138 DISSERTATION SECOND. [fart i. 



cut the area of a semi-ellipsis in a given ratio by a line 

 drawn through the focus, is the geometrical problem into 

 which he showed that the above inquiry ultimately re- 

 solved. . As if he had been answerable for the proceedings 

 of nature, the difficulty of this question was considered as 

 an argument against his theory, and he himself seems 

 somewhat to have felt it as an objection, especially when 

 he found that the best solution he could obtain was no 

 more than an approximation. With all his power of in- 

 vention, Kepler was a mathematician inferiour to many of 

 that period ; and though he displayed great ability in the 

 management of this difficult investigation, his solution fell 

 very far short of the simplicity which it was afterwards 

 found capable of attaining. 



In addition to all this, he rendered another very impor- 

 tant service to the science of astronomy and to the system 

 of Copernicus. Copernicus, it has been already mention- 

 ed, had supposed that a force was necessary to enable 

 the earth to preserve the parallelism of its axis during its 

 revolution round the sun. He imagined, therefore, that a 

 third motion belonged to the earth, and that, besides turn- 

 ing on its axis and revolving round the sun, it had another 

 movement by which its axis was preserved always equally 

 inclined to the ecliptick. Kepler was the first to observe 

 that this third motion was quite superfluous, and that the 

 parallelism of the earth's axis, in order to be preserved, 

 required nothing but the absence of all force, as it neces- 

 sarily proceeded from the inertia of matter, and its tenden- 

 cy to persevere in a state of uniform motion. Kepler had 

 a clear idea of the inertia of body ; he was the first who 

 employed the term ; and, considering all motion as natu- 

 rally rectilineal, he concluded that when a body moves in 

 a curve, it is drawn or forced out of the straight line by 

 the action of some cause, not residing in itself. Thus he 



