62' 



CHAPTER XIII. 



ON THE DEVELOPMENT OF MATHEMATICAL THOUGHT DURING 

 THE NINETEENTH CENTURY. 



In venturino; 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 tliought 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 dillerent points of 

 view, and to think and reason on them differently. 

 Such changes have frequently been l)roug]it about by 

 the discovery of novel facts, but this alone has not 

 generally sufficed to mark also a cliange 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, luis not necessarily 

 made us think differently about tliese things in them- 

 selves : tlie theory and point of view may change without 

 any change in the oliject towards which they are directed, 



