(5) Such, then, is the style of the example in arithmetic. And let the testimony of geometry be the tabernacle that was constructed, and the ark that was fashioned, - constructed in most regular proportions, and through divine ideas, by the gift of understanding, which leads us from things of sense to intellectual objects, or rather from these to holy things, and to the holy of holies. For the squares of wood indicate that the square form, producing fight angles, pervades all, and points out security. And the length of the structure was three hundred cubits, and the breadth fifty, and the height thirty; and above, the ark ends in a cubit, narrowing to a cubit from the broad base like a pyramid, the symbol of those who are purified and tested by fire. And this geometrical proportion has a place, for the transport of those holy abodes, whose differences are indicated by the differences of the numbers set down below.

(1) As then in astronomy we have Abraham as an instance, so also in arithmetic we have the same Abraham. "For, hearing that Lot was taken captive, and having numbered his own servants, born in his house, 318 (tih)," he defeats a very great number of the enemy.

(4) On another principle, 120 is a triangular number, and consists of the equality of the number 64, [which consists of eight of the odd numbers beginning with unity], the addition of which (1, 3, 5, 7, 9, 11, 13, 15) in succession generate squares; and of the inequality of the number 56, consisting of seven of the even numbers beginning with 2 (2, 4, 6, 8, 10, 12, 14), which produce the numbers that are not squares Again, according to another way of indicating. the number 120 consists of four numbers - of one triangle, 15; of another, a square, 25; of a third, a pentagon, 35; and of a fourth, a hexagon, 45. The 5 is taken according to the same ratio in each mode. For in triangular numbers, from the unity 5 comes 15; and in squares, 25; and of those in succession, proportionally. Now 25, which is the number 5 from unity, is said to be the symbol of the Levitical tribe. And the number 35 depends also on the arithmetic, geometric, and harmonic scale of doubles - 6, 8, 9, 12; the addition of which makes 35. In these days, the Jews say that seven months' children are formed. And the number 45 depends on the scale of triples - 6, 9, 12, 18 - the addition of which makes 45; and similarly, in these days they say that nine months' children are formed.

(6) This chapter and the following are recensions and combinations of extremely ancient texts

(24) Thus the Lord, who ascended the mountain, the fourth, becomes the sixth, and is illuminated all round with spiritual light, by laying bare the power proceeding from Him, as far as those selected to see were able to behold it, by the Seventh, the Voice, proclaimed to be the Son of God; in order that they, persuaded respecting Him, might have rest; while He by His birth, which was indicated by the sixth conspicuously marked, becoming the eighth, might appear to be God in a body of flesh, by displaying His power, being numbered indeed as a man, but being concealed as to who He was. For six is reckoned in the order of numbers, but the succession of the letters acknowledges the character which is not written. In this case, in the numbers themselves, each unit is preserved in its order up to seven and eight. But in the number of the characters, Zeta becomes six and Eta seven.

(1) It were tedious to go over all the Prophets and the Law, specifying what is spoken in enigmas; for almost the whole Scripture gives its utterances in this way. It may suffice, I think, for any one possessed of intelligence, for the proof of the point in hand, to select a few examples.

(3) That ten is a sacred number, it is superfluous to say now. And if the tables that were written were the work of God, they will be found to exhibit physical creation. For by the "finger of God" is understood the power of God, by which the creation of heaven and earth is accomplished; of both of which the tables will be understood to be symbols. For the writing and handiwork of God put on the table is the creation of the world.

(525) And they appear to lead the mind towards truth? Yes, in a very remarkable manner. Then this is knowledge of the kind for which we are seeking, having a double use, military and philosophical; for the man of war must learn the art of number or he will not know how to array his troops, and the philosopher also, because he has to rise out of the sea of change and lay hold of true being, and therefore he must be an arithmetician. That is true. And our guardian is both warrior and philosopher? Certainly. Then this is a kind of knowledge which legislation may fitly prescribe; and we must endeavour to persuade those who are to be the principal men of our State to go and learn arithmetic, not as amateurs, but they must carry on the study until they see the nature of numbers with the mind only; nor again, like merchants or retail-traders, with a view to buying or selling, but for the sake of their military use, and of the soul herself; and because this will be the easiest way for her to pass from becoming to truth and being. That is excellent, he said. Yes, I said, and now having spoken of it, I must add how charming the science is! and in how many ways it conduces to our desired end, if pursued in the spirit of a philosopher, and not of a shopkeeper! How do you mean? I mean, as I was saying, that arithmetic has a very great and elevating effect, compelling the soul to reason about abstract number, and rebelling against the introduction of visible or tangible objects into the argument. You know

(2) These twelve letters, he designed, formed, combined, weighed, and changed, and created with them the twelve divisions of the heavens (namely, the zodiacal constellations), the twelve months of the year, and the twelve important organs of the frame of man, namely the right and left hands, the right and left feet, two kidneys, the liver, the gall, the spleen, the intestines, the gullet, and the stomach.

