Early Christian Sources of Platonic Geometry: Augustine (2)

The Platonist scheme which was revealed through the study of the liberal arts included, as already noted, the elements and Augustine’s treatment of them echoes the description he made slightly earlier and shows how each element relates to the others in a rational way.

The system by which Plato connects and disposes the four elements in a symmetrical order interposes the two intermediary elements of air and water between the two extremes, fire, the most mobile element, and the motionless
earth, in such a way that water is as far above earth as air is above water and fire above air.

De civitate Dei VIII. 15

Elements and numbers are an indissoluble part and expression of the universal order. Augustine also transmits the first 4 numbers of the Pythagorean tetract as signifying the basic geometric concepts of point, line, plane and solid, as well as alluding to the ‘corrationality’ to be found within the numbers themselves.

Can these [trees and animals] be made of the elements and these elements not have been made of nothing? For which among them is more ordinary and lowly than earth. Yet first it has the general form of body where a unity and numbers and order are clearly shown to be.

De musica VI. 17.57

This he demonstrates by referring to the 4 elements of geometry in which 1, a point, is extended to 2, a line, which in turn grows to 3, a plane, and 4, a solid.

From where, then, is the measure of this progression of one to four? And from where, too, the equality of the parts found in length, breadth, and height? Where, I ask, do these things come from, if not from the highest and eternal rule of numbers, likeness, equality, and order? And if you abstract these things from earth, it will be nothing. And therefore God Almighty has made earth, and earth is made from nothing.

De musica VI. 17.57

At about the time he was writing this, he was similarly proving the soul to be immaterial in his De quantitate animae by referring again to the basic constituents of geometry. Drawing much on Plotinus as well as the Christian revelation,
he reverses the development of point, line and figure back to the point as the perfection of unity concluding as follows:

Augustine: Now, then, have you ever seen with the eyes of
the body such a point, or such a line, or such width?

No, never. These things are not bodily.

Augustine: But if bodily things are seen with bodily eyes,
it must be that the soul by means of which we see
these incorporeal things is not a body,
nor like a body…

De quantitate animae 13

When dealing with the millennial theory, Augustine gives another demonstration of relating the theme of solid geometry to number.

[John] may have intended the thousand years to stand for the whole period of this world’s history, signifying the entirety of time by a perfect number. For, of course, the number 1,000 is the cube of 10, since 10 multiplied by 10 is 100, a square but plane figure; but to give height to the figure and make it solid 100 is again multiplied by 10, and we get 1,000. Moreover, it seems that 100 is sometimes used to stand for totality… If this is so, how much more does 1,000 represent totality, being the square of 10 converted into a solid figure!

De civitate Dei

At the time he wrote De ordine, Augustine already understood that numbers possessed both meaning and reason. For those in the ‘search after things divine’,

…whoever has grasped the meaning of simple and intelligible numbers will readily understand these matters.

there is in reason nothing more excellent or dominant than numbers reason is nothing else than number…

De ordine II.16.44,18.48

In his passage concerning the millennium, Augustine acknowledges 10 to be ‘a perfect number’ but it will be seen that it is no longer the only one. He also recognizes that it is to be identified with the law and that it is the sum of the first 4 numbers. This is the conclusion of an exhaustive examination of their ‘corrationality’. In an extension of Macrobius’s explanation of 3 and 4 as the first odd and even numbers, Augustine concludes that, because something, to be whole, must consist of a beginning, a middle and an end, 3 is the first whole number, in that it has an indivisible middle.

3 = 1 + 1 + 1
(see De musica I.12.20)

Yet, whilst to Macrobius and Martianus 4 is the first even number because it is the first possessing two extremes, as,

4 = 2 + 2

to Augustine it is even because it has a divisible middle,

4 = 1 + 2 + 1

(see De musica I.12.21,23)

Accordingly, ‘this great harmony is in the first 3 numbers’ because,

1 + 1 = 2, and 1 + 2 = 3, which is the next in the series, whereas,

2 + 3 = 5, which is not the next in the series.

