[268] Al-[H.]a[s.][s.][=a]r's forms, Suter, _Bibliotheca Mathematica_, Vol. II (3), p. 15. [269] Woepcke, _Sur une donnee historique_, etc., loc. cit. The name _[.g]ob[=a]r_ 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 Gob[=a]r[=i] et Haw[=a][=i]," _Atti dell' accademia pontificia dei nuovi Lincei_, Vol. XIX. The adjective applied to the forms in 5 is _gob[=a]r[=i]_ 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 ueber die Fortschritte der Mathematik_. [274] This title was first applied to Roman emperors in posthumous coins of Julius Caesar. 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 Boetius. 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 _Encyclopaedia Britannica_. [276] His father, Flavius Manlius Boethius, was consul in 487. [277] There is, however, no good historic evidence of this sojourn in Athens. [278] His arithmetic is dedicated to Symmachus: "Domino suo patricio Symmacho Boetius." [Friedlein ed., p. 3.] [279] It was while here that he wrote _De consolatione philosophiae_. [280] It is sometimes given as 525. [281] There was a medieval tradition that he was executed because of a work on the Trinity. [282] Hence the _Divus_ in his name. [283] Thus Dante, speaking of his burial place in the monastery of St. Pietro in Ciel d'Oro, at Pavia, says: "The saintly soul, that shows The world's deceitfulness, to all who hear him, Is, with the sight of all the good that is, Blest there. The limbs, whence it was driven, lie Down in Cieldauro; and from martyrdom And exile came it here."--_Paradiso_, Canto X.