INDUCTIVE EPOCH OF KEPLER. 297 



tries and epicycles, as we have already said; and'the motions in lati- 

 tude by certain librations, or alternate elevations and depressions of 

 epicycles. If a mathematician had obtained a collection of true posi- 

 tions of a planet, the form of the orbit and the motion of the star 

 would have been determined with reference to the sun as well as to 

 the earth ; but this was not possible, for though the geocentric posi- 

 tion, or the direction in which the planet was seen, could be observed, 

 its distance from the earth was not known. Hence, when Kepler 

 attempted to determine the orbit of a planet, he combined the ob- 

 served geocentric places with successive modifications of the theory of 

 epicycles, till at last he was led, by one step after another, to change 

 the epicyclical into the elliptical theory. We may observe, moreover, 

 that at every step he endeavored to support his new suppositions by 

 what he called, in his fanciful phraseology, " sending into the field a 

 reserve of new physical reasonings on the rout and dispersion of the 

 veterans ;" that is, by connecting his astronomical hypotheses with 

 new imaginations, when the old ones became untenable. We find, 

 indeed, that this is the spirit in which the pursuit of knowledge is 

 generally carried on with success ; those men arrive at truth who 

 eagerly endeavor to connect remote points of their knowledge, not 

 those who stop cautiously at each point till something compels them 

 to go beyond it. 



Kepler joined Tycho Brahe at Prague in 1600, and found him and 

 Longomontanus busily employed in correcting the theory of Mars ; 

 and he also then entered upon that train of researches which he pub- 

 lished in 1609 in his extraordinary work On the Motions of Mars. 

 In this work, as in others, he gives an account, not only of his success, 

 but of his failures, explaining, at length, the various suppositions' 

 which he had made, the notions by which he had been led to invent 

 or to entertain them, the processes by which he had proved their 



6 I will insert this passage, as a specimen of Kepler's fanciful mode of narrating 

 the defeats which he received in the war which he carried on with Mars. "Duin 

 in hunc modum de Martis motibus triumpho, eique ut plane devicto tabularum 

 carceres et equationum compedes necto, diversis nuntiatur locis, futilem victorium 

 utbellum tota mole recrudescere. Nam domiquidem hostis ut captivus contemptus, 

 rupit omnia equationum vincula, carceresque tabularum eifregit. Foris specu- 

 jatores profligerunt meas cansarum physicarum arcessitas copias earumque ji-guin 

 sxcussernnt resumta libertate. Jamque parum abfuit quia hostis fugitivus sese 

 cum rebellibus suis conjungeret meque in desperationem adigeret: nisi raptkn, 

 nciva rationum physicarum subsidia, fusis et palantibus veteribus, submisissem, et 

 qua se captivus proripuisset, omni diligentia, edoctus vestigiis v-sius nulla mora 

 iuterposita inhsesisserem." 



