Brunelleschi, Alberti and the history of perspective

Brunelleschi's test panel of the Florence Baptistery had a small hole at its vanishing point; you looked through it from behind at a mirror, and the painted building lined up with the real one.

Before the rules

Painters wanted depth long before anyone could construct it exactly. Greek and Roman painters could create a convincing sense of space, but, as the historians at the University of St Andrews note of the Hellenistic painters, there is no evidence that they understood the precise mathematical laws. Giotto, working in Italy in the early fourteenth century, followed rules of thumb: lines above eye level slope down as they go away, lines below slope up. The results look deep, but parallel lines in his pictures do not meet at one point, and the floors do not measure out correctly. Around the year 1000, the scholar Ibn al-Haytham had given the first correct explanation of vision, with light travelling from objects into the eye. He did not apply it to painting, but Renaissance artists later used his optics.

Brunelleschi's mirror

The first correct method is credited to Filippo Brunelleschi (1377 to 1446), the Florentine architect who later built the great dome of Florence Cathedral, completed in 1436. The date of his discovery is not recorded exactly: the St Andrews history puts it at about 1413, and other accounts say about 1420. He painted two demonstration panels of Florence, one of the octagonal Baptistery of San Giovanni and one of the Palazzo dei Signori. Both are lost, so we know them only from later written accounts. He understood that all parallel lines in a plane, other than the plane of the picture, run to a single vanishing point, and he worked out how the drawn size of an object depends on its distance.

His test of the Baptistery panel is the famous part. He bored a small hole through the panel at the vanishing point. The viewer stood where Brunelleschi had stood, held the panel with its painted side facing away, and looked through the hole from the back at a mirror held at arm's length. In the mirror they saw the painting. Lower the mirror and they saw the real Baptistery from the same spot; raise it again and the painted lines matched the real ones. The hole fixed the eye at the one point for which the drawing is correct, the same point the model's Eye view puts the camera on.

Alberti writes it down

Brunelleschi never wrote his method down. Leon Battista Alberti (1404 to 1472) did. His treatise De pictura, in Latin, dates from 1435; an Italian version, Della pittura, followed in 1436 and was dedicated to Brunelleschi. The two are not simply translations: the Latin book is the more technical one, written for scholars, and the Italian one is for a wider readership. Its first part gives the mathematics: the visual pyramid, the picture as a slice through it, the open window, the centric point and the tiled floor with its check by diagonals. Lorenzo Ghiberti, who knew the new ideas, filled the ten panels of the Baptistery's east doors, the Gates of Paradise (1425 to 1452), with architecture that recedes in perspective.

From there the ideas spread and became more mathematical. Piero della Francesca wrote a three-volume treatise On perspective for painting, dated by some to the 1460s and by others to the mid 1470s. Leonardo da Vinci wrote down the rules of diminution. Albrecht Dürer carried the method to Germany in his book of 1525. In 1600 Guidobaldo del Monte proved that any set of parallel lines not parallel to the picture converges to a vanishing point. Girard Desargues, in 1636 and 1639, turned perspective into the start of projective geometry, where the phrase point at infinity first appears. And in 1719 Brook Taylor gave the general definition of the vanishing point used in this course; the phrase linear perspective, already the title of his first book on the subject in 1715, was his own coinage.