The use of linear perspective in art can be traced back to Brunelleschi's now lost panels depicting the Baptistery of Florence and the Palazzo Vecchio (1425). Brunelleschi observed the buildings in a mirror and attempted to capture this plane representation faithfully. Edgerton spends much time trying to reconstruct these "demonstrations". The basic ideas of linear perspective were soon afterwards applied by Masaccio in his Trinity fresco and by Masaccio and Masolino in the Brancacci Chapel frescoes, and became widespread after 1435 when Alberti wrote the first text on linear perspective, the Della pittura. Allberti says: "I decide how large I wish the human figures in the painting to be. I divide the height of this man into three parts ... With this measure I divide the bottom line ... into as many parts as it will hold." Then we fix the "centric point" (the observers straight-ahead point on the horizon ). "The suitable position for this centric point is no higher from the base line than the height of the man ... for in this way both the viewers and the objects in the painting will seem to be on the same plane. Having placed the centric point, I draw lines from it to each of the divisions on the base line." Through the centric point we draw the horizon. "This line is for me a limit or boundary, which no quantity exceeds that is not higher than the eye of the spectator ... This is why men depicted standing in the parallel [to the horizon] furthest away are a great deal smaller than those in the nearer ones, a phenomenon which is clearly demonstrated by nature herself, for in churches we see the heads of men walking about, moving at more or less the same height, while the feet of those further away may correspond to the knee-level of those in front."
Next we learn the "costruzione legittima" construction of tiled floors, although the fact that construction lines typically need to be extended off-canvas seems to have caused some confusion. As examples of early uses of Alberti's text and somewhat unsuccessful costruzione legittimas we study two drawings by Bellini and Pisanello, where "the original perspective layout constructions can still be seen under the finishing ink". These artists "seem to have followed Alberti's instructions to the letter---to the best of their understanding".
As for the reasons for the popularity of perspective, Edgerton emphasises religious motives: "perspective rules were accepted by ... early artists because it gave their depicted scenes a sense of harmony with natural law, thereby underscoring man's moral responsibility within God's geometrically ordered universe". "Linear perspective rules themselves had to be modified of even abandoned if they conflicted with the pictures true purpose in this sense", as we see in the case of a Veneziano altarpiece, which violates perspective laws and has the centric point at waist level.
We next study how linear perspective was influenced by the science of optics. There is of course the notion, in Alberti's words, that "a painting will be the intersection of a visual pyramid". Light rays from the periphery of the pyramid need to travel longer to get to the canvas so "they weaken and lose their sharpness", Alberti explains, and "the reason for this has been discovered: as they pass through the air, these and all other visual rays are laden and imbued with lights and colors; but the air too is endowed with a certain density, and in consequence the rays get tired and lose a good part of their burden as they penetrate the atmosphere. So it is rightly said that the greater the distance, the more obscure and dark the surface appears."
Edgerton also cites an optical analogy in Dante that "upholds the wisdom of looking someone 'straight in the eye', with all its overtones of detecting another's truthfulness and communicating one's own sincerity" as an illustration of why Renaissance artists preferred the central viewpoint where walls and floor tiles tend towards the centric point in the middle of the horizon. "During the fourteenth century there had been a temporary favoring of charming oblique views. Thereafter it was as if painters wanted to recapture the solemn spirit of the old traditional Christian messages" and "came more and more to believe that things planned or seen from a central viewpoint had greater monumentality and moral authority".
Next we study the influence of cartography on linear perspective. Edgerton make a big deal of this, but many connections with painting seem quite superficial, such as a Giotto painting that appears conformal but not distance-preserving and the supposed influence of latitude-longitude grid thinking on Alberti's gridded veil method and Uccello's chalice drawing.