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
Vedi anche:
Early Christian Sources of Platonic Geometry: Augustine (1)



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