* J 



492 Journal of the Asiatic Society of Bengal. [July, 1907. 



eager to learn from me, askino^ me at tlie same time from what 

 Hindu master I had learnt those things, whilst in reality I 

 showed them what they were worth, and thoaght myself a great 

 deal superior to them, disdaining to be put on a level with them. 

 They almost thought me a sorcerer . ; . . You mostly find that 

 even the so-called scientific theorems of the Hindus are in a state 

 of utter confusion, devoid of any logical order. " 



Albiruni's statements regarding Hindu mathematics and, in 

 particular, about notation, must be read in the light of the above 

 remarks. Also it must be borne in mind that in Albiruni's time 

 the common notation in use in India was the ' numerical woi^s ' 

 system, and among the Arabs probably the * abjad ' was the popu- 

 lar notation, although in both countries the modern notation was 



possibly well established. 



"The Hindus," Albiruni says, "do not use the letters of 

 their alphabet for numerical notation, as we iTse the Arabic nota- 

 tion in the order of the Hebrew alphabet,* As in different parts 

 of India the letters have different shapes, the numeral signs, too, 

 which are called anka, diffei-. The numeral signs which we use 

 are derived from the fine forms of the Hindu sisrns.^ Sisi'ns and 



D'"^- ~^0 



figures are of no use if people do not know what they mean, but 

 the people of Kashmir mark the single leaves of their books 

 with figures Avhich look like drawings or like Chit»ese character, 



the meaning of which can only be learned by very long practice. 

 However,, they do not use them when reckoning in the sand." 

 (Then follow three pages of disquisition on the orders of 

 numbers on which he states he has written a treatise! He states 

 that the Hindus " extend the names of the orders of numbers 

 until the eighteenth order for religious reasons . * • . Some 

 Hindus maintain that there is a nineteenth order . . . ., 

 but in reality reckoning is unlimited). "The Hindus, " he goes 

 on to say, " use the numeral signs in arithmetic in the same way 

 that we do. I have composed a treatise showing how far, possi- 

 bly, the Hindus are ahead of us in this subject.^ We have al- 



ready explained that the Hindus compose their books in Slokas. 

 If, now, they wish, in their astronomical handbooks, to express 

 some numbei^ of the various orders, they express them by words 

 used to denote certain numbers either in one order alone or at the 

 same time in two orders '*.... Brahmagupta says : " If you 

 want to write one^ express it by ev^erything which is unique, 



1 I take this to mean that they did use an alphabetic notation, but dif- 

 fering in the order of the letters from the ' abjad. ' See notes above on 

 Aryabhata's notation. But the passage is ambiguous. 



^ I do not see how he was in a better position to judge on this point 

 than, say. Canon Taylor, who is certainly wrong in his conclusion. 



S Probably as regards the nomenclature of orders. In Dr. Lardner's 

 Arithmetic (1834) we read, " The names (Sanskrit) for the successive orders 

 of units is carried to a surprising extent *' Mutahhar ibn Tahr notes as a 

 cunosity a pretty high figure ascribed by Indians to the length of the world 

 (Huort p. 29). This appears to have been the distinguishing characteristic. 



* "^^6 Hindus applied the place-value to their numerical word system* 

 The Arabs kept their ahjad unmodified. See my note above- 



