[268] Andrès, ii. 92, gives on the whole the best account of the progress of numerals. The article by Leslie in the Encyclopædia Britannica is too dogmatical in denying their antiquity. That in the Encyclopædia Metropolitana, by Mr. Peacock, is more learned. Montucla is as superficial as usual; and Kästner has confined himself to the claims of Gerbert, admitting which, he is too indifferent about subsequent evidence. |Mathematical treatises.| 31. Adelard of Bath, in the twelfth century, translated the elements of Euclid from the Arabic, and another version was made by Campanus in the next age. The first printed editions are of the latter. The writings of Ptolemy became known through the same channel; and the once celebrated treatise on the Sphere by John de Sacro Bosco (Holywood, or, according to Leland, Halifax) about the beginning of the thirteenth century, is said to be but an abridgment of the Alexandrian geometer.[269] It has been frequently printed, and was even thought worthy of a commentary by Clavius. Jordan of Namur (Nemorarius) near the same time, shows a considerable insight into the properties of numbers.[270] Vitello, a native of Poland, not long afterwards, first made known the principles of optics in a treatise in ten books, several times printed in the sixteenth century, and indicating an extensive acquaintance with the Greek and Arabian geometers. Montucla has charged Vitello with having done no more than compress and arrange a work on the same subject by Alhazen; which Andrès, always partial to the Arabian writers, has not failed to repeat. But the author of an article on Vitello in the Biographie Universelle repels this imputation, which could not, he says, have proceeded from any one who had compared the two writers. A more definite judgment is pronounced by the laborious German historian of mathematics, Kästner. “Vitello,” he says, “has with diligence and judgment collected, as far as lay in his power, what had been previously known; and, avoiding the tediousness of Arabian verbosity, is far more readable, perspicuous, and methodical than Alhazen; he has also gone much farther in the science.”[271] [269] Montucla, i. 506. Biogr. Univ., Kästner. [270] Montucla. Kästner. [271] Gesch. der Mathem. ii. 263. The true name is Vitello, as Playfair has remarked (Dissertat. in Encycl. Brit.), but Vitello is much more common. Kästner is correct, always copying the old editions. |Roger Bacon.|