DESCRIPTIO GLOBI INTELLECTUALS. 281 



i^ Telluris in gyrum circumactis." He means by 

 this that he used observations of Mars made when in 

 the same point of his orbit, the earth being at the time 

 of the different observations in different points of hers. 

 The same idea of the connexion of the Copernican hy- 

 pothesis with Kepler's method, is expressed in one of 

 the complimentary stanzas prefixed to the book : 



Ccelos Keplerus ten-arum oppugnat alumnus: 

 De scalis noli quaerere: terra volat. 



Iii one of Kepler's letters to David Fabricius, noth- 

 ing ran be more decided than his rejection of the notion 

 that all motions of the heavenly bodies are in perfect 

 circles. " Quod ais non dubium quin omnes motus fiant 



I'irculum perfectum, si de compositis (id est de re- 

 alibu^ ) loquerifl, falsum : fiunt enim Copernico, ut dixi, 

 per orbitam ad latera circuli excedentem, Ptolemgeo et 

 Braheo insuper per spiras. Sin autem loqueris de com- 

 ponentibus, de fictis igitur hoc est de nullis loqueris. 

 Xihil enim in coelo circumit prater ipsum corpus pla- 

 .e, nullus orbis, nullus epicyclus : quod Braheanae 



i-onomije initiatus ignorare non potes." And it is 

 interesting to observe how clearly he distinguishes be- 

 tween the real motions and the component elements 

 into which they may be resolved. 



Until the language of modern analysis had enabled 

 us tu express the nature and properties of curves merely 

 quantitively, without reference to genesis or construc- 

 tion, it was difficult to attain to a clear way of thinking 

 as to the relation which astronomical hypotheses bear 

 to reality. In order to define the motion which actu- 

 ally takes place, it was necessary to refer to simpler 

 motions which have only an abstract or ideal existence. 

 But then it was asked, how can the result be real if the 



