Vol. Ill, No. 7.] Notes on Indian Mathematics, 495 



it for the purpose for which it was invented. Sir R. Temple has 

 shown us [Ind.Antiq. xx. 53f.] that both the old system of notation 

 and the old methods of operation are still in use in Burma, India 

 and Tibet. " To the present day," he writes, " the very crudest 

 notions of arithmetical notation largely prevail in Burma • . . . 

 thus : — 1,000,100,30,9 is used to represent 1139. In Upper Burma 

 mercantile accounts are frequently kept by the ordinary people in 



this way This peculiarity yields a possible explanation of this 



system of arithmetic, which would appear to have arisen from this 

 method of notation.'* Sir R. Temple explains that this system which 

 employs the essentials of the old notation (with modem symbols) 

 and the old methods of operation, and ignores the advantages of 

 the modern notation, is that in use amongst the Phongyis or Bur- 

 mese Buddhist priests and the astrologers — amongst those who 

 have not been educated on a foreign plan. Sir R. Temple also 



says: " Mr. S. B. Dikshit informs me that a system of arithmetic 



nearly corresponding ^ to that of the Burmese is still, he believes, 

 in vogue all over India among Hindu astrologers. A Lama showed 

 Sir R. Temple that the system taught him in the indigenous 



monastic schools in Tibet was much the same. 



I have been informed that in purely indigenous schools of the 

 present day it is common for the pupils to learn their multi- 

 plication tables up to 100 X 100, and, until a short tinle ago, in the 

 Grovernment schools of the United Provinces, the pupils were com- 

 pelled to learn at least up to 40 x 40. Mr. H. Sharp in his " Rural 

 Schools in the Central Provinces" tells us that children not only 

 learn the multiplication table as far as 100 x 100, but tables of 

 squares even higher. **I have found,** he says, "a very small 

 boy who could tell without a moment's hesitation, the square of 

 any number up to 1,000." This enormous range of tables was a 

 necessary concomitant of the old notation and its survival is a 

 curious phenomenon. 



In a recent work* we read that in the section entitled Alga- 

 rithzms of Brahmagupta's mathematics: **We have undoubtedly 

 the numeration and notation of the Hindu (t.e., oar own) system 

 given and perhaps explained." Further on we read : " In the 

 twelfth century Bhaskara composed a fuller and more valu- 

 able work (than Brahmagupta's) on arithmetic," and, " undoubted- 

 ly, there was a race of scholars dui'iug the intervening centuries 

 (between Brahmagupta and Bhaskara) to whom was due the 

 maintenance, if not the extension, of Hindu learning .... Thus 

 (through M. Bin Musa) the mathematical writings of the Hindus 

 became known to the Arabians and especially the wondrous system 

 of notation * having nine digits and a cipher, with device of place/ " 

 I give these quotations, which are severally untrue, from this 

 particular work (otherwise valuable and interesting) partly to 

 illustrate the popular misconceptions of the subject of Hindu 

 mathematics and their influence, and partly as pegs on which to 



I The differences are minor and do not affect the present queation 

 * The Story of Arithmetic — S. Carriugton, 



