710 COSMOS. 



cieed a happy influence on Fermat, and, through him, on the 

 invention of the theory of the infinitesimal calculus.* A man 

 endowed with such a mind was pre-eminently qualified by the 

 richness and mobility of his ideas,f and by the bold cosmical 

 conjectures which he advanced, to animate and augment the 

 movement which led the seventeenth century uninterruptedly 

 forward to the exalted object presented in an extended con- 

 templation of the universe. 



The many comets visible to the naked eye, from 1577 to 

 the nppearance of Halley's comet in 1607 (eight in number), 

 and the sudden apparition already alluded to of three stars 

 almost at the same period, gave rise to speculations on the 

 origin of these heavenly bodies from a cosmical vapour filling 

 the regions of space. Kepler, like Tycho Brahe, believed 

 that the new stars had been conglomerated from this vapour, 

 and that they were again dissolved in it.J Comets to which, 

 before the discovery of the elliptic orbit of the planets, he 

 ascribed a rectilinear and not a closed revolving course, were 

 regarded by him, in 1608, in his "new and singular discourse 

 on the hairy stars," as having originated from " celestial air." 

 He even added, in accordance with ancient fancies on spon- 

 taneous generation, that comets arise " as a herb springs from 



* Laplace says of Kepler's theory of the measurement of casks 

 (Stereometria doliorum,) 1615, "which, like the sand-reckoning of 

 Archimedes, develops elevated ideas on a subject of little importance;" 

 " Kepler pre"sente dans cet ouvrage des vues sur 1'infini qui ont influS sur 

 la revolution que la Geometric a eprouvee & la fin du 17 me siecle; et 

 Fermat, que Ton doit regarder comme le veritable inventeur du calcul 

 differentiel, a fonde sur elles sa belle mgthode de maximis et minimis. 

 (Precis de I'hist. de I Astronomic, 1821, p. 95)." On the geometrical 

 power manifested by Kepler in the five books of his Harmonices 

 Mundi, see Chasles, Apercu hist, des Methodes en Geometrie, 1837, 

 pp. 482-487. 



t Sir David Brewster elegantly remarks, in the aocount of Kepler's 

 method of investigating truth, that " the influence of imagination as an 

 instrument of research has been much overlooked by those who have 

 ventured to give laws to philosophy. This faculty is of greatest value in 

 physical inquiries ; if we use it as a guide and confide in its indications 

 it will infallibly deceive us; but if we employ it as an auxiliary, it will 

 afford us the most invaluable aid" (Martyrs of Science, p. 215). 



Arago, in the Annuaire, 1842, p. 434 (De la transformation des 

 Nebultuses et de la matiere diffuse en etoiles). Compare Cosmos, pp. 134 

 wid 142. 



