(14) The great Democritus to a certain degree enlarged upon the atomic theory of Leucippus. Democritus declared the principles of all things to be twofold: atoms and vacuum. Both, he asserted, are infinite--atoms in number, vacuum in magnitude. Thus all bodies must be composed of atoms or vacuum. Atoms possessed two properties, form and size, both characterized by infinite variety. The soul Democritus also conceived to be atomic in structure and subject to dissolution with the body. The mind he believed to be composed of spiritual atoms. Aristotle intimates that Democritus obtained his atomic theory from the Pythagorean doctrine of the Monad. Among the Eleatics are also included Protagoras and Anaxarchus.

(6) Lucas saitth:—You speak only about four natures; and each one of you observes something concerning these. Now, I testify unto you that all things which God hath created are from these four natures, and the things which have been created out of them return into them, In these living creatures are generated and die, and all things take place as God hath predestinated. Democritus, the disciple of Lucas, answereth:—Thou hast well spoken, O Lucas, when dealing with the four natures! Then satith AritsLEus:—O Democritus, since thy knowledge was derived from Lucas, it is presumption to speak among those who are well acquainted with thy master!

Lucas answereth:—Albeit Democritus received from me the science of natural things, that knowledge was derived from the philosophers of the Indies and from the Babylonians; I think he surpasses those of his own age in this learning.

The Turba answereth:—When he attains to that age* he will give no small satisfaction, but being in his youth he should keep silence.

(16) The principles of all things he conceived to be three in number: God, matter, and ideas. Of God he said: "What He is I know not; what He is not I know." Matter he defined as the subject of generation and corruption; idea, as an incorruptible substance--the intellect of God. Wisdom he considered the sum of the virtues. Among the prominent members of the Socratic sect were Xenophon, Æschines, Crito, Simon, Glauco, Simmias, and Cebes. Professor Zeller, the great authority on ancient philosophies, has recently declared the writings of Xenophon relating to Socrates to be forgeries. When The Clouds of Aristophanes, a comedy written to ridicule the theories of Socrates, was first presented, the great Skeptic himself attended the play. During the performance, which caricatured him seated in a basket high in the air studying the sun, Socrates rose calmly in his seat, the better to enable the Athenian spectators to compare his own unprepossessing features with the grotesque mask worn by the actor impersonating him.

(40) While Pythagoras, in accordance with others of his day, practiced divination (possibly arithmomancy), there is no accurate information concerning the methods which he used. He is believed to have had a remarkable wheel by means of which he could predict future events, and to have learned hydromancy from the Egyptians. He believed that brass had oracular powers, because even when everything was perfectly still there was always a rumbling sound in brass bowls. He once addressed a prayer to the spirit of a river and out of the water arose a voice, "Pythagoras, I greet thee." It is claimed for him that he was able to cause dæmons to enter into water and disturb its surface, and by means of the agitations certain things were predicted.

(2) “There was a man among them [i. e. among the Pythagoreans] who was transcendent in knowledge, who possessed the most ample stores of intellectual wealth, and who was in the most eminent degree the adjutor of the works of the wise. For when he extended all the powers of his intellect, he easily beheld every thing, as far as to ten or twenty ages of the human race.”

(3) These things say, if occasion serves, and if possible, O Apollophanes, refute them, and to me, who was then both present with thee, and saw and judged and wondered with thee at them all. And in truth Apollophanes begins prophesying at that time, I know not whence, and to me he said, as if conjecturing the things taking place, "these things, O excellent Dionysius, are requitals of Divine deeds." Let so much be said by us by letter; but you are capable, both to supply the deficiency, and to bring eventually to God that distinguished man, who is wise in many things, and who perhaps will not disdain to meekly learn the truth, which is above wisdom, of our religion.

