158 JAMES A. WEISHEIPL 



considers the sun, moon and stars; therefore mathematics also 

 is a part of natural science. In reply Aristotle distinguished 

 purely mathematical definitions from those of natural science; 

 this is sufficient to establish the sciences as distinct. In confir- 

 mation Aristotle pointed to the quasi-physical character of 

 optics, harmonics and astronomy, which he called to, ^vo-tKajxepa 

 Twv fiadrjixaTcov (Phys., II, 2, 194a7) . Modern translators give 

 the more probable rendering of this phrase as " the more 

 physical of the branches of mathematics." It was in this sense 

 that Averroes (text. comm. 20) and St. Albert (ibidem) had 

 understood the text, William of Moerbeke, however, rendered 

 this phrase with equal grammatical correctness as magis physica 

 quam matheviatica. This translation presented St. Thomas 

 with the opportunity of explaining how astronomy, harmonics 

 and optics pertain, in a certain sense, rather to natural science 

 than to mathematics: 



Sciences of this kind, although they are intermediate between 

 natural science and mathematics, are here described by the Philoso- 

 pher as more natural than mathematical, because each thing is 

 denominated and specified by its ultimate term; hence since investi- 

 gation in these sciences terminates in natural matter, though by 

 means of mathematical principles, they are more natural than 

 mathematical. . . . Hence astronomy is more natural than mathe- 

 matical.-^ 



Both St. Albert and St. Thomas recognized two tj^es of 

 astronomy: mathematical astronomy, such as was studied by 

 Eudoxus, Ptolemy and others, and physical astronomy, such as 

 Aristotle discussed in the Physics and De caelo et mundo. This 

 latter astronomy was considered an integral part of natural 

 philosophy. Unlike mathematical astronomy, physical astrono- 

 my attempts to discover all the physical causes of celestial 

 phenomena, the ultimate efficient and final cause as well as the 

 material and intrinsic formal cause. For Albert and Thomas 

 physical astronomy alone indicates the real system of the uni- 

 verse. The difficulties involved in discovering the real system 



" In 11 Phys., lect. 3, nn. 8-9. See also Sum. theol., II-II, q. 9, a. 2 ad 3. 



