1 86 A Short History of Astronomy [Ca. vn. 



shaded and unshaded portions of the figure represent equal 

 areas each corresponding to the motion of the planet during 

 a month. Kepler's triumph at arriving at this result is 

 expressed by the figure of victory in the corner of the 

 diagram (fig. 61) which was used in establishing the last 

 stage of his proof. 



FIG. 60. Kepler's second law. 



141. Thus were established for the case of Mars the two im- 

 portant results generally known as Kepler's frst two laws : 



1. The planet describes an ellipse, the sun being in one focus. 



2. The straight line joining the planet to the sun sweeps out 

 equal areas in any two equal intervals of time. 



The full history of this investigation, with the results 

 already stated and a number of developments and results 

 of minor importance, together with innumerable digressions 

 and quaint comments on the progress of the inquiry, was 

 published in 1609 in a book of considerable length, the 

 Commentaries on the Motions of Mars* 



142. Although the two laws of planetary motion just 

 given were only fully established for the case of Mars, 



* Astronomia Nova 00-10X07777-0? seu Physica Coelestis, tradita Com- 

 mentariis de Motibus Stellae Martis. Ex Observationibus G. V. 

 Tychonis Brahc. 



