The signatures of the cathedral builders
Every stonemason bore a mark, and every mark fitted into a "mother key", a circle geometry of triangle and square.
A mason’s mark is a sign cut into worked stones, sculptures and buildings in the Middle Ages, above all on churches and cathedrals. After his training, each stonemason received a mark for life from his lodge. With it the “free masons” signed their work. Many of these marks can still be seen today. Similar ones are known from antiquity.
The mother key
The Viennese engineer Franz von Rziha (1831–1897) believed he had deciphered the secret of these marks. According to him, every mason’s mark fits into a mother key, the emblem of the principal lodge where the mason had trained. The mother key is a symmetrical geometry within a circle. The individual’s mark is just a small section of it.
A basic grid in the manner of a mother key: circle, two triangles, two squares and a twelve-pointed star around a common centre. Every mark follows the lines of such a net.
By no means all masons’ marks can be derived this way. There were great regional and period differences, and many marks come from craftsmen of small workshops without a mother key.
The lodge saying
A traditional saying of the Cologne cathedral lodge describes exactly this interplay in verse. It speaks of cord and ruler running through the compass circle everywhere, of finding “three in four” and going through the one into the centre, and out of the centre again through the three and the four into the circle. Its core reads:
Ein Punct, der in den Cirkel geht,
der im Quadrat und Dreyangel steht.
(A point that enters into the circle, that stands in the square and the triangle.) Whoever hits this point, the saying continues, has the whole art. Whoever does not understand it has learned in vain. The saying is thus a building instruction: triangle, square and circle, all laid around the same centre.
Circle, triangle and square among Rosicrucians and Freemasons
How circle, triangle and square are geometrically connected is shown by a Rosicrucian woodcut of 1617, the Rebis or “philosophical egg” (reproduced under Freemasonry). At the bottom lies a winged sphere with a triangle and a square drawn in it. On it a dragon, image of the forces of nature and of the human passions that must be mastered. On the dragon stands a two-headed being that looks like a conjoined twin but represents a hermaphrodite, Hermes and Aphrodite, with a male and a female head. Rosicrucians still use triangle, square and circle today, for instance in the emblem of the Lectorium Rosicrucianum.
The hermaphrodite holds compass and square, a good hundred years before the first Grand Lodge of the Freemasons was founded in London in 1717, whose chief emblem these two tools are. The compass, the movable tool for drawing circles and spheres, stands for the male-active triangle, the square for the female-passive four-sided figure. Laid over each other as in the Rebis, triangle and square are part of a twelve-gon, for 12 is the least common multiple of 3 and 4:
Triangle (compass, spirit, 3) and square (square, matter, 4) laid over each other: their vertices are vertices of a twelve-gon, for 12 is the least common multiple of 3 and 4.
Twelve was and is holy in Christian mysticism: twelve disciples, twelve tribes of Israel, twelve gates of the heavenly Jerusalem, and the twelve signs of the zodiac. Added together, spirit (3) and matter (4) give the holy seven. The image mirrors the Platonic idea of God as geometer and the mystic’s longing to live by divine principles and so approach divine perfection. Circle, triangle and square have always carried the idea of creation. And the numerals 1, 2, 3 and 4 on the sphere point to the lattice of triangles and squares that densely packed spheres form (see Space filling without gaps).
From stonemason to lodge
From the tradition of the builders’ lodges came the speculative Freemasonry of modern times, which works with polygons and star polygons as symbols (see Freemasonry). On the other hand, the geometry of the mother keys is partly identical with the geometry of sphere packings and their crystal lattices, which consist only of triangles and squares (see Circle, triangle and square). So the path through the masons’ marks also leads back to circle and sphere, and thus to the tetractys. The circle closes.