INTRODUCTION. 11 



numbers, measure, harmony, and contrarieties. Things are 

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

 sentation (piprjo-is ) of them. The boundless capacity for repe- 

 tition, and "the illimitability of numbers, is typical of the cha- 

 racter of eternity and of the infinitude of nature. The essence 

 of things may be recognized in the form of numerical rela- 

 tions : their alterations and metamorphoses as numerical 

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

 nature of all substances in the universe, and their different 

 stages of metamorphosis, to corporeal forms, and these again 

 to the simplest triangular plane figures. 14 But in reference 

 to ultimate principles (the elements, as it were, of the 

 elements), Plato exclaims, with modest diffidence, "God 

 alone, and those whom he loves among men, know what 

 they are." Such a mathematical mode of treating physical 

 phenomena, together with the development of the atomic 

 theory, and the philosophy of measure and harmony, have 

 long obstructed the development of the physical sciences, and 

 misled fanciful inquirers into devious tracks, as is shown in 

 the history of the physical contemplation of the universe. 

 " There dwells a captivating charm, celebrated by all anti- 

 quity, in the simple relations of time and space, as manifested 

 in tones, numbers, and lines." 15 



The idea of the harmonious government of the universe 

 reveals itself in a distinct and exalted tone throughout the 

 writings of Aristotle. All the phenomena of nature are de- 

 picted in the Physical Lectures (Auscultationes PhysiccB] as 

 moving, vital agents of one general cosmical force. Heaven and 



14 Compare on this portion of Plato's mathematical physics, 

 Bockh De platonico syst. ccelestium globorum, 1810 et 1811; 

 Martin, Etudes sur le Timee, torn. ii. pp. 234-242; and 

 Brandis in the Geschichte der Griechisch-Romischen Philo- 

 sophic, Th. ii. Abth. i. 1844, 375. 



16 Cosmos, vol. ii. p. 736, note ; compare also Gruppe 

 Ueber die Fragments des Archytas, 1840, s. 33. 



