Characterizing a Sanskrit Mathematical Commentary: An exploration of Pṛthūdaka‘s Vāsanābhāṣya on progressions

Agathe Keller (1)

1 SPHERE UMR 7219 - Sciences, Philosophie, Histoire

Exploring what could have been the particularity of Sanskrit mathematical commentaries in the larger landscape of the scholarly commentaries of South Asia, this article explores how Pṛṭhūdaka (ca. 850) carries out 'explanations' on two mathematical verses of Brahmagupta's Theoretical Astronomical Treatise of the True Brāhma [School] (Brāhmasphuṭasiddhānta-628) concerning progressions. As the commentator explores in many different ways the scope of the rule, a multiplicity of meanings is drawn out, among which one may find the interpretation of a progresssion as a pile of areas of rectangles within a 'proof', or the reading of one procedure as being an algebraical consequence of a previous one. It is within examples and their variations that such mathematical explorations are made, and these may very well be the textual particularity of mathematical commentaries in South Asia.

Mots clés: explanation; upapanna; vāsanā; commentary; Pṛthūdaka; Brahmagupta; bhāṣya; progressions; średdhi; algebraical proof; geometrical representation of arithmetical progressions

Domaines: Histoire, Philosophie et Sociologie des sciences; Histoire et perspectives sur les mathématiques [math.HO]

Agathe Keller. Characterizing a Sanskrit Mathematical Commentary: An exploration of Pṛthūdaka‘s Vāsanābhāṣya on progressions. Karine Chemla; Glenn Most. Mathematical Commentaries in The Ancient World. A global perspective, Cambridge University Press, pp.96-140, 2022, 978-1-108-83957. ⟨10.1017/9781108884488.003⟩. ⟨halshs-03101614⟩