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Updated: May 12, 2025


They abstained from animal food with the abhorrence of Pythagoreans, their drink was a pure simple element, they were vomited once a week, took physic or a glyster every third day, spent the forenoon in algebraical calculations, and slept from four o'clock till midnight, that they might then take the field with that cool serenity which is the effect of refreshment and repose.

TETRACTYS. A figure used by Pythagoras, consisting of ten points, arranged in a triangular form so as to represent the monad, duad, triad, and quarterniad. It was considered as very sacred by the Pythagoreans, and was to them what the tetragrammaton was to the Jews.

The Pythagoreans held that there is a peculiar sacredness in the number ten. Just as the Babylonians of the early day and the Hegelian philosophers of a more recent epoch saw a sacred connection between the number seven and the number of planetary bodies, so the Pythagoreans thought that the universe must be arranged in accordance with the number ten.

The gamma, Γ, or Greek letter G, is said to have been sacred among the Pythagoreans as the initial of Γεωμειρία or Geometry. Vide Oliver, Hist. Init. p. 68, note.

The Pythagoreans knew the properties of parallels and proved the theorem that the sum of the three angles of any triangle is equal to two right angles. Lastly, the Pythagoreans discovered the existence of the incommensurable or irrational in the particular case of the diagonal of a square in relation to its side.

It is said, also, that Numa built the temple of Vesta, which was intended for a repository of the holy fire, of a circular form, not to represent the figure of the earth, as if that were the same as Vesta, but that of the general universe, in the center of which the Pythagoreans place the element of fire, and give it the name of Vesta and the unit; and do not hold that the earth is immovable, or that it is situated in the center of the globe, but that it keeps a circular motion about the seat of fire, and is not in the number of the primary elements; in this agreeing with the opinion of Plato, who, they say, in his later life, conceived that the earth held a lateral position, and that the central and sovereign space was reserved for some nobler body.

What! not know the great Polemo of Rhodes, the friend of Plotinus, the pupil of Theagenes, the disciple of Thrasyllus, the hearer of Nicomachus, who was of the school of Secundus, the doctor of the new Pythagoreans? Not feel the presence in Sicca of Polemo, the most celebrated, the most intolerable of men?

If men were not Christians, they would choose, I think, to be Pythagoreans, were it for nothing but the slight chance they would enjoy of passing into some state of existence not in a remote degree different from that which they have declared themselves sick of a thousand times before they died.

XXII. Yet, how desirous he was of friendship, though at the same time he dreaded the treachery of friends, appears from the story of those two Pythagoreans: one of these had been security for his friend, who was condemned to die; the other, to release his security, presented himself at the time appointed for his dying: "I wish," said Dionysius," you would admit me as the third in your friendship."

Some of the Pythagoreans, if not Pythagoras himself, held that the earth is a sphere, and that the apparent daily revolution of the sun and stars is really due to a motion of the earth, though at first this motion of the earth was not supposed to be one of rotation about an axis.

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