________________
82
INDIAN ANTIQUARY, VOL. XXXIII, 1904; APPENDIX.
[$ 34, B.
In 1877, I agreed with him, and Keen likewise concurred, but explained the 4 and 5 as combinations of four and five strokes, arranged in the form of letters. But BURNELL differed entirely. He denied that the older "cavo-numerals," with the exception of rare cases, resemble letters, and dwelt strongly on the impossibility of finding a principle, according to which the Akşaras of the MSS. have been converted into numerals. He further pointed out the general agreement of the principles of the Indian system with those of the Demotic notation of the Egyptians. From this fact, as well as from the resemblance [78] of the Demotic signs for 1 to 9 to the corresponding Indian symbols, be inferred that the cave-numerals" have been borrowed from Egypt, and after farther modifications have been converted into Akşaras. Finally, E. C. BAYLEY tried to show in his lengthy essay, quoted above, that, thongh the principles of the Indian system have been derived from the bieroglyphic notation of the Egyptians, the majority of the Indian symbols have been borrowed from Phoenician, Bactrian, and Akkadian figures or letters, while for a few a foreign origin is not demonstrable.
BAYLEY's explanation offers great difficulties, inter alia by the assumption that the Hindus borrowed from four or five different, partly very ancient and partly more modern, sources. Bat the comparative table of the Egyptian and Indian signs given in his paper, and his remarks about the agreement of their methods in marking the hundreds, induce me to give up BHAGVĀNLĀL's hypothesis, and to adopt, with certain modifications, the view of BORNELL, with whom also BARTH concurs. It seems to me probable that the Brāhma numeral symbols are derived from the Egyptian Hieratic figures, and that the Hindus effected their transformation into Aksaras, because they were already accustomed to express numerals by words (compare below, $ 35, A).
This derivation, the details of which, however, still present difficulties and cannot be called certain, has been given in Appendix II. to the 2nd edition of my Indian Studies No. III. But two other important points may be considered as certain : -- (1) That the varying forms in the Asoka edicts show these numerals to have had a longer history in the 3rd century B. C.; and (2) that the signs have been developed by Brahmanical schoolmen, since they include two forms of the Upadhmaniya, which without doubt has been invented by the teachers of the Sikşā.
B. - The decimal notation, For the decimal notation, now occasionally called ankapalli, the Hindus used originally the ankas or the units of the ancient system, together with the cipher or naught, which originally consisted of the sünyalindu, the dot (marking a blank, see below, $ 35, E), called by abbreviated names sünya and lindu (see BW.). Very likely this system is an invention of the Hindu mathematicians and astronomers, made with the help of the Abacus (BURNELL, BAYLEY). If HOERNLE's very probable estimate of the antiquity of the arithmetical treatise, contained in the Bakhshäli MS., is correct, its invention dates from the beginning of our era or even earlier. For, in that work the decimal notation is used throughout. At all events, it was known to Varāhamibira (6th century A. D.), who employs the word anka, " the decimal figures," in order to express the numeral 9 (Pai casiddhāntikā, 18, 33; compare below, $ 35, A). Its most important element, the cipher or naught, is mentioned in Subandhu's Vāsavadatta, which Bāna (about A. D. 620) praises as a famous book. Subandhu compares the stars with "ciphers (sünyabindavah) which the Creator, while calculating the value of) the universe, on account of the absolute wortbleesness of the Samsāra marked with his chalk, the crescent of the moon, all over the firmament which the darkness made similar to a skin blackened with ink." The cipher, known to Sabandbu, of course consisted of a dot, like that of the Bakshäli MS. (plate IX, B, col. IX.). 1 IA. 6, 143.
9 BESIP, 65, note 1. * Compare HOERNLE'S orplanation, Seventh Oriental Congress, Aryan Sectiou, 192; IA. 17, 36. • IA, 17, 88.
• Vieavadatta (od. F. E, HALL), p. 182.
