[325] The title page of Calandri (1491), for example, represents Pythagoras with these numerals before him. [Smith, _Rara Arithmetica_, p. 46.] Isaacus Vossius, _Observationes ad Pomponium Melam de situ orbis_, 1658, maintained that the Arabs derived these numerals from the west. A learned dissertation to this effect, but deriving them from the Romans instead of the Greeks, was written by Ginanni in 1753 (_Dissertatio mathematica critica de numeralium notarum minuscularum origine_, Venice, 1753). See also Mannert, _De numerorum quos arabicos vocant vera origine Pythagorica_, Nuernberg, 1801. Even as late as 1827 Romagnosi (in his supplement to _Ricerche storiche sull' India_ etc., by Robertson, Vol. II, p. 580, 1827) asserted that Pythagoras originated them. [R. Bombelli, _L'antica numerazione italica_, Rome, 1876, p. 59.] Gow (_Hist. of Greek Math._, p. 98) thinks that Iamblichus must have known a similar system in order to have worked out certain of his theorems, but this is an unwarranted deduction from the passage given. [326] A. Hillebrandt, _Alt-Indien_, p. 179. [327] J. C. Marshman, loc. cit., chaps. i and ii. [328] He reigned 631-579 A.D.; called Nu['s][=i]rw[=a]n, _the holy one_. [329] J. Keane, _The Evolution of Geography_, London, 1899, p. 38. [330] The Arabs who lived in and about Mecca. [331] S. Guyard, in _Encyc. Brit._, 9th ed., Vol. XVI, p. 597. [332] Oppert, loc. cit., p. 29. [333] "At non credendum est id in Autographis contigisse, aut vetustioribus Codd. MSS." [Wallis, _Opera omnia_, Vol. II, p. 11.] [334] In _Observationes ad Pomponium Melam de situ orbis_. The question was next taken up in a large way by Weidler, loc. cit., _De characteribus_ etc., 1727, and in _Spicilegium_ etc., 1755. [335] The best edition of these works is that of G. Friedlein, _Anicii Manlii Torquati Severini Boetii de institutione arithmetica libri duo, de institutione musica libri quinque. Accedit geometria quae fertur Boetii_.... Leipzig.... MDCCCLXVII. [336] See also P. Tannery, "Notes sur la pseudo-geometrie de Boece," in _Bibliotheca Mathematica_, Vol. I (3), p. 39. This is not the geometry in two books in which are mentioned the numerals. There is a manuscript of this pseudo-geometry of the ninth century, but the earliest one of the other work is of the eleventh century (Tannery), unless the Vatican codex is of the tenth century as Friedlein (p. 372) asserts. [337] Friedlein feels that it is partly spurious, but he says: "Eorum librorum, quos Boetius de geometria scripsisse dicitur, investigare veram inscriptionem nihil aliud esset nisi operam et tempus perdere." [Preface, p. v.] N. Bubnov in the Russian _Journal of the Ministry of Public Instruction_, 1907, in an article of which a synopsis is given in the _Jahrbuch ueber die Fortschritte der Mathematik_ for 1907, asserts that the geometry was written in the eleventh century.