[347] De ratione abaci. In this he describes "quandam formulam, quam ob honorem sui praeceptoris mensam Pythagoream nominabant ... a posterioribus appellabatur abacus." This, as pictured in the text, is the common Gerbert abacus. In the edition in Migne's Patrologia Latina, Vol. LXIII, an ordinary multiplication table (sometimes called Pythagorean abacus) is given in the illustration.
[348] "Habebant enim diverse formatos apices vel caracteres." See the reference to Gerbert on p. 117.
[349] C. Henry, "Sur l'origine de quelques notations mathématiques," Revue Archéologique, 1879, derives these from the initial letters used as abbreviations for the names of the numerals, a theory that finds few supporters.
[350] E.g., it appears in Schonerus, Algorithmus Demonstratus, Nürnberg, 1534, f. A4. In England it appeared in the earliest English arithmetical manuscript known, The Crafte of Nombrynge: "¶ fforthermore ye most vndirstonde that in this craft ben vsid teen figurys, as here bene writen for ensampul,
[351] Friedlein ed., p. 397.
[352] Carlsruhe codex of Gerlando.
[353] Munich codex of Gerlando.
[354] Carlsruhe codex of Bernelinus.
[355] Munich codex of Bernelinus.