The reputation of the Italian Renaissance painter and mathematician Piero della Francesca (hereafter Piero) has risen dramatically from near oblivion in the Early Modern period to the present when he is judged as nearly equal to Leonardo da Vinci and Michelangelo Buonarroti, especially in regard to technical excellence and writing. In his paintings and his treatises Piero achieved the fullest expression of Quattrocento perspective, which he had derived from his capacious understanding of Greek geometry. Born into a family of artisans-shopkeepers of leather in the Tuscan town of Borgo San Sepolcro (today Sansepolcro) c. 1412, Piero began with several small projects in his native town in the 1430s. He served in Florence as an assistant to Domenico Veneziano in 1439 where he came in contact with the achievements of Masaccio, Donatello, Brunelleschi, and other artists in Florence, though he never became strictly a Florentine painter. He sojourned throughout central Italy in the 1440s and 1450s, receiving commissions in Ferrara, Ancona, Rimini, Arezzo, Rome, and Sansepolcro. After his two sojourns in Rome in the 1450s, Piero became increasingly interested in the representation of classical values and especially Roman architecture and in learning Greek geometry. In the decade of the 1470s he was often in the court of Federico da Montefeltro in Urbino, accepting commissions from the ruler and consulting manuscripts in his library. In the history of mathematics, he is now recognized as an indispensable participant in the revival of Greek geometry and as one of the few individuals in 15th-century Europe with extensive knowledge of both Euclid and Archimedes. In the last three decades of his life (d. 1492) Piero wrote treatises on commercial mathematics and geometry (Trattato d’abaco), perspective in painting (De prospectiva pingendi), and a reflection on several classical procedures and problems in Greek geometry (Libellus de quinque corporibus regularibus), as well as copying the Opera of Archimedes.
Comparative analysis in Greek geometry
