PREFACE. XI 



ment of the modern analysis by the latter but also to convey 

 a competent knowledge of those great methods ; while in 

 both lives, especially that of D'Alembert, there is further 

 presented a strong recommendation of mathematical pur- 

 suits, by showing the gratification which they are fitted 

 to bestow. Great as is the value of Montucla's History, 

 in the light of a didactic work, many readers have lamented 

 not more that he left it unfinished, and the latter half very 

 unsatisfactorily edited, than that he did not enter more 

 fully into the detailed statement of the subject, in several 

 of the earlier portions. 



By such historical and critical works, then, the desire and 

 the acquisition of science is promoted ; and surely no more 

 important duty can be performed, than that of affording 

 both the excitement and the gratification, in however 

 moderate a degree. They who are wholly incapable of 

 advancing science themselves, may help others to the 

 knowledge of what the great masters have done ; and they 

 may do this best by not disdaining the office of elementary 

 explanation and discussion. Two thousand years ago, the 

 wisest of the ancients was said to have brought philoso- 

 phy down from heaven to earth ; certainly, he chiefly 

 valued himself on his constant efforts to stir up in men's 

 minds the desire of knowledge.* What he found necessary 

 with regard to the nature of the subject, we in our day may 

 perceive to be equally necessary because of the clouds in which 

 great men, almost unavoidably, involve their scientific 

 researches. The mathematical writings of Newton and his 

 immediate successors require to be made plain, and also to 

 be illustrated by comparative discussion, in order both to 

 show exactly what they accomplished, and to excite an in- 

 telligent curiosity respecting their labours. This has been 



* Cic. Acad., Qu. i. 4, Tusc. v. 4. 



