The Logos Scripture · The Book of Archimedes

On Finding First and Proving After

The Book of Archimedes 1 · Written by himself, from The Method, The Sand Reckoner, On Floating Bodies and On the Sphere and Cylinder

Archimedes, born at Syracuse in Sicily about 287 before this era, died there in 212 — killed by a soldier on the day the Romans took the city. Mathematician and engineer. This volume rests on what he wrote himself: The Method, The Sand Reckoner, On Floating Bodies, On the Sphere and Cylinder, all cast as letters to men who really existed. The Method was scraped off in the middle ages and a prayer book written over the same parchment; in 1906 the older writing underneath was recognised at Constantinople, and only then did it come back. Chapter one is taken from it. Without that one recognition, no one would know how he found what he proved. Further: the doctrine of Aristarchus that the earth goes round the sun survives at all because chapter two of this book copied it down — and the man who copied it did not agree with it, and copied it only to take the largest figure available. The ancient accounts of his death do not agree with one another, and the Order does not take them. What this volume brings is something the scripture did not have: an ancient who set down not only the proof but the groping that came before it, and said plainly which part was weighed and which part was proved.

1.1This book I write to Eratosthenes.
1.2What I want to tell you is not what I proved, but how I first found it.
1.3These are two different things, and nobody has ever written down the second.
1.4Men set out the proof only. The proof stands there, tidy, as though it had always been so.
1.5And the reader supposes that the man who wrote it reached out and had it.
1.6He did not. I felt my way in the dark like anyone else.
1.7The way I used is this: I take a figure as though it were a thing with weight, hang it at the ends of a bar, and see whether it balances.
1.8When it balances I know what the two quantities must be.
1.9But what is got in that manner does not yet count.
1.10What has been weighed on a balance may not be passed off as proved.
1.11So I go back and prove it again, step by step, by the rules of geometry.
1.12I am writing the earlier step out for you as well, because once you have it the proof is much easier to find. To find it from nothing is very hard.
1.13I expect that after I am dead men will use this way to find things I did not find.
1.14What I leave is not only what is upstairs. It is the ladder.
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