[550] L'État des sciences en France, depute la mort du Roy Robert, arrivée en 1031, jusqu'à celle de Philippe le Bel, arrivée en 1314, Paris, 1741.
[551] Discours sur l'état des lettres en France au XIIIe siecle, Paris, 1824.
[552] Aperçu 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 für 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 Paläographie, 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.
[559] Woepcke, "Sur une donnée historique," etc., loc. cit., and "Essai d'une restitution de travaux perdus d'Apollonius sur les quantités irrationnelles, d'après des indications tirées d'un manuscrit arabe," Tome XIV des Mémoires présentés par divers savants à l'Académie des sciences, Paris, 1856, note, pp. 6-14.