Alberti's theories of perspective
Assess the impact on 15th Century painting of Alberti's theories of perspective
Alberti (1404-72), an accomplished mathematician and geometrician wrote his book Della Pittura in 1435. This treatise on painting included a discussion of the laws of mathematical perspective for artists. This gave perspective a scientific basis and made spatial measurement accurate for the first time.
Perspective is the technique used to represent a three dimensional world on a two dimensional surface. The construction consisted of orthogonals, transversals, horizon line and vanishing point. These together created an accurate system to graph the space of the picture, such as the apparent shrinking in size of objects, and convergence of parallel lines as they recede from the viewer.
Battle of San Romano (1445) by Paolo Uccello, the broken lances follow the lines of the orthogonal, as do the horse's necks. The dead soldier lies face down, foreshortened along an orthogonal. The exception to this is where the horses are viewed sideways. The perspective of horses and men then appears to be foreshortened so that they recede into depth.

Paolo Uccello, Deluge, c. 1445--47, fresco, Sta. Maria Novella, Florence.
Uccello advanced the language of Alberti's theory, not just the space construction, but also applied to objects developed through foreshortening. The Deluge (c1445-47), consisted of two scenes in one lunette, the corridor between them creating a perfect Albertian perspectival cone, providing orthogonals. The ladder floating in the water creates two further orthogonals. The diminishing figures added to the effect. Uccello showed his skills at perspective rendering, by the emphasis on the mazzochio, which is drawn in perspective. There is one around the neck of the second figure on the left, and another on the head of the woman in the centre.
Uccello studied Alberti's theory of perspective, but at the same time revealed the weaknesses of the system, by the use of anomalies in his perspective. This can be evident in The Miracle of the Host (1468). This painting has been set in two scenes within the same space. The first scene set in the interior of the shop uses the tiled floor and roof beams to establish orthogonals and transversals. However, scene two illustrates the weakness of the Albertian scheme. The interior scene in the living room is shown from a point of view slightly to the right of the wall so the street can be seen - the floor tiles, as a result, become flattened at the left, and seems to tilt upwards.
Another 15th century artist, Piero della Francesca, reflected his mathematical fascinations and exercise in perspective drawing through his artworks. Piero was deeply influenced by Alberti, and he extended the mathematical basis of his method and wrote De Perspective di Pingudi.
The Flagellation (c. 1463-4), the architectural setting of the portico and the buildings surrounding the square, and the pattern of the inlaid marble floor, have been constructed according to precise mathematical principles. Pictorially, it is so accurate that it is possible to reconstruct the plan of the floor. The orthogonals are projected from the braccia divisions in the baseline but Piero put the vanishing point lying below the hips of the figures rather than at eye level as Alberti suggests.

Piero della Francesca, The Flagellation, 1463--4.
As Anthony Blunt said in his Artistic Theory in Italy (1450-1600): "The artist of the early Quattrocento to whose ideas he expresses were entirely occupied with exploring the visible universe that they had so recently discovered. What they needed was practical adviceˇK and that is exactly what Alberti gave them".
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