Page:Indian mathematics, Kaye (1915).djvu/47

 Initial vowels are sometimes used as ciphers also. The earliest example of this modified system is of the twelfth century. Slight variations occur. (d) The word-symbol notation.—A notation that became extraordinarily popular in India and is still in use was introduced about the ninth century, possibly from the East. In this notation any word that connotes the idea of a number may be used to denote that number: e.g. Two may be expressed by nayana, the eyes, or karņa, the ears, etc.; seven by aśva, the horses (of the sun); fifteen by tithi, the lunar days (of the half month); twenty by nakha, the nails (of the hands and feet); twenty-seven by nakshatra the lunar mansions; thirty-two by danta, the teeth; etc., etc. (e) The modern place-value notation.—The orthodox view is that the modern place-value notation that is now universal was invented in India and until recently it was thought to have been in use in India at a very early date. Hindu tradition ascribes the invention to God! According to Maçoudi a congress of sages, gathered together by order of king Brahma (who reigned 366 years), invented the nine figures! An inscription of A.D. 595 is supposed to contain a genuine example of the system. According to, the "Indian figures" were known in Syria in A.D. 662; but his authority makes such erroneous statements about "Indian" astronomy that we have no faith in what he says about other "Indian" matters. Certain other mediæval works refer to 'Indian numbers' and so on. On the other hand it is held that there is no sound evidence of the employment in India of a place-value system earlier than about the ninth century. The suggestion of 'divine origin' indicates nothing but historical ignorance; Maçoudi is obviously wildly erratic; the inscription of A.D. 595 is not above suspicion and the next inscription with an example of the place-value system is nearly three centuries