Linear Perspective

Artists in the Renaissance did not in fact discover linear perspective, persay. In fact, the ancient Romans had depicted depth in their paintings hundreds of years earlier, but the technique was lost to artists in the Middle Ages and the early Christian Era. It was only once society's attention was turned back towards our world and ourselves, that artistic attention could be given to men and the man-made. This led naturally to the need for depth expression in art, and the rediscovery of methods by which three dimensionality could be depicted.

These methods were overlapping, changing size and placement, linear perspective, relative hue and value, and atmospheric perspective. 

Overlapping was the simplest of these, and the subtlest in effect. While intersecting the lines of an object in the background, the artist was able to produce a very subtle sense that the one was layered on top of the other within their not-quite two-demensional plane.

Placement had already been employed, but with the addition of the principal that objects shrink in all directions with distance from the eye, changing size was applied and the impact of placement was far more fully appreciated.

Linear perspective took the changing size element a step further with the introduction of the vanishing point. This tool allowed the painter to use a real or imagined point as the terminal of what the viewer could see in the painting. It allowed the painting to represent along lines of perspective in just the way that the painter would see it before him or in his mind's eye. Once coupled with the mathematical discovery of the rate at which the size of an object seems to change with distance and place allowed for dynamic representations of architectural elements.

Hue and value also have an impact, as warm hues seem closer to the mind of the viewer, and cool hues seem farther away. Colors near to each other on the value scale also appear closer when interpreted by our brain, whereas sharply contrasting values suggest definition and separation, distance between each other.