New Atheist discussions of the history of science are almost always based on some form of the Conflict Thesis. Despite the fact this conception of an eternal “warfare between science and religion” has long since been rejected by historians of science, anti-theists have an emotional commitment to this dusty nineteenth century idea, with most naively accepting it without question while a few struggle to prop it up in the face of the consensus of modern historians that it is simplistic, biased nonsense. And few New Atheist attempts at sustaining it proceed without invoking the Archimedes Palimpsest.
This is a thirteenth century manuscript of liturgical prayers from Orthodox rites called a Euchologion which, in 1899, Johan Heiberg realised was at least in part a palimpsest of Archimedes – i.e. the text of an earlier copy of works by Archimedes had been erased and the parchment recycled, with the Euchologion texts written over it. Most importantly, Heiberg then produced a transcription between 1910 and 1915 that showed the overwritten text included an otherwise unknown lost work by Archimedes, The Method of Mechanical Theorems. This caused great excitement in scholarly circles at the time, though it did not become better known to a wider audience until the high tech imaging study of the palimpsest by the Walters Art Museum in Baltimore from 1999-2008 got extensive media coverage. In 2003 the science program NOVA aired a TV documentary, “The Genius of Archimedes – The Palimpsest” telling the story of the manuscript and featuring detailed coverage of the Walters Art Museum investigations. Both the media coverage and documentary played up the “unique mathematical work destroyed to make a medieval prayer book” angle and so cue predictable New Atheist outrage.
“13th Century Monks were Dicks”
At the Beavis and Butt-Head end of New Atheism we have the Reddit subgroup /r/atheism, which periodically goes into paroxysms over the Archimedes Palimpsest each time another of its angry teenage apostates hears the story and expresses spluttering fury. So in posts there like this one we get comments like “ancient wisdom eradicated by a moron who believed in fairy tales” and “a good metaphor for the Middle Ages” or “[and] Christians claim that the church is what preserved ancient knowledge” or, best of all, “13th century monks were dicks like that”. These are fairly typical of the way the Palimpsest is usually invoked in New Atheist discussions – “Archimedes came up with calculus but the Church destroyed the only manuscript with this in it, so the Church retarded human progress”. This is often accompanied with paeans to where science and technology could have been today if the Church had not done this (colonies on Mars, cities in the sky etc.), more or less along the lines of the “Destruction of the Great Library of Alexandria” myth.
But, to be fair, occasionally these rants are interrupted by more level-headed atheists who point out the problems with this idea (as we see in that /r/atheism thread). The key one of these is that, while the Archimedes text certainly was erased by one thirteenth century cleric, the manuscript he was recycling was copied by a tenth century one. So it makes very little sense to howl condemnations of the terrible destruction of this ancient learning in the Middle Ages, when this palimpsest is actually good evidence of its preservation in that period.
To understand this we need to go beyond blurts on Reddit and TV snippets and look at the history of the transmission of Archimedes’ work down the centuries. Archimedes of Syracuse was justly famous in the ancient world as a great mathematician and geometer who also applied his mathematics to astronomy (typical in the period, as astronomy was considered a branch of mathematics) and to engineering (which was very atypical for an ancient philosopher). Despite this, however, his works were not widely read and therefore not widely copied. This is in part because he wrote in Doric Greek, the dialect of his native Syracuse, rather than the Attic form that was more common across the later Greek-speaking and Greek-literate world. It is also because his works were highly technical, and understandable to only a few specialists. In a period where books had to be copied by hand, the number of copies of any given work is determined by who can read the text and who wants to. As admired and famous as Archimedes was, both the dialect his works were written in and the technicality of their contents meant that his readership was always very small, and the numbers of copies of them were therefore going to be correspondingly tiny. With this in mind, it’s actually remarkable that they have survived at all.
We owe virtually all our knowledge of Archimedes to a burst of interest in him by a number of sixth century scholars in the Eastern Roman Empire. The first of these was Eutocius of Ascalon (c. 480-c.540) who copied and wrote commentaries on three of Archimedes’ works and one on the Conics of Apollonius. Eutocius travelled widely within the Eastern Empire and was in contact with a number of its most prominent scholars. It is not absolutely certain that he was a Christian, though the fact that he uses the Christian benediction “God-leading” (In Apollonium II, 356.3), dedicates his commentary on Plane Equilibria to “the most noble Peter” (a Christian name), and called the Christian scholar Anthemius of Tralles “my dearest friend” and “dear comrade” in another work indicates that he probably was. His friend Anthemius was an interesting scholar in his own right who, when he wasn’t annoying his neighbour with his thunder and lightning and earthquake-simulation machines, wrote a treatise on burning-glasses and lenses, and described the string construction of the ellipse. In 532 AD, along with his colleague Isidore of Miletus, he was chosen by the emperor Justinian to design and build Hagia Sophia – one of the greatest masterpieces of pre-modern architecture.
