Sacred Geometry and Ghematria: Golden Ratio in San Galgano Abbey
A concentric circle to the primitive circle C1, amplifying the latter according to a golden increment: $C_2 = C_1' = C_1 \times 1.618$. The extension of the sides of the rectangle/transept meets this second circle C2, determining 8 specific points that indicate the position of the relative columns around the crossing of the transept. The union of these points through straight lines establishes the other dimensions of the Abbey: the width of the side naves (B), the length of the transept (D), the depth of the chapels (E). To conclude the constructive scheme of the plan, it is necessary to fix the width of the transept (D) and the average width of the bays (M). Therefore we proceed as follows: A circle C3 tangent to the length of the transept is inscribed (i.e., on the main axis of the Temple, the decumanus) and it is always amplified in a golden manner obtaining the circle $C_4 = C_3' = C_3 \times 1.618$ (Fig. 8). The intersection and contact of circle C4 with the geometric grid determines and concludes the proportioning of the transept/apse, establishing the average width of the naves (M), a width that spreads - like an echo - 7 times along the main axis of the temple determining the length of the nave. **Ghematria and Geometry - 1st Part (Leo and Zadik)** The esoteric Tradition of Israel bases much of its speculation and meditation on the properties of language, particularly on the use of profound reflection applied to the Pentateuch and the inspired Prophetic writings, which can reveal the mysteries of Divine Will and guide the steps of spiritual evolution of Humanity. The wise Masters of the Cabalistic Tradition were not by chance called the Masters of the Name (Baal ha-Shem) because they knew the secret techniques of alphabetical revolution suitable for understanding the occult meanings of sacred texts and extracting divine and angelic names to be used in ritualism and mystical ascension of the Merkabah. These systems of revolution, passed from the Hebrew Cabalistic environment to the Greek and then Latin ones, inspirers of Giordano Bruno when he wrote the famous treatises on mnemonics and magic seals, were already used by Raymond Lull and later became famous in modern times as a cryptographic system treated by Abbot Trithemius of Sponheim in his work entitled Steganographia. Although modern cryptographic studies have seen nothing more than a linguistic mechanism to conceal secret messages for political purposes, economic interests, or for personal protection, much more is hidden in the Traditional systems of Cabala which, through 4 main procedures, distill the essence of the Words of Revelation (Sacred Scripture), opening the shell of the literal form to reveal the essence of the divine message. The methods provided for this sacred decipherment are the following: • **Temurah**: that is, the possibility of changing the position of letters in a word forming new terms, but with complementary essential meaning. • **Notarikon**: the formation of synthetic terms composed of the initial or final letters of the words composing a sentence (called acrostic in Greek), or vice versa the decomposition of a term composed of a definite number of letters into as many words whose initials correspond to those of the taken term. • **Ghematria**: the comparison of terms or phrases through the numerical equivalence of the terms that compose them, possible by virtue of the fact that in the Hebrew alphabet each letter has a corresponding numerical value and identifies such number. • **Ziruph**: the revolution of the order of alphabetical letters according to a progressive displacement of the letter considered initial. Ghematria, which we treat in this article, is one of the most intriguing alphabetic-mathematical systems. The term Ghematria (in Hebrew גימטריא) is associated with the Greek term Geometry, probably from a time when the arithmetical idea of number did not exist separate from its visual geometric idea. Geometry can be considered the expression of number in form, so also Ghematria can be understood as the relationship between number and its formal-verbal expression, number being an abstract concept of a power. Number wears the garment of the letter and with it it is possible to pronounce it, visualize it and invoke it for sacred, mystical and theurgical purposes. To each Hebrew letter, we have said it many times, corresponds an idea, a hieroglyph and a number. But, to be more precise, letters in the Hebrew language are numbers. This identity between letters and numbers allows for mathematical operations, which we usually conceive as purely...