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Short Notes - 2
ARHAT VACANA Kundakunda Jñanapitha, Indore
A LITTLE KNOWN 19TH CENTURY STUDY OF THE GANITA-SARA-SAMGRAHA
Prof. R.C. Gupta*
It is now well-known that Mallana (about A.D. 1100) wrote a Telugu version of the famous Sanskrit work the Ganita - sāra-samgragha (= GSS) of the Jaina Mathematician Mahāvirācārya. Mallana's father was Sivvana and mother Gaurama. His grand - father had received a land-grant from the Eastern Chalukya king Rājarāja Narendra who ruled the Vengi kingdom from 1022 to 1062. Mallana's version of the GSS was not simply its Telugu rendering but contained changes and additions. He seems to have given the name Sāra - samgrah-ganita to his translation which is usually and popularly called Pavuluriganitamu (= PG) after the name of the village to which Mallana belonged. It is the first Telugu work on mathematics. In spite of its importance, only a part of is has been published. Recently the Telugu Academy has entrusted a scholar to edit and bring out the PG fully.
One natural change made by Mallana was to replace the name of Mahāvirācārya's deity Jina by his own diety Siva. Also Mahāvirā's list of 24 decuple terms was extended to 36 tems ending with Mahāsamudra or Sagara (= 1035). Mallana was also justified in adding the units and measures which were prevalent locally. He also added relevant material to mathematical exposition. For example, informing the necklaces of digits, Mahāvirā formed (GSS, 11.2) the necklace 12345654321 by multiplying 27994681 by 441, while Mallana got it by squaring 111111 and gave some longer necklaces. It is only after a critical edition of PG is prepared, that will be able to know the full changes and additions made by Mallana from GSS to PG. But one thing is quite clear - any study of PG will also be essentially a study of GSS on which PG is based.
It so happened that about two centuries ago, a scholar-officer named Benjamin Heyne obtained a copy of the PG. He tried to understand the work with the help of an instructor who possessed the best practical knowledge of the science (of land measurements) as it existed in India. Since Hayne was interested in land - measures and revenue of the country, he translated the sixth chapter entitled Ksetra Ganita from PG into English. This was published as 'A free Translation of the Chetri Ganitam or Field Measuring of the Hindoos', which was included in the Tracts of India (London, 1814).
It seems that he translated only a portion of the chapter but has included lot of land measures e.g. Kunta = one square bamboo = 4096 square feet.
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277, 14 (2-3), 2002
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