That this monumental church was designed by two scholars of Archimedes is no surprise: it is a testament to his mathematics. Isidore is also the scholar we can thank for the first compilation of Archimedes’ works, which seem to have until then circulated separately or been included in other texts, and it appears all later editions can be traced to his editing work. Thanks to this Christian scholar, we can next trace the transmission of Archimedes to the school of Leo the Mathematician (c. 790-c. 869), who (as his nickname would suggest) taught mathematics along with a range of other disciplines, including Aristotelian logic, astronomy, medicine and philology. He is also credited with making mechanical automata and a levitating throne for the emperor, which dazzled visiting barbarian emissaries to Constantinople long after his death. Leo’s school copied and used the editions of Archimedes compiled by Isidore of Miletus, and three manuscripts that emerged from this school – called by modern scholars the Codex A, Codex B and Codex C collections – were the source texts of all later copies and editions of Archimedes’ work. It was a copy of the Codex C collection, written a little over a century after Leo’s time, that became Archimedes Palimpsest.
All this shows that the sneering about thirteenth century monks being “dicks” because this copy of Codex C got recycled is completely absurd. Far from “destroying” or “suppressing” the work of Archimedes, we have a succession of Christian scholars and an even longer succession of Christian scribes to thank for its preservation. It’s thanks to Eutocius, Anthemius, Isidore and Leo and the scribes who came after them that we can read these technical works they lovingly studied, annotated and, most of all, painstakingly copied. To cast “Christians” as the villains in this story is totally ludicrous and gets things backwards – they are actually the heroes.
“The Chart” and Guess Who
Since the Palimpsest is supposed to be just part of a wider narrative about “Christians destroying ancient learning”, the fact that this is the opposite of what happened does not deter the proponents of this virulent myth. One of the most notorious of them is a person called Jim Walker who maintains the site NoBeliefs.com: a collection of news snippets, videos and articles for “freethinkers”. This means Walker’s section on “Religion & History” is a grab bag of anti-Muslim prejudice, well-worn counter-Creationist material and the usual New Atheist pseudo history, with selective quotes “proving” that the notoriously anti-Christian Adolf Hitler was actually a Christian, some Jesus Mythicism and an infamous piece entitled “The Myth of Christianity Founding Modern Science and Medicine (And the Hole Left by the Christian Dark Ages)“. Here the term “Dark Ages” is used in its outdated and erroneous sense of “the Middle Ages generally”, and the whole article is a melange of the usual pseudo-historical gibberish, with the standard myths about Hypatia and Giordano Bruno being martyrs for science, a garbled and cartoonish version of the Galileo affair and a litany of other caricatures and clichés, all supported by references to popular authors and non-specialists. The crowning achievement of this bizarre article, however, is its presentation of a graph that purports to show “the advancement of science through time”:
The idea that you could plot something as subjective as “scientific advancement” on a graph is silly enough, but all this graphic illustrates is its creators’ limited knowledge and bizarre prejudices. As a result it has been widely mocked ever since it appeared (prompting defensive responses from Walker which just make things worse). It has become the butt of hundreds of jokes over the years on the Reddit group /r/badhistory , where it has been dubbed “The Chart” and where the collection of outdated clichés it illustrates is nicknamed “Chartism”.
