During the Middle Ages, one of the overriding religious goals of people throughout Europe was to create places of worship that soared heavenward and were filled with holy light that shined in through walls of stained glass. To achieve this revolutionary vision, the builder-architects of the Gothic era had to figure out how to make the somber religious buildings of the preceding Romanesque period less massive. They had to invent, through trial and error, a way to concentrate gravitational forces into “point” supports so that exterior walls could open to daylight and thereby bring the believer closer to God.

To achieve these goals several revolutions in architectural thinking had to occur. First, the architects of the middle ages introduced the idea of masonry ribs at the roof level. Not only did these ribs cross the nave at right angles to the rows of stone columns bordering the central space, but diagonal stone ribbing triangulated the structure and added strength. A triangular configuration cannot deform, while a rectangular one can. Consequently, the Gothic era introduced a kind of structural spaceframe that would be taken to even greater heights in the modern era when iron, then steel, allowed architectural structures to become truly spidery in a thoroughly triangulated network of lightweight struts. Then the architects had to figure out how to buttress the spindly stone piers that started to replace the massive exterior walls so they wouldn’t collapse under the horizontal thrust of windstorms and earthquakes and of the arching roof structure itself.

Gothic masons invented the angled, arching buttress as illustrated in the photograph above. These "flying buttresses" captured the horizontal thrust from the roof that was amassing at the exterior wall and carried that potentially destructive force out and down into the earth. These daring diagonal members that the world had never before seen were a stunning re-envisioning of architectural structure. No longer were massive walls the only way to build. No longer was the right angle the only way to conceive the relationship of beam to column. A triangulated exoskeleton of structural members allowed the cathedral builders of Europe to create holy spaces that could rise skyward.

Gothic structures certainly fostered the evolution of diagonal thinking but at the same time, the very orthogonality of the relationship between the nave and the transept cemented the notion of the rightness of the right angle in the minds of the bowing believers. The priest’s symbolic raising of the cross on which Christ was crucified branded the right angle as a divine geometry that should never be transgressed. Even the language of the time fostered the holiness of the right angle. It can therefore be seen that the inexorable march toward the flowering of Diagonality in the modern era took steps both forward and backward until it was freed of its bonds at the end of the 19th century and exploded onto the cultural scene at the outset of the 20th century.