Reading Algorithms in Sanskrit: How to Relate Rule of Three, Choice of Unknown, and Linear Equation?
Texts in India were transmitted in the context of oral transmissions. A consequence is that their transmission implied memorization. In the written texts that are available to us, it is difficult to locate a precise section on a specific topic if the reader does not know in advance where this section is supposed to be written. A verbal knowledge of the text is required prior to a written one. Algebraic texts in Sanskrit are thus shaped like lists of operations where the progress of the algorithm seems, at first sight, more valued than its understanding. Nevertheless, the prescription of algorithmic operations delivers some clues as to what the author expected his readers to do or to understand. This chapter presents an excerpt from the Bījagaṇitāvataṃsa written by Nārāyaṇa in 14th-century India. The example prescribes an algorithm to set up a linear equation by means of a Rule of Three. Yet, the algorithms presented in the general rule and the one used in the commentary are slightly different. These differences reveal a deep understanding and a deductive interpretation of the rule by the commentator. Tabular setting, choosing unknowns, and Rule of Three played a key role in the elaboration of the reasoning.
KeywordsAlgorithm Unknown Rule of three 14th-century India Nārāyaṇa
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