4 is admitted because,

1 + 2 + 1 = 4

Therefore, ‘one, two, three, four is the most closely connected progression of numbers’ because,

3 follows 1 and 2, and is the sum of 1 and 2;

4 follows 1, 2 and 3 and consists of 1 and 3, and twice 2; in other words,

1 + 3 = 2 x 2 = 4

Modest though this example is, such an agreement of extremes in a series with the mean, and of the mean with the extremes is called by the Greeks analogia, or proportion. This analysis was continued a decade or more later in De Trinitate when Augustine deals with 6 as a perfect number because,

1 + 2 + 3 = 6

Yet it constitutes a different kind of arithmetical perfection from the perfection of 10 as the sum of the tetrad.

At the same time, the Pythagorean powers attributed to numbers were also recognized by Augustine, albeit in Christian form. Thus In lohannis evangelicum,
3 represents the Trinity and 4 the corners of the earth. In De Trinitate,
Augustine goes on to confirm the Pythagorean significance of 6 as Creation, being the product of 2 (female) and 3 (male). Thus, the Creation was accomplished in 6 days and man was created on the sixth day. Furthermore, ‘six serves as a sort of symbol of time.’

In extending the range of perfect numbers, Augustine points out, the ‘number seven is also perfect’, being the day of God’s rest after the Creation.

There is a great deal that could be said about the perfection of the number seven three is the first odd whole number, and four the first whole even number, and seven is made up of these two For this reason the Holy Spirit is often referred to by this same number…

De civitate Dei XI.31

He thereby converts Macrobius’s Platonic attribution of 7 to the World-soul
into its Christian counterpart.

8 is repeatedly identified with a new beginning and the journey to heaven, as in De sermone Domini in monte.

‘Blessed are they who suffer persecution for justice’ (sic) sake, for their’s is the kingdom of heaven’. Perhaps this eighth maxim – which returns to the beginning, and designates the perfect man – is signified both by the circumcision on the eighth day in the Old Testament and by the Lord’s Resurrection after the Sabbath [which is indeed both the eighth day and the first] ….

De sermone Domini I.IV.12; see also Epistolae 55

Returning to 3 and 4 as root numbers,

The mystical number remained, the number twelve, because through the entire world, that is, through the four cardinal points of the world, they were going to announce the Trinity. Thus three times four…

In Iohannis evangelicum 27.10.

Again, 12,

…is significant as being the number of the patriarchs and that of the apostles because it is the product of the two parts of seven – that is, three multiplied by four…

De civitate Dei XV.20; see also XX.5

It is surely an indication of Augustine’s distinction in setting Platonic thought within a theological framework acceptable to the medieval Church that his De civitate Dei was being written at about the time Martianus was relaying in his De nuptiis the Platonic thought of late antiquity. In his turn, it will be shown that Boethius was to revert more to the encyclopedic tradition since his treatises on the liberal arts seem free from religious reference.

Autore: Nigel Hiscock
The Wise Master Builder. Platonic Geometry in Plans of Medieval Abbeys and Cathedrals
: Ashgate
Luogo: Aldershot
Anno: 2000
Pagine: 69-73
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Early Christian Sources of Platonic Geometry: Augustine (1)

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

Early Christian Sources of Platonic Geometry: Basil and Gregory

Basil (c.329-79) read philosophy and rhetoric in the young capital of the Eastern Empire, Constantinople, before continuing his studies in Athens with, among others, Julian, the apostate emperor of the Byzantines. It was only later in life, in 364, that he was ordained priest and only seven years before his premature demise that he was consecrated metropolitan of his native Caesarea, whereupon he made his younger brother Gregory (c.335-c.95) bishop of Nyssa. Before his ordination, Basil had spent some time as a hermit studying Origen and when Gregory stayed at his brother’s cell he too studied ‘his master Origen’ along with everything Basil had learned in Athens. On Basil’s death, Gregory came into his own as a churchman and teacher to the extent that he became known as the ‘Father of Fathers’. In 381 he was summoned by the Emperor Theodosius to the Second Oecumenical Council in Constantinople, as a result of which he was recognized as a principal interpreter of the emergent orthodoxy of the Eastern Church.

Of chief interest to this study is Basil’s Hexaemeron, a series of sermons on the 6 days of Creation delivered morning and evening during Lent to a congregation of workmen. As he acknowledges,

I know that many artisans, belonging to the mechanical trades, are crowding around me. A day’s labour hardly suffices to maintain them; therefore I am compelled to abridge my discourse, so as not to keep them too long from their work.

