information:extraction
Renaissance

It is generally accepted that Filippo Brunelleschi conducted a series of experiments between 1415 and 1420, which included making drawings of various Florentine buildings in correct perspective. According to Vasari and Antonio Manetti, in about 1420, Brunelleschi demonstrated his discovery by having people look through a hole in the back of a painting he had made. Through it, they would see a building such as the Florence Baptistery. When Brunelleschi lifted a mirror in front of the viewer, it reflected his painting of the buildings which had been seen previously, so that the vanishing point was centered from the perspective of the participant. Brunelleschi applied the new system of perspective to his paintings around 1425.

This scenario is indicative, but faces several problems, that are still debated.First of all, nothing can be said for certain about the correctness of his perspective construction of the Baptistery of San Giovanni, because Brunelleschi's panel is lost. Second, no other perspective painting or drawing by Brunelleschi is known. (In fact, Brunelleschi was not known to have painted at all.)Third, in the account written by Antonio Manetti in his Vita di Ser Brunellesco at the end of the 15th century on Brunelleschi's panel, there is not a single occurrence of the word "experiment".Fourth, the conditions listed by Manetti are contradictory with each other. For example, the description of the eyepiece sets a visual field of 15°, much narrower than the visual field resulting from the urban landscape described.

Soon after Brunelleschi's demonstrations, nearly every interested artist in Florence and in Italy used geometrical perspective in their paintings and sculpture, notably Donatello, Masaccio, Lorenzo Ghiberti, Masolino da Panicale, Paolo Uccello, and Filippo Lippi. Not only was perspective a way of showing depth, it was also a new method of creating a composition. Visual art could now depict a single, unified scene, rather than a combination of several. Early examples include Masolino's St. Peter Healing a Cripple and the Raising of Tabitha (c. 1423), Donatello's The Feast of Herod (c. 1427), as well as Ghiberti's Jacob and Esau and other panels from the east doors of the Florence Baptistery. Masaccio (d. 1428) achieved an illusionistic effect by placing the vanishing point at the viewer's eye level in his Holy Trinity (c. 1427), and in The Tribute Money, it is placed behind the face of Jesus. In the late 15th century, Melozzo da Forlì first applied the technique of foreshortening (in Rome, Loreto, Forlì and others).

This overall story is based on qualitative judgments, and would need to be faced against the material evaluations that have been conducted on Renaissance perspective paintings.Apart from the paintings of Piero della Francesca, which are a model of the genre, the majority of 15th century works show serious errors in their geometric construction. This is true of Masaccio's Trinity fresco and of many works, including those by renowned artists like Leonardo da Vinci.

As shown by the quick proliferation of accurate perspective paintings in Florence, Brunelleschi likely understood (with help from his friend the mathematician Toscanelli), but did not publish, the mathematics behind perspective. Decades later, his friend Leon Battista Alberti wrote De pictura (c. 1435), a treatise on proper methods of showing distance in painting. Alberti's primary breakthrough was not to show the mathematics in terms of conical projections, as it actually appears to the eye. Instead, he formulated the theory based on planar projections, or how the rays of light, passing from the viewer's eye to the landscape, would strike the picture plane (the painting). He was then able to calculate the apparent height of a distant object using two similar triangles. The mathematics behind similar triangles is relatively simple, having been long ago formulated by Euclid. Alberti was also trained in the science of optics through the school of Padua and under the influence of Biagio Pelacani da Parma who studied Alhazen 's Book of Optics. This book, translated around 1200 into Latin, had laid the mathematical foundation for perspective in Europe.

Piero della Francesca elaborated on De pictura in his De Prospectiva pingendi in the 1470s, making many references to Euclid. Alberti had limited himself to figures on the ground plane and giving an overall basis for perspective. Della Francesca fleshed it out, explicitly covering solids in any area of the picture plane. Della Francesca also started the now common practice of using illustrated figures to explain the mathematical concepts, making his treatise easier to understand than Alberti's. Della Francesca was also the first to accurately draw the Platonic solids as they would appear in perspective. Luca Pacioli 's 1509 Divina proportione (Divine Proportion), illustrated by Leonardo da Vinci, summarizes the use of perspective in painting, including much of Della Francesca's treatise. Leonardo applied one-point perspective as well as shallow focus to some of his works.

Two-point perspective was demonstrated as early as 1525 by Albrecht Dürer, who studied perspective by reading Piero and Pacioli's works, in his Unterweisung der Messung ("Instruction of the Measurement").