Walker’s article is so stuffed full of nonsense it would take a lengthy article to dissect its full stupidity, which is why science fiction writer and blogger Mike Flynn did just that back in 2009, in a piece titled “The Age of Unreason“. Of course, Walker had invoked the Archimedes Palimpsest and made some ridiculous statements about it and so Flynn responded in detail. Walker’s article reads:
“Recently scholars recovered an ancient text called The Archimedes Palimpsest, a codex written by Archimedes that revealed that the Greeks knew about infinity (both infinities and infinitesimals) long before the advent of Christianity. Ironically a monk had used the Archimedes papers to create a prayer book. A monk (or monks) scraped off the Archimedes text and wrote prayers in Greek in its place (the monks reused parchment in those days because of its durability and value). Although it may not have been the intent of the monks to destroy Archimedes’ text, the codex remained hidden for centuries until modern scientists found a way to retrieve the hidden text. Had the monks understood the Archimedes codex, they probably would have recognized its importance and protected it. The embarrassing question remains: why didn’t they? Imagine how different the world might look today if, instead of overwriting the codex, they had developed Archimedes’ math hundreds of years before Leibniz and Newton invented calculus in the late 1600s?” (“The Myth of Christianity Founding Modern Science and Medicine”)
Leaving aside the fact that 1909 is hardly “recently”, Walker seems totally unaware of both the Palimpsest’s own history or of the transmission of the texts of Archimedes detailed above. So his “embarrassing question” is simply a stupid question. Why didn’t they recognise its importance and protect it? That is precisely what they did.
Then there is Walker’s misconception that the invention of calculus would somehow immediately or automatically follow Archimedes’ use of the method of exhaustion as he details in the Palimpsest’s unique copy of his The Method of Mechanical Theorems. This is obviously wrong, given that it did not happen in the 600 years between the death of Archimedes and the rise of Christianity under Constantine or in the 1000 years between then and the erasure of this treatise. Flynn took particular issue with Walker’s references to calculus, though he was responding to the original version of Walker’s article, which was even more ridiculous in its section on the Palimpsest. Here is the original version:
“Recently, scholars found an ancient text written by Archimedes that revealed that the Greeks knew about the concept of infinity and calculus long before the advent of Christianity. Ironically a monk had used the Archimedes papers to create a prayer book. The monk washed out the Archimedes text and wrote supernatural nonsense in its place. The Archimedes text remained hidden for centuries until modern scientists found a way to retrieve the washed out text. Without religion hiding and destroying ancient scientific texts, imagine how different the world would look today if the Church had not suppressed, just calculus alone, hundreds of centuries before Isaac Newton published the idea in 1693.” (Walker, “Myth” May 27, 2007)
Obviously Walker has since been schooled on this stupid set of claims and has adjusted it considerably, as can be seen above. After educating Walker on the facts that the Greeks did not invent calculus, that the production of the Palimpsest was not some deliberate destruction and that the Church did not “suppress calculus”, Flynn went on to instruct Walker on palimpsests:
“[T]he use of palimpsests was routine. The scratch paper was routinely scraped off (not “washed”) using a razor. (A quo, Ockham’s razor; a quo “eraser.”) Paper was cheap (once its production was automated with waterwheels and camshafts) but perishable. So was papyrus in the East. Parchment was longer-lasting, but not so cheap that it wasn’t re-used on every occasion. Those same monks (a monastery in the Sinai) who overwrote the Archimedes palimpsest were the ones who had copied the Archimedes in the first place. It was not an original from the Hellenistic era. At the time that parchment was reused, as we know from references, the complete works of Archimedes were in circulation and so there was no big deal in re-using a scratch copy. Most of the monastic palimpsests we have are overwritings of Christian works. The oldest copy of the Bible we have was erased and overwritten with the sermons of Ephraem the Syrian. Hand-made manuscripts are necessarily rare; and time and chance happened to knock off this one particular work of Achimedes. Walker cannot claim that the Orthodox monks living under muslim rule were trying to “suppress calculus” when at the same time they and others were busily copying all the other works of Archimedes (and everyone else!) .” (Flynn, “The Age of Unreason”)
Flynn is absolutely correct, though while many palimpsests were produced by scraping off the old script, it seems this one had the original writing removed by the application of a mild acidic solution using a sponge. But he is right that the perfectly commonplace recycling of this manuscript cannot be painted as “suppressing” anything, since at the same time the works of Archimedes were being copied and preserved by Christian scribes, not erased and destroyed. But someone else read this and was having none of it – enter, yet again, the inevitable Dr Richard Carrier (PhD).
It would be nice, gentle reader, to write an article for this blog where I don’t have to deal with the ubiquitous Richard Carrier, but unfortunately there is barely a piece of New Atheist bad history too crackpot or too fringe for his tastes. This indefatigable apologist for ideologically warped pseudo-history pops up virtually any time someone dares to correct nonsense like Walker’s. Of course, unlike Walker, Carrier is not actually stupid, so he had to admit that Walker’s original article was riddled with flaws (thus, we can imagine, Walker’s later recensions), but nonetheless he launched into one of his typically prolix efforts, with the evocative title “Flynn’s Pile of Boners“.
Carrier’s counterblast to Flynn is itself packed with howlers, errors of fact and hilarious blunders, that prove beyond doubt that (i) he has no detailed knowledge of the Medieval Era and (ii) this seems to be because of his obvious, irrational and admitted dislike of the period. A response to everything in his piece would take a long article of its own, or a series of them – something I will probably tackle in the future. But for now it’s worth looking at how he tried to defend Walker’s bungled handling of the Archimedes Palimpsest. Carrier begins reasonably enough, saying contra Walker, “Flynn is quite right to say the Christians did not set out to deliberately destroy scientific works.” But then we get this:
“They just showed little to no interest in them, and thus let them rot and vanish, sometimes even scraping them off and writing over them with hymns to God, as happened to the Archimedes Codex. This was not because of any hatred at Archimedes or desire to suppress his work. It was just because of a complete disinterest in that work, and a greater preference for preserving hymns to God instead. Such represents the pervasive attitude of medieval Christianity, even in the East, where this terrible “deliberate” destruction of the work of Archimedes occurred.” (Carrier, “Boners“)
As the summary of the transmission of Archimedes and its debt to a succession of Christian scholars such as Eutocius, Anthemius, Isidore and Leo and many others shows, this is total garbage. The idea that they “showed little to no interest” in [scientific works] is not just contradicted by the example of the debt we owe to those scholars for the works of Archimedes, but by similar stories that could be outlined for every single ancient scientific, mathematical, logical, historical or philosophical work Carrier has ever read – or, indeed, any ancient works at all. All of the ancient works he has read exist purely because a succession of Christian and (in many cases) Muslim scholars and scribes actually did take an “interest” in them, and painstakingly copied them out letter by letter, word by word, so that modern readers could study them. Carrier’s claim that they “let” some of them rot and vanish is a bald assertion made without basis or evidence, and it is contradicted by literally hundreds of texts that they did not let “rot and vanish”. Those who claim they did, need to look at the catalogue of Harvard’s Loeb Classical Library and explain why these supposedly uninterested and careless Christian scribes spent so much time being both interested and careful. Carrier’s claim is one of his typical ideologically-driven egregious distortions of history and one so appalling and wrong that it makes his claim to be a “historian” something of a joke. Only a biased polemicist could say something so clearly, totally and hilariously wrong.
Palimpsests and Translations
Flynn also makes the correct statement that there was nothing unusual about recycling parchment to make a new book, and notes that this happened to both Christian and “pagan” texts alike – in fact it was far more common for this to happen to Christian texts, as there were more of them to recycle. Of the many palimpsests being examined by the ongoing Sinai Palimpsests Project, focused on the collection of St Catherine’s Monastery, one of the oldest libraries in the world, most of the texts that have been written over are Christian rather than pagan. There is no pattern to which manuscripts got recycled: they were clearly chosen because they were from books which had been damaged and some of the quires could be salvaged for recycling, books which were obsolete, books of which the owner or institution had multiple copies already or books for which they had no use. Making parchment was onerous, laborious and required specialist skills and was therefore the material was expensive to buy new. Recycling it was simply more time and cost effective.
Flynn claims “[t]hose same monks (a monastery in the Sinai) who overwrote the Archimedes palimpsest were the ones who had copied the Archimedes in the first place …. At the time that parchment was reused, as we know from references, the complete works of Archimedes were in circulation and so there was no big deal in re-using a scratch copy.” Carrier seizes on this , declaring it an “excuse”:
“There is actually no good evidence for this assertion. The evidence we have actually suggests the contrary. As discussed in [Reviel Netz and William Noel’s book] The Archimedes Codex, at the time this palimpsest was made (in the 13th century), his works were so rare there may have been only two other codices in the world with Archimedean works in them, neither of which contained all the works erased in this one (much less all the works of Archimedes).”