Hexaemeron III.1

Although the sermons are systematically arranged, the final homily which should have described the creation of man seems to end prematurely and was supplemented by Gregory’s treatise De hominis opificio. Such was the importance of Hexaemeron that its teaching quickly spread to the West.
Ambrose produced an adaptation of it which was soon translated into Latin by Eustathius in about 440 and, whether or not this was the work of Basil’s already noted on Alcuin’s shelves at York, a vernacular abbreviation of Hexaemeron was produced in Anglo-Saxon in 969 by Aelfric. As has been remarked elsewhere, the circulation of shortened versions of texts can usually be taken as evidence that such texts had become standard reading. In addition to manuscripts of several of Gregory’s writings surviving from the tenth century onwards, including no less than three of De hominis opificio from the tenth century itself, this same work had already been translated into Latin by John Scotus in the previous century.

At first sight Basil appears largely to repudiate classical philosophy as he recounts how one theory about the origin of the universe became supplanted by another.

Those who have written about the nature of the universe have discussed at length the shape of the earth … all these conjectures have been suggested by cosmographers, each one upsetting that of his predecessor. It will not lead me to give less importance to the creation of the universe, that the servant of God, Moses, is silent as to shapes … Shall I then prefer foolish wisdom to the oracles of the Holy Spirit? … It is this which those seem to me not to have understood, who, giving themselves up to the distorted meaning of allegory, have undertaken to give a majesty of their own invention to Scripture …

Some have said that heaven is composed of four elements … Others have rejected this system as improbable, and introduced into the world, to form the heavens, a fifth element after their own fashioning. There exists, they say, an aethereal body which is neither fire, air, earth, nor water, nor in one word any simple body … But yet another speaker arises and disperses and destroys this theory to give predominance to an idea of his own invention. Do not let us undertake to follow them for fear of falling into like frivolities; let them refute each other, and, without disquieting ourselves about essence, let us say with Moses ‘God created the heaven and the earth’. Let us glorify the supreme Artificer for all that was wisely and skillfully made … Because … the objects which on all sides attract our notice are so marvellous, that the most penetrating mind cannot attain to the knowledge of the least of the phenomenon of this world.

Hexaemeron IX.1, I.11

Basil seems intent here on keeping the minds of his workaday congregation upon simple devotion. He lived, after all, at the time of violent religious disputes such as those caused by Julian’s apostacy and Valens’s Arianism, and
both needed to be answered by an insistence on orthodoxy, particularly concerning the Holy Trinity, rather than by raking over old arguments about classical cosmogony. In fact, it was Basil himself who has been credited with precipitating the end of the Arian dispute, to be ratified soon after his death at the Council of 381 in the presence of his brother. Given the determination to hold the line on orthodoxy which this indicates, Basil is hardly likely to have encouraged cosmological speculation from his own pulpit, especially since he considered such matters to be above the heads of his artisan audience. Certainly the tradition of teaching he inherited from Clement and Origen of knowledge being reserved for the educated, leaving faith to the uneducated, would seem to support this. Indeed, it will be shown that the early Church actually developed its liturgy in a way that protected its innermost secrets from the uninitiated.

Ambiguity in this passage over the fifth essence being ether still seems unabated for, although Basil appears to dismiss it here, when dealing elsewhere with God’s command, ‘Let there be light’, he refers to it as a matter of course.

Up it sprang to the very aether and heaven. In an instant it lighted up the whole extent of the world … For the aether also is such a subtle substance and so transparent that it needs not the space of a moment for light to pass through it … With light the aether becomes more pleasing …

Hexaemeron III. 3

Here it is surely the fifth essence, being distinct from the elements and yet associated with heaven. Later in the same homily, the implication again must surely be that ether is the substance surrounding the 7 planets which therefore fills the universe.

These circles, they say, carried away in a direction contrary to that of the world, and striking the aether, make sweet and harmonious sounds, unequalled by the sweetest melody …

Hexaemeron III.3

That such matters may sometimes be implied is clear from his treatment of the elements:

… ‘In the beginning God made heaven and earth.’ … Thus, although there is no mention of the elements, fire, water and air, imagine that they were all compounds together, and you will find water, air and fire, in the earth … Do not ask, then, for an enumeration of all the elements; guess, from what Holy Scripture indicates, all that is passed over in silence.

Hexaemeron 1.7

The underlying view here seems clearly to be Platonic as well as Christian, as it is when Basil deals with the divine order and the sensible and intelligible worlds.

