192 PHYSICAL SCIENCE IN THE MIDDLE AGES. 



column, turned back to the wall, and adhered to it in the intervening 

 space. The splendid remains of Palmyra, Balbec, Petra, exhibit end- 

 less examples of this kind of perverse inventiveness ; and show us, very 

 instructively, how the decay of art and of science alike accompany 

 this indistinctuess of ideas which we are now endeavoring to illustrate. 



4. Indistinctness of Ideas in Astronomy. — Returning to the sciences, 

 it may be supposed, at first sight, that, with regard to astronomy, we 

 have not the same ground for charging the stationary period with 

 indistinctness of ideas on that subject, since they were able to acquire 

 and verify, and, in some measure, to apply, the doctrines previously 

 established. And, undoubtedly, it must be confessed that men's 

 notions of the relations of space and number are never very indistinct. 

 It appears to be impossible for these chains of elementary perception 

 ever to be much entangled. The later Greeks, the Arabians, and the 

 earliest modern astronomers, must have conceived the hypotheses of 

 the Ptolemaic system with tolerable completeness. And yet, we may 

 assert, that during the stationary period, men did not possess the 

 notions, even of space and number, in that vivid and vigorous manner 

 which enables them to discover new truths. If they had perceived 

 distinctly that the astronomical theorist had merely to do with relative 

 motions, they must have been led to see the possibility, at least, of the 

 Copernican system ; as the Greeks, at an earlier period, had already 

 perceived it. "We find no trace of this. Indeed, the mode in which 

 the Arabian mathematicians present the solutions of their problems, does 

 not indicate that clear apprehension of the relations of space, and that 

 delight in the contemplation of them, which the Greek geometrical 

 speculations imply. The Arabs are in the habit of giving conclusions 

 without demonstrations, precepts without the investigations by which 

 they are obtained ; as if their main object were practical rather than 

 speculative, — the calculation of results rather than the exposition of 

 theory. Delambre 3 has been obliged to exercise great ingenuity, in 

 order to discover the method by which Ibn Iounis proved his solution 

 of certain difficult problems. 



5. Indistinctness of Ideas shown by Skeptics. — The same unsteadi- 

 ness of ideas which prevents men from obtaining clear views, and 

 steady and just convictions, on special subjects, may lead them to 

 despair of or deny the possibility of acquiring certainty at all, and may 

 thus make them skeptics with regard to all knowledge. Such skeptics 



= Delamb. If. A. p. 125-8. 



