The Archimedes Codex by Reviel Netz

Author:Reviel Netz
Language: eng
Format: epub
Publisher: Da Capo Press

This was a moment of magic. Consider that each treatise by Archimedes contains at least one such moment of magic and you can begin to see the measure of the man. In the Method, each proposition is just as magical. No wonder Heiberg was so excited in 1906.

Note the complex route leading to this magic.We had the thought experiment—considering geometrical objects as physical ones. And then, something even further. We had a result for pairs of slices—pairs of random lines taken of the triangle and the parabolic segment. We then moved to the triangle itself and the parabolic segment itself, each taken as a whole.

In other words, we took a proportion involving four lines and turned it into a proportion involving infinitely many lines—all the infinitely many parallel lines constituting the triangle or the parabola.

Are we allowed to do that? This question, from then on—from Archimedes’ time to our own—became the central question of mathematics. The Method, by bringing together mathematics, physics, and infinity, raised the most fundamental questions of science. It anticipated Newton’s calculus, but it also anticipated the conceptual difficulties of that calculus.

How much did Archimedes know about infinity? In June 1999, we did not know. The question on everyone’s lips: what are we going to find, further, in the Method—if anything? We needed to look inside the Palimpsest and be able finally to read it. But in June 1999, Abigail had not yet unwrapped the book. The brain was still caged inside its box, as I waited, impatiently, for it to be freed.

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