History of Hindu Mathematics: A Source Book v1.c7.s9: 9. Persistence of the Old System
History of Hindu Mathematics: A Source Book v1.c7.s9
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9. Persistence of the Old System
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The occurrence of the old system of writing numbers, with no place-value, is found generally in inscriptions upto the seventh century A.D., after which it was gradually given up in favour of the new system with place-value. Occasional use of the old system, however, is to be met with in Nepal and in some South Indian inscriptions upto the beginning of the tenth century A.D., but after this period the old system seems to have been forgotten, and completely gone out of use. In the seventh century the new system was in general use, but the old system seems to have been given preference in inscriptions. There are a number of grant plates of the eighth century A.D., in which the dates, although written in the old notation, are incorrectly inscribed, showing thereby that people had already forgotten the old system. In a grant plate of Śîlâditya VI,¹ dated the Gupta year 441 (*c.* 760 A.D.), the sign for 40, instead of the sign for 4, has been subjoined to the sign for 100 to denote 400, *i.e.*, 4,000 has been incorrectly written for 400. There is another grant plate, dated the Gâṅgeya year 183 (*c.* 753 A.D.), in which the figure 183 is wrongly written.² This plate is of special interest as it exhibits the use of the old and the new systems in the same document.³ Another very interesting instance of the use of the old and the new systems in one and the same document is the Ahar stone inscription.¹ The document records gifts made on several occasions ranging over thirty-seven years, the last entry corresponding to 905 A.D. In this inscription the old notation is used in the first six lines whilst in the following lines it has been discarded and the new place-value notation appears. It is evident from the forms that the writer did not know the old system. For instance, 200 is written by adding the subscript 2 to the letter *su* (100), instead of using a *mâtṛkâ* sign as in the old system. In the same way the sign for 10 is incorrect in so far as a small zero has been affixed to the usual sign for ten. The inscription shows that although the old system had gone out of use completely, yet people tried to use it in inscriptions, probably for the same reason that makes us use the Roman numerals in giving dates, in numbering chapters of books, and in marking the hours on the face of a clock, even upto the present day.
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¹ *IA*, VI, p. 19, (plate).
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² *EI*, III, p. 133, (plate). In this the sign of 8 is written for 80 and that of 30 for 3. The number 20 has been written by placing a dot after 2.
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³ For other instances showing admixture of both the old and the new systems, see Fleet Gupta Inscriptions, *Corpus Inscriptionum Indicarum*, III, p. 292; also *IA*, XIV, p. 351, where (800) (4) (9)=849.
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¹ C. D. Chatterjee, “The Ahar stone inscription,” *Journ. United Provinces Hist. Soc.*, 1926, pp. 83-119.