12 COSMOS. 



of all motion, and therefore of all physical phenomena. An- 

 axagoras explains the apparent raiovement of the heavenly 

 bodies frcm east to west by the assumption of a centrifugal 

 force,* on the intermassion of which, as we have already ob- 

 served, the fall of meteoric stones ensues. This hypothesis 

 indicates the origin of those theories of rotatory motion wliich 

 more than two thousand years afterward attained considera- 

 ble cosmical importance from the labors of Descartes, Huy- 

 gens, and Hooke. It would be foreign to the present work 

 to discuss whether the world- arranging Intelligence of the 

 philosopher of Clazomense indicates! the Godhead itself, or 

 the mere pantheistic notion of a spiritual principle animating 

 all nature. 



In striking contrast with these two divisions of the Ionic 

 school is the mathematical symbolism of the Pjrthagoreans, 

 which in like manner embraced the whole universe. Here, 

 in the world of physical phenomena cognizable by the senses, 

 the attention is solely directed to that which is normal in con- 

 figuration (the five elementary forms), to the ideas of num- 

 bers, measure, harmony, and contrarieties. Things are re- 

 flected in numbers which are, as it were, an imitative repre- 

 sentation {jufX7]0L^) of them. The boundless capacity for rep- 

 etition, and the illimitability of numbers, is tj'pical of the 

 character of eternity and of the infinitude of nature. The 

 essence of things may be recognized in the form of numerical 

 relations ; their alterations and metamorphoses as numerical 

 combinations. Plato, in his Physics, attempted to refer the 

 nature of all substances in the universe, and their difierent 

 stages of metamorphosis, to corporeal forms, and these, again, 

 to the simplest triangular plane figures 4 But in reference 



* Cosmos, vol. i., p. 133-135 (note), and vol. ii., p. 309, 310 (and 

 note). Simplicius, in a remarkable passage, p. 491, most distinctly 

 contrasts the centripetal with the centrifugal foi'ce. He there says, 

 "■ The heavenly bodies do not fall in consequence of the centrifugal force 

 being supei'ior to the inherent falling force of bodies and to their down- 

 ward tendency." Hence Plutarch, in his work, De Facie in Orbs 

 lAincc, p. 923, compares the moon, in consequence of its not falling to 

 the earth, to "a stone in a sling." For the actual signification of the 

 Kepix(^oriGi^ of Anaxagoras, compare Schaubach, in Anaxag. Clazom. 

 Fragm., 1827, p. 107-109. 



t Schaubach, Op. cit., p. 151-156, and 185-189. Plants are likewiso 

 Mid to be animated by the intelligence vovg ; Aristot., De Plant., i., p. 

 8 1 5, Bekk. 



X Compare on this portion of Plato's mathematical physics, B5ckh, 

 Vn Platnnico Syst. Caslesiium Glohoriim, 1810 ct 1811; Martin, £^«i/p| 

 tur le Tim^e, torn, ii., p. 234-242; and Brandis, in the Gesckichie det 

 O I iichisch-Romischen Philosophie, th. ii., ablh. i., 1844, $ 375. 



