THE MEDIEVAL MASON
The people who created this art weren't formally educated. In the early days, only forty percent of master masons could even write their name on a document. They weren't trained in formal geometry, and it's unlikely they made any calculations. They didn't know Euclid, but they worked magic with a compass and square.
Medieval cathedral builders learned their empirical art through apprenticeship. Master builders held all kinds of jealously guarded tricks of the trade -- a vast inventory of knowledge about material selection, personnel management, geometrical proportioning, load distribution, design, liturgy, and Christian tradition.
And make no mistake, those masons saw no clear boundary between things material and things spiritual. Their art flowed from their right brain. It was visual and spatial. They levitated tons of stone into the air to communicate their praise of God, and when they were finished, they embellished the nooks and crannies and high aeries of their buildings with the phantoms of their minds -- with cherubs and gargoyles and wild caricatures of one another.
http://www.uh.edu/engines/epi1530.htm