phenomena observed by astronomers. This concluding 

 portion, however, of the great work, is also interspersed 

 with geometrical reasoning of the same admirable descrip 

 tion as characterized the former, and applied to the so 

 lution of problems respecting the heavenly motions. 



Before Sir Isaac Newton appeared to enlighten man 

 kind, and to found a new era in the history of physical 

 science, the eminent men who had preceded him had made, 

 during the century immediately preceding his birth, very 

 important steps in furthering the advancement of our 

 knowledge ; and they had approached exceedingly near 

 that point which forms the most important of all his dis 

 coveries, according to a kind of law which seems to 

 regulate the progress of human improvement a law of 

 continuity, which apparently prevents any sudden, and, 

 as it were, violent change, from being made in the in 

 tellectual condition of the species, and prescribes the 

 unfolding of all great truths by slow degrees, each 

 mighty discovery being preceded by others only less 

 considerable than itself, and conducting towards it. The 

 great discoveries in pure mathematics afford striking 

 examples of this truth. That of Logarithms by Napier 

 is, perhaps, the instance in which the most considerable 

 deviation has been made from the rule ; but even here 

 there had been some curious methods of mechanical 

 calculation invented before, and the discoverer of lo 

 garithms himself had reached the point very nearly by 

 other most ingenious contrivances, before he actually 

 made his great step. 



But the Fluxionary or Differential Calculus gives a 

 remarkable exemplification of the general principle; and 

 its subsequent most important extension, the Calculus of 

 Variations, furnishes another not less striking. Ever since 

 Descartes s happy application of Algebra to Geometry had 



