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

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