Chapter XI.--The Mystical Meanings in the Proportions of Numbers, Geometrical Ratios, and Music.
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 (tie  )," he defeats a very great number of the enemy.
They say, then, that the character representing 300 is, as to shape, the type of the Lord's sign,  and that the Iota and the Eta indicate the Saviour's name; that it was indicated, accordingly, that Abraham's domestics were in salvation, who having fled to the Sign and the Name became lords of the captives, and of the very many unbelieving nations that followed them.
Now the number 300 is, 3 by 100. Ten is allowed to be the perfect number. And 8 is the first cube, which is equality in all the dimensions--length, breadth, depth. "The days of men shall be," it is said, "120 (rk) years."  And the sum is made up of the numbers from 1 to 15 added together.  And the moon at 15 days is full.
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.
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 right 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.
And the numbers introduced are sixfold, as three hundred is six times fifty; and tenfold, as three hundred is ten times thirty; and containing one and two-thirds (epidimoiroi), for fifty is one and two-thirds of thirty.
Now there are some who say that three hundred cubits are the symbol of the Lord's sign;  and fifty, of hope and of the remission given at Pentecost; and thirty, or as in some, twelve, they say points out the preaching [of the Gospel]; because the Lord preached in His thirtieth year; and the apostles were twelve. And the structure's terminating in a cubit is the symbol of the advancement of the righteous to oneness and to "the unity of the faith." 
And the table which was in the temple was six cubits;  and its four feet were about a cubit and a half.
They add, then, the twelve cubits, agreeably to the revolution of the twelve months, in the annual circle, during which the earth produces and matures all things; adapting itself to the four seasons. And the table, in my opinion, exhibits the image of the earth, supported as it is on four feet, summer, autumn, spring, winter, by which the year travels. Wherefore also it is said that the table has "wavy chains;"  either because the universe revolves in the circuits of the times, or perhaps it indicated the earth surrounded with ocean's tide.
Further, as an example of music, let us adduce David, playing at once and prophesying, melodiously praising God. Now the Enarmonic  suits best the Dorian harmony, and the Diatonic the Phrygian, as Aristoxenus says. The harmony, therefore, of the Barbarian psaltery, which exhibited gravity of strain, being the most ancient, most certainly became a model for Terpander, for the Dorian harmony, who sings the praise of Zeus thus:--
"O Zeus, of all things the Beginning, Ruler of all;
O Zeus, I send thee this beginning of hymns."
The lyre, according to its primary signification, may by the psalmist be used figuratively for the Lord; according to its secondary, for those who continually strike the chords of their souls under the direction of the Choir-master, the Lord. And if the people saved be called the lyre, it will be understood to be in consequence of their giving glory musically, through the inspiration of the Word and the knowledge of God, being struck by the Word so as to produce faith. You may take music in another way, as the ecclesiastical symphony at once of the law and the prophets, and the apostles along with the Gospel, and the harmony which obtained in each prophet, in the transitions of the persons.
But, as seems, the most of those who are inscribed with the Name,  like the companions of Ulysses, handle the word unskilfully, passing by not the Sirens, but the rhythm and the melody, stopping their ears with ignorance; since they know that, after lending their ears to Hellenic studies, they will never subsequently be able to retrace their steps.
But he who culls what is useful for the advantage of the catechumens, and especially when they are Greeks (and the earth is the Lord's, and the fulness thereof  ), must not abstain from erudition, like irrational animals; but he must collect as many aids as possible for his hearers. But he must by no means linger over these studies, except solely for the advantage accruing from them; so that, on grasping and obtaining this, he may be able to take his departure home to the true philosophy, which is a strong cable for the soul, providing security from everything.
Music is then to be handled for the sake of the embellishment and composure of manners. For instance, at a banquet we pledge each other while the music is playing;  soothing by song the eagerness of our desires, and glorifying God for the copious gift of human enjoyments, for His perpetual supply of the food necessary for the growth of the body and of the soul. But we must reject superfluous music, which enervates men's souls, and leads to variety,--now mournful, and then licentious and voluptuous, and then frenzied and frantic.
The same holds also of astronomy. For treating of the description of the celestial objects, about the form of the universe, and the revolution of the heavens, and the motion of the stars, leading the soul nearer to the creative power, it teaches to quickness in perceiving the seasons of the year, the changes of the air, and the appearance of the stars; since also navigation and husbandry derive from this much benefit, as architecture and building from geometry. This branch of learning, too, makes the soul in the highest degree observant, capable of perceiving the true and detecting the false, of discovering correspondences and proportions, so as to hunt out for similarity in things dissimilar; and conducts us to the discovery of length without breadth, and superficial extent without thickness, and an indivisible point, and transports to intellectual objects from those of sense.
