There remains to us of the memorials of antiquity, concerning that doctrine, but a single, very incomplete, and very obscure fragment. It is a collection of sentences, which are attributed to Lysis, a Pythagorian philosopher, and the friend and preceptor of Epaminondas ; but it would be impossible for us to avail ourselves of the doctrines of this precious document, without the able commentary of M. Fabre d' Olivet. Thanks to this skillful interpreter, we are able to lift a corner of the veil that covers the famous dogmas of the philosopher of Samos.(Vers Dores de Pythagore, explained and translated into French verse, by M. d'Olivet. Paris, 1813)

This commentator, in order to give a general idea of the nature of his work, explains himself as follows: " I have followed, in my translation, the Greek text, as it is given at the head of the Commentary of Hierocles, expounded by the son of Casaubon, and interpreted in Latin by Cartcrius : London edition, 1673. This work, as all those that remain to us of the ancients, has been the subject of a great number of critical and grammatical constructions. The authenticity of the greater part of it seems to be unquestioned, and although there are some variations of opinion, they are of too little importance for me to pause and consider at this time. Nor is it my place to do so ; beside, each one must do his own work.

The labor of the grammarians is complete, or must so be regarded ; for nothing would ever be finished, if we continually recommence our investigations at the same point, without being willing to rely upon the previous researches of others.

As far as possible, I have extracted literally from the Commentary of d'Olivet all that I give of the system of Pythagoras ; nevertheless, for the purpose of abbreviating, I have contented myself sometimes to analyze certain passages, which I have indicated by the suppression of the brackets.

" Pythagoras considered the universe as a unit animated by Divine intelligences, each, according to its perfections, occupying its proper sphere. It was he who designated, first of all, this totality by the Greek word Kosmos, to express the beauty, order, and regularity that therein reign. The Latins translate this word by mundus. from which we have derived the French word monde. It is from unity, considered as the principle of the world, that we get the word universe, which we apply to it.

" Pythagoras considered unity as the essential principle of all things. He designated God by the figure 1 , and matter by 2 ; so he expressed the universe by 12, because this results from the juxtaposition of the figures 1 and 2." (3e Examen.)

As on the other hand, the number 1 2 results from the multiplication of 3 by 4, the philosopher conceived the universe composed of three distinct worlds bound closely to each other, each of which was developed in four concentric spheres. The ineffable Being who, placed in the common center of these twelve spheres, filling them all without being comprehended by any of them, was God.

The four spheres from which are formed each one of its three distinct worlds, correspond to four elementary modifications of inert or amorphous matter. These primitive modifications are called fire, air, earth, and water, and are the elements which constitute all material substances.

" The application of the number 12 to express the universe, was not an arbitrary invention of Pythagoras ; it was common to the Chaldeans and Egyptians, from whom he had received it, and also to the chief nations of the earth. It was the origin of the institution of the Zodiac, the division of which into twelve constellations has been found to exist everywhere, from time immemorial " (3e Examen.)

" According to this system, absolute unity, or God, was considered the spiritual soul of the universe the essence of being - the light of lights. Between the Supreme Being and man an incalculable chain of intermediate beings was conceived, whose perfections or attributes decreased in proportion to their separation from the creative principle.(The author explains in what cases secondary spirits were angels, deities, intelligences, or demons) (3e Examen.)

"Pythagoras, in conceiving this spiritual hierarchy as a geometrical progression, regarded the beings which compose it under harmonious relations, and founded, by analogy, the laws of the universe, on those of music. He termed harmony the movement of the celestial spheres, and employed figures to express the faculties, relations, and influences of the different beings." (3e Examen.)

Everything that appeared to have an existence proper, was supposed to proceed from the reunion of three modalities. Thus, the universe, the grand whole or macrocosm, included, as we have said, three secondary worlds. Man, the little world, or microcosm, was composed, according to Pythagorean views, of a body, soul, and spirit, manifested by three distinct faculties: viz., sensibility, thought, and intelligence. On the other hand, each ternary, from the one that embraced immensity, to the one that constituted the feeblest individual, being comprised in a perfect whole - a unity, relative or absolute - concurred to form the quaternary or the sacred tetrad. (3e and 12e Examen.)

Consequently, 1 represented the active and hidden principle of all things; 2, its passive principle, or matter; 3, the totality of the faculties; and 4, the plenitude of its essence. The quaternary, was the general type of all living beings, manifesting themselves by facultative modifications. It could thus become the representative sign of any being whatever ; but the being to which it was most ordinarily applied, was man. (3e and 12e Examen.)

" The language of numbers, which Pythagoras, after the example of ancient sages, frequently employed, is now lost. The fragments of it which remain, serve rather to prove its existence, than to furnish any light on its elements ; for they who wrote these fragments, used a language that they supposed known, in the same manner that our modern savans do, when they employ algebraic characters. It would certainly be ridiculous, before having acquired any notion of these algebraic signs, to attempt to explain a problem written in them ; or what would be worse still, to attempt to employ them, without knowing their value, to lay down a proposition. But this is precisely what has been attempted, often, relative to the language of numbers. Some have pretended, not only to explain it, before having learned it, but even to write it - thus rendering themselves contemptible. The learned, finding this language thus travestied, very naturally despised it, and very unreasonably extended their contempt to the ancients who made use of it ; acting thus, in this case as in many others : creating, themselves, the alleged stupidity of the antique sciences, and ended by saying, ' antiquity was stupid.' "(The little sketch that we have given above of the language of numbers, will serve, imperfect as it is, to give an idea of the importance that the ancients attached to ternary and quaternary periods, in the determination of critical days) (3e Examen.)

