“The Forty-Seventh Proposition is older than Pythagoras. It is this: “In every right angled triangle, the sum of the squares of the base and perpendicular is equal to the square of the hypotenuse.” “The square of a number is the product of that number, multiplied by itself. Thus, 4 is the square of 2 and 9 of 3.
The first ten numbers are: 1 2 3 4 5 6 7 8 9 10
Their squares are: 1 4 9 16 25 36 49 64 81 100
And 3 5 7 9 11 13 15 17 19
are the differences between each square and that which precedes it; giving us the sacred numbers 3, 5, 7 and 9”.
“Of these numbers, the square of 3 and 4, added together, gives the square of 5; and those of 6 and 8 the square of 10; and if a right-angled triangle be formed, the base measuring 3 or 6 parts and the perpendicular 4 or 8 parts, the hypotenuse will be 5 or 10 parts; and if a square is erected on each side, these squares being subdivided into squares each side of which is one part in length, there will be as many of these in the square erected on the hypotenuse as in the other two squares together.”
“Now the Egyptians arranged their deities in Triads – The father or the spirit or Active Principle or Generative power; the Mother, or Matter, or the passive principle, or the conceptive power; and the son, issue or Product, the Universe, preceeding from the two principles. These were OSIRIS, ISIS and HORUS. In the same way PLATO gives us Thought the father; primitive matter the mother; and Kosmos the world, the son, the universe animated by a soul. Triads of the same kind are found in the Kabalah.
PLUTARCH says, in his book De Iside et Osiride, “But the better and diviner nature consists of three, - that which exists within the intellect only, and matter and that which proceeds from these, which the Greeks call Kosmos; of which three, Plato is wont to call the Intelligible, the ‘idea, Exemplar and Father’; Matter, ‘the Mother, the Nurse, and the place of receptacle of generation’; and the issue of these two, ‘The Offspring and Genesis,’” the Kosmos, “a word signifying equally beauty and order, or the universe itself.” You will not fail to notice that Beauty is symbolised by the Junior Warden in the South. Plutarch continues to say that the Eqyptians compared the universal nature to what they called the most beautiful and perfect triangle, as Plato does, in that nuptial Diagram, as it is termed, which he has introduced into his Commonwealth”.
“Then he adds that this triangle is right angled, and its sides respectively as 3, 4 and 5; and he says, “We must suppose that the perpendicular is designed by them to represent the masculine nature, the base,the feminine, and that the hypotenuese is to be looked on as the offspring of both; and accordingly the first of them will aptly enough represent OSIRIS, or the prime cause; the second ISIS, or the receptive capacity; the last, HORUS, or the common effect of the other two. For 3 is the first number which is composed of even and odd; and 4 is a square whose side is equal to the even number 2; but 5, being generated, as it were, out of the preceding numbers, 2 and 3, may be said to have an equal relation to both of them, as to its common parents.”
Morals and Dogma of the ancient and accepted Scottish Rite of Freemasonry. Prepared for the supreme council of the Thirty Third Degree, 1871 published 1919. P86 – 89. 3 - Degree of Master Mason