The Archimedes Palimpsest is a palimpsest

Palimpsest

A palimpsest is a manuscript page from a scroll or book from which the text has been scraped off and which can be used again. The word "palimpsest" comes through Latin palimpsēstus from Ancient Greek παλίμψηστος originally compounded from πάλιν and ψάω literally meaning “scraped...

 on parchment

Parchment

Parchment is a thin material made from calfskin, sheepskin or goatskin, often split. Its most common use was as a material for writing on, for documents, notes, or the pages of a book, codex or manuscript. It is distinct from leather in that parchment is limed but not tanned; therefore, it is very...

 in the form of a codex

Codex

A codex is a book in the format used for modern books, with multiple quires or gatherings typically bound together and given a cover.Developed by the Romans from wooden writing tablets, its gradual replacement...

. It originally was a copy of an otherwise unknown work of the ancient mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

, physicist

Physicist

A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...

, and engineer

Engineer

An engineer is a professional practitioner of engineering, concerned with applying scientific knowledge, mathematics and ingenuity to develop solutions for technical problems. Engineers design materials, structures, machines and systems while considering the limitations imposed by practicality,...

 Archimedes

Archimedes

Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an...

 of Syracuse

Syracuse, Italy

Syracuse is a historic city in Sicily, the capital of the province of Syracuse. The city is notable for its rich Greek history, culture, amphitheatres, architecture, and as the birthplace of the preeminent mathematician and engineer Archimedes. This 2,700-year-old city played a key role in...

 and other authors, which was overwritten with a religious text.

Archimedes lived in the third century BC, but the copy of his work was made in the tenth century AD by an anonymous scribe. In the twelfth century 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 had been 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 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

Ultraviolet

Ultraviolet light is electromagnetic radiation with a wavelength shorter than that of visible light, but longer than X-rays, in the range 10 nm to 400 nm, and energies from 3 eV to 124 eV...

, infrared

Infrared

Infrared light is electromagnetic radiation with a wavelength longer than that of visible light, measured from the nominal edge of visible red light at 0.74 micrometres , and extending conventionally to 300 µm...

, visible and raking light

Raking light

Raking light, the illumination of objects from a light source at an oblique angle or almost parallel to the surface, provides information on the surface topography and relief of the artefact thus lit...

, and X-ray

X-ray

X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...

.

In 1906 it was briefly inspected in Istanbul by the Danish

Denmark

Denmark is a Scandinavian country in Northern Europe. The countries of Denmark and Greenland, as well as the Faroe Islands, constitute the Kingdom of Denmark . It is the southernmost of the Nordic countries, southwest of Sweden and south of Norway, and bordered to the south by Germany. Denmark...

 philologist

Philology

Philology is the study of language in written historical sources; it is a combination of literary studies, history and linguistics.Classical philology is the philology of Greek and Classical Latin...

 Johan Ludvig Heiberg

Johan Ludvig Heiberg (historian)

Johan Ludvig Heiberg was a Danish philologist and historian. He is best known for his discovery of previously unknown texts in the Archimedes Palimpsest, and for his edition of Euclid's Elements that T. L. Heath translated into English...

. With the aid of black-and-white photographs he arranged to have taken, he published a transcription of the Archimedes text. Shortly thereafter Archimedes' Greek

Greek language

Greek is an independent branch of the Indo-European family of languages. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. Its writing system has been the Greek alphabet for the majority of its history;...

 text was translated into English

English language

English is a West Germanic language that arose in the Anglo-Saxon kingdoms of England and spread into what was to become south-east Scotland under the influence of the Anglian medieval kingdom of Northumbria...

 by T. L. Heath

T. L. Heath

Sir Thomas Little Heath was a British civil servant, mathematician, classical scholar, historian of ancient Greek mathematics, translator, and mountaineer. He was educated at Clifton College...

. Before that it was not widely known among mathematicians, physicists or historians. It contains:

• "On the Equilibrium of Planes"
• "Spiral Lines
  On Spirals
  On Spirals is a treatise by Archimedes in 225 BC. Although Archimedes did not discover the Archimedean spiral, he employed it in this book to square the circle and trisect an angle.-Preface:...
  
  "
• "Measurement of a Circle
  Measurement of a Circle
  Measurement of a Circle is a treatise that consists of three propositions by Archimedes. The treatise is only a fraction of what was a longer work.-Proposition one:Proposition one states:...
  
