<± DISSERTATION SECOND. [paet u. 



Mathematical sciences, well marked and distinguished by 

 great improvements, I have divided the above interval into 

 three corresponding parts. The first of these, reaching 

 from the commencement of Newton's discoveries in 1663, 

 to a little beyond his death, or to 1730, may be denominat- 

 ed, from the men who impressed on it its peculiar charac- 

 ter, the period of Newton and Leibnitz. The second, which, 

 for a similar reason, I call that of Euler and U'Alembert, 

 may be regarded as extending from 1"50 to 1780; and the 

 third, that of Lagrange and Laplace, from 1780 to 1818. 



PERIOD FIRST. 



SECTION I. 



THE NEW GEOMETRY. 



The seventeenth century, which had advanced with such 

 spirit and success in combating prejudice, detecting error, 

 and establishing truth, was destined to conclude with the 

 most splendid series of philosophical discoveries yet recorded 

 in the history of letters. It was about to witness, in sue- 

 cession, the invention of Fluxions, the discovery of the 

 Composition of Light, and of the Principle of Universal 

 Gravitation, — all three within a period of little more than 

 twenty years, and all three the work of the same individual. 

 It is to the first of these that our attention at present k 

 to be particularly directed. 



