The development of linear perspective

The history of Western painting can be read as a long argument about how to put a three-dimensional world onto a flat surface. The argument turned decisively in the workshops of Florence in the first half of the fifteenth century, when a system of construction — what came to be called la prospettiva and then perspectiva artificialis — was put together, named, taught, and used to produce the unified, measurable, mathematical space of Renaissance painting. The conventional account gives the credit to Filippo Brunelleschi and to Leon Battista Alberti, and it is essentially right, but it has to be read against the technical inheritance that the early Quattrocento inherited from antiquity and the Middle Ages, and against the continuing history of the system in the painting of the next four hundred years.

The problem of space before Brunelleschi

Greek painters had, by the late fifth century BC, developed a sophisticated practice of skiagraphia — the rendering of bodies in graded light and shadow — and of foreshortening in monumental painting; the Niobid Painter in Athens and the panel paintings of the Macedonian tombs demonstrate what a Greek painter could do. The Romans inherited this practice and extended it to the wall painting of the houses of Pompeii, Herculaneum, and the Domus Aurea; the third and fourth Pompeian styles used receding orthogonal pavements, painted architectural backdrops, and graded tones of colour to suggest depth. That classical practice was lost to the medieval Latin West in the centuries after the Germanic invasions. The Byzantine icons that dominated the Eastern and, increasingly from the twelfth century, the Western altar, the great Romanesque murals of the via lattea tradition in northern Italy, and the early Gothic frescoes of the Île-de-France kept the figures well but did not put them into a continuous, measurable space. The Giotto of the Scrovegni Chapel, working in the first years of the fourteenth century, made the most decisive break that the Trecento was to see: a painted space articulated by painted architecture and by overlapping planes of colour, with a horizon line implicit in the landscape, but not yet organised as a geometrical construction.

The late medieval painters and the early humanists knew perfectly well that the Greeks had been able to do things that they could not. The references to skiagraphia in Plutarch and the references in Pliny the Elder to the lost books of antiquity on painting were part of the humanist reading of the classics. The question that occupied the humanists of the 1390s and 1400s was how those books, and the practice they described, could be recovered. The most ambitious answer, in the centuries of the early Quattrocento, was the system that we now call linear perspective.

Brunelleschi’s demonstrations

The evidence for the early construction of the system comes from the biographer Antonio di Tuccio Manetti (1423–1497) in his Vita di Brunelleschi (c. 1480). Manetti describes two demonstrations, both carried out in Florence in the years around 1413. In the first, Brunelleschi painted a small panel of the baptistery of San Giovanni in Florence as seen from the door of the cathedral, looking east, with the east end of the cathedral’s unfinished nave on the right. He then cut a hole in the panel at the position of the viewer’s eye and held the panel up to the viewer at the spot from which it had been painted; the viewer looked through the hole at the back of the painting, which was silvered to act as a mirror, and saw the painted image superimposed on the painted image of the building behind it. The painted image and the actual building coincided.

In the second, Brunelleschi painted a small panel of the Piazza della Signoria, viewed from a point on the pavement, again with a hole in the panel and a mirror at the back. The viewer, with one eye to the hole, was meant to hold the panel with a sweep of the hand to bring it back to the eye and to convince himself that the painted image was identical to the real one. The second panel, unlike the first, is documented in the Zibaldone of the Florentine merchant Giovanni Rucellai (1403–1481), in which the earliest use of the term perspectiva in this sense appears. The system Brunelleschi had constructed is what is now called one-point linear perspective: a system in which all the orthogonals of the scene — the lines that in the actual world are parallel to each other and at right angles to the picture plane — are made to converge on a single vanishing point on the horizon, and in which the size of the figures in the picture is reduced as the square of their distance from the eye.

The paintings have been lost (the small panel of the piazza is documented in the Codex Magliabechiano of c. 1530); what survives is the system that Brunelleschi used in the architecture of the Ospedale degli Innocenti, the Pazzi Chapel, the Sagrestia Vecchia of San Lorenzo, and the great models for the dome of the cathedral that have come down to us in the Opus Dei drawings of the Opera del Duomo. Eugenio Battisti (Brunelleschi, 1976) and Arnaldo Bruschi (Brunelleschi, 1977) have reconstructed the practice from the buildings; Hubert Damisch (The Origin of Perspective, 1987 trans.) has read the practice, more daringly, as a transformation of the symbolische Form of the European picture; and Samuel Edgerton (The Renaissance Rediscovery of Linear Perspective, 1975, 1991) has read it, more concretely, as the application of optical and mathematical knowledge that the Florentine workshop shared with the medieval optical tradition of Roger Bacon and John Pecham.

