A palimpsest /ˈpælɪmpsɛst/ is a manuscript page from a scroll or book from which the text has been scraped or washed off and which can be used again.

The term has come to be used in similar context in a variety of disciplines, notably architectural archaeology and geomorphology.


The word “palimpsest” comes through Latin palimpsēstus from Ancient Greek παλίμψηστος (palímpsestos, “scratched or scraped again”) originally compounded from πάλιν (palin, “again”) and ψάω (psao, “I scrape”) literally meaning “scraped clean and used again”. Romans wrote on wax-coated tablets that could be smoothed and reused, and a passing use of the term “palimpsest” by Cicero seems to refer to this practice.


A Georgian palimpsest from the 5th or 6th century.

Because parchment prepared from animal hides is far more durable than paper or papyrus, most palimpsests known to modern scholars are parchment, which rose in popularity in Western Europe after the 6th century. Where papyrus was in common use, reuse of writing media was less common because papyrus was cheaper and more expendable than costly parchment. Some papyrus palimpsests do survive, and Romans referred to this custom of washing papyrus.[1]

The writing was washed from parchment or vellum using milk and oat bran. With the passing of time, the faint remains of the former writing would reappear enough so that scholars can discern the text (called the scriptio inferior, the “underwriting”) and decipher it. In the later Middle Ages the surface of the vellum was usually scraped away with powdered pumice, irretrievably losing the writing, hence the most valuable palimpsests are those that were overwritten in the early Middle Ages.

Medieval codices are constructed in “gathers” which are folded (compare “folio“, “leaf, page” ablative case of Latin folium), then stacked together like a newspaper and sewn together at the fold. Prepared parchment sheets retained their original central fold, so each was ordinarily cut in half, making a quarto volume of the original folio, with the overwritten text running perpendicular to the effaced text.

Modern decipherment

Faint legible remains were read by eye before 20th-century techniques helped make lost texts readable. Scholars of the 19th century used chemical means to read palimpsests that were sometimes very destructive, using tincture of gall or later, ammonium bisulfate. Modern methods of reading palimpsests using ultraviolet light and photography are less damaging.

Innovative digitized images aid scholars in deciphering unreadable palimpsests. Superexposed photographs exposed in various light spectra, a technique called “multispectral filming,” can increase the contrast of faded ink on parchment that is too indistinct to be read by eye in normal light. Multispectral imaging, undertaken by researchers at the Rochester Institute of Technology and Johns Hopkins University, recovered much of the undertext (estimated to be more than 80%) from the Archimedes Palimpsest.

At the Walters Art Museum where the palimpsest is now conserved, the project has focused on experimental techniques to retrieve the remaining text, some of which was obscured by overpainted icons. One of the most successful techniques for reading through the paint proved to be X-ray fluorescence imaging, through which the iron in the ink is revealed. A team of imaging scientists and scholars from the USA and Europe is currently using spectral imaging techniques developed for imaging the Archimedes Palimpsest to study more than one hundred palimpsests in the library of Saint Catherine’s Monastery in the Sinai Peninsula in Egypt.[2]

As a form of destruction

A number of ancient works have survived only as palimpsests.[3] Vellum manuscripts were over-written on purpose mostly due to the dearth or cost of the material. In the case of Greek manuscripts, the consumption of old codices for the sake of the material was so great that a synodal decree of the year 691 forbade the destruction of manuscripts of the Scriptures or the church fathers, except for imperfect or injured volumes. Such a decree put added pressure on retrieving the vellum on which secular manuscripts were written. The decline of the vellum trade with the introduction of paper exacerbated the scarcity, increasing pressure to reuse material.

Cultural considerations also motivated the creation of palimpsests. The demand for new texts might outstrip the availability of parchment in some centers, yet the existence of cleaned parchment that was never overwritten suggests that there was also a spiritual motivation, to sanctify pagan text by overlaying it with the word of God, somewhat as pagan sites were overlaid with Christian churches to hallow pagan ground. Or the pagan texts may have merely appeared irrelevant.

