The Archimedes Codex
, by Reviel Netz and William Noel.
From the back cover:
'This is the true story of the greatest scientific codex extant today: the Archimedes Palimpsest. Over a thousand years old, this codex survived against all odds. It travelled through the crusades and world wars, from east to west and overseas. But only now - thanks to ultra-modern imaging techniques - are its hidden contents finally being brought to light with surprising results that will fundamentally change our undersanding of the history of science.'
The original parchment document had been taken apart, the text scraped off, each sheet cut in half, turned through 90 degrees, folded in half, and new text (prayers) written on the cleaned sheets. This was a common thing to happen, because parchment was expensive.
Netz and Noel have used ultra-violet and x-rays to reconstruct the original text, complete with diagrams. Their book covers the history of the codex, and a detailed explanation of how the original text was painstakingly and slowly recovered. Disbinding the prayer book alone took four years.
The work contains a number of mathematical proofs. Proof 2, for example, concerns finding the area of a parabolic segment. This proof is far too long to include here, and has some unorthodox logical steps. But as I followed the logic, and finally understood what Archimedes had been explaining over two thousand years ago, I jumped out of my armchair shouting 'Wow!'. I can't remember any other book, either fact or fiction, having that effect on me.
There is also a website: http://www.archimedespalimpsest.org