(20) Critias: the wisest of the Seven, once upon a time declared. Now Solon—as indeed he often says himself in his poems—was a relative and very dear friend of our great-grandfather Dropides; and Dropides told our grandfather Critias as the old man himself, in turn, related to us—that the exploits of this city in olden days, the record of which had perished through time and the destruction of its inhabitants, were great and marvellous, the greatest of all being one which it would be proper

(23) Diogenes of Sinopis is remembered chiefly for the tub in the Metroum which for many years served him as a home. The people of Athens loved the beggar-philosopher, and when a youth in jest bored holes in the tub, the city presented Diogenes with a new one and punished the youth. Diogenes believed that nothing in life can be rightly accomplished without exercitation. He maintained that everything in the world belongs to the wise, a declaration which he proved by the following logic: "All things belong to the gods; the gods are friends to wise persons; all things are common amongst friends; therefore all things belong to the wise." Among the Cynics are Monimus, Onesicritus, Crates, Metrocles, Hipparchia (who married Crates), Menippus, and Menedemus.

(1) And these indeed were such as philosophized. But the greatest part of his disciples consisted of auditors whom they call Acusmatici , who on his first arrival in Italy, according to Nicomachus, being captivated by one popular oration alone, exceeded two thousand in number. These, with their wives and children, being collected into one very large and common auditory, called Homacoïon, and which for its magnitude resembled a city, founded a place which was universally called Magna Græcia. This great multitude of people likewise, receiving laws and mandates from Pythagoras as so many divine precepts, and without which they engaged in no occupation, dwelt together with the greatest general concord, celebrated and ranked by their neighbours among the number of the blessed.

At the same time, as we have already observed, they shared their possessions in common. Such also was their reverence for Pythagoras, that they numbered him with the Gods, as a certain beneficent and most philanthropic dæmon. And some indeed celebrated him as the Pythian, but others as the Hyperborean Apollo. Some again considered him as Pæon, but others as one of the dæmons that inhabit the moon; and others celebrated him as one of the Olympian Gods, who, in order to benefit and correct the mortal life, appeared to the men of those times in a human form, in order that he might extend to them the salutary light of felicity and philosophy. And indeed a greater good never came, nor ever will come to mankind, than that which was imparted by the Gods through this Pythagoras.

Hence, even now the proverb of the long-haired Samian , is applied to the most venerable man. But Aristotle relates, in his Treatise On the Pythagoric Philosophy, that such a division as the following was preserved by the Pythagoreans among their principal arcana; viz. that of rational animals one kind is a God, another man, and another such as Pythagoras. And indeed they very reasonably apprehended him to be a being of this kind, through whom a right conception and conformable to things themselves was introduced of Gods, heroes, and dæmons; of the world, the all-various motion of the spheres and stars, their oppositions, eclipses, and inequalities, their eccentricities and epicycles; of all the natures contained in the heavens and the earth, together with those that have an intermediate subsistence, whether apparent or occult.

Nor was there anything (in all this variety of information) at all contrary to the phenomena, or the conceptions of intellect. To which we may add, that all such disciplines, theories, and scientific investigations, as truly invigorate the eye of the soul, and purify the intellect from the blindness introduced by studies of a different kind, so as to enable it to perceive the true principles and causes of the universe, were unfolded by Pythagoras to the Greeks. But besides all this, the best polity, popular concord, community of possessions among friends, the worship of the gods, piety to the dead, legislation, erudition, silence, abstinence from animals, continence, temperance, sagacity, divinity, and in one word, whatever is anxiously sought after by the lovers of learning, was brought to light by Pythagoras. On all these accounts, therefore, as I have just now said, he was (every where) so transcendently admired.

(4) This therefore was the form of his wisdom which is so admirable.

