TRACT 3€.

HISTORY OF ALGEBRA.

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any other than that of Diophantus . If there be any doubtof Diophantus ’s algebra being of Greek origin, it may beworthy of remark, that at Alexandria he might have hadthe means of access to Indian literature. The Bija Ganitais, indeed, of comparatively modern date; but we mustnot forget that it is extracted from other books, as stated byMr. Davis, in the Asiatic Researches, in a very learnedarticle on the cycle of 60 years. And it is not un-likely that there are old Hindu treatises, from whichnot only the Bija Ganita, but even the algebra of Dio­ phantus , and that of the Arabs , may have been derived.

The other work, the Lilawati, as before-mentioned, ison arithmetic, mensuration, &c. In the introduction, wefind that “ the collector of the book Lilawati was BhaskerAcbarya, of Bidder city,” on the northern confines ofHindustan. And “ though the date of it is not known,yet in another book, made in the year 1105 of Salbahan,the reason of making the Lilawati is given.” In theAyeen Akbery (a Persian work on the manners, history,laws, &c, of the Hindus, translated, by Gladwin), we find“ that Acbarya among the followers of Jine, is one who ex-plains any'difficulties that may occur to noviciates;” andtherefore we may conclude that Bhasker was an instructorin mathematics. Now, the Salbahan, according to theHindu chronology, commenced Anno Dom. 80; hence thisbook must have been written in’ 11S5. But, all that can beinferred from this is, that in I1&5 they did not know whenBhasker lived.

The Lilawati begins with the first rules of arithmetic,and goes through fractions, the extraction of roots, &c,with a good deal of what we should call alligation. Likens, they mark every 3d figure from the place of units, inextracting the cube root. A part towards the end is upon“ forms,” somewhat similar it seems to our permutations.The numeral figures have been gradually' varied from theoriginal of the Hindus as in the following specimens :