KEPLER'S CELEBRATED LAWS. 307 



To fix these ideas thoroughly in our minds, and a super 

 ficial knowledge is worse than useless, let us imagine to our- 

 selves a man holding horizontally extended a tube of a certain 

 length, capable, like a telescope, of being lengthened or short- 

 ened at pleasure ; and let us fancy him pivoting upon himself, 

 in such a manner that he sweeps, every minute, exactly the 

 same area or same quantity of surface, while varying per- 

 petually the swiftness of movement and the length of the 

 tube ; this " ideal man " will have solved the problem whose 

 solution is inscribed, in ineffaceable letters, on the machinery 

 of our globe ; he will describe around him an ellipse, of which 

 he himself occupies one of the foci. 



By this method of investigation and deduction, Kepler suc- 

 ceeded in breaking up the traditionary authority of the circle 

 and of uniform movement. He broke it up for ever by two of 

 his celebrated laws, which may be rendered in the following 

 terms : 



ist, The orbit of the earth, as well as the curves described by 

 the other planets, are ellipses, one of whose foci is repre- 

 sented by the sun ; 



ad, The heliocentric vector radius of a planet describes around 

 the sun areas equal with the times ; or, in other words, the 

 surfaces described by the vector radii, in eqiial times, are 

 also equal 



The ancients had looked for equality in the movements of 



