Pythagorean Tetraktys and Masonic Delta by Arturo Reghini: The poetic formula of the Pythagorean oath has been transmitted by various authors, but its most ordinary and exact form is the following:
“No, I swear by him who has sent to our soul tetractys in which there is the source and root of eternal nature.” A variation of this formula also appears in Aurea Carmina, or Golden Verses.
The last part of “ Sacred numbers in masonic Pythagorean Tradition” 1947, first chapter.
The Pythagorean symbol of Tetractys in its schematic form of an equilateral triangle clearly coincides with the schematic form of the Masonic Delta, and also with the schematic form of the Christian symbol of Trinity. This latter assimilation comes as too easily done, especially in the case of the Eternal Father eye fitted inside. The Christian character of the masonic symbol is not much more conspicuous when, as often happens, the written tetragrammaton appears in the triangle, for example, the name of God in four letters, so designated by cabalists with the greek word, and even disappears when the triangle is located within the giant flaming five-pointed star with or Pythagorean pentalpha, as in frontispiece of Baron De Tschoudy Étoile Flamboyant, which is attributed to the ritual of fourteenth degrees of Scottish Rite.
In addition, the sacred delta, which is together with the sun and moon, one of three sublime lights of Freemasons society, as says the Apprentice ritual, is in the first-degree work between sun and moon symbols and behind the Venerable seat, while in the second-degree work is replaced by a Flaming Star. The initiatic ages of the apprentice and mate correspond to this substitution. The result is a connection between two symbols, and since no doubt, the five-pointed star is a symbol so characteristic both of the ancient Pythagorean brotherhood and Freemasonry, it results in the identification of the Masonic Delta with the Pythagorean Tetractys. To give a Christian character even to the five-pointed star one should say that this was the star shape that appeared, according to the fourth Gospel, to three Magi, Melchior, Caspar, and Balthazar, but the fourth gospel on this point does say nothing, and other Gospels, the three Synoptic Gospels, do not make the slightest mention of three Magi. And as the ancient documents prove the continuity of the Masonic tradition referring to Pythagoras, the identification of masonry with geometry, and masons’ claim to be the only ones who know sacred numbers, it seems that the identification of Masonic Delta with Pythagorean Tetractys is comforted by more weight than identification with the Christian symbol.
Among mason symbols we do not see any Christian symbol, not even the cross appears, instead and it is natural, but only symbols of architectural and numerical occupation and geometric symbols. If the masonic delta had a Christian character it would be an isolated symbol, confused, which one would not understand the existence and diversity in freemasonry. We insist on this point not only because it is right for the seriousness and serenity of critical investigation not to be misled by sympathy or antipathy, but because the misunderstanding and ignorance about it are ancient and deadly, and many rituals, instead of driving the brothers to the full understanding of symbolism, contributing in good or bad faith to prevent an interpretation that it is essential to understand masonic of symbolism.
This is not to say or see a contrast between the Pythagorean Tetractys or masonic delta and the Christian symbol of the Trinity. The Christian ternary opposition to the Pythagorean quaternion was due to the Christians’ myopic bigotry of the early centuries, and it was unjustified because, as we will see, the Pythagoreans were triad enhancers, and their practice of worship and enumerate the number three in all the things guided them in the classification of even numbers.
To summarize, two can only be achieved through addition, and only by the addition of two units. Three can only be achieved through addition, where at least one of the terms is unity. From four on all numbers can be obtained by the addition of all the terms other than a unit. The geometric representation of numbers in a three-dimensional space is perfect and ends with the number four, and since the sum 1 + 2 + 3 + 4 = 10 is the new unit of the decimal numbering system, consequently the perfection of four and ten and the Tetractys symbol. Thus Pythagoreans did not especially deal in numbers larger than ten that were expressed in language and writing by ten and previous numbers and for this reason, perhaps, they reduced to the first nine numbers the numbers greater than ten by the consideration of their pithmene or bottom, substituting to them the remaining of their division for nine or the very nine when the number was a multiple of nine: remaining easily obtained through the well-known rule of the division remaining for nine.
Since the development of numbers by addition ends with four, one must now consider the development or generation of numbers by multiplication. It seems sure that Pythagoreans did actually appeal to this canon of distinction because the number seven was sacred to Minerva since as Minerva it was a virgin and not generated, that is it was not a factor of any number (within the decade) and was not the product of a factor. Thus numbers are divided into numbers that are not products of other numbers, or prime numbers, and numbers that are products. Taking into account only the numbers within a decade, numbers are divided into four classes: the class of prime numbers within a decade, which are factors of decade numbers: and they are the two (which really is not a number) but appear as a factor of 4 of 6 of the 8 and 10, three that is a factor of 6 and 9; and 5 which is a factor of 10. The second class consists of the prime numbers less than 10 which are not factors of numbers less than 10 and is represented by only seven. The third class consists of the composed numbers, less than ten, and that factors of numbers less than 10, and is made only by the number four, which is at the same time the square of the two and a factor of 8; the fourth class is formed by composite numbers less than 10 which are compounds of other numbers without being factors within the decade, it is represented by six, eight and nine, because 2 · 3 = 6, 2 · 2 · 2 = 2 · 4 = 8 and 3 · 3 = 9. Not counting 10 and taking into account two we have four prime numbers: 2, 3, 5, 7 whose only one does not produce other numbers, and four composite numbers: 4, 6, 8, and 9 of which only one is a factor.
It is worth noting that this Pythagorean canon of distinction for numbers classification within a decade coincides perfectly with the traditional canon of distinction compliant with Vedanta for the fourfold classification of twenty-five principles or tattwa, precisely the first principle (Prakriti) which is not a production but it is productive, seven principles (Mahat, Ahamkara, and the 5 tanmatras) which are both products and productive, 16 principles (the 11 indriya, including Manas and the 5 bhuta) which are unproductive productions, and finally Purushawhich is neither production nor productive. We refer the reader to the exposure that makes René Guenon in his “The Man and his becoming according to the Vedanta”, Bari, Laterza, 1937. This same principle of distinction affects, as noted by the Colebrooke (Essais sur la Philosophie des Hindous, trans. Pauthier), the division of nature, made in Scotus Erigena De divisione Naturae, who says: “The division of Nature I believed to be established in four different species, of which the first is what creates and is created, the second is what is created and in turn creates: the third that is created and does not create, and finally the fourth what is not created nor creates. “Of course, it is not appropriate to speak of derivation, however, Pythagoras, chronologically precedes, not only Scotus Erigena but Shankaracharya too. So that leaves the established traditional character of the Pythagorean doctrine of numbers.
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