Book:Archimedes/The Method

Also known as The Method.

Subject Matter

 * Solid Geometry

Contents

 * From this theorem, to the effect that a sphere is four times as great as the cone with a great circle of the sphere as base and height equal to the radius of the sphere, I conceived the notion that the surface of any sphere is four times as great as a great circle in it; for, judging from the fact that any circle is equal to a triangle with base equal to the circumference and height equal to the radius of the circle, I apprehended that, in like manner, a sphere is equal to a cone with base equal to the surface of the sphere and height equal to the radius.

Historical Note
This work was found on a palimpsest in Constantinople in 1906, having been lost for nearly 1000 years.

It had originally been written by in the form of a letter to.

Translations and Editions

 * 1912: :

Comment

 *  The Method, so happily recovered, is of the greatest interest for the following reason. Nothing is more characteristic of the classical works of the great geometers of Greece, or more tantalizing, than the absence of any indication of the steps by which they worked their way to the discovery of their great theorems. As they have come down to us, these theorems are finished masterpieces which leave no trace of any rough-hewn stage, no hint of the method by which they were evolved. We cannot but suppose that the Greeks had analysis; yet, in general, they seem to have taken pains to clear away all traces of the machinery used and all the litter, so to speak, resulting from tentative efforts, before they permitted themselves to publish, in sequence carefully thought out, and with definitive and rigorously scientific proofs, the results obtained. A partial exception is now furnished by the Method; for here we have a sort of lifting of the veil, a glimpse of the interior of ' workshop.