… ‘In the beginning God created.’ What a glorious order!

It appears, indeed, that even before this world an order of things existed of which our mind can form an idea, but of which we can say nothing, because it is too lofty a subject for men who are but beginners and are still babies in knowledge. . . . The Creator and the Demiurge of the universe perfected His works in it, spiritual light for the happiness of all who love the Lord, intellectual and invisible natures, all the orderly arrangement of pure intelligences who are beyond the reach of our mind and of whom we cannot even discover the names.

Hexaemeron I.2, 5

You will finally discover that the world … is really the school where reasonable souls exercise themselves, the training ground where they learn to know God; since by the sight of visible and sensible things the mind is led, as by a hand, to the contemplation of invisible things.

Hexaemeron I.6

This anagogical doctrine of the path that leads from the sensible to the intelligible, or from the material to the spiritual, was not only a logical corollary of Plato’s world of Forms but, of importance to this study, it also justified religious art and architecture, as Suger was to write in explaining the design of his abbey of St Denis in the twelfth century.

Gregory’s completion of his brother’s Hexaemeron seems similarly Platonic.

Now all is beautiful and good that is closely related to the First Good … If, then, … that which is truly good is one, and the mind itself also has its power of being beautiful and good, in so far as it is in the image of the good and beautiful, and the nature, which is sustained by the mind, has the like power, in so far as it is an image of the image, it is hereby shown that our material part holds together, and is upheld when it is controlled by nature; and on the other hand is dissolved and disorganized when it is separated from that which upholds and sustains it, and is dissevered from its conjunction with beauty and goodness.

De hominis opificio XII.11

Although, like his brother, Gregory sometimes appears to refute a conventional Platonic doctrine, it reappears later albeit in slightly altered
guise. For example, in referring to humans as a microcosm of the universe, he

… how unworthy of the majesty of man are the fancies of some heathen writers, who magnify humanity as they supposed, by their comparison of it with this world! for they say that man is a little world, composed of the same elements with the universe.

De hominis opificio XVI.1

Yet when he answers:

In what then does the greatness of man consist, according to the doctrine of the Church? Not in his likeness to the created world, but in his being in the image of the nature of the Creator.

De hominis opificio XVI.2

surely he is simply equating Creator and created with Origen’s own distinction between the intelligible and sensible worlds. His description of rational man certainly appears purely Platonic:

Now since man is a rational animal, the instrument of his body must be made suitable for the use of reason …

De hominis opificio VIII.8; cf. Plato, Timaeus 44D

Likewise, in another treatise, Plato’s world of Forms lies just beneath the surface as Gregory celebrates the liberal arts as the path to virtue. A virtuous man is one who,

… has been led to the apprehension of a Master of the creation; he has taken the true Wisdom for his teacher, that Wisdom which the spectacle of the Universe suggests; and when he observed the beauty of this material sunlight he had grasped by analogy the beauty of the real sunlight….

Has a man who looks at such spectacles procured for himself only a slight power for the enjoyment of those delights beyond? Not to speak of the studies which sharpen the mind towards moral excellence, geometry, I mean, and astronomy, and the knowledge of the truth that the science of numbers gives, and every method that furnishes a proof of the unknown and a conviction of the known, and, before all these, the philosophy contained in the inspired Writings, which affords a complete purification to those who educate themselves thereby in the mysteries of God.

De infantibus praemature abreptis 377-8

Once again it may be seen that the doctrines of Plato and Clement are conveyed in the importance given by Gregory to education and purification as preparations for the ‘apprehension of a Master of the creation’ and ‘the spectacle of the Universe’. Part of this apprehension is to be gained in the understanding of numbers:

… number is nothing else than a combination of units growing into a multitude in a complete way … accordingly, in order that we may be taught by Holy Scripture that nothing is unknown to God, it tells us that the multitude of the stars is numbered by Him, not that their numbering takes place as I have described, [for who is so simple as to think that God takes knowledge of things by odd and even, and that by putting units together He makes up the total of the collective quantity?] … For to measure quantity by number is the part of those who want information. But He who knew all things before they were created needs not number as His informant. But when David says that He ‘numbers the stars’, it is evident that the Scripture descends to such language in accordance with our understanding, to teach us emblematically that the things which we know not are accurately known to God.

