Early Christian Sources of Platonic Geometry: Augustine (1)

Ambrose presumably had less need for Latinizers because of his own knowledge of Greek. It was partly this and his enthusiasm for Greek thought, both classical and Christian, and in particular the Platonists whom he regarded as the ‘aristocrats of thought’ that contributed to his standing as one of four Doctors of the Western Church.
In addition to adapting Basil’s Hexaemeron,
he eagerly collected other Greek works, especially those of Origen, from whom he acquired his own understanding of allegory. Ambrose’s contact with the Greek world evidently made his sermons the most progressive in the West and it was into this environment that Augustine (354-430) arrived in 384.

Symmachus, the Prefect of Rome and one of the leading pagans of his day, had recommended Augustine for the post in rhetoric at the court of Milan. On his arrival from Rome, however, Augustine soon fell deeply under the influence of Ambrose and his sermons. In just two turbulent years he had contemplated withdrawing from the world with a band of amateur philosophers; he had been introduced to various Neoplatonic writings in the translations of Victorinus, including probably the Enneads of Plotinus; then
having turned to Simplicianus who particularly impressed him with the earlier conversion of Victorinus, Augustine underwent his own conversion; and, following a breakdown, he penned four Dialogues during his convalescence which marked his arrival as a Christian Platonist thinker, teacher and writer.

It is of crucial importance to this study that his massive output, together with his command of classical and Christian thought and his ability to conduct an argument derived from personal reflection, ensured his place along with Gregory as the foremost authority for the Latin Church in the tenth century and either side of it.
Being comprehensive in span, his writings are concerned not only with purely theological interpretations of scripture and the Christian revelation but with Christian philosophy as well. In this he reveals the Platonic underpinning of his own thought, particularly that related to the universe, harmony and numbers, to the extent that he is credited with transmitting to the medieval Church the best account of Plato’s teaching, thereby securing its acceptance by the Church.
Among the first of the early Dialogues was De ordine. Another Platonic work, De musica,
was started a year later in 387 along with his treatise De quantitate animae. After an interval of ten years his Confessiones,
compiled over a period of four years, also contains an exposition of Platonic metaphysics. This was overlapped by his treatise De Trinitate which was written between 399 and 419. During this time he commenced his greatest undertaking, De civitate Dei,
a work of twenty-two volumes which was perhaps the most widely read of all books early in the middle ages apart from the Bible itself. It was written throughout the years 413 to 427, with what can be considered the Platonic volumes of the work, VIII-XI, coming over two years from 415. Finally, as he was nearing the end of De civitate Dei,
he issued his Retractationes in about 427.

It needs to be borne in mind, however, that since Augustine’s search for truth had already caused him several revisions, the views expressed in this huge collection of writings are neither uniform nor unchanging. For example, De ordine is a treatise dealing with the liberal arts as the path leading to comprehension of the universal order. It shows that their evolution was rational because it was orderly and it concludes with a generous tribute to Pythagoras. This and the predominance accorded the liberal arts were subsequently moderated, though by no means actually retracted, in his Retractiones. De musica, on the other hand, constitutes a six-volume work on rhythm that was meant to be complemented by a further six on melody. The first five serve as an introduction to Book VI which places number and music in a cosmological scheme that is essentially Platonic and reflects material in Timaeus. The work as left by Augustine largely follows a Greek treatise on music written in the second century by Aristides Quintilianus.
However, the Platonic content of De musica and the early Dialogues which it followed was shortly to be put into perspective in Confessiones as being but a preparation, albeit a necessary one, for understanding the Christian mysteries. This was a similar conclusion to Clement’s, yet the importance of Platonism was hardly diminished thereby, for it is abundantly evident from his later De civitate Dei that the discipline of Platonic thought and the basic precepts of its natural philosophy remained indispensable for such an understanding.

However, this did not place Platonists beyond criticism, especially those who found the idea of the Incarnation of the Son of God profoundly distasteful. Augustine recalled Simplicianus recounting how one Platonist had maintained that the quotation, “The Word was in the beginning of all things, and the Word was with God”, should be displayed in gold in every church. This was sufficient, it was argued, and some could not accept the Christian sequel that “The Word was made flesh”. Porphyry in particular was repelled by the suggestion that the Word, as Christ Incarnate, should appear as a body from a woman, bleed on the Cross and become resurrected. This earned Augustine’s dismissal:

But god, the great teacher, became of no account in the eyes of the proud [Porphyry and the Platonists] simply because “the Word became flesh

De civitate Dei X.29

I read there that the Word, God, “was born not of the flesh, but of God”. But, that “the Word was made flesh and dwelt among us” – I did not read that there that “in due time He died for the ungodly” and “that Thou didst not spare Thine Only-begotten Son, but didst deliver Him up for us all” – that is not there.

