PRELUDE TO THE EPOCH OF NEWTON. 161 



such globe ; the planets, for instance, to the sun, 

 the Medicean Stars to Jupiter. It is certain, also' 

 that circular motion gives a body a tendency to 

 recede from the center of such revolution, as we 

 find in a wheel, or a stone whirled in a sling. Let 

 us suppose, then, the planet to endeavour to ap- 

 proach the sun ; since, in the mean time, it acquires, 

 by the circular motion, a force to recede from the 

 same central body, it comes to pass, that when 

 those two opposite forces are equal, each compen- 

 sates the other, and the planet cannot go nearer to 

 the sun nor further from him than a certain deter- 

 minate space, and thus appears balanced and float- 

 ing about him." 



This is a very remarkable passage; but it will 

 be observed, at the same time, that the author has 

 no distinct conception of the manner in which the 

 change of direction of the planet's motion is regu- 

 lated from one instant to another; still less do his 

 views lead to any mode of calculating the distance 

 from the central body at which the planet would be 

 thus balanced, or the space through which it might 

 approach to the center and recede from it. There 

 is a great interval from Borelli's guesses, even to 

 Huyghens' theorems; and a much greater to the 

 beginning of Newton's discoveries. 



(England.} It is peculiarly interesting to us to 

 trace the gradual approach towards these disco- 

 veries which took place in the minds of English 

 mathematicians ; and this we can do with tolerable 

 distinctness. Gilbert, in his work, De Magnete, 



