Piero della Francesca's Treatment of Edge Distortion

In his own day, Piero della Francesca was acknowledged as a very competent mathematician. This judgement is endorsed by modern scholars.1 Indeed, it is generally considered that it was on account of its unusually high mathematical level that Piero's treatise on perspective, De prospectiva pingendi, did not appear in a printed edition during the Renaissance.2 However, the work seems to have circulated in manuscript in the sixteenth century and Daniele Barbaro (15I3-70) incorporated large parts of it into his La Pratica della Perspettiva, published in Venice in 1569.3 Barbaro shows an ambivalent attitude to his source. In his preface he dismisses Piero's work as written for idiots. Such ajudgement can hardly be taken seriously and the most charitable interpretation of the passage would seem to be that it may reflect Barbaro's impression of the intellectual level of the painters to whom Piero explicitly addressed his treatise. Nevertheless, when he comes to use Piero's work, Barbaro acknowledges his debt to his predecessor, and makes no claim to have made significant improvements upon his source. Such courtesy is by no means characteristic of the times. Piero's pupil Luca Pacioli (1445-1514?) had incorporated large quantities of his master's work into his Summa de Arithmetica... (Venice I494) and his De divina proportione (Venice I509) without acknowledgement.4 Barbaro's near contemporary Andreas Vesalius (1514-64) showed even less courtesy. De humani corporis fabrica (Basle 1543) is notorious for the author's repeated references to Galen's fallibility and his silent incorporation of what he took to be correct parts of Galen's works.5 One of the many passages of Piero's work which Barbaro incorporates, with acknowledgement but without any further development, is the final proposition (xxx) of the first