Texts most susceptible to being overwritten included obsolete legal and liturgical ones, sometimes of intense interest to the historian. Early Latin translations of Scripture were rendered obsolete by Jerome’s Vulgate. Texts might be in foreign languages or written in unfamiliar scripts that had become illegible over time. The codices themselves might be already damaged or incomplete. Heretical texts were dangerous to harbor – there were compelling political and religious reasons to destroy texts viewed as heresy, and to reuse the media was less wasteful than simply to burn the books.

Vast destruction of the broad quartos of the early centuries of our[who?] era took place in the period which followed the fall of the Roman Empire, but palimpsests were also created as new texts were required during the Carolingian renaissance. The most valuable Latin palimpsests are found in the codices which were remade from the early large folios in the 7th to the 9th centuries. It has been noticed that no entire work is generally found in any instance in the original text of a palimpsest, but that portions of many works have been taken to make up a single volume. An exception is the Archimedes palimpsest (see below). On the whole, Early Medieval scribes were thus not indiscriminate in supplying themselves with material from any old volumes that happened to be at hand.

Famous examples

  • The best-known palimpsest in the legal world was discovered in 1816 by Niebuhr and Savigny in the library of Verona cathedral. Underneath letters by St. Jerome and Gennadius was the almost complete text of the Institutes of Gaius, probably the first student’s textbook on Roman law.[4]
  • The Sana’a palimpsest is one of the oldest Qur’anic manuscripts in existence. Carbon dating indicates that the undertext (the scriptio inferior) was written probably within 15 years of the death of Prophet Muhammad. The undertext differs from the standard Qur’anic text, and is therefore the most important documentary evidence for the existence of variant Qur’anic readings.[5]
  • Among the Syriac manuscripts obtained from the Nitrian desert in Egypt, British Museum, London: important Greek texts, Add. Ms. 17212 with Syriac translation of St. Chrysostom’s Homilies, of the 9th/10th century, covers a Latin grammatical treatise from the 6th century.
  • A double palimpsest, in which a text of St John Chrysostom, in Syriac, of the 9th or 10th century, covers a Latin grammatical treatise in a cursive hand of the 6th century, which in its turn covers the Latin annals of the historian Granius Licinianus, of the 5th century, British Museum.
  • The only known hyper-palimpsest: the Novgorod Codex, where potentially hundreds of texts have left their traces on the wooden back wall of a wax tablet.
  • The Ambrosian Plautus, in rustic capitals, of the 4th or 5th century, re-written with portions of the Bible in the 9th century, Ambrosian Library.
  • Seneca, On the Maintenance of Friendship, the sole surviving fragment, overwritten by a late-6th century Old Testament.
  • The Archimedes Palimpsest, a work of the great Syracusan mathematician copied onto parchment in the 10th century and overwritten by a liturgical text in the 12th century.
  • the unique copy of a Greek grammatical text composed by Herodian for the emperor Marcus Aurelius in the 2nd century, preserved in the Österreichische Nationalbibliothek, Vienna.

Other palimpsests (New Testament)

To the present day survived about sixty palimpsest manuscripts of the Greek New Testament. Uncial codices:

Porphyrianus, Vaticanus 2061 (double palimpsest), Uncial 064, 065, 066, 067, 068 (double palimpsest), 072, 078, 079, 086, 088, 093, 094, 096, 097, 098, 0103, 0104, 0116, 0120, 0130, 0132, 0133, 0135, 0208, 0209.


The Archimedes Palimpsest is a parchment codex palimpsest, which originally was a 10th-century Byzantine copy of an otherwise unknown work of Archimedes of Syracuse and other authors. It was overwritten with Christian religious text by 13th-century monks.[1] The erasure was incomplete, and Archimedes’ work is now readable after scientific and scholarly work from 1998 to 2008 using digital processing of images produced by ultraviolet, infrared, visible and raking light, and X-ray.[2][3]


It contains:

The palimpsest also contains speeches by the 4th century BC politician Hypereides, a commentary on Aristotle‘s Categories by Alexander of Aphrodisias, and other works.[4]


Archimedes lived in the 3rd century BC, and a copy of his work was made around 950 AD in the Byzantine Empire by an anonymous scribe. In 1229, the original Archimedes codex was unbound, scraped and washed, along with at least six other parchment manuscripts, including one with works of Hypereides. The parchment leaves were folded in half and reused for a Christian liturgical text of 177 pages; the older leaves folded so that each became two leaves of the liturgical book.


