iict. i] DISSERTATION SECOND. i 



nineteenth century, I shall, in the present Part, confine 

 myself entirely, as has been done in the first Discourse, to 

 the period preceding the end of the seventeenth century, 

 or, more precisely, to that preceding the invention of the 

 fluxionary calculus, and the discovery of (he principle of 

 gravitation ; — one of the most remarkable epochas, without 

 doubt, in the history of human knowledge. 



SECTION I, 



MATHEMATICKS. 



1. Geometry. 



The great inheritance of mathematical knowledge, which 

 the ancients bequeathed to posterity could not, on the re- 

 vival of learning, be immediately taken possession of, nor 

 could even its existence be discovered, but by degrees. 

 Though the study of the Mathematicks had never been en- 

 tirely abandoned, it had been reduced to matters of very sim- 

 ple and easy comprehension, such as were merely subservient 

 to practice. There had been men who could compute the 

 area of a triangle, draw a meridian line, or even construct a 

 sun-dial, in the worst of times ; but between such skill, and 

 the capacity to understand, or the taste to relish, the de- 

 monstrations of E jclid, Apollonius, or Archimedes, there 

 was a great interval; and many difficulties were to be over- 

 come, for which much time, and much subsidiary know- 

 ledge, were necessary. The repositories of the ancient 

 treasures were to be opened, and made accessible ; the 

 knowledge of the languages was to be acquired; the manu- 

 scripts were to be deciphered ; and the skill of the gram- 



