Brahmagupta's apodictic discourse
Le discours apodictique de Brahmagupta
Résumé
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.
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