The Biblical scholar Constantin von Tischendorf visited Constantinople in the 1840s, and, intrigued by the Greek mathematics visible on the palimpsest, brought home a page of it. (This page is now in the Cambridge University Library.) It was Johan Heiberg who realized, when he studied the palimpsest in Constantinople in 1906, that the text was of Archimedes, and included works otherwise lost. Heiberg took photographs, from which he produced transcriptions, published between 1910 and 1915 in a complete works of Archimedes. Shortly thereafter Archimedes’ Greek text was translated into English by T. L. Heath. Before that it was not widely known among mathematicians, physicists or historians.

From the 1920s, the manuscript lay unknown in the Paris apartment of a collector of manuscripts and his heirs. It is not known how the palimpsest subsequently wound up in France. In 1998 the ownership of the palimpsest was disputed in federal court in New York in the case of the Greek Orthodox Patriarchate of Jerusalem v. Christie’s, Inc. At some time in the distant past, the Archimedes manuscript had lain in the library of Mar Saba, near Jerusalem, a monastery bought by the Patriarchate in 1625. The plaintiff contended that the palimpsest had been stolen from one of its monasteries in the 1920s. Judge Kimba Wood decided in favor of Christie’s Auction House on laches grounds, and the palimpsest was bought for $2 million by an anonymous buyer. Simon Finch, who represented the anonymous buyer, stated that the buyer was “a private American” who worked in “the high-tech industry”, but was not Bill Gates.[5] The German magazine Der Spiegel reported that the buyer is probably Jeff Bezos.[6]

Imaging and digitization

After imaging a page from the palimpsest, the original Archimedes text is now seen clearly

At the Walters Art Museum in Baltimore, the palimpsest was the subject of an extensive imaging study from 1999 to 2008, and conservation (as it had suffered considerably from mold). This was directed by Dr. Will Noel, curator of manuscripts at the Walters Art Museum, and managed by Michael B. Toth of R.B. Toth Associates, with Dr. Abigail Quandt performing the conservation of the manuscript.

A team of imaging scientists including Dr. Roger L. Easton, Jr. from the Rochester Institute of Technology, Dr. William A. Christens-Barry from Equipoise Imaging, and Dr. Keith Knox (then with Boeing LTS, now with USAF Research Laboratory) used computer processing of digital images from various spectral bands, including ultraviolet, visible, and infrared wavelengths to reveal most of the underlying text, including of Archimedes. After imaging and digitally processing the entire palimpsest in three spectral bands prior to 2006, in 2007 they reimaged the entire palimpsest in 12 spectral bands, plus raking light: UV: 365 nanometers; Visible Light: 445, 470, 505, 530, 570, 617, and 625 nm; Infrared: 700, 735, and 870 nm; and Raking Light: 910 and 470 nm. The team digitally processed these images to reveal more of the underlying text with pseudocolor. They also digitized the original Heiberg images. Dr. Reviel Netz of Stanford University and Nigel Wilson have produced a diplomatic transcription of the text, filling in gaps in Heiberg’s account with these images.[7]

Sometime after 1938, one owner of the manuscript forged four Byzantine-style religious images in the manuscript in an effort to increase its value. It appeared that these had rendered the underlying text forever illegible. However, in May 2005, highly focused X-rays produced at the Stanford Linear Accelerator Center in Menlo Park, California, were used by Drs. Uwe Bergman and Bob Morton to begin deciphering the parts of the 174-page text that had not yet been revealed. The production of X-ray fluorescence was described by Keith Hodgson, director of SSRL: “Synchrotron light is created when electrons traveling near the speed of light take a curved path around a storage ring—emitting electromagnetic light in X-ray through infrared wavelengths. The resulting light beam has characteristics that make it ideal for revealing the intricate architecture and utility of many kinds of matter—in this case, the previously hidden work of one of the founding fathers of all science.”[8]