  "
• "On the Sphere and Cylinder
  On the Sphere and Cylinder
  On the Sphere and Cylinder is a work that was published by Archimedes in two volumes c. 225 BC. It most notably details how to find the surface area of a sphere and the volume of the contained ball and the analogous values for a cylinder, and was the first to do so.-Contents:The principal formulae...
  
  "
• "On Floating Bodies" (only known copy in Greek)
• "The Method of Mechanical Theorems" (only known copy)
• "Stomachion" (only known copy)

The palimpsest also contains speeches by the fourth century BC politician Hypereides

Hypereides

Hypereides or Hyperides was a logographer in Ancient Greece...

, a commentary on Aristotle

Aristotle

Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...

's Categories

Categories (Aristotle)

The Categories is a text from Aristotle's Organon that enumerates all the possible kinds of thing that can be the subject or the predicate of a proposition...

 by Alexander of Aphrodisias

Alexander of Aphrodisias

Alexander of Aphrodisias was a Peripatetic philosopher and the most celebrated of the Ancient Greek commentators on the writings of Aristotle. He was a native of Aphrodisias in Caria, and lived and taught in Athens at the beginning of the 3rd century, where he held a position as head of the...

, and other works.

Mathematical content

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

Real number

In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...

 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

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

 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

Physics

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, on the center of mass

Center of mass

In physics, the center of mass or barycenter of a system is the average location of all of its mass. In the case of a rigid body, the position of the center of mass is fixed in relation to the body...

 and the law of the lever. He compared the area or volume of a figure that he knew the total mass and center of mass of with the area or volume of another figure he didn't know anything about. He divided both figures into infinitely many slices of infinitesimal

Infinitesimal

Infinitesimals have been used to express the idea of objects so small that there is no way to see them or to measure them. The word infinitesimal comes from a 17th century Modern Latin coinage infinitesimus, which originally referred to the "infinite-th" item in a series.In common speech, an...

 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

Heuristic

Heuristic refers to experience-based techniques for problem solving, learning, and discovery. Heuristic methods are used to speed up the process of finding a satisfactory solution, where an exhaustive search is impractical...

 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

Isaac Newton

Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

 and Gottfried Leibniz

Gottfried Leibniz

Gottfried Wilhelm Leibniz was a German philosopher and mathematician. He wrote in different languages, primarily in Latin , French and German ....

. Among those problems were that of calculating the center of gravity

Center of gravity

In physics, a center of gravity of a material body is a point that may be used for a summary description of gravitational interactions. In a uniform gravitational field, the center of mass serves as the center of gravity...

 of a solid hemisphere

Sphere

A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point...

, the center of gravity of a frustum

Frustum

In geometry, a frustum is the portion of a solid that lies between two parallel planes cutting it....

 of a circular paraboloid

Paraboloid

In mathematics, a paraboloid is a quadric surface of special kind. There are two kinds of paraboloids: elliptic and hyperbolic. The elliptic paraboloid is shaped like an oval cup and can have a maximum or minimum point....

, and the area of a region bounded by a parabola

Parabola

In mathematics, the parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface...

 and one of its secant line

Secant line

A secant line of a curve is a line that intersects two points on the curve. The word secant comes from the Latin secare, to cut.It can be used to approximate the tangent to a curve, at some point P...

s. (For explicit details, see Archimedes' use of infinitesimals

Archimedes' use of infinitesimals

The Method of Mechanical Theorems is a work by Archimedes which contains the first attested explicit use of infinitesimals. The work was originally thought to be lost, but was rediscovered in the celebrated Archimedes Palimpsest...

.)

When rigorously proving theorems, Archimedes often used what are now called Riemann sum

Riemann sum

In mathematics, a Riemann sum is a method for approximating the total area underneath a curve on a graph, otherwise known as an integral. It mayalso be used to define the integration operation. The method was named after German mathematician Bernhard Riemann....

s. In On the Sphere and Cylinder

On the Sphere and Cylinder

On the Sphere and Cylinder is a work that was published by Archimedes in two volumes c. 225 BC. It most notably details how to find the surface area of a sphere and the volume of the contained ball and the analogous values for a cylinder, and was the first to do so.-Contents:The principal formulae...

, 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 didn't know about differentiation, so he couldn't 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

Johannes Kepler

Johannes Kepler was a German mathematician, astronomer and astrologer. A key figure in the 17th century scientific revolution, he is best known for his eponymous laws of planetary motion, codified by later astronomers, based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican...