Confessiones V.II.9.14

That all gods should be worshipped, as urged by Plato, was also repudiated by Augustine together with the doctrine of metempsychosis. Porphyry was again criticized for upholding both these teachings along with Origen who, as recently as 400, had been criticized at a council in Alexandria for some of his

Despite these differences, it can be seen that the two traditions remained essentially compatible. This was still partly explained by the belief that Plato may have learnt some scripture in Egypt,
a belief based on what was taken to be internal evidence as, for example, when Augustine compares Timaeus with Genesis:

“In the beginning God made heaven and earth. But the earth was invisible and unformed, and there was darkness over the abyss, and the spirit of God soared above the water (Genesis 1.1f)”. Now in the Timaeus, the book in which he writes about the creation of the world, Plato says that God in that work first brought together earth and fire (Timaeus 31B); and it is obvious that for Plato fire takes the place of the sky Plato goes on to say that water and air were the two intermediaries whose interposition effected the junction of those two extremes
(Timaeus 32B). This is supposed to be his interpretation of the biblical statement: “The spirit of God soared above the water”.

De civitate Dei VIII. 11

And when God declared, “I am He who is ” (Exodus 3,14), it was the “truth Plato vigorously maintained and diligently taught”. Augustine’s own exegesis of Plato’s moral philosophy acknowledged that, to Platonists, the highest good was to be found not in the mind or body, but in God, and that goodness, being equated with virtue, is only to be found through knowledge of God.”

[Platonists] acknowledge a God who transcends any kind of soul, being the maker not only of this visible – heaven and earth, in the familiar phrase – but also of every soul whatsoever, a God who gives blessedness to the rational and intelligent soul – the class to which the human soul belongs – by giving it a share in his unchangeable and immaterial light.

De civitate Dei, VIII.1

Platonists assert that the true God is the author of the universe, the source of the light of truth, and the bestower of happiness.

De civitate Dei VIII.5

His synthesis of the two traditions appears as effortless as Clement’s had been.

The philosophy that is true has no other function than to teach what is the First Principle of all things – Itself without beginning, – and how great an intellect dwells therein, and what has proceeded therefrom for our welfare, but without deterioration of any kind. Now, the venerated mysteries teach that this First Principle is one God omnipotent, and that He is tripotent, Father and Son and Holy Spirit.

De ordine II.5.6

In his expositions of the cosmos, the elements, the liberal arts and the understanding of numbers, it may be seen that Augustine again very much continues the teaching of Clement.

But what are the higher things ? Where there is no time, because there is no change, and from where times are made and ordered and changed, initiating eternity as they do when the turn of the heavens comes back to the same state, and the heavenly bodies to the same place, and in days and months and years and centuries and other revolutions of the stars obey
the laws of equality, unity and order. So terrestrial things are subject to celestial, and their time circuits join together in harmonious succession for a poem of the universe.

De musica VI. 11.29

In this is contained the original sense of universe as unus versus,
namely one that is turning.

From him derives every mode of being, every species, every order, all measure, number and weight he has not left them without a harmony of their constituent parts, a kind of peace.

De civitate Dei V.11, paraphrasing Wisdom 11.20

there is nothing which is not brought into being by him, from whom comes all form, all shape, all order …

De civitate Dei XI. 15

However, understanding the orderliness of the creation and what a Christian’s attitude towards it should be was naturally difficult, particularly following the shock of the sack of Rome in 410 which prompted the writing of De civitate Dei. In achieving such an understanding, Augustine evidently differs somewhat from Clement for, whereas Clement excluded the uneducated from the path to knowledge, Augustine seems prepared to include anyone even at the risk of holding back the educated.

If only the weak understanding of the ordinary man did not stubbornly resist the plain evidence of logic and truth! The result is that we are forced very often to give an extended exposition of the obvious …

De civitate Dei II. 1; see also VII. Pref.

In all these branches of study, therefore, all things were being presented to reason as numerically proportioned Then, reason gained much coinage and preconceived a great achievement; it ventured to prove the soul immortal. It treated diligently of all things. It came to feel that it possessed great power, and that it owed all its power to numerical proportions. Something wondrous urged it on. And it began to suspect that it itself was perhaps the very number by which all things are numbered, or if not, that this number was there whither it was striving to arrive But, false images of the things which we number drift away from that most hidden something by which we ennumerate, snatch our attention to themselves, and
frequently make that hidden something slip away even when it has been already in our grasp.