It is also said, that of the sciences which the Pythagoreans honored, music, medicine and divination, were not among the least. But they were habitually silent and prompt to hear, and he who was able to hear [in a proper manner] was praised by them. Of medicine, however, they especially embraced the diætetic species, and in the exercise of this were most accurate. And in the first place, indeed, they endeavoured to learn the indications of symmetry, of labor, food, and repose. In the next place, with respect to the preparation of food, they were nearly the first who attempted to employ themselves in it, and to define the mode in which it should be performed. The Pythagoreans likewise employed cataplasms more frequently than their predecessors; but they in a less degree approved of medicated ointments. These however they principally used in the cure of ulcerations. But incisions and burnings they admitted the least of all things. Some diseases also they cured by incantations. Pythagoras, however, thought that music greatly contributed to health, if it was used in a proper manner. The Pythagoreans likewise employed select sentences of Homer and Hesiod for the amendment of souls. But they thought it was necessary to retain and preserve in the memory things which they had learnt and heard; and that it was requisite to be furnished with disciplines and auditions, to as great an extent as there was an ability of learning and remembering; the former of these being the power by which knowledge is obtained, but the latter, the power by which it is preserved. Hence, they very much honored the memory, abundantly exercised, and paid great attention to it. In learning too, they did not dismiss what they were taught, till they had firmly comprehended the first rudiments of it; and they recalled to their memory what they had daily heard, after the following manner: A Pythagorean never rose from his bed till he had first recollected the transactions of the former day; and he accomplished this by endeavouring to remember what he first said, or heard, or ordered his domestics to do when he was rising, or what was the second and third thing which he said, heard, or commanded to be done. And the same method was adopted with respect to the remainder of the day. For again, he endeavoured to recollect who was the first person that he met, on leaving his house, or who was the second; and with whom he in the first, or second, or third place discoursed. And after the same manner he proceeded in other things. For he endeavoured to resume in his memory all the events of the whole day, and in the very same order in which each of them happened to take place. But if they had sufficient leisure after rising from sleep, they tried after the same manner to recollect the events of the third preceding day. And thus they endeavoured to exercise the memory to a great extent. For there is not any thing which is of greater importance with respect to science, experience and wisdom, than the ability of remembering. From these studies therefore, it happened that all Italy was filled with philosophers, and this place, which before was unknown, was afterwards on account of Pythagoras called Magna Græcia. Hence also it contained many philosophers, poets, and legislators. For the rhetorical arts, demonstrative reasonings, and the laws written by them, were transferred from Italy to Greece. Those likewise who make mention of physics, adduce as the principal physiologists Empedocles and the Elean Parmenides. Those too, who wish to cite sentences, pertaining to the conduct of human life, adduce for this purpose the conceptions of Epicharmus. And nearly all philosophers make use of these. Thus much therefore concerning the wisdom of Pythagoras, how in a certain respect he very much impelled all his auditors to the pursuit of it, as far as they were adapted to its participation, and how perfectly it was delivered by him.

(1) I wish, in the next place, to reply to such assertions as calumniate divine prediction. For you compare with it “ certain other methods which are conversant with the prediction of future events .” To me, however, it does not appear to be any thing honourable if a certain natural aptitude is ingenerated in us to the indication of the future, just as in animals there is a foreknowledge of earthquakes, or winds, or tempests. For an innate presage of this kind is the consequence of acuteness of sensation, or sympathy, or some other conjoint motion of the physical powers, and is not attended with any thing venerable and supernatural. Nor if some one, by human reasoning, or artificial observation, conjectures from signs those things of which the signs are indicative (as physicians foreknow that a fever will take place from the systole and torpor of the pulse), neither does he appear to me to possess any thing honourable and good. For he conjectures after a human manner, and concludes from our reasoning power about things which are acknowledged to be effected naturally, and forms a judgment not very remote from the corporeal-formed order. Hence, if there is in us a certain natural presentiment of the future, in the same manner as in all other animals, this power is clearly seen to energize; this presentiment does not in reality possess any thing which is most blessed. For what is there among the things which are implanted in us by nature in the realms of generation that is a genuine, perfect, and eternal good?

(1) Universally, however, it deserves to be known, that Pythagoras discovered many paths of erudition, and that he delivered an appropriate portion of wisdom conformable to the proper nature and power of each; of which the following is the greatest argument. When Abaris, the Scythian, came from the Hyperboreans, unskilled and uninitiated in the Grecian learning, and was then of an advanced age, Pythagoras did not introduce him to erudition through various theorems, but instead of silence, auscultation for so long a time, and other trials, he immediately considered him adapted to be an auditor of his dogmas, and instructed him in the shortest way in his treatise On Nature, and in another treatise On the Gods. For Abaris came from the Hyperboreans, being a priest of the Apollo who is there worshipped, an elderly man, and most wise in sacred concerns; but at that time he was returning from Greece to his own country, in order that he might consecrate to the God in his temple among the Hyperboreans, the gold which he had collected.