Perhaps Carrier was working from faulty memory, but this is a strange reading of what Netz and Noel’s book says. They certainly argue that there were not many copies of any of Archimedes’ works around in the thirteenth century, but they also make the point that this had always been the case, even in ancient times, for the reasons covered above (see Netz and Noel, The Archimedes Codex: How a Medieval Prayer Book Is Revealing the True Genius of Antiquity’s Greatest Scientist, 2007, p. 71). Carrier’s odd reference to “only two other codices in the world with with Archimedean works in them” seems to be either a misreading or a mis-remembering of Netz and Noel’s discussions of the three collections of works by Archimedes that were edited by the school of Leo the Mathematician – dubbed Codex A, Codex B and Codex C by modern scholars. These three collections continued to be copied, and the book that became the Palimpsest was a copy of the Codex C collection made 100 years or so after Leo’s time. Somehow Carrier has misread all this as Netz and Noel saying there were only three copies of these editions, which is totally wrong.
In fact, around the time that this copy of Codex C was being recycled into the Palimpsest, a number of very important new copies of Archimedes’ other works were being made, but this time in the West. Like many technical works in Greek, those of Archimedes had been completely lost in the chaos of the fall of the Western Roman Empire, and he was known to western scholars mainly through passing mentions and references which give his name as “Ersemides” or “Arsamithes”, indicating these probably came via Arabic. His work began to return to the west thanks to the remarkable translation programs of the Twelfth Century Revival, when Gerard of Cremona (1114–1187) included The Measurement of the Circle in the over 90 works he translated into Latin from Arabic (Gerard seems to be another medieval Christian who did not receive Carrier’s memo about how he was supposed to let ancient scientific works “rot and vanish”). He also translated the Verba filiorum, which was an Arabic reworking of Archimedes’ On the Sphere and the Cylinder. These and the hundreds of other Greek, Roman and Muslim works that the vigorous scholars of medieval Europe did not allow to “rot and vanish” stimulated a great appetite for still more such books, and for better editions of them. By the thirteenth century western scholars were finding their Latin translations via Arabic and (often) Syriac intermediaries inadequate, and there was a desire to find the original Greek texts to produce better translations.
This need was first filled by William of Moerbeke (1215/35? – c.1286), a remarkable Flemish Dominican who learned Greek and travelled to the Byzantine Empire, where he sought out and translated into Latin a whole range of important philosophical and technical works. Many of these were already widely known through inferior translations from Arabic, but others were brought back into western circulation for the first time since the Late Roman Era or even before. These included copies of the works collected in the Codex A and Codex B editions from the school of Leo, though not the Codex C works, obviously. This means that not only is Carrier completely wrong that there were “only two other [Archimedean] codices in the world” in the thirteenth century, but copies of the works of Archimedes were being passed from Byzantine scholars to their western counterparts and eagerly received in western Europe.
But Carrier stumbles on:
“Even if there were other manuscripts, there certainly were none in the monastery where this palimpsest was made, so the decision was not based on the monks’ belief that there were plenty of others. The monks just didn’t care about the texts they were erasing. And that’s why those texts were almost all lost (until we were able to recover them from this palimpsest using modern technology, a gift of mere luck). So both Flynn and Walker are wrong: the text wasn’t erased by an attempt to ‘suppress calculus’, but neither was it erased in the belief that the text wouldn’t be lost. It was erased quite simply because no one cared anymore.”
This, too, is nonsense. Flynn never actually posited that the eraser of the Codex C material that became the Archimedes Palimpsest somehow knew there were other copies of Archimedes’ work, he simply notes (correctly) that the erasure was done in the context of copies of Archimedes continuing to be made. But both Flynn and Carrier are wrong when they talk about this erasure being done by “monks” in some “monastery”. Flynn seems to be under the impression that the Palimpsest was produced in “a monastery in the Sinai” and Carrier follows him in this misconception with his fantasies about “the monastery where this palimpsest was made” and his magic telepathy about what the “monks” were thinking. In fact, all the evidence indicates that the Palimpsest was produced in Jerusalem, probably in a smaller church and most likely by an impoverished priest.
Netz and Noel’s popular book traces the history of the manuscript that became the Palimpsest from its production in Constantinople some time in the tenth century to the Patriarchate of Jerusalem, probably in the wake of the Fourth Crusade’s sack and occupation of the Imperial capital in 1204. Exactly how it came into the possession of a priest who recycled it as his liturgical prayer book is unknown, but several of the prayers and responses in this Euchologion were specific to the use of churches in Jerusalem. What is known is when the Euchologion was completed – the bottom of folio 1 verso of the manuscript carries a colophon giving the date as April 13, 1229.
It is interesting that this date was just a month after the Holy Roman Emperor Frederick II took control of the city from the Ayyubid sultanate and was crowned King of Jerusalem, ending the Sixth Crusade. Perhaps the disruptions of war in the preceding months had made parchment particularly expensive, or perhaps the priest who created the Euchologion was simply very poor. Either way, he took parchment from several books and re-purposed them for his liturgical manual. The six texts he recycled were a mixture, both pagan and Christian – a book of speeches by the Attic orator Hyperides, a tenth century philosophical commentary on Aristotle’s Categories, a hagiography, a Menaion (book of monthly offices said by a priest) and two unidentified texts. There is no indication here of any particular preference for non-Christian works, in fact his interest seems to have been mainly to get parchment of sufficient size and quality for his purpose. As Walters Art Museum conservator Abigail Quandt observes:
“There are several reasons why a manuscript would have been taken apart and the parchment written over to make a new book. The texts might be obscure or difficult to understand; they might be out of date or no longer relevant to their owners’ present needs; or the pages might be worn or the bindings dilapidated and not worth repairing. Almost the entire Archimedes Codex was incorporated into the palimpsest, so it is likely the book was disbound and the parchment erased for this specific purpose. The manuscript was a good candidate for several reasons: the text was irrelevant to its present owners; the parchment was in good condition since the book had been little used; there were no incised writing lines to interfere with the legibility of the prayers; and finally the dimensions of the written area of the original text were just the right size for the prayer book.” (Abigail Quandt, ” The Making of the Euchologion” in The Archimedes Palimpsest Volume 1: Catalogue and Commentary, Eds. Reviel Netz, William Noel, Nigel Wilson and Natalie Tchernetska, Cambridge, 2011, p. 81)
So basically the manuscripts this priest in Jerusalem chose to recycle were the right size, in good condition and easy to clean and cover with new text. That an abstruse technical work of mathematics was probably of as little use to this parish priest as a fragment of a book of ancient speeches or an old Menaion tells us precisely nothing about the general attitudes of thirteenth century Christian scholars to Archimedes, despite Carrier’s confident historical telepathy regarding his imaginary “monks”. The fact that William of Moerbeke was in the Greek east just 31 years later, seeking and translating complex Archimedean works directly from the Greek to feed the western medieval hunger for this material tells us far more. Of course Carrier says nothing of this, probably because that level of detail is well beyond his high-school level grasp of medieval history and his irrational prejudice against the Middle Ages for being too “Christian” for his tastes. Unlike a real historian, Carrier simply cannot get over his biases and it makes him sloppy, unreliable and wilfully ignorant of the relevant material.
The moral of this story is that historical analysis that draws on single examples taken out of all context is usually crap. None of the Reddit-level atheists who get steamed up about the Palimpsest and what they think it represents have enough grasp of the material and its background to understand the real history here. People like Walker possibly could grasp that background, but are too driven by irrational bias and fixed a priori assumptions to actually do so – even when corrected he clings to his distorted interpretation. But the person who comes out of this looking the worst is Carrier. Here is someone who, as he and his acolytes remind us constantly, has a doctorate in history from Columbia, yet his treatment of his topic is riddled with basic errors of fact and shows absolutely no grasp of the medieval historical context at all. And we are apparently meant to genuflect before him as a “historian”. To paraphrase Forrest Gump, “Historian is what historian does.” Yet again, Carrier’s irrational prejudices and wilful ignorance means that what he has produced on the Palimpsest is pseudo-history, at best.
Marshall Clagettt (ed.), Archimedes in the Middle Ages, (University of Wisconsin, 1964)
Marshall Clagett, “William of Moerbeke: Translator of Archimedes”, Proceedings of the American Philosophical Society, Vol. 126, No. 5 (Oct. 21, 1982), pp. 356-366
Pier Daniele Napolitani, “Between Myth and Mathematics: The Vicissitudes of Archimedes and his Work”, Lettera Matematica, October 2013, Volume 1, Issue 3, pp 105–112
Reviel Netz & William Noel, The Archimedes Codex : How a Medieval Prayer Book is Revealing the True Genius of Antiquity’s Greatest Scientist, (Capo Press, 2007)
Reviel Netz, William Noel, Nigel Wilson and Natalie Tchernetska (Ed.s) The Archimedes Palimpsest, 2 Vols, (Cambridge, 2011)