PREFACE vii 



infinite the positive evidence and practical fecundity 

 which we to-day know that it implied. 



On the other hand, the astronomy of position, a 

 science which is purely mathematical, is subordinated 

 to an astrology which seemed explanatory because it 

 entirely filled the frames prepared by the verbalism 

 of the Aristotelian categories. 



Ancient science has in this way missed the very 

 thing which, to us, seems the essential condition of 

 knowledge, the connection between the mathematical 

 and the physical, between calculation and experiment. 

 On that depend twenty centuries of history. Rome 

 remained totally indifferent to the purely disinterested 

 speculative spirit which the followers of Pythagoras 

 and Plato carried to its highest expression in mathe- 

 matical research. She deliberately circumscribed the 

 horizon of science by her anxiety for immediate utility, 

 as is shown by an almost tragic statement by Cicero, 

 quoted by M. Reymond. The spiritual decadence 

 linked to the triumph of Roman imperialism, only 

 ended with the Renaissance, when Hellenizing savants 

 re-opened the book of exact Science at the page where 

 the Greeks of Syracuse and Alexandria had left it 

 unfinished. 



Such considerations show clearly the utility of a work 

 as skilfully adapted to its object as this which we have 

 the honour of presenting to the public. Thanks to 

 it, our men of letters will have the means of com- 

 pleting and rectifying their knowledge of antiquity, 

 supporting it by an understanding of the mental sub- 

 structure which will enable them at last to appreciate 

 the order and solidity of the whole edifice. But it is 

 addressed also to our young men of science. From 

 lack of official institutions in harmony with a general 

 survey of human knowledge, they are, for the most 

 part, left in ignorance of the history of science, incap- 

 able of following the way opened up by our com- 



