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No. II]
MATHEMATICS OF NEMICANDRA.
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chieftain of the famous King Bhoja of Dhārā (in Malwa). He then composed a short treatise of twenty-six verses, entitled Laghu Dravyasamgraha, for a merchant named Soma and subsequently enlarged it into Brhad-Dravyasamgraha. Our author lived long before the time of King Bhoja. The present article on the mathe. matics of Nemicandra Siddhānta-cakravarti is based wholly on materials furnished by his Gommațasāra and Trilokasāra. So the difference of opinions about his other works just noted does not affect us in the least. It may be mentioned by the way that there is nothing of mathematical interest in the Dravyasamgraha.
Nemicandra as mathematician
· Except the Trilokasāra which treats of the cosmography of the Jaiņas, other works of Nemicandra are devoted to the Jaiva philosophy. As is shown by his title, Siddhānta cakravartā ("Paramount Lord in the Siddhāntas or Jaina Scriptures”), Nemicandra was highly learned in Jaina Scriptures and is still recognised by all as a great authority on them. It appears that he had a fair knowledge also of mathematics. He is found to have employed the law of indices, summation of series, mensuration formulæ for a circle and its segment, and permutations and combinations. It is true that most of those results were not new but were known to the anterior Hindu mathematicians. But if we remember that Nemicandra was essentially a philosopher and a saint, the so much knowledge of an abstruse secular science, as displayed by him, will appear very commendable. Some of his results in combinations we have not so far found in any Hindu work before the fourteenth century of the Christian era.
Arithmetical Notations
From early times there were devised in India various methods for expressing numbers, such as by means of (1) names of things, 1 For a comprehensive account of the nominal notation or word numerals
see the following articles of the author : " Sabda-samkhyā Praņāli ” in the Bangiya Sahitya Párigad Patrikā, 1335 B. S. (=1928-29 A.C.), pp. 8-30 " Näma-samkhyā," Ibid, 1337 B,S., pp. 7-27.
