The Logos Scripture · The Book of Archimedes

On Floating

The Book of Archimedes 3 · 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.

3.1Put a thing into water and the water pushes up against it.
3.2With how much force? I want that said exactly.
3.3The thing put in has pushed some water out of the way.
3.4The force with which the water lifts it is equal to the weight of the water pushed out of the way.
3.5Not more and not less. Exactly that much.
3.6Therefore, if the thing is lighter than the same bulk of water it will float, and will settle until the part pressed under displaces water weighing as much as the whole of it.
3.7If it is heavier than the same bulk of water it will sink, and once under, the weight it seems to lose equals the weight of the water it displaced.
3.8These sentences I did not observe. I derived them, out of the nature of water itself.
3.9Let me say why this matters.
3.10Hold a thing in your hand and you do not know its weight. You know only that it presses on your hand.
3.11Put it in water, and the water answers a question for you that you could not answer yourself.
3.12A thing that cannot be measured may be measured by way of another thing that can.
3.13That way of proceeding is worth a great deal more than this one result.
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