(20) The two chapters which are numbered by M. Naville as 136 A and 136 B are represented in the later recensions by a single chapter, which has been made out of them. There is very much obscurity in the ancient texts, though the MSS. containing them are numerous, and the more recent versions are quite as difficult to understand. We must be satisfied for the present by a strict literal and grammatical translation, wherever this amount of success is attainable. The royal sarcophagus 32 of the British Museum gives the latest form of 136 A

(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) "Child, copy this book for the temple at Diospolis in hieroglyphic characters, and call it the Eighth Reveals the Ninth."

(4) "For the Muse was not then Greedy of gain or mercenary; Nor were Terpsichore's sweet, Honey-toned, silvery soft-voiced Strains made merchandise of." Now those instructed among the Egyptians learned first of all that style of the Egyptian letters which is called Epistolographic; and second, the Hieratic, which the sacred scribes practise; and finally, and last of all, the Hieroglyphic, of which one kind which is by the first elements is literal (Kyriologic), and the other Symbolic. Of the Symbolic, one kind speaks literally by imitation, and another writes as it were figuratively; and another is quite allegorical, using certain enigmas.

(4) From two letters, or forms He composed two dwellings; from three, six; from four, twenty-four; from five, one hundred and twenty; from six, seven hundred and twenty; from seven, five thousand and forty; and from thence their numbers increase in a manner beyond counting; and are incomprehensible. These seven are Planets of the Universe, the Sun, Venus, Mercury, Moon, Saturn, Jupiter, and Mars; the seven days are the days of creation; and these an the seven gateways of a man, two eyes, two ears, two nostrils and a mouth, through which he perceives by his senses.

(8) But only to a few of them is shown what those things are which are contained in the mystery. Rightly then, Plato, in the Epistles, treating of God, says: "We must speak in enigmas that should the tablet come by any mischance on its leaves either by sea or land, he who reads may remain ignorant." For the God of the universe, who is above all speech, all conception, all thought, can never be committed to writing, being inexpressible even by His own power. And this too Plato showed, by saying:

(1) The simple letters are twelve, namely: He, Vau, Zain, Heth, Teth, Yod, Lamed, Nun, Samech, Oin, Tzaddi, and Quoph; they represent the fundamental properties, eight, hearing, smell, speech, desire for food, the sexual appetite, movement, anger, mirth, thought, sleep, and work. These symbolize also twelve directions in space: northeast, southeast, the east above, the east below, the northwest, southwest, the west above, the west below, the upper south, the lower south, the upper north, the lower north. These diverge to all eternity, and an as the arms of the universe.

(14) Again, that the Spring is called "flowery," from its nature; and Night "still," on account of rest; and the Moon" Gorgonian," on account of the face in it; and that the time in which it is necessary to sow is called Aphrodite by the "Theologian." In the same way, too, the Pythagoreans figuratively called the planets the "dogs of Persephone;" and to the sea they applied the metaphorical appellation of "the tears of Kronus." Myriads on myriads of enigmatical utterances by both poets and philosophers are to be found; and there are also whole books which present the mind of the writer veiled, as that of Heraclitus On Nature, who on this very account is called "Obscure." Similar to this book is the Theology of Pherecydes of Syrup; for Euphorion the poet, and the Causes of Callimachus, and the Alexandra of Lycophron, and the like, are proposed as an exercise in exposition to all the grammarians.

(481) 999 To say: Look-out, His-face-behind-him, ferry N. over. 999 The two reed-floats of heaven are placed, that N. may ferry over therewith to R`, to the horizon. 999 The two reed-floats of heaven were placed for R`, that he might ferry over therewith to Horus of the gods, to the horizon. 1000 The two reed-floats of heaven are placed for N., 1000 that N. may ferry over therewith to R`, to the horizon. 1000 N. will ferry over to his station on the eastern side of the sky, 1000 in its northern region, among the imperishable stars, 1000 who stand on (by?) their d`m-sceptres, who stand (?) on their eastern standard. 1001 N. will stand among them. 1001 The brother of N. is the moon, the mother (mtw) of N. is the morning star. 1001 Give thine arm to N., that he may live.

(3) Thence the prophecies and oracles are spoken in enigmas, and the mysteries are not exhibited incontinently to all and sundry, but only after certain purifications and previous instructions.

(1) ALTHOUGH in the writings of Moses the spirit has kept the deepest mysteries secret, hidden and concealed in the letter, yet all is so very regularly described that there is no defect at all in the order thereof.