the negative numbers" has been dealt with by translators and commentators from Maximus Planudes onwards. eng dcterms.accessRights open access dcterms.creator Barner, Klaus dcterms.isPartOf Mathematische Schriften Kassel ger dcterms.isPartOf 05, 04 ger
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