(24) Pythagoras taught that friendship was the truest and nearest perfect of all relationships. He declared that in Nature there was a friendship of all for all; of gods for men; of doctrines one for another; of the soul for the body; of the rational part for the irrational part; of philosophy for its theory; of men for one another; of countrymen for one another; that friendship also existed between strangers, between a man and his wife, his children, and his servants. All bonds without friendship were shackles, and there was no virtue in their maintenance. Pythagoras believed that relationships were essentially mental rather than physical, and that a stranger of sympathetic intellect was closer to him than a blood relation whose viewpoint was at variance with his own. Pythagoras defined knowledge as the fruitage of mental accumulation. He believed that it would be obtained in many ways, but principally through observation. Wisdom was the understanding of the source or cause of all things, and this could be secured only by raising the intellect to a point where it intuitively cognized the invisible manifesting outwardly through the visible, and thus became capable of bringing itself en rapport with the spirit of things rather than with their forms. The ultimate source that wisdom could cognize was the Monad, the mysterious permanent atom of the Pythagoreans.

(3) "The Pythagoreans indeed go farther than this, and honour even numbers and geometrical diagrams with the names and titles of the gods. Thus they call the equilateral triangle head-born Minerva and Tritogenia, because it may be equally divided by three perpendiculars drawn from each of the angles. So the unit they term Apollo, as to the number two they have affixed the name of strife and audaciousness, and to that of three, justice. For, as doing an injury is an extreme on the one side, and suffering one is an extreme on the on the one side, and suffering in the middle between them. In like manner the number thirty-six, their Tetractys, or sacred Quaternion, being composed of the first four odd numbers added to the first four even ones, as is commonly reported, is looked upon by them as the most solemn oath they can take, and called Kosmos." (Isis and Osiris.)

(59) Theon of Smyrna declares that the ten dots, or tetractys of Pythagoras, was a symbol of the greatest importance, for to the discerning mind it revealed the mystery of universal nature. The Pythagoreans bound themselves by the following oath: "By Him who gave to our soul the tetractys, which hath the fountain and root of ever-springing nature."

(64) Pythagoras saith: How marvellous is the diversity of the Philosophers in those things which they formerly asserted, and in their coming. together {or agreement], in respect of this small and most common-thing, wherein the precious thing is concealed! And if the vulgar knew, O all ye investigators of this art, the same small and vile thing, they would deem it a lie! Yet, if they knew its efficacy, they would not vilify it, but God hath concealed this from the crowd* lest the world should be devastated.

(54) The most famous of the Pythagorean fragments are the Golden Verses, ascribed to Pythagoras himself, but concerning whose authorship there is an element of doubt. The Golden Verses contain a brief summary of the entire system of philosophy forming the basis of the educational doctrines of Crotona, or, as it is more commonly known, the Italic School. These verses open by counseling the reader to love God, venerate the great heroes, and respect the dæmons and elemental inhabitants. They then urge man to think carefully and industriously concerning his daily life, and to prefer the treasures of the mind and soul to accumulations of earthly goods. The verses also promise man that if he will rise above his lower material nature and cultivate self-control, he will ultimately be acceptable in the sight of the gods, be reunited with them, and partake of their immortality. (It is rather significant to note that Plato paid a great price for some of the manuscripts of Pythagoras which had been saved from the destruction of Crotona. See Historia Deorum Fatidicorum, Geneva, 1675.)

(42) Iamblichus gathered thirty-nine of the symbolic sayings of Pythagoras and interpreted them. These have been translated from the Greek by Thomas Taylor. Aphorismic statement was one of the favorite methods of instruction used in the Pythagorean university of Crotona. Ten of the most representative of these aphorisms are reproduced below with a brief elucidation of their concealed meanings.

(3) Anaxacoras saith:—I make known that the beginning of all those things which God hath created is weight and proportion,* for weight rules all things, and the weight and spissitude of the earth is manifest in proportion; but weight is not found except in body. And know, all ye Turba, that the spissitude of the four elements reposes in the earth; for the spissitude of fire falls into air, the spissitude of air, together with the spissitude received from the fire, falls into water; the spissitude also of water, increased by the spissitude of fire and air, reposes in earth. Have you not observed how the spissitude of the four elements is conjoined in earth? The same, therefore, is more inspissated than all.

Then saith the Turba: —Thou hast well spoken. Verily the earth is more inspissated than are the rest. Which, therefore, is the most rare of the four elements and is most worthy to possess the rarity of these four?

He answereth:—Fire is the most rare among all, and thereunto cometh what is rare of these four. But air is less rare than fire, because it is warm and moist, while fire is warm and dry; now that which is warm and dry is more rare than the warm and moist. They say unto him: —Which element is of less rarity than air?

He answereth:—Water, since cold and moisture inhere therein, and every cold humid is of less rarity than a warm humid.

Then do they say unto him:—Thou hast spoken truly. What, therefore, is of less rarity than water?

He answereth:-—Earth, because it is cold and dry, and that which is cold and dry is of less rarity than that which is cold and moist.

PyTHAGoRAS saith:—Well have ye provided, O Sons of the Doctrine, the description of these four natures,* out of which God hath created all things. Blessed, therefore, is he who comprehends what ye have declared, for from the apex of the world he shall not find an intention greater than his own! Let us, therefore, make perfect our discourse.

They reply:—Direct every one to take up our speech in turn. Speak thou, O Pandolfus!

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