226 MB. R. HAELEY ON IMFOSSIBLE 



the Vijcu-ganitaj and the remaining records of ancient 

 Oriental science. Of these circumstances, one is afforded 

 by the first example of a quadratic equation, which occurs 

 in the Vija-ganita. That example is as follows : — (see pp. 

 211-12 of Algebra, with Arithmetic and Mensuration, from 

 the Sanscrit of Brahmegupta and Bhascara. Translated 

 by Henry Thomas Colebrooke, Esq., F.R.S., &c. &c. &c. 

 London: Murray, 1817. * * *) 



" * The square root of half the number of a swarm of 

 bees is gone to a shrub of jasmin, and so are eight-ninths 

 of the whole swarm : a female is buzzing to one remaining 

 male that is humming within a lotus, in which he is con- 

 fined, having been allured to it by its fragrance at night. 

 Say, lovely woman, the number of bees ? ' 



** To solve this problem, we are directed to * put the 

 number of the swarm of bees ya, v, 2.' In this expression, 

 ya is an abbreviation of yavat-tavat, of which the literal sig- 

 nification is, ' so much as,' and of which the meaning is an 

 unknown quantity ; v indicating that ya is to be squared, 

 and 2, that twice the square is to be taken. In modern 

 notation, this assumption would be represented by 2^' ; 

 but, the qiccesitum of the problem being the number of bees 

 in the swarm, why was not ya 1 (or a) taken to repre- 

 sent that number ? It was not to avoid fractions, because, 

 with that assumption, fractions occur in the statement of 

 the question, and, moreover, such a purpose would only 

 account for the occurrence of the co-efficient 2. As little 

 was that assumption a capricious or accidental one, as we 

 may see from the next example in the Vija-ganita. (Cole- 

 brooke, p. 212, Art. 133; and pp. 30 — 1,) which is: — 



** * The son of Pritha, exasperated in combat, shot a 

 quiver of arrows to slay Carna. With half his arrows he 

 parried those of his antagonist ; with four times the square 

 root of the quiver full, he killed his horse ; with six arrows 

 he slew Salya ; with three he demolished the umbrella. 



