THEIR MYSTICISM. 217 



abundant and defective, — were, by a willing submission to an enthu- 

 siastic bias, connected with the notions of good and beauty, which 

 were suggested by the terms expressing their relations ; and principles 

 resulting from such a connection were woven into a wide and complex 

 system. It is not necessary to dwell long on this subject ; the mere 

 titles of the works which treated of it show its nature. Archytas 10 is 

 said to have written a treatise on the number ten : Telauge, the daugh- 

 ter of Pythagoras, wrote on the number four. This number, indeed, 

 which was known by the name of the Tetractys, was very celebrated in 

 the school of Pythagoras. It is mentioned in the " Golden Verses," 

 which are ascribed to him : the pupil is conjured to be viituous, 



Nai na tov ifiCTepa ^v^a trapaldvTa rcrpaKTvv 

 Tlayav atvvdov <fi6<Tt<i>; .... 



By him who statnpt The Four upon the mind,— 

 The Four, the fount of nature's endless stream. 



In Plato's works, we have evidence of a similar belief in religious 

 relations of Number; and in the new Platonists, this doctrine was es- 

 tablished as a system. Proclus, of whom we have been speaking, 

 founds his philosophy, in a great measure, on the relation of Unity and 

 Multiple ; from this, he is led to represent the causality of the Divine 

 Mind by throe Triads of abstractions ; and in the development of one 

 part of this system, the number seven is introduced. 1 ' " The intelligi- 

 ble and intellectual gods produce all things triadically ; for the monads 

 in these latter are divided according to number ; and what the monad 

 was in the former, the number is in these latter. And the intellectual 

 gods produce all things hebdomically ; for they evolve the intelligible, 

 and at the same time intellectual triads, into intellectual hebdomads, 

 and expand their contracted powers into intellectual variety." Seven 

 is what is called by arithmeticians a prime number, that is, it cannot 

 be produced by the multiplication of other numbers. In the language 

 of the New Platonists, the number seven is said to be a virgin, and 

 without a mother, and it is therefore sacred to Minerva. The number 

 six is a perfect number, and is consecrated to Venus. 



The relations of space were dealt with in like manner, the Geomet- 

 rical properties being associated with such physical and metaphysical 

 notions as vague thought and lively feeling could anyhow connect 

 with them. We may consider, as an example of this, 12 Plato's opinion 



10 Mont. ii. 123. » Procl. v. 3, Taylor's translation. >2 Stanley, Hist. Phil. 



