(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.

(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.

(2) Certain of the secret schools in the world today are perpetuations of the ancient Mysteries, and although it is quite possible that they may possess some of the original numerical formulæ, there is no evidence of it in the voluminous writings which have issued from these groups during the last five hundred years. These writings, while frequently discussing Pythagoras, show no indication of a more complete knowledge of his intricate doctrines than the post-Pythagorean Greek speculators had, who talked much, wrote little, knew less, and concealed their ignorance under a series of mysterious hints and promises. Here and there among the literary products of early writers are found enigmatic statements which they made no effort: to interpret. The following example is quoted from Plutarch:

(6) This uncertainty shared by all true students of the subject proves conclusively that it is unwise to make definite statements founded on the indefinite and fragmentary information available concerning the Pythagorean system of mathematical philosophy. The material which follows represents an effort to collect a few salient points from the scattered records preserved by disciples of Pythagoras and others who have since contacted his philosophy.

(9) Now Pythagoras made an epitome of the statements on righteousness in Moses, when he said, "Do not step over the balance;" that is, do not transgress equality in distribution, honouring justice so.

(9) As is so often the case with genius, Pythagoras by his outspokenness incurred both political and personal enmity. Among those who came for initiation was one who, because Pythagoras refused to admit him, determined to destroy both the man and his philosophy. By means of false propaganda, this disgruntled one turned the minds of the common people against the philosopher. Without warning, a band of murderers descended upon the little group of buildings where the great teacher and his disciples dwelt, burned the structures and killed Pythagoras.

(3) The wrong assertions that I have uttered, and the wrong resistance which I have offered: let them not be imputed to me

(49) VI. Having departed from your house, turn not back, for the furies will be your attendants. Pythagoras here warns his followers that any who begin the search for truth and, after having learned part of the mystery, become discouraged and attempt to return again to their former ways of vice and ignorance, will suffer exceedingly; for it is better to know nothing about Divinity than to learn a little and then stop without learning all.

(18) The study of geometry, music, and astronomy was considered essential to a rational understanding of God, man, or Nature, and no one could accompany Pythagoras as a disciple who was not thoroughly familiar with these sciences. Many came seeking admission to his school. Each applicant was tested on these three subjects, and if found ignorant, was summarily dismissed.

(53) Timaeus: Now all triangles derive their origin from two triangles, each having one angle right and the others acute ; and the one of these triangles has on each side half a right angle marked off by equal sides, while the other has the right angle divided into unequal parts by unequal sides. These we lay down as the principles of fire and all the other bodies, proceeding according to a method in which the probable is combined with the necessary; but the principles which are still higher than these are known only to God and the man who is dear to God.

(12) Having then from nature abundant means for examining the statements made, we ought to discover the sequence of the truth. Wherefore also we are rightly condemned, if we do not assent to what we ought to obey, and do not distinguish what is hostile, and unseemly, and unnatural, and false, from what is true, consistent, and seemly, and according to nature. And these means must be employed in order to attain to the knowledge of the real truth.

(12) During his youth, Pythagoras was a disciple of Pherecydes and Hermodamas, and while in his teens became renowned for the clarity of his philosophic concepts. In height he exceeded six feet; his body was as perfectly formed as that of Apollo. Pythagoras was the personification of majesty and power, and in his presence a felt humble and afraid. As he grew older, his physical power increased rather than waned, so that as he approached the century mark he was actually in the prime of life. The influence of this great soul over those about him was such that a word of praise from Pythagoras filled his disciples with ecstasy, while one committed suicide because the Master became momentarily irritate over something he had dome. Pythagoras was so impressed by this tragedy that he never again spoke unkindly to or about anyone.

(11) After Pythagoras of Samos, its founder, the Italic or Pythagorean school numbers among its most distinguished representatives Empedocles, Epicharmus, Archytas, Alcmæon, Hippasus, Philolaus, and Eudoxus. Pythagoras (580-500? B.C.) conceived mathematics to be the most sacred and exact of all the sciences, and demanded of all who came to him for study a familiarity with arithmetic, music, astronomy, and geometry. He laid special emphasis upon the philosophic life as a prerequisite to wisdom. Pythagoras was one of the first teachers to establish a community wherein all the members were of mutual assistance to one another in the common attainment of the higher sciences. He also introduced the discipline of retrospection as essential to the development of the spiritual mind. Pythagoreanism may be summarized as a system of metaphysical speculation concerning the relationships between numbers and the causal agencies of existence. This school also first expounded the theory of celestial harmonics or "the music of the spheres." John Reuchlin said of Pythagoras that he taught nothing to his disciples before the discipline of silence, silence being the first rudiment of contemplation. In his Sophist, Aristotle credits Empedocles with the discovery of rhetoric. Both Pythagoras and Empedocles accepted the theory of transmigration, the latter saying: "A boy I was, then did a maid become; a plant, bird, fish, and in the vast sea swum." Archytas is credited with invention of the screw and the crane. Pleasure he declared to be a pestilence because it was opposed to the temperance of the mind; he considered a man without deceit to be as rare as a fish without bones.