Passing therefore through Italy, and seeing Pythagoras, he especially assimilated him to the God of whom he was the priest. And believing that he was no other than the God himself, and that no man resembled him, but that he was truly Apollo, both from the venerable indications which he saw about him, and from those which the priest had known before, he gave Pythagoras a dart which he took with him when he left the temple, as a thing that would be useful to him in the difficulties that would befal him in so long a journey. For he was carried by it, in passing through inaccessible places, such as rivers, lakes, marshes, mountains, and the like, and performed through it, as it is said, lustrations, and expelled pestilence and winds from the cities that requested him to liberate them from these evils.

We are informed, therefore, that Lacedæmon, after having been purified by him, was no longer infested with pestilence, though prior to this it had frequently fallen into this evil, through the baneful nature of the place in which it was built, the mountains of Taygetus producing a suffocating heat, by being situated above the city, in the same manner as Cnossus in Crete. And many other similar particulars are related of the power of Abaris. Pythagoras, however, receiving the dart, and neither being astonished at the novelty of the thing, nor asking the reason why it was given to him, but as if he was in reality a God himself, taking Abaris aside, he showed him his golden thigh, as an indication that he was not [wholly] deceived [in the opinion he had formed of him;] and having enumerated to him the several particulars that were deposited in the temple, he gave him sufficient reason to believe that he had not badly conjectured [in assimilating him to Apollo].

Pythagoras also added, that he came [into the regions of mortality] for the purpose of remedying and benefiting the condition of mankind, and that on this account he had assumed a human form, lest men being disturbed by the novelty of his transcendency, should avoid the discipline which he possessed. He likewise exhorted Abaris to remain in that place, and to unite with him in correcting [the lives and manners] of those with whom they might meet; but to share the gold which he had collected, in common with his associates, who were led by reason to confirm by their deeds the dogma, that the possessions of friends are common . Thus, therefore, Pythagoras unfolded to Abaris, who remained with him, as we have just now said, physiology and theology in a compendious way; and instead of divination by the entrails of beasts, he delivered to him the art of prognosticating through numbers, conceiving that this was purer, more divine, and more adapted to the celestial numbers of the Gods.

He delivered also to Abaris other studies which were adapted to him. That we may return, however, to that for the sake of which the present treatise was written, Pythagoras endeavoured to correct and amend different persons, according to the nature and power of each. All such particulars therefore as these, have neither been transmitted to the knowledge of men, nor is it easy to narrate all that has been transmitted to us concerning him.

(1) Of his wisdom, however, the commentaries written by the Pythagoreans afford, in short, the greatest indication; for they adhere to truth in every thing, and are more concise than all other compositions, so that they savour of the ancient elegance of style, and the conclusions are exquisitely deduced with divine science. They are also replete with the most condensed conceptions, and are in other respects various and diversified both in the form and the matter. At one and the same time likewise, they are transcendently excellent, and without any deficiency in the diction, and are in an eminent degree full of clear and indubitable arguments, accompanied with scientific demonstration, and as it is said, the most perfect syllogism; as he will find to be the case, who, proceeding in such paths as are fit, does not negligently peruse them.

This science, therefore, concerning intelligible natures and the Gods, Pythagoras delivers in his writings from a supernal origin. Afterwards, he teaches the whole of physics, and unfolds completely ethical philosophy and logic. He likewise delivers all-various disciplines, and the most excellent sciences. And in short there is nothing pertaining to human knowledge which is not accurately discussed in these writings. If therefore it is acknowledged, that of the [Pythagoric] writings which are now in circulation, some were written by Pythagoras himself, but others consist of what he was heard to say, and on this account are anonymous, but are referred to Pythagoras as their author;—if this be the case, it is evident that he was abundantly skilled in all wisdom.

