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D'ALEMBERT. 



THE pleasures of a purely scientific life have often 

 been described ; and they have been celebrated with 

 very heartfelt envy by those whose vocations pre- 

 cluded or interrupted such enjoyments, as well as 

 commended by those whose more fortunate lot gave 

 them the experience of what they praised ; but it may 

 be doubted, if such representations can ever apply to 

 any pursuits so justly as to the study of the mathe- 

 matics. In other branches of science the student is 

 dependent upon many circumstances over which he 

 has little control. He must often rely on the reports 

 of others for his facts ; he must frequently commit to 

 their agency much of his inquiries ; his research may 

 lead him to depend upon climate, or weather, or the 

 qualities of matter, which he must take as he finds it ; 

 where all other things are auspicious, he may be with- 

 out the means of making experiments, of placing nature 

 in circumstances by which he would extort her secrets ; 

 add to all this the necessarily imperfect nature of in- 

 ductive evidence, which always leaves it doubtful if 

 one generalization of facts shall not be afterwards 

 superseded by another, as exceptions arise to the rule 

 first discovered. But the geometrician* relies entirely 

 on himself; he is absolute master of his materials ; his 

 whole investigations are conducted at his own good 

 pleasure, and under his own absolute and undivided 



* It may be as well to adopt the expression always used on the conti- 

 nent, to denote the cultivation of mathematical science : " Ce grand geo- 

 metre," is a phrase now universally understood and applied to mathema- 

 ticians of every description. 



