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HISTORY OF ALGEBRA.

TRACT 33.

Ayeen Ackbcry, and in D’Herbelot. Abul Fuzl gives a iistof Sanscrit books, which were translated into Persian inAkbar’s time; among which the Leelawuttee is the only ma-thematical work.

From a comparison of the algebra of the Arabians andGreeks, and that of the modern Europeans, with the Per-sian translations of the Beej Gunnit and Leelawuttee, itwould probably appear, that the algebra of the Arabs isquite different from that of Diophantus, and not taken theone from the other: that if the Arabs did learn from theIndians, as is most probable, they did not borrow largelyfrom them ; that the Persian translations of the Beej Gunnitand Leelawuttee contain principles, w'bich are sufficient forthe solution of any propositions in the Arabian, or in theDiophantine algebra ; that these translations contain propo-sitions, which are not to be solved on any principles thatcould be supplied by the Arabian or the Diophantine alge-bra ; and that the Hindoos were further advanced in somebranches of this science than the modern Europeans, withall their improvements, till the middle of the eighteentheentury.

On Senes, with Extracts from the Leelawuttee.

In the translation of the Leelawmttee there is a chapteron combinations, and another on progressions, as in thefollowing specimens:—

Combinations.

“ To find the number of mixtures of different things.”

“ If it be required to add different things together, sothat all the combinations, arising from their addition, maybe known, this is. the rule:”

“ First write them all, with 1, in order; and below ivrite1 the last opposite the first in order. Then divide the firstterm of the first line by the number which is opposite to itin the second line ; the quotient will be the number of com-