The Transformation of a Handbook into Tables: The Brahmatulyasāranī and the Karanakutūhala of Bhāskara (2015)
Type of ContentJournal Article
PublisherUniversity of Canterbury. Mathematics and Statistics
AuthorsMontelle, C., Plofker, K.show all
Brahmatulyasarani is the name most often given to a set of tables (Sanskrit sarani/sarini, kosthaka) based on Bhaskara II's astronomical handbook Karanakutuhala or Brahmatulya (epoch 1183 CE), which in turn is a condensed and simplified adaptation of the same author's treatise Siddh anta siromani. The name Brahmatulya means "equal or corresponding to the Brahma," i.e., the Brahmapaksa school of astronomy adhered to by Bhaskara II, which follows the parameters of the Brahmasphutasiddh anta of Brahmagupta (628 CE). The Brahmatulyasarani tables record Brahmapaksa-derived values of planetary mean motions with orbital and geographical corrections for computing their true motions for a given terrestrial location, topics which are addressed in chapters 1-2 of the Karanakutuhala. There are at least five extant manuscripts of the tables of the Brahmatulyasarani, some with occasional expository details in table headers and marginal notes. A brief description of their contents has been published by Pingree [1968, 36-37] based on the manuscripts described in tables 1-4 below; we have used also the so-called Karanakutuhala-sarini in BORI 501/1895-1902. A critical edition of the tables based on these five manuscripts is currently in preparation. One of the Brahmatulyasarani manuscripts also contains (S29, ff. 6r-6v) the only currently known copy of ten verses explaining the use of the tables, plus a colophon and two post-colophon verses on astrological matters; it was copied by an otherwise unknown scribe named Malukacandra. It consists of an invocation and prescribed algorithms for accomplishing fundamental tasks of astronomy: computing planetary mean longitudes measured along the ecliptic for a given date, correcting them for orbital anomalies reckoned from the so-called manda and sighra apogees (see the technical analysis for verses 4-7) while interpolating linearly between tabulated values, and reducing arcs to the appropriate trigonometric quadrant. A few different verse meters are used, primarily sardulavikridita and upajati : several of the verses draw on corresponding text in Karanakutuhala chapter 2 for their style and/or content. In the present paper, we provide a critical edition with transcription, translation, and technical commentary for this very terse explanatory text.
CitationMontelle, C., Plofker, K. (2015) The Transformation of a Handbook into Tables: The Brahmatulyasāranī and the Karanakutūhala of Bhāskara. SCIAMVS: Sources and Commentaries in Exact Sciences, 16, pp. 1-34.
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