There have been many attempts to intepret the sacred geometry of Chartres. John James applies a series of geometrical figures to the plan. He explains that the Middle Ages gloried in multiplicity as part of the divine order, and "hence we should not be surprised when we find more than one geometric system inhabiting the one place, each flowing over the other, while being locked together at a few essential points like the labyrinth and the altar, which tehreby express the mosts acred and meaningful locations in the building."
Some interpreters go much further and relate the proportions and dimensions of the cathedral to what they regard as the "lost knowledge" of the Druids, the builders of the Temple of Solomon and the Order of the Knights Templar.
The basis of the design in the early Middle Ages was the application of a standard dimension or module, multiplying, sub-dividing and combining it. The unit of measurement, however, varied from place to place, from trade to trade and from one master builder to another. The basic dimensions was often the Roman foot (295 mm) but could be the Teuton foot or the French pied du roi, or the pes manualis, or foot-and-hand which was six-fifths of the Roman foot. Several of these modules were used by the various masters of Chartres. Added to this variety, there were several different systems of proportion in the Gothic period. John Harvey explains that "the two main systems were known as ad quadratum, based upon a square, and ad triangulum based on the equilateral triangle. Applied to the cross-section of a church, the system ad triangulum naturally resulted in a lower, more squat proportion of height and width."
Small wonder that the unravelling of the immensely complex geometry of a building like Chartres is the labour of a lifetime.