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Brahmagupta’s Apodictic Discourse

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Bibliographic Details
Title: Brahmagupta’s Apodictic Discourse
Authors: Kichenassamy, Satyanad
Contributors: Kichenassamy, Satyanad
Source: Ganita Bharati. 41:1-21
Publisher Information: Printspublications Private Limited, 2020.
Publication Year: 2020
Subject Terms: Discourse Analysis, Brahmagupta, derivations, [MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM], Apodicticité, 16. Peace & justice, linear congruences, kuṭṭaka, algebraic identities, [SHS.HISPHILSO] Humanities and Social Sciences/History, Philosophy and Sociology of Sciences, [MATH.MATH-HO] Mathematics [math]/History and Overview [math.HO], history of mathematics, Lemme de Gauss, algebra in several variables, [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]
Description: We continue our analysis of Brahmagupta’s Brāhmasphuṭasiddhānta (India, 628), that had shown that each of his sequences of propositions should be read as an apodictic discourse: a connected discourse that develops the natural consequences of explicitly stated assumptions, within a particular conceptual framework. As a consequence, we established that Brahmagupta did provide a derivation of his results on the cyclic quadrilateral. We analyze here, on the basis of the same principles, further problematic passages in Brahmagupta’s magnum opus, regarding number theory and algebra. They make no sense as sets of rules. They become clear as soon as one reads them as an apodictic discourse, so carefully composed that they leave little room for interpretation. In particular, we show that (i) Brahmagupta indicated the principle of the derivation of the solution of linear congruences (the kuṭṭaka) at the end of chapter 12 and (ii) his algebra in several variables is the result of the extension of operations on numbers to new types of quantities – negative numbers, surds and “non-manifest” variables.
Document Type: Article
Other literature type
File Description: application/pdf
ISSN: 0970-0307
DOI: 10.32381/gb.2019.41.1-2.1
Access URL: https://hal.archives-ouvertes.fr/hal-03147427v2/file/20-GB-repr.pdf
Accession Number: edsair.doi.dedup.....e70983af73f92feda9c408fb16306feb
Database: OpenAIRE
Description
Abstract:We continue our analysis of Brahmagupta’s Brāhmasphuṭasiddhānta (India, 628), that had shown that each of his sequences of propositions should be read as an apodictic discourse: a connected discourse that develops the natural consequences of explicitly stated assumptions, within a particular conceptual framework. As a consequence, we established that Brahmagupta did provide a derivation of his results on the cyclic quadrilateral. We analyze here, on the basis of the same principles, further problematic passages in Brahmagupta’s magnum opus, regarding number theory and algebra. They make no sense as sets of rules. They become clear as soon as one reads them as an apodictic discourse, so carefully composed that they leave little room for interpretation. In particular, we show that (i) Brahmagupta indicated the principle of the derivation of the solution of linear congruences (the kuṭṭaka) at the end of chapter 12 and (ii) his algebra in several variables is the result of the extension of operations on numbers to new types of quantities – negative numbers, surds and “non-manifest” variables.
ISSN:09700307
DOI:10.32381/gb.2019.41.1-2.1