T his is a fascinating account of the nearly unbelievable ups and downs of the ‘‘Archimedes Palimpsest,’’ a Byzantine codex containing, under the text of a prayer book, a small library of unique ancient texts, including exceptionally important Archimedes treatises. The account is written in alternating chapters by William Noel, Curator of Manuscripts at the Walters Art Museum, Baltimore, and Reviel Netz, Professor of Classics and Philosophy at Stanford University. The story of the three known codices with works of Archimedes is told in the chapters written by Noel. The story begins with Archimedes, a prominent citizen of Syracuse, a Greek city in Sicily, sending letters with a number of his mathematical works for further distribution to colleagues in Alexandria, such as Conon, Dositheus and Eratosthenes. Archimedes was killed in 212 BC, when Syracuse fell to the invading Romans, but copies of his works, written on papyrus scrolls, continued to circulate. Early in the sixth century A.D., Eutocius wrote commentaries to some of Archimedes’s works: Sphere and Cylinder I-II, Measurement of the Circle and Balancing Planes. At about this time, the texts of some of Archimedes’s treatises that were still around were transferred from papyrus scrolls to a new and less fragile medium with greater capacity, codices made of stacks of folded parchment sheets stitched together. A new change of medium in the ninth century involved the transition from majuscule to minuscule, lowercase script. Manuscripts written in the older script were often destroyed. After centuries of neglect, a revival of interest in Archimedes’s texts in the Byzantine Renaissance in the ninth and tenth centuries may be one of the reasons for the survival of three codices with Archimedes treatises, now called Codices A, B and C. A and B both contain the treatises Balancing Planes and Quadrature of the Parabola, while B also contains On Floating Bodies, and A also contains Sphere and Cylinder, Measurement of the Circle, Spiral Lines, Conoids and Spheroids, and Sand-Reckoner. Today, both A and B are lost, but copies of A still survive, and so does a Latin translation of B, made in 1269 by William of Moerbeke, a Franciscan friar. After being lost for nearly a millennium (as is now known, after having spent several centuries being used as any other prayer book at the monastery of St. Sabas in the Judaean desert), Codex C sensationally resurfaced in 1899, when a few lines of a partially erased text visible under the text of a medieval prayer book were reproduced in a catalog of manuscripts in the library of the Metochion of the Holy Sepulcher in Constantinople. The Dane J. L. Heiberg, a prominent Greek scholar, recognized the lines as being taken from a work of Archimedes. Subsequently he went to Constantinople, where he could verify that the prayer book was a palimpsest, with the text of the prayer book written above