Geometry, especially Gothic cathedral geometry, has many meanings in different periods. In simple terms, geometry is the science of shapes and figures. In the medieval period, that of Gothic art, geometry was known as "line" among journeymen builders. It was used by the worker and the architect (the master builder) to design the plan and elevation of Gothic buildings, cathedrals, abbeys, churches and so on. Villard de Honnecourt gives examples of these techniques in his notebook, with a Gothic cathedral choir alongside a Gothic elevation, as well as various geometric networks. Regulating tracings are, for some, a secret geometrical concept that can be used to draw the plans of a Gothic cathedral, including its footprint and the design of the choir, nave, apse and chevet. They can be ad quadratum or ad triangulum, i.e. based on a square or a triangle. The layout of Gothic elevations demonstrates the use of an esoteric geometric system capable of designing the elevation of any medieval Gothic cathedral. Simple geometric figures such as squares, triangles and circles can be found in these layouts. They are assembled to form polygons, geometric constructions that are the true signature of Gothic art. The floor plans, for their part, are governed by the symbol of the triple enclosure, that of the heavenly Jerusalem.
On a Gothic cathedral site, the builder uses a knotted rope, a compass, a ruler and a square. This is the secret of the Gothic art known to Villard de Honnecourt. Freemasonry claims knowledge of the geometrical lines used by cathedral builders, without being able to provide historical proof. Similarly, many Gothic cathedrals housed labyrinths under their vaults, evoking the myth of Theseus and the Minotaur. Their geometry, however, does not seem to be linked to the master plan used by medieval master builders. Labyrinths are part of the ornamental vocabulary of cathedrals, but not a signature of Gothic art. Hopscotch refers to the triple enclosure and the labyrinth, to a geometric, symbolic and esoteric concept. It is at once a symbol, a geometric layout and a guide to Gothic cathedrals. It indicates a path to follow inside a sanctuary to gather tellurism.
In his notebook, Villard de Honnecourt offers drawings whose geometry is similar to that of hopscotch and the triple enclosure.
As can be observed in all traditions, springs are associated with the idea of religion, and as such are the object of worship. They can be found near Gothic churches and cathedrals, as well as most ancient sanctuaries and megaliths. In Lourdes, they manifest themselves in the form of a grotto and a spring, while in Chartres Cathedral, they are evoked by the crypt, the underground cavern and the puits des Saints-Forts. These are not the only similarities with Gothic cathedrals. Symbolic analogies are often drawn between covered walkways and church naves, with the menhir evoking the church steeple. Archaeologically, these similarities make sense. As Auguste Choisy put it: "The first churches had only an altar raised over a crypt containing the remains of a martyr". In this respect, they resemble a dolmen, whose covering table overhangs the burial chamber. The sanctuary is an archetype. One of our greatest artists, Auguste Rodin, wrote in his book Les cathédrales de France: "There is in the Cathedral all the simple beauty of the menhir that announces it. Unquestionably, the Romanesque and Gothic blocks are very reminiscent, in a large way, of Druidic stones". You'll find all these themes and more in Pierre Bellenguez's book "Les cathédrales retracées".