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Person: Della Francesca, Piero

Piero della Francesca was an Italian artist who pioneered the use of perspective in Renaissance art and went on to write several mathematical treatises.

Mathematical Profile (Excerpt):

• Although today he is always known as Piero della Francesca, he would have been known in his lifetime as Piero di Benedetto de' Franceschi.
• As these arguments illustrate, there is no definite evidence when Piero was born, sources giving dates between 1406 and 1422.
• Details of Piero's schooling remain conjecture, but we can deduce something of its nature from the skills he displayed as an adult.
• Also it is clear that Piero's Italian writing lacked style, and was rather simple and elementary.
• This suggests that Piero did not spend that long at school and it confirms his lack of Latin since those who could write fluent Latin developed a style when writing Italian that reflected Latin structure.
• However, as an adult he had read Euclid's Elements and had some knowledge of the works of Archimedes and, since no Italian versions were available in Piero's day, he must have learnt enough Latin in later life to read these works.
• The boy Piero probably received the same schooling as did thousands of other Italians of his background, but it was a surprisingly rich and diverse education.
• The adult Piero may have learned enough Latin to enable him to read Latin mathematical texts with their specialised vocabulary.
• The key seems to be that Piero continued to learn throughout his life.
• One has the impression that Piero retained everything - the saints' legends read in school, the mathematics of abbaco school, his creative explorations into ancient geometry - and that all his learning enriched his painting.
• Documents Banker has found show that Piero worked as the assistant of Antonio d'Anghiari in the 1430s.
• In June of the following year Benedetto received payment for Piero's work "painting the poles of the candles".
• Benedetto received further payments for work carried out by Piero over the following years during which he was clearly working as an assistant to Antonio.
• The fact that Piero is described as a "painter" in this document indicates that Piero was not an apprentice by this time but rather an assistant.
• The real problem is that, fascinating as all the evidence about Piero's youth is, whatever dates are proposed, there always seems to remain some difficulties.
• A document dated 8 January 1438, again signed by Benedetto, ends Piero's association with Antonio acknowledging that payment has been received for Piero's work on three separate churches and chapels in and around Borgo San Sepolcro.
• His labour in the artisan culture remained formative in Piero's life and art, not withstanding his great later achievements in painting, mathematics, and geometry that required access to and participation in an elite culture.
• Piero left Borgo San Sepolcro and went to Florence where, in 1439, he was assisting Domenico Veneziano in painting the chapel of Santa Egidio, in Santa Maria Novella.
• It was this contact with the early Renaissance art of Florence that provided the foundation of Piero's own style.
• It is not known whether Piero assisted Domenico for the whole work but we know he received payment for his contribution to painting the first mural on 12 September 1439.
• In June 1441 Domenico began work on a second fresco in the chapel and by this time Piero is listed as a member of the town council in Borgo San Sepolcro.
• In 1445 the Compagnia della Misericordia, a guild whose aim was to help the poor and unfortunate, commissioned him to paint an altarpiece in their church at Borgo San Sepolcro.
• The commission stated that the work was to be completed within three years, but it was not finished until 1462, seventeen years after Piero began.
• The image painted by Piero depicts the Virgin protecting members of the guild under her cloak.
• Piero only worked intermittently on the altarpiece, undertaking many other commissions during these years.
• Alberti, like Piero, was deeply interested in perspective and the two must have exchanged ideas on this topic while in Rimini.
• One of Piero's most famous works (many would say his most famous) is the Story of the True Cross cycle, begun around 1457.
• The decorations had been started by a popular, but rather workmanlike, painter Bicci di Lorenzo, in the late 1440s; it was probably after Bicci died in 1452 that Piero was called in.
• Not only do the frescos show that Piero is complete master of perspective but they also show a remarkable treatment of light.
• Piero uses light, combining shadow and shade, to make the figures 3-dimensional.
• Piero painted many frescos in the Vatican, later destroyed when replaced by works by Raphael, and in the Basilica di Santa Maria Maggiore.
• After leaving Rome, Piero returned to his home town where he undertook a number of commissions before he went to Loreto to begin decorating the vault of the sacristy with Domenico Veneziano.
• Piero's The Flagellation of Christ, painted in Urbino around 1460, is now considered a masterpiece.
• When it made its first appearance in art historical literature some time after, Piero was, surprisingly enough, considered more a technician than an artist.
• Piero produced other remarkable paintings, including the Resurrection painted in Borgo San Sepolcro around 1563.
• Federico was blind in his right eye so Piero shows him in profile so as not to give offence.
• Piero spent the last years of his life in his home town, becoming prior of the Confraternita di San Bartolomeo in 1480.
• We now give a description, contributed by J V Field, of Piero's mathematical works.
• Piero almost certainly wrote all three works in the vernacular (his native dialect was Tuscan), and all three are in the style associated with the tradition of 'practical mathematics', that is, they consist largely of series of worked examples, with rather little discursive text.
• (All these modern names are due to Johannes Kepler (1619).) Piero appears to have been the independent re-discoverer of these six solids.
• Piero is determined to show that this technique is firmly based on the science of vision (as it was understood in his time).
• He accordingly starts with a series of mathematical theorems, some taken from the optical work of Euclid (possibly through medieval sources) but some original to Piero himself.
• There are many diagrams and illustrations, but unfortunately none of the known manuscripts has illustrations actually drawn by Piero himself.
• None of Piero's mathematical work was published under his own name in the Renaissance, but it seems to have circulated quite widely in manuscript and became influential through its incorporation into the works of others.
• Much of Piero's algebra appears in Pacioli's Summa (1494), much of his work on the Archimedeans appears in Pacioli's De divina proportione (1509), and the simpler parts of Piero's perspective treatise were incorporated into almost all subsequent treatises on perspective addressed to painters.

Born June 1420, Borgo San Sepolcro (now Sansepolcro, Italy). Died 12 October 1492, Borgo San Sepolcro (now Sansepolcro, Italy).

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Tags relevant for this person:

Geometry, Origin Italy

Thank you to the contributors under CC BY-SA 4.0!

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@J-J-O'Connor

@E-F-Robertson

@J-V-Field

References

Adapted from other CC BY-SA 4.0 Sources:

1. O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive