The book under review is a German translation of *The Archimedes Codex: Revealing the Secrets of the World’s Greatest Palimpsest* (Weidenfeld and Nicolson / Orion Publishing Group, London, 2007).

In 1910-1913 Johan Ludvig Heiberg published two volumes of his revised edition of the *Archimedes opera omnia cum commentaria Eutocii*, which for many years become the standard reference for works of the greatest ancient mathematician. For this edition he utilized a newly discovered palimpsest dated to the tenth century, then kept in the famous Metochion library of the Church of the Holy Sepulcher in Constantinople, and mostly containing the works of Archimedes. He studied the original for a short period only but later managed to transcribe the text on the basis of photographs and published the results in 1907-1909.^{1} Though he recovered quite a lot of extremely difficult text, the works of Archimedes which thus came to light were still very lacunose. Besides, Heiberg was not able to read some of the text because of the later binding of the book.

Then the manuscript was lost — apparently stolen from the library during or after the First World War — until it had recently appeared again and, despite protests from the Greek government, sold by American auctioneers to an anonymous “collector” (“Mister B.”) in 1998 for more than $2 million, and deposited by its new owner at the Walters Art Museum (Baltimore, USA) for conservation, imaging and scholarly study in 1999. Discussion of this event (as such a typical example of shameless speculation on the cultural heritage), and the scholarly work which has been going ever since, are conveniently available at the web site of the Archimedes Palimpsest project.

I will just briefly recollect the circumstances and outline the book content.

The oldest surviving manuscript of Archimedes suffered at least twice, first being covered with prayers and all these things which replaced science and culture in the dark ages of European civilization and then mutilated by contemporary barbarians, its new owners, who covered some of its pages with forged pictures, taken from a printed book, apparently to make the book more valuable and kept it in such bad condition that the manuscript was on the edge of complete destruction when it finally was given to the specialists.

The international team of researchers in their attempts to recover the content of the invaluable manuscript had to overcome numerous obstacles and had to apply a variety of advanced research techniques. Recent study and recovery of the text revealed that the manuscript in question, a prayer book (the Euchologion), completed in April 1229, apparently in Constantinople and now containing 174 parchment folios, was made of at least seven treatises by Archimedes (the Equilibrium of Planes, Spiral Lines, The Measurement of the Circle, Sphere and Cylinder, On Floating Bodies, The Method of Mechanical Theorems, and the Stomachion). For three (“On Floating Bodies”, “The Method of Mechanical Theorems”, and the “Stomachion”) the palimpsest is the unique source.^{2} Another five leaves, palimpsested for the Euchologion, were taken from a work by the fourth century B.C. Attic Orator Hyperides, previously known only from papyrus fragments and from quotations of his work by other authors.^{3} Six folios came from a philosophical treatise,^{4} four folios belonged to a liturgical book, and twelve further pages came from two different books, the text of which has yet to be deciphered.^{5}

The book under review outlines both the story of the Archimedes palimpsest studies and the works by Archimedes in a very simple interpretation, accessible to general reader with no special education. It contains, for instance, interesting though elementary information on the technique of book production in antiquity and the Middle Ages and could be of interest to undergraduates approaching the history of ancient civilization for the first time, and some readers would probably enjoy an introductory story, illustrated by personal observations and specimens of e-mail correspondence, told by Noel in the first chapter of the book, entitled “Archimedes in America” (pp. 9-29).

This story is followed by an introductory chapter by Netz (30-67), outlining the life and works of Archimedes in the light of new studies. Netz believes that the most interesting features of Archimedes’ thought, still of interest today, are his approach to infinity and his developing mathematical models on the basis of physical world. Netz gives simple examples of Archimedes methods and techniques (squaring of the circle, indirect proofs, quadrature of a parabola, potential infinity, etc.), and continues the subject in consequent chapters: the fourth chapter (pp. 91-120) turns to Archimedes diagrams; Chapters six (141-159) and eight (184-203) deal with “The Method of Mechanical Theorems”, while Chapter ten (230-256) is concerned with the “Stomachion”. This matter is sufficiently well known both to specialists and general reader, and the highly original although often speculative and over-generalizing position taken by Netz, is amply presented in his recent publications and the first volume of his translation of the works of Archimedes.^{6}

The third chapter (pp. 69-90) concisely outlines an imaginary story of the transmission of Archimedes’ works from Syracuse and Alexandria to Constantinople and the translation of them first from a roll to a codex and then from majuscule to minuscule script. The subject is continued in Chapter 5 (pp. 121-140) where attempt is made to sketch a (more sizable but still quite shady) modern history of Archimedes’ works, starting with the Constantinopolitan tragedy of 1204 and a Latin translation of Archimedes by Wilhelm of Moerbeke (1269) and finishing with a detailed description of how it was discovered and published by Heiberg, lost and then recently “rediscovered” and came under the hammer. In the seventh chapter (pp.161-182) we find a detailed description of the physical condition of the manuscript as well as difficulties which the scholars (especially Abigail Quandt of the Walters Art Museum) faced in the process of its conservation and restoration.

