306 HISTORY OF FORMAL ASTRONOMY. 



appeared like models of the Solar System; but disclosing unexpected 

 objects, as the Ring of Saturn, and the Spots of the Sun. The art of 

 observing made rapid advances, both by the use of the telescope, and 

 by the sounder notions of the construction of instruments which Tycho 

 introduced. Copernicus had laughed at Rheticus, when he was dis- 

 turbed about single minutes ; and declared that if he could be sure to 

 ten minutes of space, he should be as much delighted 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, 5 " the Divine Goodness has given us 

 in Tycho an observer so exact that this error of eight minutes is im- 

 possible, we must be thankful to God for this, and turn it to account. 

 And these eight minutes, which we must not neglect, will, of them- 

 selves, enable us to reconstruct the whole of astronomy." In addition 

 to other improvements, the art of numerical calculation made an in- 

 estimable advance by means of Napier's invention of Logarithms ; and 

 the progress of other parts of pure mathematics was proportional 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 

 unsystematized facts. The science was, therefore, forced along by a 

 strong impulse on all sides, and its career assumed a new character. 

 Up to this point, the history of European Astronomy was only the 

 sequel of the history of Greek Astronomy ; for the heliocentric system, 

 as we have seen, had had a place among the guesses, at least, of the 

 inventive and acute intellects of the Greek philosophers. But the dis- 

 covery of Kepler's Laws, accompanied, as from the first they were, with 

 a conviction that the relations thus brought to light were the effects 

 and exponents of physical causes, led rapidly and irresistibly to the 

 Mechanical Science of the skies, and collaterally, to the Mechanical 

 Science of the other parts of Nature : Sound, and Light, and Heat ; 

 and Magnetism, and Electricity, and Chemistry. The history of these 

 Sciences, thus treated, forms the sequel of the present work, and will 

 be the subject of the succeeding volumes. And since, as I have said, 

 our main object in this work is to deduce, from the history of science, 

 the philosophy of scientific discovery, it may be regarded as fortunate 

 for our purpose that the history, after this point, so far changes its 

 aspect as to offer new materials for such speculations. The details of 



5 De Stella Martis, c. 19. 



