Page:The Hindu-Arabic Numerals (1911).djvu/76

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THE HINDU-ARABIC NUMERALS

tradition has so persistently assigned to Boethius (c. 500 A.D.), and which he would naturally have received, if at all, from these same Neo-Pythagoreans or from the sources from which they derived them. Furthermore, Woepcke points out that the Arabs on entering Spain (711 A.D.) would naturally have followed their custom of adopting for the computation of taxes the numerical systems of the countries they conquered,^[1] so that the numerals brought from Spain to Italy, not having undergone the same modifications as those of the Eastern Arab empire, would have differed, as they certainly did, from those that came through Bagdad. The theory is that the Hindu system, without the zero, early reached Alexandria (say 450 A.D.), and that the Neo-Pythagorean love for the mysterious and especially for the Oriental led to its use as something bizarre and cabalistic; that it was then passed along the Mediterranean, reaching Boethius in Athens or in Rome, and to the schools of Spain, being discovered in Africa and Spain by the Arabs even before they themselves knew the improved system with the place value.

↑ E.g., they adopted the Greek numerals in use in Damascus and Syria, and the Coptic in Egypt. Theophanes (758–818 A.D.), Chronographia, Scriptores Historiae Byzantinae, Vol. XXXIX, Bonnae, 1839, p. 575, relates that in 699 A.D. the caliph Walīd forbade the use of the Greek language in the bookkeeping of the treasury of the caliphate, but permitted the use of the Greek alphabetic numerals, since the Arabs had no convenient number notation: καὶ ἐκώλυοε γράφεσθαι Ἑλληνιοτὶ τοὺς δημοσίους τῶν λογοθεοίων κώδικας, ἀλλ' Ἀραβίοις αὐτὰ παρασημαίνεσθαι, χωρὶς τῶν ψήφων, ἐπειδὴ ἀδύνατον τῇ ἐκείνων γλώσσῃ μονάδα ἢ δυάδα ἢ τριάδα ἢ ὀκτώ ἥμιου ἢ τρία γράφεσθαι· διὸ καὶ ἕως σήμερόν εἰσιν οὺν αὐτοῖς νοτάριοι Χριστιανοί. The importance of this contemporaneous document was pointed out by Martin, loc. cit. Karabacek, "Die Involutio im arabischen Schriftwesen," Vol.CXXXV of Sitzungsberichte d. phil.-hist. Classe d. k. Akad. d. Wiss., Vienna, 1896, p. 25, gives an Arabic date of 868 A.D. in Greek letters.

[1] E.g., they adopted the Greek numerals in use in Damascus and Syria, and the Coptic in Egypt. Theophanes (758–818 A.D.), Chronographia, Scriptores Historiae Byzantinae, Vol. XXXIX, Bonnae, 1839, p. 575, relates that in 699 A.D. the caliph Walīd forbade the use of the Greek language in the bookkeeping of the treasury of the caliphate, but permitted the use of the Greek alphabetic numerals, since the Arabs had no convenient number notation: καὶ ἐκώλυοε γράφεσθαι Ἑλληνιοτὶ τοὺς δημοσίους τῶν λογοθεοίων κώδικας, ἀλλ' Ἀραβίοις αὐτὰ παρασημαίνεσθαι, χωρὶς τῶν ψήφων, ἐπειδὴ ἀδύνατον τῇ ἐκείνων γλώσσῃ μονάδα ἢ δυάδα ἢ τριάδα ἢ ὀκτώ ἥμιου ἢ τρία γράφεσθαι· διὸ καὶ ἕως σήμερόν εἰσιν οὺν αὐτοῖς νοτάριοι Χριστιανοί. The importance of this contemporaneous document was pointed out by Martin, loc. cit. Karabacek, "Die Involutio im arabischen Schriftwesen," Vol.CXXXV of Sitzungsberichte d. phil.-hist. Classe d. k. Akad. d. Wiss., Vienna, 1896, p. 25, gives an Arabic date of 868 A.D. in Greek letters.

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