Sacred Geometry and the Law of Three

Pistoia: Archeosophica; Benassai Alessandro. 1996. La genesi svelata. Pistoia: Archeosophica. The point indeed cannot be divided. The point as that which has no parts is the definition provided by Euclid in the first book of the Elements. The moment of Initiation, the symbol of Ra, the Word in the Sun, the Eye of the World. From the Point, source of every manifestation, originate 3 rays, effect of the interior Divine disposition that originates Three Divine Personalities or hypostases. The One becomes Tri-Unity: the Almighty Father, the All-wise Son and the Divine All-loving Mother. A mathematical representation of the process of passage from Unity to Ternary is represented by the extraction of the cube root of unity on an algebraically closed field like that of complex numbers $\mathbb{C}$, i.e. $\sqrt[3]{1} = \{1, \omega, \omega^2\}$, where $\omega = e^{2i\pi/3}$ and $\omega^2 = e^{4i\pi/3}$. A graphical representation of the cube roots of unity is represented in Fig. 2. Through the interior motion, indicated by the cube root, the One $1$ appears as Three $3$ on the circumference. The Three points symbolize the Three divine Personalities of a single indivisible Essence, the Archè or Absolute. From Ternary to Sacred Triangle In the previous paragraph we analyzed the passage from One to Three in the specific case of the creative act. More generally, the Ternary identifies the "Law of Three" in all its possible manifestations, whether of uncreated order, created, cosmic or individual. If, through the use of geometry, we want to study the implications of this law, we must resort to the use of 3 identical and equidistant points (Fig.3). In synthesis, the three points represent the three Entities or also the three Forces through which the Ternary acts: active, passive and neutral; or masculine, feminine and androgynous; or also future, past and present; thesis, antithesis and synthesis; etc. In all its manifestations the Ternary always expresses a force that acts as positive, one as negative and a third, identified with the upper point (Fig.3), which acts as a conciliating form towards the two previous antithetical ones. The two forces, projective and receptive, represented by the points on the horizontal line, are balanced by a third element orthogonal to the ground of conflict and which expresses its conciliating and also neutralizing force. Every dualism is the horizontal, visible projection of a superior Ternary whose conciliating element is invisible. The Three points (Fig.3 right) are identical and therefore identify every possible expression of the original Ternary. The moment instead when we distinguish them, assigning a symbol or number to each of them (Fig.3 left), it is said that the Ternary is realized to use a mathematical term, that is identified in one of its specific representations. Realizing the abstract Ternary by identifying it with Numbers 1, 2 and 3 which, in this adimensional context, have a precise meaning: the One $1$ identifies the "Origin of Numbers", the Two $2$ the "Firstborn of Even Numbers" or "Feminine" and the $3$, instead, the "Firstborn of Odd Numbers" or "Masculine". These Three Entities, identified by Numbers 1, 2 and 3 belong to an adimensional and formless world, but possess a first, essential, geometric structure. From the Three points we can therefore draw lines or segments that unite them reciprocally and that synthetically represent all the possible relationships that these entities can have. The mutual relationships of the three vertices 1, 2 and 3 identify an equilateral Triangle. The mutual possible relationships among these Numbers are infinite, but for our discourse we will choose the simplest relationship expressed by the operation of addition, so that the three relationships or the three relations originated by the elements of the Ternary 1, 2 and 3 will be expressed by the Numbers $1 + 2 = 3$; $1 + 3 = 4$; $2 + 3 = 5$; that is by the Numbers of the Sacred Triangle. From an abstract symbolic representation we therefore pass to a formal geometric representation, actually drawing a Triangle, no longer equilateral, but scalene with sides or segments of dimension 3, 4 and 5, that is the Sacred Triangle. The passage from "informal" or abstract to "formal" or concrete corresponds to the passage from the "world of essences" to the "world of phenomena", from the "formless world" to the "world of form": from the equilateral Triangle which with its symmetry identifies a perfection and a reality outside of time, to the Sacred Triangle which with its thrust identifies an evolutionary cycle in time and forms. The Sacred Triangle maintains its seminal origin from the Ternary 1, 2 and 3. Indeed, let us consider the circle $C$ inscribed in the Sacred Triangle. As in every right triangle with legs $a$ and $b$ and hypotenuse $c$, the radius $r_C$ of such circle will be given by $r_C = \frac{a + b - c}{2}$;