De ordine II. 15.43

If a man does not yield to these images, and if he reduces to simple, true and certain unity all the things that are scattered far and wide throughout so many branches of study, then he is most deserving of the attribute learned. Then, without being rash, he can search after things divine …

De ordine II.16.44

Open though this may be for anyone to attempt, Augustine both warns of the difficulties that lie ahead and at the same time describes the milestones that must be attained in order to succeed:

… no one ought to aspire to a knowledge of those matters without that twofold science, so to speak – the science of right reasoning and that of the power of numbers.

De ordine II.18.47

only a rare class of men is capable of using [reason] as a guide to the knowledge of God or of the soul; either of the soul within us or of the world-soul.

De ordine II.11.30

If you have a care for order you must return to those verses, for instruction in the liberal arts produces devotees more alert and steadfast and better equipped for embracing

De ordine I.8.24

But since all the liberal arts are learned partly for practical use and partly for the knowledge and contemplation of things, to attain the use of them is very difficult except for some very gifted person who even from boyhood has earnestly and constantly applied himself.

De ordine II.16.44

Autore: Nigel Hiscock
The Wise Master Builder. Platonic Geometry in Plans of Medieval Abbeys and Cathedralsl
: Ashgate
Luogo: Aldershot
Anno: 2000
Pagine: 64-69


Early Christian Sources of Platonic Geometry: the Latin Encyclopedists

In the foregoing sections, it has been shown that the passage of Platonic and Neoplatonic thought from Alexandria to Asia Minor and the Greek Fathers produced writings of sufficient importance that they were immediately to find their way to the West, reaching not only Ambrose in Milan but Rome as well, whence the teachings of Origen were to spread in the translations of Rufinus. In the meantime, however, Neoplatonism had already reached Rome with the arrival of Plotinus in 244.

It was Plotinus’s pupil, Porphyry (233-c.300), a leading Neoplatonist himself, who edited the work of his master and whose own writings included commentaries on Timaeus and apparently the Elementa as well. Writing in Greek though living in Rome, he was to be highly regarded by Augustine as a pagan philosopher, though this was a tribute Augustine was to qualify because of Porphyry’s anti-Christian stance, manifest for example in his treatise Adversus Christianos.

Marius Victorinus, who taught rhetoric in Rome and became a Christian convert in the middle of the fourth century, translated writings of Plotinus and other Neoplatonists into Latin which may have numbered among the works of Victorinus recorded by Alcuin at York. He was in touch with
Simplicianus, the priest in Milan who prepared Ambrose for baptism the year before the latter became bishop of that city in 374.

At about the time of Victorinus’s conversion, Chalcidius was producing his celebrated Timaeus translation and commentary, copies of which, as already stated, were a necessary possession for all medieval libraries of note.
This was in spite of the text ending prematurely at a point which immediately precedes Plato’s treatment of the elements and the regular solids. Nevertheless, the work remained the most important of all Platonic sources for the Latin middle ages.

This was followed by two more Platonic works of hardly less importance, namely the Commentarii in Ciceronis Somnium Scipionis of Macrobius and Martianus’s De nuptiis Philologiae et Mercurii. Macrobius’s Commentarii,
second only to Chalcidius’s, was written late in the fourth century or early in the fifth based on a lost commentary on Timaeus by Porphyry. Yet it is less a commentary than an encyclopedia of Neoplatonism illustrated with diagrams. Its starting-point is Plato’s Republic,
Cicero’s original work also being entitled De republica,
and it is with Scipio’s Dream that he ends it as an obvious counterpart to Plato’s Vision of Er. Martianus’s De nuptiis was approximately contemporary, being written between 410 and 439, and uses the allegorical marriage between Philology and Mercury as a setting for summarizing the seven liberal arts, in which each appears personified as a bridesmaid at the wedding.

