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tind the simplicity and universality of the conclusion, de- 

 rives its principal claim on our consideration from the ferti- 

 lity with which it supplies new deductions, each successively 

 •unfolding new properties, and pointing out relations hitherto 

 -unobserved. Thus every step that we ascend in the progress 

 i^F discovery, at the same time that it gives us a more com- 

 manding view of the ground that we have passed, enables 

 us to catchaglimpee of some more elevated pinnacle, which 

 the interposing objects had hitherto prevented us from ob- 

 serving, and when at length we have obtained the possession 

 -erf" ithis 'eminence, we value it chiefly as it facilitates our ap- 

 proach to a summit Still more elevated and remote. The 

 •discovery, for which fPythagoras thanked the gods by the 

 -sacrifice of a whole hecatomb, was entitled to the gratitude 

 of future mathematicians -for consequences of which the phi- 

 losopher himself could 'have had no conception, for establish- 

 ing the connection between arithmetic and geometry, and 

 Opening the passage to trigonometrical computation. The 

 -exultation, which drew from Archimede the proud exclama- 

 'tion '* EvpfiKct," has long been lost in the ardor of ulterior 

 ^discovery ; and his method of eKhaustions, beautiful and ac- 

 curate, and scientific as it is, retains it's place in the list of 

 great discoveries principally from it's having given birth to 

 the method of indivisibles, and prepared the way for the 

 more extensive and philosophical reasonings of the immortal 

 Newton. The observations and researches of every one 

 whose name is mentioned in the history of Science, from the 



