1882.] Br. A. F. U. Iloernle— 0/i a lirch-larh Manuscript, 109 



early lost to Hindu civilization through the Muhammadan conquests, 

 during which it was a common practice to bury MSS. to save them from 

 destruction, the Bakhshali MS. may be referred to the 8th or 9th century 

 A. D. 



" I have looked over all the leaves of the MS. that remain, and have 

 carefully read and transcribed about one-third. I have thus seen enough 

 of the fragment to make sure that the whole of it treats of Arithmetic 

 (including apparently Mensuration), though incidentally a few rules of 

 Algebra are noticed. The latter refer to the solution of indeterminate 

 problems {kuttaha). The arithmetical problems are of various sorts; e. g., 

 on velocity, alligation, profit and loss, etc. I may give one or two exam- 

 ples : thus " A and B run 5 and 9 yojanas a day respectively, and A is 

 allowed a start of 7 days or 35 yojanas ; when will A and B meet ?" 

 Or, " A and B earn 1\ and \\ dindras a day respectively ; A makes a pre- 

 sent of 10 dindras to B; how soon will their possessions be equal?" 

 An example of an algebraical problem is : '^ A certain quantity, whether 

 6 be added to it or 7 be subtracted from it, is a square ; what is that 

 quantity?" The solution, given in this case, is 11 ; for 11 + 5 = 16 or 

 4^, and 11 — 7 = 4 or 2^. The fragment, however, evidently does not con- 

 tain the whole of the treatise on Arithmetic ; for many subjects, commonly 

 treated in Hindu arithmetical works, do not appear to occur in it ) and 

 this is confirmed by the numbers of the rules (or sutras, as they are called). 

 The earliest numbered sutra that I have noticed is the 9th, and from 

 internal evidence I conclude, — though the numbers are lost, — that the 7th 

 and 8th rules are also preserved. The latest number I have met is the 

 57th. 



" The method observed in the treatment of the problems is as follows : 

 first a rule is given, introduced by the word siitra ; next follow one, or 

 more, examples, introduced by tadd, and stated both in words and in arith- 

 metical notation ; the latter is sometimes indicated by the term sthdpana ; 

 next follows a solution in words, which is always called karana " opera- 

 tion" ; and lastly comes the proof, generally expressed in notation, and 

 called pratydyana or pratyaya. This method differs considerably from that 

 used in other Hindu arithmetical treatises, e, g., in those of Bhaskara and 

 Brahmagupta. The latter also use different terms ; instead of tadd, exam- 

 ples are called by them uddesa or uddharana ; instead of sthdpana they 

 have nydsa; harana 2CCi^ pratydyana oy pratyaya are not used at all. The 

 term sutra they employ occasionally, but in most cases they say karana- 

 sutra ; which latter term may contain a reference to a karana-\NQ)\i\L such as 

 that in the Bakhshali MS. There are, also, some differences in the 

 method of notation as used in this MS. and as commonly established. 

 Division is indicated by placing one quantity under another without a line 