In April 2007, it was announced that a new text had been found in the palimpsest, which was a commentary on the work of Aristotle attributed to Alexander of Aphrodisias. Most of this text was recovered in early 2009 by applying principal component analysis to the three color bands (red, green, and blue) of fluorescent light generated by ultraviolet illumination. Dr. Will Noel said in an interview: “You start thinking striking one palimpsest is gold, and striking two is utterly astonishing. But then something even more extraordinary happened.” This referred to the previous discovery of a text by Hypereides, an Athenian politician from the fourth century BC, which has also been found within the palimpsest.[4] It is from his speech Against Diondas, and was published in 2008 in the German scholarly magazine Zeitschrift für Papyrologie und Epigraphik, vol. 165, becoming the first new text from the palimpsest to be published in a scholarly journal.[9]

The transcriptions of the book were digitally encoded using the Text Encoding Initiative guidelines, and metadata for the images and transcriptions included identification and cataloging information based on Dublin Core Metadata Elements. The metadata and data were managed by Dr. Doug Emery of Emery IT.

On October 29, 2008, (the tenth anniversary of the purchase of the palimpsest at auction) all data, including images and transcriptions, were hosted on the Digital Palimpsest Web Page for free use under a Creative Commons License,[10] and processed images of the palimpsest in original page order were posted as a Google Book.[11] In late 2011 it was the subject of the Walters Art Museum exhibit “Lost and Found: The Secrets of Archimedes”.[12]

Mathematical content

Ostomachion is a dissection puzzle in the Archimedes Palimpsest (shown after Suter from a different source; this version must be stretched to twice the width to conform to the Palimpsest)

The most remarkable of the above works is The Method, of which the palimpsest contains the only known copy.

In his other works, Archimedes often proves the equality of two areas or volumes with Eudoxus‘ method of exhaustion, an ancient Greek counterpart of the modern method of limits. Since the Greeks were aware that some numbers were irrational, their notion of a real number was a quantity Q approximated by two sequences, one providing an upper bound and the other a lower bound. If you find two sequences U and L, with U always bigger than Q, and L always smaller than Q, and if the two sequences eventually came closer together than any prespecified amount, then Q is found, or exhausted, by U and L.

Archimedes used exhaustion to prove his theorems. This involved approximating the figure whose area he wanted to compute into sections of known area, which provide upper and lower bounds for the area of the figure. He then proved that the two bounds become equal when the subdivision becomes arbitrarily fine. These proofs, still considered to be rigorous and correct, used geometry with rare brilliance. Later writers often criticized Archimedes for not explaining how he arrived at his results in the first place. This explanation is contained in The Method.

The method that Archimedes describes was based upon his investigations of physics, on the center of mass and the law of the lever. He compared the area or volume of a figure of which he knew the total mass and center of mass with the area or volume of another figure he did not know anything about. He divided both figures into infinitely many slices of infinitesimal width, and balanced each slice of one figure against a corresponding slice of the second figure on a lever. The essential point is that the two figures are oriented differently, so that the corresponding slices are at different distances from the fulcrum, and the condition that the slices balance is not the same as the condition that they are equal.

Once he shows that each slice of one figure balances each slice of the other figure, he concludes that the two figures balance each other. But the center of mass of one figure is known, and the total mass can be placed at this center and it still balances. The second figure has an unknown mass, but the position of its center of mass might be restricted to lie at a certain distance from the fulcrum by a geometrical argument, by symmetry. The condition that the two figures balance now allows him to calculate the total mass of the other figure. He considered this method as a useful heuristic but always made sure to prove the results he found using exhaustion, since the method did not provide upper and lower bounds.

