Sallust said that after a State has been corrupted by luxury and idleness, it may by its mere greatness bear up under the burden of its vices. But even while he wrote, Rome, of which he spoke, had played out her masquerade of freedom. Other causes than luxury and sloth destroy Republics. If small, their larger neighbors extinguish them by absorption. If of great extent, the cohesive force is too feeble to hold them together, and they fall to pieces by their own weight. The paltry ambition of small men disintegrates them. The want of wisdom in their councils creates exasperating issues. Usurpation of power plays its part, incapacity seconds corruption, the storm rises, and the fragments of the incoherent raft strew the sandy shores, reading to mankind another lesson for it to disregard.
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 hypothenuse."
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 hypothenuse 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 hypothenuse 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, proceeding 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.