[269] Woepcke, Sur une donnée historique, etc., loc. cit. The name ġobār is not used in the text. The manuscript from which these are taken is the oldest (970 A.D.) Arabic document known to contain all of the numerals.
[270] Silvestre de Sacy, loc. cit. He gives the ordinary modern Arabic forms, calling them Indien.
[271] Woepcke, "Introduction au calcul Gobārī et Hawāī," Atti dell' accademia pontificia dei nuovi Lincei, Vol. XIX. The adjective applied to the forms in 5 is gobārī and to those in 6 indienne. This is the direct opposite of Woepcke's use of these adjectives in the Recherches sur l'histoire cited above, in which the ordinary Arabic forms (like those in row 5) are called indiens.
These forms are usually written from right to left.
[272] J. G. Wilkinson, The Manners and Customs of the Ancient Egyptians, revised by S. Birch, London, 1878, Vol. II, p. 493, plate XVI.
[273] There is an extensive literature on this "Boethius-Frage." The reader who cares to go fully into it should consult the various volumes of the Jahrbuch über die Fortschritte der Mathematik.
[274] This title was first applied to Roman emperors in posthumous coins of Julius Cæsar. Subsequently the emperors assumed it during their own lifetimes, thus deifying themselves. See F. Gnecchi, Monete romane, 2d ed., Milan, 1900, p. 299.
[275] This is the common spelling of the name, although the more correct Latin form is Boëtius. See Harper's Dict. of Class. Lit. and Antiq., New York, 1897, Vol. I, p. 213. There is much uncertainty as to his life. A good summary of the evidence is given in the last two editions of the Encyclopædia Britannica.
[276] His father, Flavius Manlius Boethius, was consul in 487.
[277] There is, however, no good historic evidence of this sojourn in Athens.