But it is said that he very much applied himself to geometry among the Egyptians. For with the Egyptians there are many geometrical problems; since it is necessary that from remote periods, and from the time of the Gods themselves, on account of the increments and decrements of the Nile, those that were skilful should have measured all the Egyptian land which they cultivated. Hence also geometry derived its name. Neither did they negligently investigate the theory of the celestial orbs, in which likewise Pythagoras was skilled. Moreover, all the theorems about lines appear to have been derived from thence. For it is said that what pertains to computation and numbers, was discovered in Phœnicia. For some persons refer the theorems about the celestial bodies to the Egyptians and Chaldeans in common.

It is said therefore, that Pythagoras having received and increased all these [theories,] imparted the sciences, and at the same time demonstrated them to his auditors with perspicuity and elegance. And he was the first indeed that denominated philosophy, and said that it was the desire, and as it were love of wisdom. But he defined wisdom to be the science of the truth which is in beings. And he said that beings are immaterial and eternal natures, and alone possess an efficacious power, such as incorporeal essences. But that the rest of things are only homonymously beings, and are so denominated through the participation of real beings, and such are corporeal and material forms, which are generated and corrupted, and never truly are.

And that wisdom is the science of things which are properly beings, but not of such as are homonymously so. For corporeal natures are neither the objects of science nor admit of a stable knowledge, since they are infinite and incomprehensible by science, and are as it were, non-beings, when compared with universals, and are incapable of being properly circumscribed by definition. It is impossible however to conceive that there should be science of things which are not naturally the objects of science. Hence it is not probable that there will be a desire of science which has no subsistence, but rather that desire will be extended to things which are properly beings, which exist with invariable permanency, and are always consubsistent with a true appellation.

For it happens that the perception of things which are homonymously beings, and which are never truly what they seem to be, follows the apprehension of real beings; just as the knowledge of particulars follows the science of universals. For he who knows universals properly, says Archytas, will also have a clear perception of the nature of particulars. Hence things which have an existence are not alone, nor only-begotten, nor simple, but they are seen to be various and multiform. For some of them are intelligible and incorporeal natures, and which are denominated beings; but others are corporeal and fall under the perception of sense, and by participation communicate with that which has a real existence. Concerning all these therefore, he delivered the most appropriate sciences, and left nothing [pertaining to them] uninvestigated.

He likewise unfolded to men those sciences which are common [ to all disciplines ,] as for instance the demonstrative, the definitive, and that which consists in dividing, as may be known from the Pythagoric commentaries. He was also accustomed to pour forth sentences resembling Oracles to his familiars in a symbolical manner, and which in the greatest brevity of words contained the most abundant and multifarious meaning, like the Pythian Apollo through certain oracles, or like nature herself through seeds small in bulk, the former exhibiting conceptions, and the latter effects, innumerable in multitude, and difficult to be understood. Of this kind is the sentence, The beginning is the half of the whole , which is an apothegm of Pythagoras himself.

But not only in the present hemistich, but in others of a similar nature, the most divine Pythagoras has concealed the sparks of truth; depositing as in a treasury for those who are capable of being enkindled by them, and with a certain brevity of diction, an extension of theory most ample and difficult to be comprehended, as in the following hemistich:

(1) That which follows after this, we shall no longer discuss generally, but direct our attention particularly to the works resulting from the virtues of Pythagoras. And we shall begin in the first place from the Gods, as it is usual to do, and endeavour to exhibit his piety, and the admirable works which he performed. Let this, therefore, be one specimen of his piety, which also we have before mentioned, that he knew what his soul was, and whence it came into the body, and also its former lives, and that of these things he gave most evident indications. After this also, let the following be another specimen; that once passing over the river Nessus with many of his associates, he spoke to it, and the river in a distinct and clear voice, in the hearing of all his followers, answered, Hail Pythagoras!

Farther still, nearly all historians of his life confidently assert, that in one and the same day he was present at Metapontum in Italy, and Tauromenium in Sicily, and discoursed in common with his disciples in both places, though these cities are separated from each other by many stadia both by land and sea, and cannot be passed through in a great number of days. The report, also, is very much disseminated, that he showed his golden thigh to the Hyperborean Abaris, who said that he resembled the Apollo among the Hyperboreans, and of whom Abaris was the priest; and that he did this in order that Abaris might apprehend this to be true, and that he was not deceived in his opinion.

