INDUCTIVE EPOCH OF KEPLEK. 29 



o 



though some of the features are exaggerated, and some too feebly 

 marked. His spirit of invention was undoubtedly very fertile and 

 ready, and this and his perseverance served to remedy his deficiency in 

 mathematical artifice and method. But the peculiar physiognomy is 

 given to his intellectual aspect by his dwelling in a most prominent 

 manner on those erroneovs trains of thought which other persons con- 

 ceal from the world, and often themselves forget, because they find 

 means of stopping them at the outset. In the beginning of his book 

 (Argumenta Capituin) he says, " if Christopher Columbus, if Magel- 

 lan, if the Portuguese, when they narrate their wanderings, are not 

 only excused, but if we do not wish these passages omitted, and should 

 lose much pleasure if they were, let no one blame me for doing the 

 same." Kepler's talents were a kindly and fertile soil, which he culti- 

 vated with abundant toil and vigor ; : but with great scantiness of agri- 

 cultural skill and implements. Weeds and the grain throve and flour- 

 ished side by side almost undistinguished; and he gave a peculiar 

 appearance to his harvest, by gathering and preserving the one class of 

 plants with as much care and diligence as the other. 



Sect. l.-^Kepler's Discovery of his Third Law. 



I SHALL now'give some account of Kepler's speculations and discov- 

 eries. The first discovery which he attempted, the relation among the 

 successive distances of the planets from the sun, was a failure ; his doc- 

 trine being without any solid foundation, although propounded by him 

 with great triumph, in a work which he called Mysterium Cosmoyrapld- 

 cttm, and which was published in 1590. The account which he gives 

 of the train of his thoughts on this subject, namely, the various sup- 

 positions assumed, examined, and rejected, is curious and instructive, 

 for the reasons just stated ; but we shall not dwell upon these essays, 

 since they led only to an opinion now entirely abandoned. The doc- 

 trine which professed to give the true relation of the orbits of the dif- 

 ferent planets, was thus delivered : 3 " The orbit of the earth is a circle : 

 round the sphere to which this circle belongs, describe a dodecahedron ; 

 the sphere including this will give the orbit of Mars. Round Mars 

 describe a tetrahedron ; the circle including this will be the orbit of 

 Jupiter. Describe a cube round Jupiter's orbit ; the circle including 

 this will be the orbit of Saturn. Now inscribe in tna Earth's orbit an 

 f.osahedron ; the circle inscribed in it will be the orbit of Venus. In- 



L. U. K. Kepler, 0. 