Contra Eunomium librum II 293

Autore: Nigel Hiscock
The Wise Master Builder. Platonic Geometry in Plans of Medieval Abbeys and Cathedralsl
: Ashgate
Luogo: Aldershot
Anno: 2000
Pagine: 56-61

Early Christian Sources of Platonic Geometry: Clement of Alexandria (2) and other Greek Fathers

Therefore just as the equation of the law with perfection appears safe so, it seems, can references to law and perfection be equated with 10.

It may also be seen that the meaning of number was as integral to Clement’s universal view as it had been to those of Pythagoras and Plato, the sole distinction between them being that he acknowledged his authority to be biblical as well as Platonic.

They say, then, that the character representing 300 is, as to shape, the type of the Lord’s sign.. Now the number 300 is 3 by 100. Ten is allowed to be the perfect number…

‘The days of men shall be,’ it is said, ‘120 years’ (Genesis 6.3). And the sum is made up of the numbers from 1 to 15 added together.

Stromateis VI. 11

Numbers were not endowed with specific significance arbitrarily. For example, because the Greek letter T served as the numeral for 300 and resembled a cross, 300 became regarded as the Lord’s sign. Yet numbers were also held to be expressions of the divine order because of the order to be found within them. If the tetrad was given importance partly because the sum of the first 4 numbers is 10, then 120 was important partly because it is the sum of the first 15 numbers. Moreover, Clement continues:

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 in succession generates squares; and of the inequality of the number 56, consisting of seven of the even numbers beginning with 2, which produce the numbers that are not squares.

Stromateis VI. 11

In other words,

64 + 56 = (8 x 8) + (7 x 8) = 120

64 is composed thus:

1 + 3 = 4, + 5 = 9, + 7 = 16, + 9 = 25, + 11 = 36, + 13 = 49, + 15 = 64

where each sum is a square number which, when added to the next odd number in the series, produces the next square number in the series. As for the series of the first 7 even numbers adding up to 56, each sum, whilst being even, is not square.

2 + 4 + 6 + 8 +10+ 12+ 14 = 56

2 + 4 = 6; 4 + 6 = 10; 6 + 8 = 14; 8 + 10 = 18; 10 + 12 = 22

Following this, Clement continues:

Again, according to another way of indicating, the number 120 consists of four numbers – of one triangular, 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.

Stromateis VI. 11

It can be seen that in this apparently numerical analysis, geometry is clearly implicit. In addition to the importance given to numbers when they relate rationally to each other, the relationship is perceived and expressed in geometric terms, with the concept of figurate numbers standing for square, triangular and polygonal arrangements of numbers, originally in the form of pebble figures. This, together with the inherent order to be found in numbers themselves was to be treated by the Latin encyclopedists and Augustine.

Clement’s successor at the Didascaleon was his former pupil Origen (c.185-c.254) who went on to study philosophy under Ammonius Saccas. He in turn had abandoned an earlier conversion to Christianity and was a Neoplatonist.
One result of Origen’s varied education was a certain flexibility in calling upon the authority of Plato, not invariably, but when it supported his own theological speculations. In a huge output of literature, these were largely a development of Clement’s and organized into his famous treatise, De principiis, which enjoyed particular influence in both the West and the East. Before they caught the attention of Ambrose and others in Italy, Origen’s ideas had spread to Cappadocia reaching the generation of Basil the Great and his brother Gregory of Nyssa and, although some of his ideas were soon to be condemned, his main thesis remained intact.
Ammonius Saccas also taught Platonic philosophy in Alexandria to the Greek Egyptian Plotinus (c.205-70) whose principal contribution lies in incorporating Plato’s thought with Aristotle’s methods and in bringing to this his own theories concerning progressive planes of spiritual existence. As the doctrine of emanation, this was to have a profound effect on mystical thinkers, setting him among the greatest of the Neoplatonists. Care, it should be said, needs to be taken in the understanding of Neoplatonism as a term, since it is comprehensive rather than specific, referring to various individual developments of Platonic thought, some of which are more Christian than Platonic, or more theological than philosophical, or more mystical than intellectual, or vice versa. Despite such distinctions, however, Neoplatonists at the time called themselves Platonists. As for Plotinus, his importance for this study is that in 244 he moved to Rome, where he taught and eventually died, and it was in Italy that Augustine may well have read his essay On Beauty from his Enneads (I, VI).

