Until recently one of the most neglected branches of the western esoteric tradition, sacred geometry began to experience a renaissance in the last two decades of the twentieth century and is becoming a known factor again in the alternative scene. The links between geometry and spirituality go back to the beginnings of geometrical study in the western world, for Pythagoras, the first known teacher of geometry in the Greek world, gained his knowledge of the art in Egypt and Babylon and taught it to students as a sacred mystery surrounded by religious taboos and disciplines. See Pythagorean Brotherhood.

The principles behind classical sacred geometry remain essential to the tradition today. The laws governing form in geometrical constructions are understood by sacred geometers as expressions of the same timeless patterns experienced by mystics in their meditations and visions. The most significant of these laws express themselves in irrational ratios. The most widely known of these ratios is pi, π, the ratio between the diameter of a circle and its circumference. The others that have been central to sacred geometry since ancient times are 1/√2, the ratio between the side of a square and its diagonal; 1/√3, the ratio between the side of an equilateral triangle and twice its height; √5, the ratio between the side of a double square and its diagonal; and phi, φ, the Golden Proportion, the ratio a/b that makes a/b=b/(a+b). These ratios appear constantly in nature and art.

From its Pythagorean sources, sacred geometry became common in the ancient world and was preserved by Christian monks through the chaos that followed the collapse of the Roman Empire in the West. As the first stone cathedrals rose above European cities in the early Middle Ages, the stonemasons who put this lore into practical use became expert in the symbolic dimensions of geometry as well. While the fusion of practical and symbolic geometry went out of use in most of Europe with the rise of the universities and a growing separation between the educated and working classes, in the cultural backwater of Scotland guilds of stonemasons survived into the seventeenth century with significant elements of the old lore intact, and eventually gave rise to Freemasonry. See Freemasonry, origins of.

Medieval stonemasons evolved two schools of sacred geometry, based on different systems of proportion. One, the ad quadratim (“by the square”) system, used the relationship between squares and diagonals as the basis for its designs; the other, the ad triangulum (“by the triangle”) system, used equilateral triangles and hexagons for the same purpose. The two rival systems each had partisans, and quarrels, sometimes descending to the level of fist-fights, sometimes broke out between stonemasons of different schools working on the same building project. The Scottish stonemasons’ guilds that gave rise to modern Freemasonry were partisans of the ad quadratim system, which is why right angles and squares play such a central part in Masonic symbolism. Continental stonemasons’ guilds aligned with the ad triangulum approach may have had an influence on later systems of high degree Masonry, which may explain the greater importance of equilateral triangles in the higher Masonic degrees. See high degrees.

Long before Freemasonry emerged out of the operative stonemasons’ guilds, however, sacred geometry became an integral part of the Renaissance occult tradition. Magicians of the Renaissance used geometry as one of many tools to bring themselves into harmony with the entire cosmos and call down universal powers into the human world. These methods passed at the end of the Renaissance into the underworld of occult secret societies, where they fused with Masonic lore to become essential elements of magical work. Practices based on sacred geometry remain a significant part of the teachings of many occult secret societies today; the pentagram, for example, derives its role in ritual magic from the Golden Proportion geometries that define it. By the nineteenth century, however, very few people in the occult scene understood the geometrical principles behind their rituals and practices. See Magic; Pentagram.

The revival of sacred geometry in the western world began with the work of one man, French occultist R.A. Schwaller de Lubicz (1887–1961). After decades of involvement in occult and alchemical circles in Paris and elsewhere, Schwaller went to Egypt, where he found that the geometries of ancient Egyptian art and architecture provided him with a symbolic language perfectly suited to express mystical teachings. His studies there resulted in a series of brilliant if difficult works on the subject, which introduced traditional sacred geometry to the modern occult tradition. In the 1970s, several English writers researching leys and other earth mysteries stumbled across old treatises on the subject, notably William Stirling’s forgotten 1897 classic The Canon, and introduced the fundamentals of sacred geometry to a wider audience. Since that time, books on the subject have proliferated; some excellent work has been done, though certain authors have mixed sacred geometry with the wilder and less useful ends of the modern rejected knowledge industry, with dubious results. The field remains lively at present, and has begun to influence certain schools of architecture and design. See Leys; rejected knowledge; Schwaller de Lubicz, René Aor.

SOURCE:

The Element Encyclopedia of Secret Societies : the ultimate a-z of ancient mysteries, lost civilizations and forgotten wisdom written by John Michael Greer – © John Michael Greer 2006

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