The philosopher of Samos admitted two eternal, uncreated essences : namely, spirit and matter ; and by the agency of these two principles he explains the various phenomena of sensibility, intelligence, and thought. " Whenever any one has pretended, or shall pretend to found the universe on the existence of one sole nature, material or spiritual, and deduces from the hypothesis, the explanation of all phenomena, he encounters, and always will encounter insurmountable difficulties. It has always been by asking what is the origin of good and evil, that an irresistible overthrow has been given to all systems of this kind, from Moschus,

Leucippus, and Epicurus, down to Spinosa and Leibnitz: from Parnienides, Zeno of Elea, and Chrysippus, down to Berkley and Kant." (31e Examen.)

" Hornogenity in nature was, with the unity of God, one of the greatest secrets of the mysteries. Pythagoras founded this homogenity on the unity of the spirit, with which it is penetrated, and from which all our souls, according to him, took their origin. This dogma, which he had received from the Chaldeans, and the priests of Egypt, was admitted by all the sages of antiquity, as is amply shown at length by Stanley and the judicious Eeausobre. Those sages established a harmony in principle, and a perfect analogy between heaven and earth, the intelligible and the sensible, divisible and indivisible substances, in such a manner that what transpires in one of the regions of the universe, or of the modifications of the primordial ternary, was the exact image of what transpired in the other. Beside, I must say, that it is on the homogenity of nature that rest, in principle, all the occult sciences, of which the four principal ones are connected with the human quaternar, beign theurgy, astrology, magic, and chemistry." - (28e Examen.)

" Man, in this system, was considered as holding the middle between intellectual and sensible things, the last of superior and the first of inferior beings, free to move upward or downward, as influenced by the passions that control the power of the will to ascend or descend. Sometimes they bring him into union with immortals, and, by his return to virtue, enable him to recover his proper position ; and again, sometimes replunging him into mortal association, and by transgression of the divine laws, cause him to be stripped of his dignity. It is based on this rule, that we find everywhere, though differently explained, the foundation of the dogma of the transmigration of souls. This dogma, explained in the mysteries of antiquity, and received by all the people, has been so disfigured by what the moderns have called metempsychosis, that it would surpass very much the limits of these comments to give it an explanation that could be understood." - (32e Examen.)

" This same philosopher taught that the soul has a body, which is given to it according to its good or bad nature, by the interior labor of its faculties. He calls this body the subtle car of the soul, and says that the mortal body is only a gross envelope." - (37e Examen.) ( We shall show, at proper time and place, the analogy that exists between this doctrine and that of the monads invented by Leibnitz)

The indefinite perfectibility of nature, founded on the homogenity of its essence, is also one of the dogmas of the Pythagorian school, that moderns have appropriated, and which they have fortified by considerations nearly demonstrative. Among those who have developed it with most success, we cite Leibnitz, Lecat, Ch. Bonnet, Buffon, Linaeus, Kant, Schelling, and lastly, the author of the articles, " Nature" and " Animal," of the Nouveau Dictionaire d'Histoire Naturelle. The following is his explanation : (35e Examen.)

" All animals and plants are only modifications of an original animal or vegetable. Man is the point of union between divinity and matter, connecting heaven and earth. The light of wisdom and intelligence that beams in his thoughts, is reflected on nature. He is the bond of communication between all beings.''

" There may have been a time when the insect, the shell-fish, or the unclean reptile, knew no master in the universe, and found itself at the head of organized beings. Who knows if, in the eternal night of ages, the scepter of the world shall not pass from the hands of man into those of a being more perfect and worthy to bear it. It may be that the race of black, now secondary, was once the ruler of the earth, before the white race was created. If nature has successively accorded empire to the species more and more perfect which she has created, why should she stop now ? Who shall define the limits of her power ? She is ruled by God alone, and it is his might and hand that governs her.(See the " Nouveau Diet. d'Hist. Nat.," at the word Nature--Same work, at the word Animal )

Attracted by the grandeur, beauty, and connection of these ideas, I have given to the extracts of the doctrine of Pythagoras a more considerable extension than I was willing to, but the precious illumination that is found there, on a multitude of things and opinions that are supposed new, have repaid the reader, I hope, and will recompense him more and more hereafter. A system which embraces and unites, by a common bond, God, the universe, time, and eternity ; which includes an explanation of all the phenomena of nature, if not true, at least acceptable, at an epoch when nothing could be put in parallel with it, but the gross mythology of pagan priests - such a system, I say, was well calculated to captivate, at once, the imagination and understanding. It is now easy to conceive the admiration and enthusiasm of the adepts, in proportion to their progress in the autopsy of the mysteries, and their submission, respect, and gratitude toward the superior man who initiated them into such lofty conceptions, seems entirely reasonable and natural.

From History of Medicine by P. V. Renouard M.D.