The Hindu-Arabic Numerals c9.136

c9.136

⁶ The most noteworthy of these was for a long time Cantor (*Geschichte*, Vol. I., 3d ed., pp. 587–588), who in his earlier days even believed that Pythagoras had known them. Cantor says (*Die römischen Agrimensoren*, Leipzig, 1875, p. 130): "Uns also, wir wiederholen es, ist die Geometrie des Boetius echt, dieselbe Schrift, welche er nach Euklid bearbeitete, von welcher ein Codex bereits in Jahre 821 im Kloster Reichenau vorhanden war, von welcher ein anderes Exemplar im Jahre 982 zu Mantua in die Hände Gerbert's gelangte, von welcher mannigfache Handschriften noch heute vorhanden sind." But against this opinion of the antiquity of MSS. containing these numerals is the important statement of P. Tannery, perhaps the most critical of modern historians of mathematics, that none exists earlier than the eleventh century. See also J. L. Heiberg in *Philologus, Zeitschrift f. d. klass. Altertum*, Vol. XLIII, p. 508. Of Cantor's predecessors, Th. H. Martin was one of the most prominent, his argument for authenticity appearing in the *Revue Archéologique* for 1856–1857, and in his treatise *Les signes numéraux* etc. See also M. Chasles, "De la connaissance qu'ont eu les anciens d'une numération décimale écrite qui fait usage de neuf chiffres prenant les valeurs de position," *Comptes rendus*, Vol. VI, pp. 678–680; "Sur l'origine de notre système de numération," *Comptes rendus*, Vol. VIII, pp. 72–81; and note "Sur le passage du premier livre de la géométrie de Boèce, relatif à un nouveau système de numération," in his work *Aperçu historique sur l'origine et le devéloppement des méthodes en géométrie*, of which the first edition appeared in 1837.