INDUCTIVE EPOCH OF KEPLER. 443 



the other two laws with which Kepler's name is 

 associated. 



Sect. 3. Kepler's Discovery of Ms First and Second 

 Lares. Elliptical Theory of the Planets. 



THE propositions designated as Kepler's first and 

 second laws are these: that the orbits of the 

 planets are elliptical; and that the areas de- 

 scribed, or swept, by lines drawn from the sun to 

 the planet are proportional to the times employed 

 in the motion. 



The occasion of the discovery of these laws was 

 the attempt to reconcile the theory of Mars to the 

 theory of eccentrics and epicycles; the event of it 

 was the complete overthrow of that theory, and the 

 establishment, in its stead, of the Elliptical Theory 

 of the planets. Astronomy was now ripe for such 

 a change. As soon as Copernicus had taught men 

 that the orbits of the planets were to be referred to 

 the sun, it obviously became a question, what was 

 the true form of these orbits, and the rule of 

 motion of each planet in its own orbit. Copernicus 

 represented the motions in longitude by means of 

 eccentrics and epicycles, as we have already said; 

 and the motions in latitude by certain librations, or 

 alternate elevations and depressions of epicycles. 

 If a mathematician had obtained a collection of 

 true positions of a planet, the form of the orbit, and 

 the motion of the star would have been determined 



