as a mark of logical purity and rigor. Had the real or 

 supposed advantages of introducing motion into geo- 

 metrical conceptions been suggested to Euclid, we may 

 suppose him to have replied that the theorems of space 

 are independent of time ; that the idea of motion neces- 

 sarily implies time, and that, in consequence, to avail 

 ourselves of it would be to introduce an extraneous 

 element into geometry. 



It is quite possible that the contempt of the ancient 

 philosophers for the practical application of their science, 

 which has continued in some form to our own time, 

 and which is not altogether unwholesome, was a pow- 

 erful factor in the same direction. The result was that, 

 in keeping geometry pure from ideas which did not 

 belong to it, it failed to form what might otherwise have 

 been the basis of physical science. Its founders missed 

 the discovery that methods similar to those of geometric 

 demonstration could be extended into other and wider 

 fields than that of space. Thus not only the develop- 

 ment of applied geometry but the reduction of other 

 conceptions to a rigorous mathematical form was indefi- 

 nitely postponed. 



Astronomy is necessarily a science of observation 

 pure and simple, in which experiment can have no place 

 except as an auxiliary. The vague accounts of striking 

 celestial phenomena handed down by the priests and 

 astrologers of antiquity were followed in the time of the 

 Greeks by observations having, in form at least, a rude 

 approach to precision, though nothing like the degree of 

 precision that the astronomer of today would reach with 

 the naked eye, aided by such instruments as he could 

 fashion from the tools at the command of the ancients. 



IT 



