ALEXANDRIAN SCIENCE. 



various mathematical labours of Archimedes would require more space 

 than we can here afford. His genius has justly been regarded as one 

 of the greatest the annals of science can exhibit. 



Archimedes perished in the fall of his city to the Romans, B.C. 212. 

 Marcellus, the Roman general, raised over his grave a monument 

 bearing a cylinder and a sphere. Nearly a century and a half after- 

 wards Cicero, who greatly admired the genius of Archimedes, had to 

 make a minute search in order to discover the burial-place of the 

 philosopher, which he found neglected and overgrown with vegetation. 

 Thus, he remarks to the Syracusans, the memorial of their greatest 

 citizen would have remained unknown had it not been shown to them 

 by a man from Arpinum. 



Scarcely had the career of Archimedes prematurely closed at Syra- 

 cuse before the school of Alexandria witnessed the commencment of 

 that of another famous geometer, APOLLONIUS OF PERGA (c. B.C. 200). 

 His works were regarded by the ancients as the full sources of all 

 geometrical science, and among these works his treatise on the conic 

 sections has most contributed to his celebrity. He appears to have 

 been the first who perceived that the circle, ellipse, parabola, and 

 hyperbola could be formed by different sections of the same cone. 

 The sections of the cone are now so familiar to us that the merit of 

 this discovery is liable to be underrated. Apollonius investigated a 

 multitude of the properties of these curves. Every section of a cone 



FIG. 14. 



made by a plane passing through the vertex is bounded by two straight 

 lines passing through that point. If the cone be cut by another plane 

 parallel to one of those just mentioned, the section will be the curve 

 called the hyperbola. If the cone be cut by a plane parallel to any 

 one which passes through its vertex without intersecting the cone, the 

 section is an ellipse or a circle, according as the plane is inclined, or 

 is perpendicular to the axis of the cone. See Fig. 14. The Conic 

 Sections of Apollonius consisted of eight books, of which only seven 

 remain, and three of these are known only through an Arabic version* 



