Bhāskara I's versified solutions of a linear indeterminate equation

Abstract : At the end of Bhāskara's 7th century commentary on the mathematical part of the Āryabhaṭīya 91 verses provide solutions of linear indeterminate equations using astral parameters. The number of civil days and the number of revolutions elapsed since the beginning of the Kali Yuga are computed knowing specific mean positions of the Sun, the Moon, the Moon's Apogee, the Moon's ascending node, Mars, Mercury, Jupiter, Venus, Saturn, and the Moon's Anomaly. Other computed elements concern intercalary months, intercalary days, omitted days and the sun's declination. This article provides an English translation of the verses, an explanation and exploration of the data provided. It shows how the verses are used to tabulate data in a compact form. I propose these tables had two aims: first to be used as a tool when solving more elaborate equations; and second as an exploration of the ratios between planet positions and time elapsed, if not a more general exploration of the numbers involved in these ratios.
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Agathe Keller. Bhāskara I's versified solutions of a linear indeterminate equation. Indian Journal of History of Science, 2014, 49 (2), pp.97-126. ⟨halshs-00760116v2⟩

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