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CHAPTER XIII. 



ON THE DEVELOPMENT OF MATHEMATICAL THOUGHT DURING 

 THE NINETEENTH CENTURY. 



IN venturing upon the last and most abstract portion of i. 



History of 



the great domain of Scientific Thought of the century, it thought. 

 may be well to remind the reader that it is not a history 

 of science but a history of thought that I am writing. 

 When dealing in the foregoing chapters with mani- 

 fold discoveries, drawn promiscuously from the various 

 natural sciences, I have done so only to show how the 

 scientific mind has, in the course of the period, come 

 to regard the things of nature from different points of 

 view, and to think and reason on them differently. 

 Such changes have frequently been brought about by 

 the discovery of novel facts, but this alone has not 

 generally sufficed to mark also a change in the manner 

 of reasoning on and thinking about them. The increase 

 in the number of natural species, of the chemical ele- 

 ments or of the smaller planets, has not necessarily 

 made us think differently about these things in them- 

 selves : the theory and point of view may change without 

 any change in the object towards which they are directed, 



