KEPLER: HIS LIFE AND WORKS. 



By M. Bertr.Os'D, Mcmhcr of the French Academy of Sciences* 



ITranslated for the Smiihsonian Insiitution hij C. A. Alexander.'] 



The liigLest laws of the jihysical workl have been established by 

 geometers ; the hyj)otheses on which those laws rest acquire real import- 

 ance only after having been submitted to their decision ; and yet the 

 progress of natural i)hilosophy would have been impossible if the great 

 men to whom they are due, imbued only with a geometrical spirit, had 

 regarded only its inflexible rigor. 



Let us imagine a geometer initiated in the most elevated theories of 

 abstract science. I speak not merely of a disciple of Euclid and Archi- 

 medes, but an intelligent reader of Jacobi and of Abel ; and let us supi)ose 

 that, while a stranger to every idea of astronomy, he should undertake 

 to peuetrate by his own independent efforts the general structui-e of the 

 universe and the arrangement of its parts. Let us place him, moreover, 

 in the most favorable conditions ; let us admit that, free in spirit as Co- 

 pernicus, he reposes not in the deceptive represeutatious of the senses 

 which, veiling from us the movements of the earth, have caused its 

 immobility to be so long regarded as an axiom : what impossibilities 

 will present themselves to his imagination ! Borne along by an un- 

 known movement, perceiving no fixed direction, no stable basis on 

 which to rely for the determination of distances, he finds himself with- 

 out data for the solution of the problem. Our geometer will attain, 

 perhaps, to a conception of our own incommensurable littleness ; but, 

 l^erceiviug no certain route, he will stop short by assertiug in the name 

 of a science which he believes infallible, because it leaves notliing to 

 hazard, that, whatever the genius of man and the resoui^ces with which 

 art may endow his organs, our path through space is to him as undis- 

 coverable as would be that of a grain of dust borne on the wind to the 

 animalcules which inhabit it. 



Happily Pascal has gone too far in asserting that what transcends 

 geometry lies beyond our reach. Tliis discouraging ai)preciation takes 

 no account of a sentiment Implanted in the depths of the hunmn soul ; 

 a sentiment which sustained Copernicus after having inspired Pytha- 

 goras. Outside of all demonstration, in effect man believes in the har- 

 mony of the universe and the simplicity of its mechanism ; and, although 

 imagination stands in strong contrast to geometry, the history of as- 

 tronomy presents them to us united in a strict alliance ; the former sus- 

 tained by well-regulated reason, in some sort outstripping truth in order 

 to reveal, as if by intuition, the beauty and general order of the system 

 of worlds; the latter exerting its powers to test the true and the false, 

 and by separating one from the other, finally to arrive at certainty. 



The situation of the astronomer who seeks to divine the symmetrical 

 and regular order of the celestial bodies, ])resents a certain degree of an- 

 alogy vrith that of the philologist who, with unkiu:)wn characters before 



"Mc'ruoires dc VAcadeinie de Sciences de Vlnstitut Imperial de France, t. xxxv, l^^'oG. 



