Piero della Francesca is also asserted by Vasari to have been one of the most profound mathematicians of his day, and to have improved perspective and the management of light by an adaptation of geometrical principles to painting. The latter of these opinions has been received, and constitutes the highest claim of this master upon the historians of art. The point has not as yet been illustrated by any writer competent to pronounce with accuracy upon such pretensions,[*144] but the merit of having shown how to ameliorate perspective, especially in architectural design, is generally granted to Piero. Pascoli and others have regarded him as its father. Lanzi thinks him the first who revived the ancient Greek notion of rendering geometry subject to painting in general, although Brunelleschi, Paolo Uccelli, and others had already applied the same principles with less science to architectural details; and he combats the priority in these respects asserted by Lomazzo for Foppa of Brescia. The claims of Leon Battista Alberti,[*145] the architect, seem to have been settled by Vasari's opinion that distance was better described by his pen than delineated by his pencil. The same author enlists our sympathy in favour of Il Borghese, representing him as defrauded of his fame by an unscrupulous scholar, Fra Luca Pacioli, a Franciscan, who, after learning from him mathematics, availed himself of his instructor's after blindness to plagiarise his manuscripts, and eventually published them as his own.[*146] Into this controverted matter we need not enter, further than to pronounce with Tiraboschi, Rosini, and Gaye a verdict of _not proven_, and to observe that the celebrity attained by the friar's scientific works ought to reflect some merit upon his instructor. Yet justice to both parties requires us to extract the generous testimony volunteered to the painter by his pupil, in dedicating to Duke Guidobaldo his Summa de Arithmetica, Geometria, &c.: "Perspective, if closely looked into, would certainly be nothing without the aid of geometry, as has been fully demonstrated by Pietro di Franceschi, our contemporary, and the prince of modern painting. During his assiduous service in your Excellency's family, he composed his short treatise on the art of painting and the power of linear perspective, which is now deservedly placed in your library, rich with books in every branch." These, surely, are not the words of a literary pirate; indeed, Vasari's whole account is vague and confused. After telling us that Pacioli had appropriated the matter of Piero's many MSS., then existing at Borgo San Sepolcro, he adds that most of his writings were deposited in the Urbino library, where it is obvious that neither he nor those who have repeated his assertions ever sought them. After every possible search, I have reason to believe that that library now contains but two treatises by Il Borghese, nor have I found any evidence of others having ever been there.