Sacred Geometry

I. What Sacred Geometry Is

Τί ἐστιν ἡ Ἱερὰ Γεωμετρία

Γεωμετρία is the measuring of the earth, γῆ and μέτρον, and the Greeks said where they got it. Herodotus reports that Sesostris divided the land of Egypt into equal square plots, taxed each one, and sent surveyors to measure what the Nile carried away each year; "from this, in my opinion, the Greeks learned the art of measuring land".¹ Proclus, drawing on Eudemus's history, says the same: geometry was first discovered among the Egyptians, originated in the remeasuring of their lands, and was carried to Greece by Thales.² Zevism holds that one must stand at the source, and the source of this science is Egyptian measure made Greek proof.

What the Greeks added was the reason geometry is sacred. Plato, in the Republic, has Socrates say that geometry is knowledge of what always is, and that it draws the soul toward truth and produces the philosophic understanding that directs upward what is now wrongly directed downward.³ Philolaus, the first Pythagorean whose words survive, said that all things that are known have number, and that without number nothing can be understood or known.⁴ The figures on these pages are number made visible. A triangle is 3 seen; a cube is 8 corners, 12 edges and 6 faces seen at once; the Tetractys is 1, 2, 3 and 4 laid in rows. To draw a figure exactly is to see what a number is.

The tradition that the entrance to Plato's Academy bore the words "let no one ignorant of geometry enter" is recorded only in late antiquity and the Byzantine period, 9 centuries after Plato, and is cited here for what it is: the memory of a school in which geometry was the threshold of philosophy.⁵ This section is built on the same assumption. The figures are the threshold, and the threshold is where one begins.

II. How the Study Is Arranged

Ἡ Τάξις τῆς Μελέτης

The study is graded. It begins at 1 and ascends, and no layer assumes a figure that an earlier layer hasn't built. Level I takes the figures of the first 10 numbers in order: the point and the circle, the line and the vesica, the triangle, the square and the cross, the pentagon and the pentacle, the hexagon and the hexagram, the heptagon and the 7 circles, the octagon and the eight-pointed star, the enneagon and the square of 9, the Tetractys and the Decad. Level II is the golden section, the proportion the pentagon and the decagon share. Level III raises the plane into the body: the 5 Platonic solids and the grid of circles from which they can be drawn. Level IV is the sphere, the body of the Cosmos, and the return to the point.

Every page has the same parts. The Figure gives the definition and the theorem, from Euclid where Euclid has it. The Construction gives the steps, with ruler and compass where they suffice and an honest note where they don't. Number and Form connects the figure to its figurate number and to the Temple's numerology. In the Ancient Witnesses sets the figure among its sources, Greek, Egyptian, Babylonian and later, with the dates stated and the late attributions marked as late. The Zevist Reading reads the figure through the Temple's teaching of the soul, the elements, the Gods and Ma'at. A contemplation follows, aligned with the Temple's guide to the numbers in magick and meditation, and then a table of exact measures and a numbered list of sources with links to the texts.

Every diagram is computed, not drawn by hand. The polygons are placed by angle, the stars by stepping, the solids by rotating their coordinates and projecting them, with hidden edges dashed; the proportions are exact to the pixel, and the measures in the tables were checked by calculation against the standard references. The pages follow the black and white themes of the site, and the figures follow the theme with them.

III. Numerology and Geometry

Ἀριθμολογία καὶ Γεωμετρία

The Temple's Zevist Numerology reads the 10 fundamental numbers, from the Monad to the Decad, through the Theology of Arithmetic and the Temple's own core meanings; its pages show each number as a figure of dots.⁶ This section is the geometry of those figures. Each of the first 10 layers opens with the band of its number, carrying the Temple's core meanings and a link to the number's page, and reads the figure as that number's shape: the point under the Monad, the line under the Dyad, the plane under the Triad and the solid under the Tetrad, as the Pythagoreans ordered them.⁷ The Tetractys of Layer 10 gathers all 4, and the Temple's Tetractys symbol page is its companion; the Pythagorean Star page is the companion of Layer 5; the Equal-Armed Cross, the Triskelion, Infinity and the Chakra Cross stand beside their layers.⁸

Numerology says what a number means; geometry shows what it does. Three is spirit, divinity and the first union in the Temple's reading, and the triangle is the first figure that encloses anything. Seven is the virgin and the armour of the just, and the heptagon is the first polygon that ruler and compass can't draw. Eight is the firm foundation and the Divine Mother, and the cube is 2 × 2 × 2. The 2 readings confirm each other at every layer, and that agreement, between the Theology of Arithmetic and the Elements, is the subject of the section.

IV. The Instruments

Τὰ Ὄργανα

Euclid allows 2 tools, the straightedge and the compass, and 3 postulates to use them: a line between any 2 points, a line extended, a circle about any centre with any distance.⁹ With these the first 6 layers can be drawn and so can the octagon, the decagon and every doubling; the heptagon and the enneagon can't, and the pages say so, with Gauss's rule and the ancient constructions that bent it. A reader who follows the constructions with real instruments will learn more than one who reads them, which is why each page gives the steps. The compass is the Monad's tool and the straightedge the Dyad's, and between them they make everything up to the sphere.

V. Standing Sources

Αἱ Πηγαί

The texts cited throughout are open and checkable. Euclid's Elements is cited from the Greek of Heiberg on Perseus and the English of Heath in D. E. Joyce's edition; Plato, Aristotle, Herodotus, Diogenes Laertius and Plutarch from Perseus and the Scaife Viewer; the Theology of Arithmetic from the Greek on Wikisource; Proclus from Morrow's translation; the Pythagorean tradition from the Stanford Encyclopedia of Philosophy; the mathematics from MathWorld and MacTutor; and the objects from the collection databases of the British Museum and the Ashmolean. Where a claim is popular and unsupported, the page names it and sets it aside.

1. Herodotus, Histories II.109. English (Godley) · Greek.
2. Proclus, Commentary on the First Book of Euclid's Elements, Prologue II (Friedlein 64.16 to 65.11), translated by Glenn R. Morrow (Princeton, 1970). archive.org.
3. Plato, Republic VII, 527b. English (Shorey) · Greek.
4. Philolaus, fragment B4, in Carl Huffman, "Philolaus", Stanford Encyclopedia of Philosophy. plato.stanford.edu.
5. The inscription is first reported in the 6th-century commentators on Aristotle (Elias and Philoponus) and later by Tzetzes; see Henri Dominique Saffrey, "ΑΓΕΩΜΕΤΡΗΤΟΣ ΜΗΔΕΙΣ ΕΙΣΙΤΩ: une inscription légendaire", Revue des Études Grecques 81 (1968) 67 to 87. Persée.
6. Temple of Zeus, Zevist Numerology and its 10 number pages, 1 · The Monad to 10 · The Decad.
7. Sextus Empiricus, Against the Physicists II 278 to 282. Greek, Scaife Viewer.
8. Temple of Zeus, Our Symbols: The Tetractys, The Pythagorean Star and the Two Orientations, The Equal-Armed Cross, The Triskelion, Infinity and the Temple of the Sun, The Chakra Cross and Descending Power.
9. Euclid, Elements I, Postulates 1 to 3. Joyce, Book I.

VI. The Path of Study

14 figures in 4 levels. Begin at Layer 1 and ascend.