Using this method, Archimedes was able to solve several problems now treated by integral calculus, which was given its modern form in the seventeenth century by Isaac Newton and Gottfried Leibniz. Among those problems were that of calculating the center of gravity of a solid hemisphere, the center of gravity of a frustum of a circular paraboloid, and the area of a region bounded by a parabola and one of its secant lines. (For explicit details, see Archimedes’ use of infinitesimals.)

When rigorously proving theorems, Archimedes often used what are now called Riemann sums. In “On the Sphere and Cylinder,” he gives upper and lower bounds for the surface area of a sphere by cutting the sphere into sections of equal width. He then bounds the area of each section by the area of an inscribed and circumscribed cone, which he proves have a larger and smaller area correspondingly. He adds the areas of the cones, which is a type of Riemann sum for the area of the sphere considered as a surface of revolution.

But there are two essential differences between Archimedes’ method and 19th-century methods:

  1. Archimedes did not know about differentiation, so he could not calculate any integrals other than those that came from center-of-mass considerations, by symmetry. While he had a notion of linearity, to find the volume of a sphere he had to balance two figures at the same time; he never figured out how to change variables or integrate by parts.
  2. When calculating approximating sums, he imposed the further constraint that the sums provide rigorous upper and lower bounds. This was required because the Greeks lacked algebraic methods that could establish that error terms in an approximation are small.

A problem solved exclusively in the Method is the calculation of the volume of a cylindrical wedge, a result that reappears as theorem XVII (schema XIX) of Kepler‘s Stereometria.

Some pages of the Method remained unused by the author of the palimpsest and thus they are still lost. Between them, an announced result concerned the volume of the intersection of two cylinders, a figure that Apostol and Mnatsakanian have renamed n = 4 Archimedean globe (and the half of it, n = 4 Archimedean dome), whose volume relates to the n-polygonal pyramid.

In Heiberg’s time, much attention was paid to Archimedes’ brilliant use of indivisibles to solve problems about areas, volumes, and centers of gravity. Less attention was given to the Stomachion, a problem treated in the palimpsest that appears to deal with a children’s puzzle. Reviel Netz of Stanford University has argued that Archimedes discussed the number of ways to solve the puzzle, that is, to put the pieces back into their box. No pieces have been identified as such; the rules for placement, such as whether pieces are allowed to be turned over, are not known; and there is doubt about the board. The board illustrated here, as also by Netz, is one proposed by Heinrich Suter in translating an unpointed Arabic text in which twice and equals are easily confused; Suter makes at least a typographical error at the crucial point, equating the lengths of a side and diagonal, in which case the board cannot be a rectangle. But, as the diagonals of a square intersect at right angles, the presence of right triangles makes the first proposition of Archimedes’ Stomachion immediate. Rather, the first proposition sets up a board consisting of two squares side by side (as in Tangram). A reconciliation of the Suter board with this Codex board was published by Richard Dixon Oldham, FRS, in Nature in March, 1926, sparking a Stomachion craze that year. Modern combinatorics reveals that the number of ways to place the pieces of the Suter board to reform their square, allowing them to be turned over, is 17,152; the number is considerably smaller – 64 – if pieces are not allowed to be turned over. The sharpness of some angles in the Suter board makes fabrication difficult, while play could be awkward if pieces with sharp points are turned over. For the Codex board (again as with Tangram) there are three ways to pack the pieces: as two unit squares side by side; as two unit squares one on top of the other; and as a single square of side the square root of two. But the key to these packings is forming isosceles right triangles, just as Socrates gets the slave boy to consider in Plato‘s Meno – Socrates was arguing for knowledge by recollection, and here pattern recognition and memory seem more pertinent than a count of solutions. The Codex board can be found as an extension of Socrates’ argument in a seven-by-seven-square grid, suggesting an iterative construction of the side-diameter numbers that give rational approximations to the square root of two. The fragmentary state of the palimpsest leaves much in doubt. But it would certainly add to the mystery had Archimedes used the Suter board in preference to the Codex board. However, if Netz is right, this may have been the most sophisticated work in the field of combinatorics in Greek antiquity. Either Archimedes used the Suter board, the pieces of which were allowed to be turned over, or the statistics of the Suter board are irrelevant.

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