The ninth chapter (206-229), about imaging of the manuscript, I find the most fascinating. After the process of restoration was complete in 2000, several groups of scholars tried to apply various imaging techniques intended to bringing out the under text of the palimpsest. The method of multispectral imaging consisted of creating a large number of pictures of a given area taken at different wavelengths of light which allowed the scholars, applying certain algorithm, first, to highlight the Archimedes ink and make it more discernable and, second, to make the prayer book ink look like the parchment. Another and more successful method was applied by Roger Easton, Keith Knox, and William Christens-Barry, who devised a special apparatus for imaging the Palimpsest in a more effective way. They realized that the solution was not to make the prayer book text disappear as people thought before.but to clearly differentiate this text from the Archimedes text which lies underneath it. The imagers combined two different wavelengths of light: the Red channel of the visible spectrum (RGB light), which makes the Archimedes text disappear almost completely; and the blue channel from Ultra-violet florescent light (i. e. the light invisible as such but which emits in the blue part of the visible spectrum when directed against parchment). Combining an image taken in the Red channel of RGB light with an image of the blue channel of Ultra-violet fluorescent light, the imagers succeeded in separating texts which now appeared in three different colors: the parchment become white, because it reflects both of these lights, the prayer book appears black, because it absorbs both red light and blue light, and the under text comes out red, because it absorbs the blue light but reflects the red light. The results are illustrated here, and the process is described in all necessary technical details on the website.

This method did not help in case of the text that was hidden on the four pages containing the forged 20th-century paintings. The results, as described in the last chapter of the book (pp. 257-274, esp. 260ff), were achieved by Uwe Bergmann of the Stanford Linear Accelerator Center in California by means of a considerably more advanced technique, the so-called X-ray fluorescence method. Cf. this page — a most extraordinary achievement.

On the basis of some editorial descriptions found in the Internet I gather that the original English edition of the book contains 16 pages of color photos, which are entirely omitted in the present German translation. The publisher must have had its practical reasons for this, but in this case the omission is truly unfortunate, since only color pictures can properly illustrate the technique of its imaging.

To sum up, in the book under review a Stanford historian of ancient science R. Netz, and the director of the Archimedes Palimpsest Project W. Noel make the story of discovery, conservation and imaging of the manuscript, as well as some preliminary scholarly results, accessible for the general reader interested in the history of science and new technologies of recovering ancient texts. The book can be recommended to the libraries and individuals and constitutes a welcome addition to our understanding of the ancient science.

**Notes**

1. Cf. Heiberg J. L. “Eine neue Schrift des Archimedes”, *Hermes* XLII (1907) 235-297, the edition referred, and some other works.

2. Aside from some parts of four works by Archimedes, known from other sources, the palimpsest contains substantial passages of the Method; the treatise On floating bodies, previously known only in Latin translation, and a fragment of the Stomachion, partially preserved in Arabic.

3. Cf. pp. 225-227 of the book under review; N. Tchernetska, “New Fragments of Hyperides from the Archimedes Palimpsest”, *Zeitschrift für Papyrologie und Epigraphik*, vol. 154, 2005, pp.1-6; and an outline by J. Hermann.

4. R. W. Sharples suggests that this could even be a fragment of a lost commentary to the Categories by Alexander of Aphrodisias.

5. The manuscripts of Archimedes, we know today, are reasonably traced back by the scholars to the circle of Leo the Mathematician (died after 869) who taught at the Magnaura school and who is said to collect a great library of mathematical works, while the Prayer book is dated to April 14, 1229 on the basis of a colophon on the bottom of folio 1 verso of the manuscript (cf. p. 183 and 273ff).

6. Some anachronistic and propagandist statements by Netz mar the overall very favorable picture (passim, esp. 282ff). He believes for instance that Archimedes anticipated both the integral and differential analysis, knew and used in his mathematics actual infinity, etc. Cf. a detailed review of Netz’ methods and approaches: Acerbi F., “Archimedes and the Angel: Phantom Paths from Problems to Equations”, *Aestimatio* 2 (2005) 169-226, and his recent works: 1. Reviel Netz, *The Works of Archimedes: Translated into English, together with Eutocius’ Commentaries, with Commentary, and Critical Edition of the Diagrams.* Vol. 1: The Two Books On the Sphere and the Cylinder. Cambridge: Cambridge University Press, 2004 (reviewed by Eleanor Dickey at BMCR 2004.07.14 and at by N. Sidoli *Aestimatio* 1 (2004) 148-162)

2. Reviel Netz, *The Shaping of Deduction in Greek Mathematics*. “Ideas in Context”, 51. Cambridge: Cambridge University Press, 1999 (reviewed by Daryn Lehoux, BMCR 2000.02.17)

3. Reviel Netz, *The Transformation of Mathematics in the Early Mediterranean World: From Problems to Equations*. Cambridge: Cambridge University Press, 2004 (reviewed BMCR 2004.10.25)