Autore: Nigel Hiscock
The Wise Master Builder. Platonic Geometry in Plans of Medieval Abbeys and Cathedralsl
: Ashgate
Luogo: Aldershot
Anno: 2000
Pagine: 54-56

Early Christian Sources of Platonic Geometry: Clement of Alexandria (1)

It was the cultural crucible of Alexandria that initiated early Christianity to Platonic thought. In the first century of the new era, the writings of Philo Judaeus, a Greek-speaking Jew, attempted the conciliation of the Hellenic and Judaic traditions of learning, a process continued by Clement (c.150-c.215) in the next century. As a Greek philosopher and convert to Christianity, Clement compared both traditions with each other and with the emergent teachings of Christianity. As a result, he was the first to appreciate how much the writings of Plato and the evangelists John and Paul had in common. Recognized as the leading Christian scholar of his day and the foremost exponent of natural philosophy from the Christian point of view prior to Augustine, Clement was able to produce the synthesis of classical and Christian thought which gave birth to Christian Platonism. This was developed by his most famous pupil, Origen, and provided the theological foundations for the writings in the East of the Cappadocian Fathers as well as for Augustine in the West. Although it has to be admitted that Clement’s own work might not have been read much in the middle ages, his teaching was nevertheless to reach the West through Cassian’s adaptations in the fifth century which were soon to be consulted by Benedict himself. Through Origen’s writing, it was also to reach Ambrose in Greek and thence Augustine, along with translations by Rufinus, some of which were also known to Augustine. The result of this was to be the permanent acceptance of Christian Platonism by the Latin Church. In these early centuries, it not only answered the pagan reaction of Porphyry and Julian, it also gave Christian faith its intellectual content and, such was its enduring appeal, it was to reach its culmination in the cathedral school of Chartres nine hundred years after Clement died.

Clement’s forum was the Didascaleon, or Catechetical School, in Alexandria of which he became head. It had only recently been opened by Pantaenus, also a Christian convert and a Pythagorean, with the purpose of promoting Christian studies for educated converts in opposition to the paganism of Alexandria’s Museum and the esoteric cabalism of the Gnostics. Accordingly, the methods of classical philosophy were applied to a curriculum
which included philosophy, mathematics and scripture. Education was the path to knowledge, or gnosis,
which led to freedom. The union of knowledge with ‘right reason’ led to virtue just as the union between the human and divine spirit resulted in love. Thus Plato’s three-part division of rational, moral and natural philosophy found its place in Clement’s school.

For the uneducated, a state of grace was still possible through the acceptance of faith but from them, however, gnosis should be concealed:

For Plato also thought it not lawful for ‘the impure to touch the pure.’ 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.

Clement, Stromateis V.4

… even those myths in Plato . . . are to be expounded allegorically, not absolutely in all their expressions, but in those which express the general sense. And these we shall find indicated by symbols under the veil of allegory.

Stromateis V.9

Clement found as much authority for obfuscation in the scriptures:

But since this tradition is not published alone for him who perceives the magnificence of the word; it is requisite, therefore, to hide in a mystery the wisdom spoken, which the Son of God taught. . . . because, ‘even now I fear,’ as it is said, ‘to cast the pearls before swine, lest they tread them underfoot, and turn and rend us’ (Matthew VII.6). For it is difficult to exhibit the really pure and transparent words respecting the true light, to swinish and untrained hearers. For scarcely could anything which they could hear be more ludicrous than these to the multitude; nor any subjects on the other hand more admirable or more inspiring to those of noble nature.

Stromateis 1.12

In retrospect, such determined concealment of gnosis from the uninitiated might arguably be confused with the secret societies of the Gnostics themselves, particularly since Clement often refers to the followers of ‘the true philosophy’ as Gnostics. However, this would be a modern misperception, since Clement had simply decided to combat Gnosticism with his own invention of Christian Gnosticism. When he writes:

Then [the Preaching of Peter, an apocryphal book] adds: ‘Worship this God not as the Greeks’ – signifying plainly, that the excellent among the Greeks worshipped the same God as we, but that they had not learned by perfect knowledge that which was delivered by the Son.’

Stromateis VI.5 [my italics]

Clement makes clear his regard for gnosis as ‘perfect knowledge’, as opposed to the arcane superstitions of the Gnostics.

