Piero's most enigmatic painting is "Flagellation of Christ", a small panel painting perhaps also produced for Federico da Montefeltro. The setting for the New Testament drama is the portico of Pontius Pilate's palace in Jerusalem. Curiously, the focus of the composition is not Christ but the group of three large figures in the foreground, whose identity scholars still debate.
The influences here come from further a field than Tuscany. The painting shows the impact of Northern European painting. Piero painted with tempera early in his career, but for later works like this one he began working in oil. Along with the use of brown under-painting for the figures, this shows a familiarity with Netherlandish and Flemish work. This is reinforced by the slim figure of Christ, who lacks the square muscularity of contemporary depictions from Italy, and is more reminiscent of paintings by artists like Hugo van der Goes.
The diptych of the Dukes of Urbino is one of the most famous works of art of the Italian Renaissance. Painted by Piero della Francesca, it depicts Federico da Montefeltro and his wife Battista Sforza. The Duke of Montefeltro, leader of mercenaries, skillful strategist and a great patron, turned Urbino into a refined and renowned cultural center.
The first works that can be found of Piero della Francesca as a painter can be found in 1439. This is when he was apprenticing under Domencio Veneziano, assisting him in painting the chapel of S. Egidio, in S. Maria Novella of Florence. He then was found to have executed some extensive frescoes in the Vatican; although these were destroyed when Raphael undertook the same walls for his “Liberation of St. Peter.” In by 1451 he was painting on his own. There is a fresco in Rimini by Piero della Francesca from 1451 that still remains.
In his autograph works Piero was a perfectionist, creating precise, logical and light-filled images (although analysis of their perspective schemes shows that these were always subordinated to narrative effect). However he often delegated important passages of works (e.g. the Arezzo frescoes) to an ordinary, even incompetent, assistant.
The first really practical treatise on perspective painting was Piero's "De Prospectiva Pingendi". The series of perspective problems posed and solved builds from the simple to the complex in a very methodical way. In Book I, after some elementary constructions to introduce the idea of the apparent size of an object being actually its angle subtended to the eye, and referring to Euclid's "Elements", Book I and VI, and Euclid's "Optics", he turns, in Proposition 13, to the representation of a square lying flat on the ground in front of the viewer. What should the artist actually draw?
Piero della Francesca's perspective treatise is the first of its kind--as far as we know and, it would seem, as far as Piero knew also. It is called "On perspective for painting" to make clear that we are concerned not with ordinary natural optics, which at this time was sometimes known as 'common perspective' (perspectiva communis), but with the special kind used by painters. As we shall see, Piero takes care to show that this new part of perspective should be seen as a legitimate extension of the older established science.
His work is the embodiment of rational, calm, monumental painting in the Italian early Renaissance, an age in which art and science were indissolubly linked through the writings of Leon Battista Alberti. Born two generations before Leonardo da Vinci, Piero was similarly interested in the scientific application of the recently discovered rules of perspective to narrative or devotional painting, especially in fresco, of which he was an imaginative master; and although he was less universally creative than Leonardo and worked in an earlier idiom, he was equally keen to experiment with painting technique.
Francesca received a scientific education where he excelled in the fields of mathematics and geometry. This led into his development as a painter. He had a stronger science background then either of his contemporaies, Paolo Uccello or Andrea Mategna. His study of linear perspective led to him fixing rectangular planes in a precise order and measuring them. This led him to paint objects and people in true proportional height.
Della Fransesca was blessed with a privileged childhood and he was able to study with painters in and around Florence, where he could view the sculptures and paintings of the great masters, such as Donatello and Fra Angelico. Della Fransesca was especially talented in perspective; his paintings are noted for the care he took in painting backgrounds for his figures
Piero planned his compositions almost entirely by his sense of the exact and lucid structures defined by mathematics. He believed that the highest beauty resides in forms that have the clarity and purity of geometric figures. Toward the end of his long career, Piero, a skilled geometrician, wrote the first theoretical treatise on systematic perspective, after having practiced the art with supreme mastery for almost a lifetime.