224 SCIENCE IN GRECO-ROMAN ANTIQUITY 



to closer grips with truth, hence an important problem 

 presents itself : How did the savants of the Renaissance 

 succeed in filling up the gap which, to the Greek mind, 

 existed between physics and mathematics ? How did 

 they succeed in reconciling the requirements of the 

 Greek theory of axioms with the no less irresistible 

 data of experience. 



This question may be answered in a few words as 

 follows. As we have seen, Greek science had two 

 requirements : 



1. A rigorous chain of propositions ; 



2. A collection of ideas which serves as the basis of 

 this chain of reasoning and whose logical truth is 

 convincing to the mind. 



The scientists of the Renaissance maintained the 

 first of these two requirements in its integrity, but 

 they partially modified the second. 



In every science the connection between proposi- 

 tions must be. rigorous, there can be no dispute on this 

 point. 



However, the primary notions (axioms, definitions) 

 which form the basis of the reasoned deduction are 

 not necessarily logically clear ; a constant verification 

 by experience is sufficient to make them valid. We 

 do not know, for instance, what motion is in itself, 

 but if we can decompose it into certain measurable 

 elements (time, space), and if this decomposition is 

 useful and accounts for observed facts, we can include 

 it in our primary notions. 



By proceeding in this fashion the scientists of the 

 Renaissance succeeded in constituting a science which 

 was both rational and experimental. The aim which 

 they pursued more or less consciously was to make the 

 mathematical conceptions less rigid so as to adapt 

 them to the interpretation of mechanical and physical 

 facts ; and to create a type of law which, whilst allow- 

 ing of rigorous deductions, expresses the real con- 



