Page:Indian mathematics, Kaye (1915).djvu/41

 VI. 22. According to the Hindus the modern place-value system of arithmetical notation is of divine origin. This led the early orientalists to believe that, at any rate, the system had been in use in India from time immemorial; but an examination of the facts shows that the early notations in use were not place-value ones and that the modern place-value system was not introduced until comparatively modern times. The early systems employed may be conveniently termed (a) the Kharoshthī, (b) the Brāhmī, (c) Āryabhata's alphabetic notation, (d) the word-symbol notation. (a) The Kharoshthī script is written from right to left and was in use in the north-west of India and Central Asia at the beginning of the Christian era. The notation is shown in the accompanying table. It was, apparently, derived from the Aramaic system and has little direct connection with the other Indian notations. The smaller elements are written on the left. (b) The Brāhmī notation is the most important of the old notations of India. It might appropriately be termed the Indian notation for it occurs in early inscriptions and was in fairly common use throughout India for many centuries, and even to the present day is occasionally used. The symbols employed varied somewhat in form according to time and place, but on the whole the consistency of form exhibited is remarkable. They are written from left to right with the smaller elements on the right. Several false theories as to the origin of these symbols have been published, some of which still continue to be recorded. The earliest orientalists gave them place-value, but this error soon