It is evident that the use of the numeral signs does not of itself imply an acquaintance with the Arabic calculation, though it was a necessary step to it. Signs bearing some resemblance to these (too great for accident) are found in MSS. of Boethius, and are published by Montucla, (vol. i. planch. ii.) In one MS. they appear with names written over each of them, not Greek, or Latin, or Arabic, or in any known language. These singular names, and nearly the same forms, are found also in a manuscript well deserving of notice,--No. 343 of the Arundel MSS., in the British Museum, and which is said to have belonged to a convent at Mentz. This has been referred by some competent judges to the twelfth, and by others to the very beginning of the thirteenth century. It purports to be an introduction to the art of multiplying and dividing numbers; quicquid ab abacistis excerpere potui, compendiose collegi. The author uses nine digits, but none for ten, or zero, as is also the case in the MS. of Boethius. Sunt vero integri novem sufficientes ad infinitam multiplicationem, quorum nomina singulis sunt superjecta. A gentleman of the British Museum, who had the kindness, at my request, to give his attention to this hitherto unknown evidence in the controversy, is of opinion that the rudiments, at the very least, of our numeration are indicated in it, and that the author comes within one step of our present system, which is no other than supplying an additional character for zero. His ignorance of this character renders his process circuitous, as it does not contain the principle of juxtaposition for the purpose of summing; but it does contain the still more essential principle, a decuple increase of value for the same sign, in a progressive series of location from right to left. I shall be gratified if this slight notice should cause the treatise, which is very short, to be published, or more fully explained. [264] Montucla, whom several other writers have followed, erroneously places this work in the beginning of the fifteenth century. |Proofs of them in thirteenth century.|