546 COSMOS. 



by the acquisition of new organs, arrived at a more exact 

 knowledge of the movements of the planetary system. Many 

 centuries however elapsed before any advance was made 

 towards a knowledge of the absolute size, form, mass, and 

 physical character of the heavenly bodies. 



Many of the astronomers of the Alexandrian Museum were 

 not only distinguished as geometricians, but the age of the 

 Ptolemies was, moreover, a most brilliant epoch in the prose- 

 cution of mathematical investigations. In the same century 

 there appeared Euclid, the creator of mathematics as a science, 

 Apollonius of Perga, and Archimedes who visited Egypt and 

 was connected through Conon with the school of Alexandria. 

 The long period of time which leads from the so-called geo- 

 metrical analysis of Plato, and the three conic sections of 

 Mensechmes,** to the age of Kepler and Tycho Brahe, Euler 

 and Clairaut, d' Alembert and Laplace, is marked by a series of 

 mathematical discoveries, without which the laws of the motion 

 of the heavenly bodies and their mutual relations in the 

 regions of space would not have been revealed to mankind. 

 While the telescope serves as a means of penetrating space, 

 and of bringing its remotest regions nearer to us, mathe- 

 matics, by inductive reasoning, have led us onwards to the 

 remotest regions of heaven, and brought a portion of them 

 within the range of our possession ; nay, in our own times 

 so propitious to extension of knowledge the application of all 

 the elements yielded by the present condition of astronomy 

 has even revealed to the intellectual eye a heavenly body, and 

 assigned to it its place, orbit, and mass, before a single tele- 

 scope had been directed towards it.f 



* Idelcr, on Eudoxus, s. 23. 



t The Planet discovered by Le Verrier, 