Whilst Somnium Scipionis is among the works most frequently referred to in early medieval manuscripts and is itself among the most common manuscripts from that time, so De nuptiis was perhaps the most widely used schoolbook, its popularity during the ninth and tenth centuries being matched by that of Somnium Scipionis possibly from early in the tenth. Their influence in transmitting Plato’s cosmology was second only to Chalcidius partly as a result of expositions of number theory that deal not only with numerical relationships but with their powers as well, the attributes of the Pythagorean decad for example and the discovery of his musical ratios being relayed extensively in medieval literature. This is not to say that the transmission was exact and unvarying since tradition was always open to interpretation and development. For example, Plato’s and Clement’s concept of 7 planets revolving around an eighth, which is Earth, becomes in Somnium Scipionis 7
planets revolving within an eighth which is an all-encompassing celestial sphere. This is composed of 5 zones. Because justice is even-handed, to Clement it was represented by 4, by Martianus 2 and by Macrobius 8. 7, being a virgin number, is identified with Pallas Athene. In De nuptiis, 9 is also a perfect number and signifies the Muses. Nevertheless, it seems fair to say that these are additions to, not an undermining of, the basic precepts, for these remained those of Pythagoras and Plato as recognized by Martianus.

Meanwhile the august company of the gods… acknowledged [Arithmetic] herself… to be in very truth the procreator of the gods. And the host of philosophers, too, who stood nearby – in particular, Pythagoras, with all his disciples, and Plato,
expounding the cryptic doctrines of his Timaeus – worshipped the lady with words of mystic praise….

Martianus, De nuptiis 803

According to this whole tradition as transmitted, 1 is confirmed as the monad and the generator of numbers. 2, being the first departure from unity, represents discord and is the female number because it lacks a middle term.
3 is male because it possesses a middle term and is therefore the first number that is wholly odd. In other words, because,

1 + 1 + 1=3,

it is the first number comprising a mean and two extremes; it also stands for the triangle and the three divisions of the soul.
By the same reasoning, 4 is the first number wholly even because it is the first consisting of two means; it is the terminal number of the tetrad as well as that of the geometric elements of point, line, plane and solid; it represents the quadrangle and the
4 elements and seasons.

The pentad comes next, the number assigned to the universe. This identification is reasonable, for after the four elements, the universe is a fifth body of a different nature.

Martianus, De nuptiis 735

To this Macrobius adds that 5,

. . . alone embraces all things that are and seem to be

Macrobius, Commentarii, 1.6.19

Yet in conveying Plato’s association of the macrocosm with the human microcosm, Martianus adds that 5 also stands for marriage, being the sum of the male and female numbers, as well as the sum of the human senses. 6 is a perfect number because it is the sum of its parts. In other words,

1 x 2 x 3 = 1 + 2 + 3 = 6

Moreover, it is the product of the male and female numbers and so signifies creation. Because 7 begets no numbers in the decad,
it is virgin; as the sum of 3 + 4, it is the number by which the World-Soul is generated, according to Timaeus;
and, the Moon being the seventh planet, it also relates to the phases of the Moon measured in 7-day periods and the lunar stages of each month.
8 is the first cube and is perfect because it has 6 surfaces.

(10 is) the highest degree of perfection of all numbers…

Macrobius, Commentarii, 1.6.76

It contains within itself all numbers with their varied attributes and degrees of perfection…

De nuptiis 742

Interestingly, it is important to note that Martianus has Geometry preceding Arithmetic at the wedding. Her Book is the longest in the work and contains more geography than geometry, yet it does incorporate a ten-page summary of Euclid’s Elementa. Here a classification of angles, planes and solids leads to a description of how solids are generated from planes. Having described the basic solids, among which are found the pyramid and cube, Martianus concludes with the ‘noble’ figures of the octahedron, dodecahedron and icosahedron. Not surprisingly, geometric thinking finds its counterpart in arithmetic for, just as the sphere is recognized as containing all other figures, and in particular the regular solids, so 10 contains all numbers. And since geometric solids are recognized as being based upon plane figures, this would explain Macrobius’s allusion to 5 embracing all things.
Because 5 is the first figurate number of the pentagon, which is the plane figure of the dodecahedron which signifies the universe, Macrobius seems clearly to be associating 5 directly with the macrocosm, as indeed does Martianus.

Had Augustine written his text-books on the liberal arts, he would undoubtedly have belonged to the encyclopedic tradition of his near-contemporaries Macrobius and Martianus. As it is, his importance for the present study is arguably even greater, not only for transmitting Platonic thought within a theological framework but also for securing thereby its acceptance by the Church. Consequently, his contribution will be considered next.

Autore: Nigel Hiscock
The Wise Master Builder. Platonic Geometry in Plans of Medieval Abbeys and Cathedralsl
: Ashgate
Luogo: Aldershot
Anno: 2000
Pagine: 61-64