Alberti’s costruzione legittima

The system that Brunelleschi had used in the workshop was first published in a Latin treatise by his friend Leon Battista Alberti, De pictura (1435, dedicated to Brunelleschi himself), and in an Italian paraphrase of the same text, Della pittura (1436, dedicated to Filippo Strozzi the Elder and to the humanist Giannozzo Manetti). Book I of the treatise sets out the mathematical principles — the projection of a three-dimensional body onto a plane through a point — and Book II the practical method of construction that Alberti called the costruzione legittima and that is still taught as the standard method in most academies of painting in Europe. The picture, on Alberti’s account, is a finestra (window): a transparent plane through which the viewer looks at the world on the other side, and on which the visible body is plotted by the straight lines that connect the contour of the body to the eye. The point in the picture that corresponds to the eye is the centrale; the horizontal line through it is the horizon; the lines from the centrale to the body are the raggi (rays); the lines in the picture parallel to the rays are the orthogonals; the lines in the picture perpendicular to the orthogonals are the fughe (recedes).

The costruzione legittima was, in the countryside, taught and learnt through the use of a velo — a net of black threads stretched in a frame — that the artist held between the model and a single eye, and through which the model was plotted point by point. Cennino Cennini’s Il Libro dell’Arte (c. 1390), the great handbook of the late Trecento workshop, knew nothing of the velo; Alberti’s treatise knew it well, and the velo was to remain the standard teaching instrument in the workshops of the Italian peninsula, and then of the academies of France, until the nineteenth century.

Mathematics, optics, and the painted world

Alberti’s system was, on its own terms, a Euclidean application of optics to painting, and it had the consequence that the art of painting could be treated as a branch of mathematics. The centrale is a point; the raggi are straight lines; the fughe are at right angles to the raggi; the orizzonte is the locus of all the points at infinity. Piero della Francesca’s De prospectiva pingendi (written in the 1470s, first printed 1502) and Luca Pacioli’s De divina proportione (Venice, 1509, with its famous illustrations of the regular solids by Leonardo) took the consequence further and made the perspective construction a chapter in a much larger mathematical philosophy. The De prospectiva pingendi is, in the end, a treatise on projective geometry as much as a treatise on painting: Piero demonstrates the construction of a perspective from a point in a different position, from a greater or lesser distance, from a different elevation, and from a system of light; he uses the costruzione legittima to construct the regular solids in foreshortening; and he offers a number of “practical rules” (most notoriously, the rule that the size of a body varies inversely as the distance) that painters of the next four hundred years were to dispute in their own textbooks.

The deepest theoretical issue that the system raised was the relationship between the perspective of the eye and the perspective of the picture, and it is the question that Panofsky (Perspektive als symbolische Form, 1927, trans. Perspective as Symbolic Form, 1991) made famous: whether the system was a description of the world as it actually is, or a description of the world as it appears to the human subject. The Florentine tradition took the system to be both: the construction of the picture is a mathematical description of an empirical fact, and the empirical fact is the working of the human eye. The Florentine picture, on Panofsky’s reading, is a symbolische Form of the modern, subjective, finite, located observer. The reading is controversial, but the system it discusses is not.

Practice: from Masaccio to Raphael

The first great painting constructed in Alberti’s system is Masaccio’s Trinity of c. 1427 in the church of Santa Maria Novella, in which the painted architecture of the chapel is constructed to the same modular system as the Brunelleschian architecture of the building. The vanishing point of the barrel vault is at the feet of the crucified Christ; the proportions of the chapel are those of a real chapel in the same church; the two donors, kneeling in the foreground, are at the scale of the actual people they are meant to represent. Paolo Uccello’s Battle of San Romano of the 1430s and the elaborate foreshortening of his perspective studies of lances are the Quattrocento’s most famous celebrations of the system as a system; Piero della Francesca’s Flagellation of c. 1455, in which the two simultaneous scenes of the Flagellation and of the conversation of the Jews are constructed in a single perspective, is the most sophisticated. The Brancacci Chapel frescoes (c. 1425) and the Tribute Money of Masaccio are the first great demonstration of the system in a multi-figure narrative.

The High Renaissance took the system and made it the foundation of a new pictorial rhetoric. Leonardo’s Last Supper (1495–1498) is a perspective construction in which the orthogonals converge on a point at the right temple of Christ; Raphael’s School of Athens (1509–1511) is a perspective construction in which the two great coffered vaults converge on a point between Plato and Aristotle; Michelangelo’s Sistine Chapel ceiling (1508–1512) is a perspective construction of the ignudi that organises the whole flat surface of the vault as a continuous, receding architecture. The Venetian school — Giovanni Bellini, Giorgione, Titian — used the Florentine system with greater or lesser strictness; Tintoretto’s Last Supper of 1592–1594 in San Giorgio Maggiore is a deliberately broken perspective, in which the multiple vanishing points are the rhetorical and theological argument of the painting.