Vol. lII,':lT(i. 7.] 2 "^'^otes^oH Indian Mathematics. 477' 



[iV^,^.] 



use 



language witL. any 

 people have generally follo^^^d the same lines, some indication 



Would probably appear in the language. "-' , . 



In the early stages of any language^ we generally find that 

 the smaller elements of the higher numbers are expressed first. 

 Thus we'have'^u;o and himd seofontig in Alfred's Chronicle for our 

 modern seventy -"two; and the Gennans still keep to this old 

 fashion much more than we do. In Herodotus we find such ex- 

 amples as the following : iirra Kat StrjKoatat Kai ;^iXtat ; and in Sans*' 



krit there are numberless examples with the names of the smallei' 

 numbers placed first. Such examples as fifteen^ quinta decima^ 

 tryodaca^ dreizehn^ etc^ etc., are found in many languages. 

 .;. The popular idea that the order of our (European) arith- 

 m'etical notation is the moi^e natural and convenient order ^ is not 

 correct. Our order is. inconvenient and clumsy -and the reverse 

 order would be much more suitable ,^ If >ve adopted the reverse 

 order we should write the present year of the Christian era 7091 

 instead of* 1907. The order in which we do write our numbers is 

 contrary to the nature of our script and has been imposed on us 

 by a people with a right to left script; This conclusion, if gene- 

 rally 



appear to dispose of the 

 question as to the notation in use being of Indian origin. But 

 there are many complications that liave to be cleared away. In 

 some cases the scx^ipts in use have actually changed in their order 

 of writing, but as this was, in nxost instances, long before arithme- 

 tical notation was well developed, it does not gi^eatly affect the 

 ^question. In the time of Herodotus houstrophedon writing had 

 vanished and the left to right order had been generally adopted. 

 Herodotus therefore followed the natural order in writing his 

 smaller elements first. The Greek notation of the time also 



followed the same plan. We have numerous examples on coins 



^uch as A n P ( = l-f 80-f-lpO) and H I ( = 8 + 10,). However, 

 ^ome time about the beginning of the Christian era, a change 

 took place and both the number, words and symbols began to be 

 written in the reverse order, e.^., P S ( = 100 + 60 + 9). Here 

 is a change that complicates mattei's and which, as far as I 

 jaiqw, has not yet been explained. , ' ^ 



But the notations that are of special interest to us now are 

 those that immediately preceded our modem notation in India, 

 J^irst thez^e is the notation that may be termed ' old Indian.'^ It 

 is a decimal notation, but does not recognise the value of position, 

 ,and separate sets of symbols were used for the units, tens, 

 hundreds, etc,, e.g.^ two hundred' and twenty-two was expressed 



wTitten 

 first as in . the example just given, where Y^ is equivalent to 200, 



by T 7^ and so otu 



9 to 20 and r^ to 2. TLas order was in opposition to the early 



-*— - 



,:_i 



1 So stated to be by Sir E. C. Bajley. 

 . : 2 See Ferry'a Practical Mathematics and' any work on th^ theory of 

 iiambers. , . - , 



* Sometimes called BrahmTj or ' numerical Bymbols.' 



i 



