The top layer of writing in this 700-year-old book describes Christian prayers. But underneath, almost obliterated, are the only surviving copies of many of the works of the ancient Greek mathematician Archimedes.

The picture on the left is an ordinary photograph, with the Archimedes text barely visible. The picture on the right is a multi-spectral image, and the Archimedes text and diagrams are mostly legible.

Sometime after Johan Heiberg examined the book in 1906, someone painted gold-leaf images over four of the pages (left). Multispectral imaging couldn't peer beneath the reflective metal paint, but x-ray fluorescence imaging revealed the underlying text (right).

Archimedes computed the area of the curved figure (left) by enclosing it in a bigger one with straight edges (right). He then examined random slices to compute the volume—using the concept of actual infinity.