INDUCTIVE EPOCH OF NEWTON. 171 



that the emanation of the earth carries a projected 

 stone along with the motion of the earth, just in the 

 same way as it carries the moon in her orbit ; and 

 that this force is greater on the stone than on the 

 moon, because the distance is less. 



The Proposition in which Newton has stated the 

 discovery of which we are now speaking, is the 

 fourth of his third Book: "That the moon gravi- 

 tates to the earth, and by the force of gravity is 

 perpetually deflected from a rectilinear motion, and 

 retained in her orbit." The proof consists in the 

 numerical calculation, of which he only gives the 

 elements, and points out the method; but we may 

 observe, that no small degree of knowledge of the 

 way in which astronomers had obtained these ele- 

 ments, and judgment in selecting among them, were 

 necessary: thus, the mean distance of the moon 

 had been made as little as fifty-six and a half semi- 

 diameters of the earth by Tycho, and as much as 

 sixty-two and a half by Kircher: Newton gives 

 good reasons for adopting sixty-one. 



The term " gravity," and the expression " to gra- 

 vitate," which, as we have just seen, Newton uses of 

 the moon, were to receive a still wider application 

 in consequence of his discoveries ; but in order to 

 make this extension clearer, we consider it as a 

 separate step. 



4. Mutual Attraction of all the Celestial Bodies. 

 If the preceding parts of the discovery of gravi- 

 tation were comparatively easy to conjecture, and 



