362 The Life of the Spider 



tion proclaimed, * Eadem mutata resurgo : I 

 rise again like unto myself.' Geometry would 

 find it difficult to better this splendid flight of 

 fancy towards the great problem of the hereafter. 



There is another geometrical epitaph no less 

 famous. Cicero, when quaestor in Sicily, search- 

 ing for the tomb of Archimedes amid the thorns 

 and brambles that cover us with oblivion, recog- 

 nized it, among the ruins, by the geometrical 

 figure engraved upon the stone : the cylinder 

 circumscribing the sphere. Archimedes, in fact, 

 was the first to know the approximate relation 

 of circumference to diameter ; from it he 

 deduced the perimeter and surface of the circle, 

 as well as the surface and volume of the sphere. 

 He showed that the surface and volume of the 

 last-named equal two-thirds of the surface and 

 volume of the circumscribing cylinder. Dis- 

 daining all pompous inscription, the learned 

 Syracusan honoured himself with his theorem 

 as his sole epitaph. The geometrical figure 

 proclaimed the individual's name as plainly 

 as would any alphabetical characters. 



To have done with this part of our subject, 

 here is another property of the logarithmic 



