[547] "Sinistrorsum autera scribimus in hac arte more arabico sive iudaico, huius scientiae inventorum." [Curtze, loc. cit., p. 7.] The Plimpton manuscript omits the words "sive iudaico." [548] "Non enim omnis numerus per quascumque figuras Indorum repraesentatur, sed tantum determinatus per determinatam, ut 4 non per 5,..." [Curtze, loc. cit., p. 25.] [549] C. Henry, "Sur les deux plus anciens traites francais d'algorisme et de geometrie," Boncompagni _Bulletino_, Vol. XV, p. 49; Victor Mortet, "Le plus ancien traite francais d'algorisme," loc. cit. [550] _L'Etat des sciences en France, depute la mort du Roy Robert, arrivee en 1031, jusqu'a celle de Philippe le Bel, arrivee en 1314_, Paris, 1741. [551] _Discours sur l'etat des lettres en France au XIII^e siecle_, Paris, 1824. [552] _Apercu historique_, Paris, 1876 ed., p. 464. [553] Ranulf Higden, a native of the west of England, entered St. Werburgh's monastery at Chester in 1299. He was a Benedictine monk and chronicler, and died in 1364. His _Polychronicon_, a history in seven books, was printed by Caxton in 1480. [554] Trevisa's translation, Higden having written in Latin. [555] An illustration of this feeling is seen in the writings of Prosdocimo de' Beldomandi (b. c. 1370-1380, d. 1428): "Inveni in quam pluribus libris algorismi nuncupatis mores circa numeros operandi satis varios atque diversos, qui licet boni existerent atque veri erant, tamen fastidiosi, tum propter ipsarum regularum multitudinem, tum propter earum deleationes, tum etiam propter ipsarum operationum probationes, utrum si bone fuerint vel ne. Erant et etiam isti modi interim fastidiosi, quod si in aliquo calculo astroloico error contigisset, calculatorem operationem suam a capite incipere oportebat, dato quod error suus adhuc satis propinquus existeret; et hoc propter figuras in sua operatione deletas. Indigebat etiam calculator semper aliquo lapide vel sibi conformi, super quo scribere atque faciliter delere posset figuras cum quibus operabatur in calculo suo. Et quia haec omnia satis fastidiosa atque laboriosa mihi visa sunt, disposui libellum edere in quo omnia ista abicerentur: qui etiam algorismus sive liber de numeris denominari poterit. Scias tamen quod in hoc libello ponere non intendo nisi ea quae ad calculum necessaria sunt, alia quae in aliis libris practice arismetrice tanguntur, ad calculum non necessaria, propter brevitatem dimitendo." [Quoted by A. Nagl, _Zeitschrift fuer Mathematik und Physik, Hist.-lit. Abth._, Vol. XXXIV, p. 143; Smith, _Rara Arithmetica_, p. 14, in facsimile.] [556] P. Ewald, loc. cit.; Franz Steffens, _Lateinische Palaeographie_, pp. xxxix-xl. We are indebted to Professor J. M. Burnam for a photograph of this rare manuscript. [557] See the plate of forms on p. 88. [558] Karabacek, loc. cit., p. 56; Karpinski, "Hindu Numerals in the Fihrist," _Bibliotheca Mathematica_, Vol. XI (3), p. 121.