Page:The Life of the Spider.djvu/392

 searching for the tomb of Archimedes amid the thorns and brambles that cover us with oblivion, recognized 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. Disdaining 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 spiral. Roll the curve along an indefinite straight line. Its pole will become displaced while still keeping on one straight line. The endless scroll leads to rectilinear progression; the perpetually varied begets uniformity.

Now is this logarithmic spiral, with its curious properties, merely a conception of the