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CHAPTER I. 



ON THE INDISTINCTNESS OF IDEAS OF THE 

 MIDDLE AGES. 



THAT firm and entire possession of certain clear 

 and distinct general ideas which is necessary to 

 sound science, was the character of the minds of 

 those among the ancients who created the several 

 sciences which arose among them. It was indis- 

 pensable, that such inventors should have a 

 luminous and steadfast apprehension of certain 

 general relations, such as those of space and num- 

 ber, order and cause ; and should be able to apply 

 these notions with perfect readiness and precision 

 to special facts and cases. It is necessary that 

 such scientific notions should be more definite 

 and precise than those which common language 

 conveys; and in this state of unusual clearness, 

 they must be so familiar to the philosopher, that 

 they are the language in which he thinks. The 

 discoverer is thus led to doctrines which other 

 men adopt and follow out, in proportion as they 

 seize the fundamental ideas, and become acquainted 

 1 with the leading facts. Thus Hipparchus, con- 

 ceiving clearly the motions and combinations of 

 motion which enter into his theory, saw that the 