(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.)

(11) His surviving disciples attempted to perpetuate his doctrines, but they were persecuted on every hand and very little remains today as a testimonial to the greatness of this philosopher. It is said that the disciples of Pythagoras never addressed him or referred to him by his own name, but always as The Master or That Man. This may have been because of the fact that the name Pythagoras was believed to consist of a certain number of specially arranged letters with great sacred significance. The Word magazine has printed an article by T. R. Prater, showing that Pythagoras initiated his candidates by means of a certain formula concealed within

(5) And the disciples of Aristotle say that some of their treatises are esoteric, and others common and exoteric. Further, those who instituted the mysteries, being philosophers, buried their doctrines in myths, so as not to be obvious to all. Did they then, by veiling human opinions, prevent the ignorant from handling them; and was it not more beneficial for the holy and blessed contemplation of realities to be concealed? But it was not only the tenets of the Barbarian philosophy, or the Pythagorean myths. But even those myths in Plato (in the Republic, that of Hero the Armenian; and in the Gorgias, that of Aeacus and Rhadamanthus; and in the Phoedo, that of Tartarus; and in the Protagoras, that of Prometheus and Epimetheus; and besides these, that of the war between the Atlantini and the Athenians in the Atlanticum) r are to be expounded allegorically, not absolutely n in all their expressions, but in those which ex press the general sense. And these we shall find indicated by symbols under the veil of allegory. Also the association of Pythagoras, and the twofold intercourse with the associates which designates the majority, hearers (akousmatikoi), and the others that have a genuine attachment to philosophy, disciples (224> aqhmatikoi, yet signified that something was spoken to the multitude, and something concealed from them. Perchance, too, the twofold species of the Peripatetic teaching - that called probable, and that called knowable - came very near the distinction between opinion on the one hand, and glory and truth on the other.

(11) To Pythagoras music was one of the dependencies of the divine science of mathematics, and its harmonies were inflexibly controlled by mathematical proportions. The Pythagoreans averred that mathematics demonstrated the exact method by which the good established and maintained its universe. Number therefore preceded harmony, since it was the immutable law that governs all harmonic proportions. After discovering these harmonic ratios, Pythagoras gradually initiated his disciples into this, the supreme arcanum of his Mysteries. He divided the multitudinous parts of creation into a vast number of planes or spheres, to each of which he assigned a tone, a harmonic interval, a number, a name, a color, and a form. He then proceeded to prove the accuracy of his deductions by demonstrating them upon the different planes of intelligence and substance ranging from the most abstract logical premise to the most concrete geometrical solid. From the common agreement of these diversified methods of proof he established the indisputable existence of certain natural laws.

(39) The Neo-Pythagorean school flourished in Alexandria during the first century of the Christian Era. Only two names stand out in connection with it--Apollonius of Tyana and Moderatus of Gades. Neo-Pythagoreanism is a link between the older pagan philosophies and Neo-Platonism. Like the former, it contained many exact elements of thought derived from Pythagoras and Plato; like the latter, it emphasized metaphysical speculation and ascetic habits. A striking similarity has been observed by several authors between Neo-Pythagoreanism and the doctrines of the Essenes. Special emphasis was laid upon the mystery of numbers, and it is possible that the Neo-Pythagoreans had a far wider knowledge of the true teachings of Pythagoras than is available today. Even in the first century Pythagoras was regarded more as a god than a man, and the revival of his philosophy was resorted to apparently in the hope that his name would stimulate interest in the deeper systems of learning. But Greek philosophy had passed the zenith of its splendor; the mass of humanity was awakening to the importance of physical life and physical phenomena. The emphasis upon earthly affairs which began to assert itself later reached maturity of expression in twentieth century materialism and commercialism,

(38) If a man's thoughts are unsteady, if he does not know the true law, if his peace of mind is troubled, his knowledge will never be perfect.

(47) But that in some things I write otherwise than they, I do it not out of selfwill or conceit and supposition, doubting whether it be so or no. I dare not make any doubt herein, neither can any man instruct me herein.