202 W. A. WALLACE 



mathematical explanation of eccentrics and epicycles, however, 

 he is still at a loss for a physical explanation as to why this 

 peculiar motion of the heavenly bodies occurs, and in seeking 

 such an explanation has recourse to his concept of " composite 

 motion." 



In this treatment, as in De elementis, there is again a lack 

 of quantitative analysis. Theodoric's argument is in fact very 

 brief, and merely suggestive of an analogy that might obtain 

 between straight-line motions and circular ones when both are 

 considered as natural motions. He first notes that there is a 

 certain relativity to be found in linear gravitational motions, 

 when the principles of such motions are considered precisely as 

 related to the surrounding environment.^^ If extrinsic factors 

 introduce a type of composition into motions that should be 

 simple when explained in terms of their intrinsic principles 

 alone, he sees no reason why a similar type of composition 

 might not also be found in circular motions: 



If this is the case in such straight-line motions, as has been said, 

 it is not extraordinary or incomprehensible to interpret the Phi- 

 losopher's [Aristotle's] treatment of circular motion, when he speaks 

 of it as rotating about a center, as not to mean the exact center of 

 the universe, but the natural center of any natural circle in which 

 there is something having the nature of a terminus, as for example 

 the mid-point of the revolution, insofar as a revolution includes in 

 its very notion movement to a point and away from a point, both 

 being vmderstood with reference to the center of the circle. ... If 

 therefore different relations to various termini can introduce com- 

 position into straight-line motions, so also different centers can 



'^ Cap. 16, U 59ra-b: Quia in talibus transformacionibus que sunt recti motus 

 attenditur fercio aliquis terminus — nichil enini tali motu incipit moveri secundum 

 naturam quod non potest perveiiire ad terminum secundum naturam intentum — 

 hinc est quod in talibus motis secundum diversitatem talium terminorum invenitur 

 nonnulla distraccio et aliquis recessus a pura et omnimoda simplicitate, ne talia 

 corpora, quamvis habeantur per simplicibus, ad eosdem terminos vel secundum 

 eosdem moveantur. Videmus enim alium esse terminum ad quem naturaliter 

 movetur ignis in regione sua, quia ad superficiem infimam spere lune, alium autem 

 terminum perpendimus ad quem movetur aer in spera sua, qui si esset in spera 

 ignis ab ea recedet naturaliter. Et ita videmus diversitatem terminorum in aqua 

 et in terra quoad proprias secundum naturam regiones eorum. 