Ten thousand other more divine and more admirable particulars likewise are uniformly and unanimously related of the man : such as infallible predictions of earthquakes , rapid expulsions of pestilence and violent winds, instantaneous cessations of the effusion of hail, and a tranquillization of the waves of rivers and seas, in order that his disciples might easily pass over them. Of which things also, Empedocles the Agrigentine, Epimenides the Cretan, and Abaris the Hyperborean, receiving the power of effecting, performed certain miracles of this kind in many places. Their deeds, however, are manifest. To which we may add, that Empedocles was surnamed an expeller of winds ; Epimenides, an expiator ; and Abaris, a walker on air ; because being carried on the dart which was given to him by the Hyperborean Apollo, he passed over rivers and seas and inaccessible places, like one walking on the air.

Certain persons likewise are of opinion, that Pythagoras did the same thing, when in the same day he discoursed with his disciples at Metapontum and Tauromenium. It is also said, that he predicted there would be an earthquake from the water of a well which he had tasted; and that a ship which was sailing with a prosperous wind, would be merged in the sea. And let these, indeed, be the indications of his piety.

(1) It is also said, that Pythagoras was the first who called himself a philosopher; this not being a new name, but previously instructing us in a useful manner in a thing appropriate to the name. For he said that the entrance of men into the present life, resembled the progression of a crowd to some public spectacle. For there men of every description assemble with different views; one hastening to sell his wares for the sake of money and gain; but another that he may acquire renown by exhibiting the strength of his body; and there is also a third class of men, and those the most liberal, who assemble for the sake of surveying the places, the beautiful works of art, the specimens of valor, and the literary productions which are usually exhibited on such occasions.

Thus also in the present life, men of all-various pursuits are collected together in one and the same place. For some are influenced by the desire of riches and luxury; others by the love of power and dominion; and others are possessed with an insane ambition for glory. But the most pure and unadulterated character, is that of the man who gives himself to the contemplation of the most beautiful things, and whom it is proper to call a philosopher. He adds, that the survey of all heaven, and of the stars that revolve in it, is indeed beautiful, when the order of them is considered. For they derive this beauty and order by the participation of the first and the intelligible essence.

But that first essence is the nature of number and reasons [i. e. productive principles,] which pervades through all things, and according to which all these [celestial bodies] are elegantly arranged, and fitly adorned. And wisdom indeed, truly so called, is a certain science which is conversant with the first beautiful objects, and these divine, undecaying, and possessing an invariable sameness of subsistence; by the participation of which other things also may be called beautiful. But philosophy is the appetition of a thing of this kind. The attention therefore to erudition is likewise beautiful, which Pythagoras extended, in order to effect the correction of mankind.

(38) Among the celebrities who visited the oracle of Delphi were the immortal Apollonius of Tyana and his disciple Damis. He made his offerings and, after being crowned with a laurel wreath and given a branch of the same plant to carry in his hand, he passed behind the statue of Apollo which stood before the entrance to the cave, and descended into the sacred place of the oracle. The priestess was also crowned with laurel and her head bound with a band of white wool. Apollonius asked the oracle if his name would be remembered by future generations. The Pythoness answered in the affirmative, but declared that it would always be calumniated. Apollonius left the cavern in anger, but time has proved the accuracy of the prediction, for the early church fathers perpetuated the name of Apollonius as the Antichrist. (For details of the story see Histoire de la Magie.)

(2) For time always proceeding the divine mode of knowledge becomes evanescent, through being frequently mingled and contaminated with much of what is mortal. This divine mode is indeed [in astrology also], and a certain clear indication of truth, though it is but small, is at the same time preserved in it. For it places before our eyes manifest signs of the mensuration of the divine periods, when it predicts the eclipses of the sun and moon, and the concursions of the moon with the fixed stars, and when the experience of the sight is seen to accord with the prediction. Moreover, the observations of the celestial bodies through the whole of time, both by the Chaldeans and by us, testify that this science is true. Indications, also, more known than these might be adduced, if the present discussion was precedaneously about these particulars. But as they are superfluous, and do not pertain to the knowledge of the peculiar dæmon, I shall, as it is fit so to do, omit them, and pass on to things more appropriate than these.