OF THE UNIVERSE. EPOCH OP THE PTOLEMIES. 177 



epoch of the cultivation of mathematical knowledge. There 

 flourished in the same century Euclid the creator of mathe- 

 matics as a science, Apollonius of Perga, and Archimedes, 

 who visited Egypt and was connected through Conon with 

 the Alexandrian school. The long path of time which 

 leads from what is called the geometric analysis of Plato, and 

 the three conic sections of Mensechmes, ( 275 ) to the age of 

 Kepler and Tycho, Euler and Clairaut, d'Alembert and 

 Laplace, is marked by a series of mathematical discoveries, 

 without which the laws of the motions of the heavenly 

 bodies, and their mutual relations in space, would never 

 have been disclosed to mankind. The telescope pierces 

 pace, and brings distant worlds near through our sense of 

 vision. Mathematical knowledge forms a no less powerful 

 instrument of another class : ever leading us onward through 

 the connection of ideas, it conducts us to those distant re- 

 gions of space, of part of which it has taken secure posses- 

 sion. In our own times so favoured in the extension of 

 knowledge, by the application of all the resources afforded 

 l>y modern astronomy, a heavenly body has even been 

 seen by the intellectual eye, and its place, its path, and its 

 mass pointed out, before a single telescope had been directed 

 towards it. W 