'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

Tom M. Apostol

Tom Mike Apostol is a Greek-American analytic number theorist and professor at the California Institute of Technology.He was born in Helper, Utah in 1923. His parents, Emmanouil Apostolopoulos and Efrosini Papathanasopoulos, originated from Greece. Mr...

 and Mnatsakanian

Mamikon Mnatsakanian

Mamikon Mnatsakanian is Project Associate at Project Mathematics! at California Institute of Technology.He received a Ph.D. in physics in 1969 from Yerevan State University, where he became professor of astrophysics...

 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 infinitesimals to solve problems about areas, volumes, and centers of gravity. Less attention was given to the Stomachion

Ostomachion

Ostomachion, also known as loculus Archimedius and also as syntomachion, is a mathematical treatise attributed to Archimedes. This work has survived fragmentarily in an Arabic version and in a copy of the original ancient Greek text made in Byzantine times...

, a problem treated in the palimpsest that appears to deal with a children's puzzle. Reviel Netz of Stanford University

Stanford University

The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...

 has argued that Archimedes discussed the number of ways to solve the puzzle, that is, to put the pieces back in 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

Tangram

The tangram is a dissection puzzle consisting of seven flat shapes, called tans, which are put together to form shapes. The objective of the puzzle is to form a specific shape using all seven pieces, which may not overlap...

). A reconciliation of the Suter board with this Codex board was published by Richard Dixon Oldham

Richard Dixon Oldham

Richard Dixon Oldham FRS was a British geologist who made the first clear identification of the separate arrivals of P-waves, S-waves and surface waves on seismograms and the first clear evidence that the Earth has a central core.-Life:Born on 31 July 1858 to Thomas Oldham, a Fellow of the Royal...

, FRS, in Nature in March, 1926, sparking a Stomachion craze that year. Modern combinatorics

Combinatorics

Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...

 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

Socrates

Socrates was a classical Greek Athenian philosopher. Credited as one of the founders of Western philosophy, he is an enigmatic figure known chiefly through the accounts of later classical writers, especially the writings of his students Plato and Xenophon, and the plays of his contemporary ...

 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 a 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.

Modern history

The Biblical scholar Constantine 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

Johan Ludvig Heiberg (historian)

Johan Ludvig Heiberg was a Danish philologist and historian. He is best known for his discovery of previously unknown texts in the Archimedes Palimpsest, and for his edition of Euclid's Elements that T. L. Heath translated into English...

 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 transcripts, published between 1910 and 1915 in a complete works of Archimedes. It is not known how the palimpsest subsequently wound up in France.

From the 1920s, the manuscript lay unknown in the Paris apartment of a collector of manuscripts and his heirs. 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

Orthodox Patriarch of Jerusalem

The Greek Orthodox Patriarch of Jerusalem is the head bishop of the Orthodox Church of Jerusalem, ranking fourth of nine Patriarchs in the Eastern Orthodox Church. Since 2005, the Orthodox Patriarch of Jerusalem has been Theophilos III...

v. Christie's

Christie's

Christie's is an art business and a fine arts auction house.- History :The official company literature states that founder James Christie conducted the first sale in London, England, on 5 December 1766, and the earliest auction catalogue the company retains is from December 1766...

, Inc. At some time in the distant past, the Archimedes manuscript had lain in the library of Mar Saba

Mar Saba

The Great Lavra of St. Sabbas the Sanctified, known in Arabic as Mar Saba , is a Greek Orthodox monastery overlooking the Kidron Valley in the West Bank east of Bethlehem. The traditional date for the founding of the monastery by Saint Sabas of Cappadocia is the year 483 and today houses around 20...

, 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

Kimba Wood

Kimba Maureen Wood is a United States federal judge for the United States District Court for the Southern District of New York.-Early life and education:...

 decided in favor of Christie's Auction House on laches

Laches (equity)

Laches is an "unreasonable delay pursuing a right or claim...in a way that prejudices the [opposing] party" When asserted in litigation, it is an equitable defense, or doctrine...

 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. (The German magazine Der Spiegel

Der Spiegel

Der Spiegel is a German weekly news magazine published in Hamburg. It is one of Europe's largest publications of its kind, with a weekly circulation of more than one million.-Overview:...

reported that the buyer is probably Jeff Bezos

Jeff Bezos

Jeffrey Preston "Jeff" Bezos is the founder, president, chief executive officer , and chairman of the board of Amazon.com.-Early life and background:...

