The Book of Archimedes 2 · 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.
2.1It is said that the sand cannot be numbered.
2.2Those who say it do not mean that there is a great deal of sand. They mean that the number of the grains is no number at all.
2.3I mean to show that this is not so.
2.4I shall not count sand. What I shall show is that even the largest heap of it falls inside what can be numbered.
2.5First there must be numbers large enough. The ones we have will not do, so I shall build a new set.
2.6I begin at ten thousand; ten thousand times ten thousand makes one new unit, and so I pile them up, tier upon tier.
2.7Having built them, I take them to fill something very large: the whole sphere of the heavens, packed with sand.
2.8To know how large that sphere is, I must know how far off the sun and moon and stars are.
2.9So I set down what the several schools of the day say, and take the largest.
2.10The largest is that of Aristarchus of Samos. He says the sun stands still, the earth moves, and the earth goes round the sun.
2.11I do not accept what he says. But his figure is the largest, and for this reckoning I must use the largest.
2.12And I find that the sand filling such a sphere does not exceed a certain one of the numbers I have built.
2.13It can be numbered. That is all.
2.14I say this not for the sake of sand but for the sake of the words cannot be numbered. When a man says a thing cannot be numbered, it is usually only that the numbers in his hand are not long enough.