death by J. Roediger
and A. Mueller. The first volume contains the Arabic text and the second
volume contains critical notes upon it.

[266] Like those of line 5 in the illustration on page 69.

[267] Woepcke, _Recherches sur l'histoire des sciences mathematiques chez
les orientaux_, loc. cit.; _Propagation, _p. 57.

[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] I