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During this time We see in the service of naturalism a development that was to revolutionize art. Indeed, it defined most painting up to the twentieth century (and still holds sway in realistic painting). This was the discovery of linear or vanishing-point perspective in Florence. The principles of it were first demonstrated around 1413 by architect Filippo Brunelleschi (who later gained fame for the technical feat of designing and erecting the immense dome of Florence Cathedral). But it was architect and man of letters Leon Battista Alberti who first described the underlying geometry and a simple method in his treatise On Painting in 1435. This system was further refined by Piero della Francesca, Leonardo, and Durer.

Early pioneers devised a system of looking at the world as if through a framed window, in which the painting’s panel (or picture plane) is the “glasspane.” They even devised frames with grids through which the artist looked at (and could even trace) the subject to be depicted. This was not a very scientific approach, but it allowed the artist to observe and gauge the phenomenon of foreshortening. Artists had previously noticed that if, say, you gaze at the interior of a long room, the sides of the room appear to move inward, while the floor appears to move up and the ceiling down, so the wall at the far end of the room appears to be smaller than a theoretical wall on the spot where you are standing.

What Brunelleschi and Alberti discovered was that–to take our example–while your side walls are in reality pallel, if in your drawing you extend the lines of their receding top and bottom edges to a horizontal line denoting the far horizon opposite your eye level, the lines of the walls all appear to meet in a single vanishing point. With the further help of geometry they developed a system to measure “depth” in the picture. Thus it became possible to depict objects with exact dimensions placed in a measurable three-dimensional space and to draw all objects to proper scale. The result is a rendition of visual reality quite like what you see with one eye closed, or like that produced in a photograph. It’s not exactly the way humans see, for we have stereoscopic vision, among other things. But it presents a convincing, readable, and systematic two-dimensional representation of three-dimensionality.

Early systems of linear perspective used a single vanishing point in the center of the picture. The system for working out the depth easily resulted in the checkerboard floors and street-grounds often found in Early Italian Renaissance paintings. But the single vanishing point system works only for simple scenes in which all planes depicted in depth are parallel to each other and all planes depicted in width are parallel to the picture plane. Any plane at a different angle would result in another vanishing point. To obtain greater naturalism, a system evolved years later that used two vanishing points (or even more) to achieve round-the-corner or up hill and down dale effects.

When linear perspective was first introduced, Florentine artists seized upon it with fervor, for here they not only had a method to render a scene in correct perspective, re-creating almost exactly what the eye sees, but they felt they had found the key to unlock the divine order of the cosmos. Since at least the time of Pythagoras in ancient Greece, people had believed that the universe was ordered–was held together, in a sense–by sacred numerical relationships and proportions, by sacred geometry. Here the artist-architects of the Renaissance seemed to have found basic principles underlying the structure of reality. No wonder they had such confidence that man as a creative being was capable of achieving divinity. Here they could experience and vicariously participate in the very process of the mathematical creation of the universe through the re-creation of “worlds” of harmony in their own works.

Geometric relations, mathematical proportion, and the mysticism of numbers played an important part in how painters designed their pictures and architects their buildings. They made the underlying structure itself embody central ideas or themes (Piero della Francesca’s paintings demonstrate this most markedly).

Brunelleschi reportedly made two paintings to demonstrate the principles of perspective he discovered, but these are now lost. His good friend the sculptor Donatello was apparently the first to use Brunelleschi’s findings, though rather erratically; this was in his bronze relief Feast of Herod (1423-27).

It was another friend of Brunelleschi’s, the short-lived Masaccio, who made the earliest extant painting utilizing the new perspective technique consistently. The Holy Trinity With the Virgin, St. John, and Donors (c. 1425-28), a fresco on a wall of the Santa Maria Novella Church in Florence, creates the illusion of a two-tiered chapel. The bottom of this, with the tomb and skeleton of Adam, appears to jut into the space of the church in which the viewer stands. The upper part creates the optical illusion of an additional barrel-vaulted wing to the church, a “chapel of Golgatha” that houses the crucified Christ, God the Father looming behind him, and the dove of the Holy Spirit between them, with Saint John and Mary flanking the scene. The overall arrangement makes literal the Trinity through the use of the triangle–or, more exactly, the intersection of two triangles at the apex, one in the spiritual chapel and the other linking the spiritual dimension with the earthly one. Masaccio’s perspectival tour de force thus served as a most effective vehicle through which a viewer could contemplate the mysteries of the Trinity, the Incarnation, and the process of redemption.