29. We have in the last chapter made no mention of the physical sciences, because little was to be said, and it seemed expedient to avoid breaking the subject into unnecessary divisions. It is well known that Europe had more obligations to the Saracens in this, than in any other province of research. They indeed had borrowed much from Greece, and much from India; but it was through their language that it came into use among the nations of the west. Gerbert, near the end of the tenth century, was the first who, by travelling into Spain, learned something of Arabian science. A common literary tradition ascribes to him the introduction of their numerals, and of the arithmetic founded on them, into Europe. This has been disputed, and again re-asserted, in modern times.[263] It is sufficient to say here, that only a very unreasonable scepticism has questioned the use of Arabic numerals in calculation during the thirteenth century; the positive evidence on this side cannot be affected by the notorious fact, that they were not employed in legal instruments, or in ordinary accounts; such an argument, indeed, would be equally good in comparatively modern times. These numerals are found, according to Andrès, in Spanish manuscripts of the twelfth century; and, according both to him and Cossali, who speak from actual inspection, in the treatise of arithmetic and algebra by Leonard Fibonacci Pisa, written in 1202.[264] This has never been printed. It is by far our earliest testimony to the knowledge of algebra in Europe; but Leonard owns that he learned it among the Saracens. “This author appears,” says Hutton, or rather Cossali, from whom he borrows, “to be well skilled in the various ways of reducing equations to their final simple state by all the usual methods.” His algebra includes the solution of quadratics. [263] See Andrès, the Archæologia, vol. viii., and the Encyclopædias, Britannic and Metropolitan, on one side, against Gerbert; Montucla, i. 502, and Kästner, Geschichte der Mathematik, i. 35, and ii. 695, in his favour. The latter relies on a well-known passage in William of Malmsbury concerning Gerbert: Abacum certe primus a Saracenis rapiens, regulas dedit, quæ a sudantibus abacistis vix intelliguntur; upon several expressions in his writings, and upon a manuscript of his geometry, seen and mentioned by Pez, who refers it to the twelfth century, in which Arabic numerals are introduced. It is answered, that the language of Malmsbury is indefinite, that Gerbert’s own expressions are equally so, and that the copyist of the manuscript may have inserted the cyphers.