.)
At the Walters Art Museum

Walters Art Museum

The Walters Art Museum, located in Baltimore, Maryland's Mount Vernon neighborhood, is a public art museum founded in 1934. The museum's collection was amassed substantially by two men, William Thompson Walters , who began serious collecting when he moved to Paris at the outbreak of the American...

 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

Mold

Molds are fungi that grow in the form of multicellular filaments called hyphae. Molds are not considered to be microbes but microscopic fungi that grow as single cells called yeasts...

). 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 Easton from the Rochester Institute of Technology

Rochester Institute of Technology

The Rochester Institute of Technology is a private university, located within the town of Henrietta in metropolitan Rochester, New York, United States...

, Dr. Bill Christens-Barry from Equipoise Imaging, and Dr. Keith Knox with Boeing LTS used computer processing of digital images from various spectral bands, including ultraviolet and visible light, 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

Stanford University

The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...

 and Nigel Wilson have produced a diplomatic transcription of the text, filling in gaps in Heiberg's account with these images. All images are currently hosted on the website.

Sometime after 1938, one owner of the manuscript forged four Byzantine-style

Byzantine art

Byzantine art is the term commonly used to describe the artistic products of the Byzantine Empire from about the 5th century until the Fall of Constantinople in 1453....

 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

Stanford Linear Accelerator Center

The SLAC National Accelerator Laboratory, originally named Stanford Linear Accelerator Center, is a United States Department of Energy National Laboratory operated by Stanford University under the programmatic direction of the U.S...

 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

Fluorescence

Fluorescence is the emission of light by a substance that has absorbed light or other electromagnetic radiation of a different wavelength. It is a form of luminescence. In most cases, emitted light has a longer wavelength, and therefore lower energy, than the absorbed radiation...

 was described by Keith Hodgson, director of SSRL. "Synchrotron light

Synchrotron light

A synchrotron light source is a source of electromagnetic radiation produced by a synchrotron, which is artificially produced for scientific and technical purposes by specialized particle accelerators, typically accelerating electrons...

 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."

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

Aristotle

Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...

 attributed to Alexander of Aphrodisias

Alexander of Aphrodisias

Alexander of Aphrodisias was a Peripatetic philosopher and the most celebrated of the Ancient Greek commentators on the writings of Aristotle. He was a native of Aphrodisias in Caria, and lived and taught in Athens at the beginning of the 3rd century, where he held a position as head of the...

. 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

Hypereides

Hypereides or Hyperides was a logographer in Ancient Greece...

, an Athenian politician from the fourth century BC, which has also been found within the palimpsest. 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.

The transcriptions of the book were digitally encoded using the Text Encoding Initiative

Text Encoding Initiative

The Text Encoding Initiative is a text-centric community of practice in the academic field of digital humanities. The community runs a mailing list, meetings and conference series, and maintains a technical standard, a wiki and a toolset....

 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

Creative Commons

Creative Commons is a non-profit organization headquartered in Mountain View, California, United States devoted to expanding the range of creative works available for others to build upon legally and to share. The organization has released several copyright-licenses known as Creative Commons...

 License, and processed images of the palimpsest in original page order were posted as a Google Book. In late 2011 it was the subject of the Walters Art Museum exhibit "Lost and Found: The Secrets of Archimedes".

External links

• The Archimedes Palimpsest Project Web Page
• Digital Palimpsest on the Web
• The Nova Program outlined
• The Nova Program teacher's version
• The Method: English translation (Heiberg's 1909 transcription)
• Did Isaac Barrow read it?
• May 2005 Stanford Report: Heather Rock Woods, "Archimedes manuscript yields secrets under X-ray gaze" May 19, 2005
• Will Noel: Restoring The Archimedes Palimpsest (YouTube), Ignite (O'Reilly), August 2009
• The Greek Orthodox Patriarchate of Jerusalem v. Christies’s Inc., 1999 U.S. Dist. LEXIS 13257 (S.D. N.Y. 1999) (via Archive.org)
• Eureka! 1,000-year-old text by Greek maths genius Archimedes goes on display Daily Mail
  Daily Mail
  The Daily Mail is a British daily middle-market tabloid newspaper owned by the Daily Mail and General Trust. First published in 1896 by Lord Northcliffe, it is the United Kingdom's second biggest-selling daily newspaper after The Sun. Its sister paper The Mail on Sunday was launched in 1982...
  
  , October 18, 2011.