|South Kensington tube station, on the District Line, London. Click to "embiggen"|
All elements that are perpendicular to the viewing frame converge at a single point (a vanishing point) on the horizon.
Ancient artists - the Greeks, the Egyptians - were aware of this phenomenon, and many works of art from those era show attempts to depict a sense of depth in a two-dimensional work. Medieval and Byzantine artists also tinkered with these ideas - but in many works, the relative status of certain figures caused these spatial ideas to be applied inconsistently. When you have to draw saints or donors larger than ordinary people, you tend to get the proportions out of whack.
It wasn't until the Eleventh Century that somebody figured out the math of perspective. The Islamic scientist and mathemetician Alhazan - born Abu Ali Al-Hazan ibn Al-Hasan ibn Al-Haytham in the city of Basra in what is now Iraq - was a civil servant working in Cairo. He developed the modern science of optics, studied the anatomical function of the human eye, and is credited with being the first scientist to explain how rays of light work.
Expanding on the writings of Alhazan, Italian artists such as Lorenzo Ghiberti and Fillipo Brunelleschi developed the geometrical methods of drawing in perspective.
As a theatre student in college, my design professors used to assign me the trick of turning a floor plan into a graphic rendering, by simply using the geometrical formulae of perspective drawing. Or - conversely - to take a Renaissance perspective drawing and turn it into a spatial floor plan.
A photo like this one makes my fingers itch for drafting pencil and a T-square, to see if I can do it again.