# Book:Archimedes/The Method

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## Archimedes:

## Archimedes: *The Method of Mechanical Theorems*

Published $\text {c. 250 BCE}$.

Also known as *The Method*.

### Subject Matter

### Contents

Contains $15$ propositions illustrating Archimedes' technique for making his geometrical discoveries:

- Proposition $6$: Center of Gravity of Solid Hemisphere
- Proposition $15$: Volume in Common between Two Equal Cylinders with Perpendicular Intersecting Axes

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## Historical Note

This work was found by Johan Ludvig Heiberg on a palimpsest in Constantinople in $1906$, having been lost for nearly $1000$ years.

It had originally been written by Archimedes in the form of a letter from Archimedes to his friend Eratosthenes of Cyrene.

The manuscript it appeared on was sold in $1998$ to a private buyer for $2$ million dollars.

## Translations and Editions

## Critical View

*, 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 Archimedes' workshop.*

## Sources

- 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.3$: Democritus (ca. $\text {460}$ – $\text {370}$ B.C.) - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.5$: Archimedes (ca. $\text {287}$ – $\text {212}$ B.C.) - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {B}.6$: How Archimedes Discovered Integration - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $2$: The Logic of Shape: Archimedes