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Leonardo was a trader, who had learned the art during his voyages to Barbary, and his treatise and that of Mahommed were the sole literature on the subject up to the year 1494, when Fra Luca Pacioli da Borgo brought out his volume treating of Arithmetic and Algebra as well. This was the first printed work on the subject. After the invention of printing the interest in Algebra grew rapidly.
This handsome man of thirty, in the fur-trimmed vest and red cap, with the dark eyes, long locks, and refined thoughtful face, touched with an air of melancholy, may well be the brilliant cavalier who played so great a part at the Moro's court, the patron of Leonardo and Luca Pacioli, and the loyal servant of Duchess Beatrice.
As a statesman, let each man judge him as he pleases; a foreigner will hesitate to pronounce what was due to human guilt and what to circumstances in the fate of Florence, but no more unjust charge was ever made than that in the field of culture Lorenzo was the protector of mediocrity, that through his fault Leonardo da Vinci and the mathematician Fra Luca Pacioli lived abroad, and that Toscanella, Vespucci, and others at least remained unsupported.
French Italian chroniclers alike own the fascination of his handsome presence and extol the gentilezza of this very perfect knight. Leonardo da Vinci and Luca Pacioli the mathematician had in him a noble, generous patron, and Baldassare Castiglione, who knew him in his youth at Milan, has enshrined his memory in the pages of his "Cortigiano."
It ends with information as to house-rent, letters of credit and exchange, tables of interest, games of chance, mensuration, and weights and measures. In an appendix Cardan examines critically the work of Fra Luca Pacioli da Borgo, an earlier writer on the subject, and points out numerous errors in the same.
Thausing tells us his work shows certain resemblances to that of Luca Pacioli, a companion of Leonardo's, who may have been the "man who is willing to teach me the secrets of the art of perspective," and whom Duerer in 1506 travelled from Venice to Bologna to see; it is even possible that he saw Leonardo himself in the latter town.
But his love of art and learning was as great as ever, and Fra Luca Pacioli, the able mathematician, who came to Milan in 1496, and dedicated his treatise of La Divina Proporzione to Lodovico, describes the laudable and scientific duel of famous and learned men, that was held on the 9th of February, 1498, in the Castello of Milan "that invincible fortress of the glorious city which is a residence worthy of His Excellency."
As a statesman, let each man judge him as he pleases; a foreigner will hesitate to pronounce what in the fate of Florence was due to human guilt and what to circumstances, but no more unjust charge was ever made than that in the field of culture Lorenzo was the protector of mediocrity, that through his fault Leonardo da Vinci and the mathematician Fra Luca Pacioli lived abroad, and that Toscanella, Vespucci, and others remained at least unsupported.
Leonardo's Cenacolo, we learn from his friend Pacioli, was at length finished, and preparations were being made for casting his great horse in bronze, but the master himself was chiefly engaged in the study of hydraulics, and was writing a treatise on motion and water-power.
But even so, Italy, at the close of the fifteenth century, with Paolo Toscanelli, Luca Pacioli and Leonardo da Vinci, held incomparably the highest place among European nations in mathematics and the natural sciences, and the learned men of every country, even Regiomontanus and Copernicus, confessed themselves its pupils.
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