460 HISTORY OF FORMAL ASTRONOMY. 



ten minutes of space, he should be as much de- 

 lighted as Pythagoras was when he discovered the 

 property of the right-angled triangle. But Kepler 

 founded the revolution which he introduced on a 

 quantity less than this. "Since," he says 4 , " the divine 

 goodness has given us in Tycho an observer so exact 

 that this errour of eight minutes is impossible, we 

 must be thankful to God for this, and turn it to 

 account. And these eight minutes, which we must 

 not neglect, will, of themselves, enable us to recon- 

 struct the whole of astronomy." In addition to 

 other improvements, the art of numerical calcu- 

 lation made an inestimable advance by means of 

 Napier's invention of Logarithms ; and the progress 

 of other parts of pure mathematics was propor- 

 tional to the calls which astronomy and physics 

 made upon them. 



The exactness which observation had attained 

 enabled astronomers both to verify and improve the 

 existing theories, and to study the yet unsystema- 

 tized facts. The science was, therefore, forced along 

 by a strong impulse on all sides. We now proceed 

 to speak of the new path into which this pressure 

 forced it ; but, in order to this, we must first trace 

 the rise and progress of the Science of Mechanics. 



4 De Stella Mortis, c. 19. 