Clement’s three main works constitute a progression in which the acquiring of gnosis leads to an understanding of Logos, the Word. Protreptikos exhorts the reader to renounce paganism; Paedagogus instructs him in Christian ethics; whilst the major part is Stromateis, a miscellany of essays devoted to a higher knowledge of God and his creation. In these works he repeatedly refers to and quotes from Timaeus and other Dialogues as well as scripture. Of the Protreptikos and Paedagogus,
a tenth-century manuscript has been noted in the Bibliotheque Nationale in Paris together with an eleventh-century manuscript of Stromateis in the Laurentian Library in Florence.

The origins of philosophy are succinctly stated by Clement:

From Pythagoras Plato derived the immortality of the soul; and he from the Egyptians.

Stromateis VI.2

However, the composition of the universe and the nature of the 4 elements had, even since Aetius, become somewhat muddled. Although he writes:

And indeed the most elementary instruction of children embraces the interpretation of the four elements ….

Stromateis V.8

And Athamas the Pythagorean having said, ‘Thus was produced the beginning of the universe; and there are four roots – fire, water, air, earth: for from these is the origination of what is produced’. . . .

Stromateis VI.2

he continues,

Empedocles of Agrigentum wrote:

‘The four roots of all things first do thou hear – Fire, water, earth, and ether’s boundless height: For of these all that was, is, shall be, comes.’

Stromateis VI.2

Nevertheless, despite an apparent confusion between ether and air here, Clement himself seemed clear enough in his previous chapter when he repeated the colours associated with the 4 elements – blue for air, purple for water, scarlet for fire and linen for earth.
Interestingly, this reveals that the atmospheric elements are chromatically – as well as physically and geometrically – related to each other and distinct from the element earth. For just as fire can cause water to evaporate into air and cooling can cause water to condense in air, so the purple of water is a synthesis of the red and blue of fire and air and their geometric solids are also relations of each other in that they are each enclosed by the regular triangle, quite distinct therefore from the colour and cube of earth. Plato’s relation of the macrocosm of the universe to the microcosm of the human also seems preserved by Clement, particularly when it is remembered that the number 10 was equated with perfection.

And the perfect inheritance belongs to those who attain to ‘a perfect man,’ according to the image of the Lord.

And there is a ten in man himself.

Stromateis VI.14, 16; see also V.6

In this passage, Clement then refers to the 5 senses and adds to them another 5, namely power of speech, power of reproduction, spirit received through creation, rule of the soul, rule of the Holy Spirit through faith.

Thus the Platonic Christian appears complete, the conjunction of the two traditions seeming to be effortless.

If then we consider, virtue is, in power, one. But it is the case, that when exhibited in some things, it is called prudence, in others temperance, and in others manliness or righteousness. By the same analogy, while truth is one, in geometry there is truth of geometry; in music, that of music; and in the right philosophy, there will be Hellenic truth. But that is the only authentic truth, unassailable, in which we are instructed by the Son of God.

Stromateis 1.20

The synthesis of the two traditions was evidently derived at least partly from the belief that Plato himself had had sight of certain scriptures. Several of Clement’s essays are devoted to the theme of Greeks borrowing from Hebrews, or of the two traditions at least coinciding. Nevertheless they were still distinguishable:

Rightly, then, to the Jews belonged the Law, and to the Greeks Philosophy, until the Advent ….

Stromateis VI. 17

That scripture associated the Law with 10 is evident above all in the Decalogue, or Ten Commandments. More than being a mere list of rules, however, the Commandments were regarded as an image of heaven and, in this aspect, they are to be identified with the same Pythagorean number of perfection. As Clement writes:

But law is the opinion which is good, and what is good is that which is true, and that which is true is that which finds ‘true being,’ and attains to it. … In accordance with which, namely good opinion, some have called law, right reason, which enjoins what is to be done and forbids what is not to be done. . . . That ten is a sacred number, it is superfluous to say now.

Stromateis 1.25, VI. 16

Therefore just as the equation of the law with perfection appears safe so, it seems, can references to law and perfection be equated with 10.

Autore: Nigel Hiscock
The Wise Master Builder. Platonic Geometry in Plans of Medieval Abbeys and Cathedralsl
: Ashgate
Luogo: Aldershot
Anno: 2000
Pagine: 50-54