The studies of philosophy, therefore, and philosophy itself, are aids in treating of the truth. For instance, the cloak was once a fleece; then it was shorn, and became warp and woof; and then it was woven. Accordingly the soul must be prepared and variously exercised, if it would become in the highest degree good. For there is the scientific and the practical element in truth; and the latter flows from the speculative; and there is need of great practice, and exercise, and experience.
But in speculation, one element relates to one's neighbours and another to one's self. Wherefore also training ought to be so moulded as to be adapted to both. He, then, who has acquired a competent acquaintance with the subjects which embrace the principles which conduce to scientific knowledge (gnosis), may stop and remain for the future in quiet, directing his actions in conformity with his theory.
But for the benefit of one's neighbours, in the case of those who have proclivities for writing, and those who set themselves to deliver the word, both is other culture beneficial, and the reading of the Scriptures of the Lord is necessary, in order to the demonstration of what is said, and especially if those who hear are accessions from Hellenic culture.
Such David describes the Church: "The queen stood on thy right hand, enveloped in a golden robe, variegated;"  and with Hellenic and superabundant accomplishments, "clothed variegated with gold-fringed garments."  And the Truth says by the Lord, "For who had known Thy counsel, hadst Thou not given wisdom, and sent Thy Holy Spirit from the Highest; and so the ways of those on earth were corrected, and men learned Thy decrees, and were saved by wisdom?" For the Gnostic knows things ancient by the Scripture, and conjectures things future: he understands the involutions of words and the solutions of enigmas. He knows beforehand signs and wonders, and the issues of seasons and periods, as we have said already. Seest thou the fountain of instructions that takes its rise from wisdom? But to those who object, What use is there in knowing the causes of the manner of the sun's motion, for example, and the rest of the heavenly bodies, or in having studied the theorems of geometry or logic, and each of the other branches of study?--for these are of no service in the discharge of duties, and the Hellenic philosophy is human wisdom, for it is incapable of teaching  the truth--the following remarks are to be made. First, that they stumble in reference to the highest of things--namely, the mind's free choice. "For they," it is said, "who keep holy holy things, shall be made holy; and those who have been taught will find an answer."  For the Gnostic alone will do holily, in accordance with reason all that has to be done, as he hath learned through the Lord's teaching, received through men.
Again, on the other hand, we may hear: "For in His hand, that is, in His power and wisdom, are both we and our words, and all wisdom and skill in works; for God loves nothing but the man that dwells with wisdom."  And again, they have not read what is said by Solomon; for, treating of the construction of the temple, he says expressly, "And it was Wisdom as artificer that framed it; and Thy providence, O Father, governs throughout."  And how irrational, to regard philosophy as inferior to architecture and shipbuilding! And the Lord fed the multitude of those that reclined on the grass opposite to Tiberias with the two fishes and the five barley loaves, indicating the preparatory training of the Greeks and Jews previous to the divine grain, which is the food cultivated by the law. For barley is sooner ripe for the harvest than wheat; and the fishes signified the Hellenic philosophy that was produced and moved in the midst of the Gentile billow, given, as they were, for copious food to those lying on the ground, increasing no more, like the fragments of the loaves, but having partaken of the Lord's blessing, and breathed into them the resurrection of Godhead  through the power of the Word. But if you are curious, understand one of the fishes to mean the curriculum of study, and the other the philosophy which supervenes. The gatherings  point out the word of the Lord.
"And the choir of mute fishes rushed to it,"
says the Tragic Muse somewhere.
"I must decrease," said the prophet John,  and the Word of the Lord alone, in which the law terminates, "increase." Understand now for me the mystery of the truth, granting pardon if I shrink from advancing further in the treatment of it, by announcing this alone: "All things were made by Him, and without Him was not even one thing."  Certainly He is called "the chief corner stone; in whom the whole building, fitly joined together, groweth into an holy temple of God,"  according to the divine apostle.
I pass over in silence at present the parable which says in the Gospel: "The kingdom of heaven is like a man who cast a net into the sea and out of the multitude of the fishes caught, makes a selection of the better ones." 
And now the wisdom which we possess announces the four virtues  in such a way as to show that the sources of them were communicated by the Hebrews to the Greeks. This may be learned from the following: "And if one loves justice, its toils are virtues. For temperance and prudence teach justice and fortitude; and than these there is nothing more useful in life to men."
Above all, this ought to be known, that by nature we are adapted for virtue; not so as to be possessed of it from our birth, but so as to be adapted for acquiring it.