The Archimedes Palimpsest is a palimpsest on parchment in the form of a codex which originally was a copy of an otherwise unknown work of the ancient mathematician, physicist, and engineer Archimedes of Syracuse and other authors. Archimedes lived in the third century BC, but the copy was made in the 10th century by an anonymous scribe. In the 12th century the codex was unbound and washed, in order that the parchment leaves could be folded in half and reused for a Christian liturgical text. It was a book of nearly 90 pages before being made a palimpsest 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 using digital processing of ultraviolet, X-ray, and visible light. A palimpsest is a manuscript page, scroll, or book that has been written on, scraped off, and used again. ... German parchmenter, 1568 Parchment is a material for the pages of a book or codex, made from fine calf skin, sheep skin or goat skin. ... First page of the Codex Argenteus A codex (Latin for block of wood, book; plural codices) is a handwritten book, in general, one produced from Late Antiquity through the Middle Ages. ... Leonhard Euler is considered by many to be one of the greatest mathematicians of all time A mathematician is the person whose primary area of study and research is the field of mathematics. ... ... For the Technical Symposium of NITK Surathkal Engineer , see Engineer (Technical Fest). ... Archimedes (Greek: c. ... Syracuse (Italian, Siracusa, ancient Syracusa - see also List of traditional Greek place names) is a city on the eastern coast of Sicily and the capital of the province of Syracuse, Italy. ... The 3rd century BC started the first day of 300 BC and ended the last day of 201 BC. // The Pyramid of the Moon, one of several monuments built in Teotihuacán Early 3rd century BC or later - Theater, Epidauros is built. ... As a means of recording the passage of time, the 10th century was that century which lasted from 901 to 1000. ... (11th century - 12th century - 13th century - other centuries) As a means of recording the passage of time, the 12th century was that century which lasted from 1101 to 1200. ... The word leitourgia is derived from the two Greek words, leos and ergon. Leos, meaning the people of God and Ergon meaning the work. ... UV redirects here. ... In the NATO phonetic alphabet, X-ray represents the letter X. An X-ray picture (radiograph) taken by Röntgen An X-ray is a form of electromagnetic radiation with a wavelength approximately in the range of 5 pm to 10 nanometers (corresponding to frequencies in the range 30 PHz...

In 1906 it was briefly inspected in Constantinople and was published, from photographs, by the Danish philologist Johan Ludvig Heiberg (1854–1928); shortly thereafter Archimedes' Greek text was translated into English by Thomas Heath. Before that it was not widely known among mathematicians, physicists, or historians. It contains: 1906 (MCMVI) was a common year starting on Monday (see link for calendar). ... Map of Constantinople. ... Philology is the study of ancient texts and languages. ... 1854 (MDCCCLIV) was a common year starting on Sunday (see link for calendar). ... Year 1928 (MCMXXVIII) was a leap year starting on Sunday (link will display full calendar). ... The English language is a West Germanic language that originates in England. ... Thomas Little Heath (October 5, 1861 - March 16, 1940) was a mathematician, classical scholar, historian of ancient Greek mathematics, and translator. ...

• "Equilibrium of Planes"
• "Spiral Lines"
• "The Measurement of the Circle"
• "Sphere and Cylinder"
• "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 4th century BC politician Hypereides, and a commentary on Aristotle's Categories by Alexander of Aphrodisias.[1] Hypereides (c. ... Aristotle (Greek: Aristotélēs) (384 BC – March 7, 322 BC) was a Greek philosopher, a student of Plato and teacher of Alexander the Great. ... Categories (or Categoriae) is a text from Aristotles Organon that enumerates all the possible kinds of thing which can be the subject or the predicate of a proposition. ... Alexander of Aphrodisias, a pupil of Aristocles of Messene, was the most celebrated of the Greek commentators on the writings of Aristotle. ...

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 his method of double contradiction: assuming that the first is bigger than the second leads to a contradiction, as does the assumption that the first be smaller than the second; so the two must be equal. These proofs, still considered to be rigorous and correct, used what we might now consider secondary-school 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. This article or section does not adequately cite its references or sources. ... Table of Geometry, from the 1728 Cyclopaedia. ...

Essentially then, the method consists in dividing the two areas or volumes in infinitely many stripes of infinitesimal width, and "weighing" the stripes of the first figure against those of the second. He considered this method as a useful heuristic but always made sure to prove the results found in this manner using the unrelated and rigorous geometrical methods mentioned above. In mathematics, an infinitesimal, or infinitely small number, is a number that is smaller in absolute value than any positive real number. ...

He was able to solve problems that would now be treated by integral calculus, which was formally invented in the 17th century by Isaac Newton and Gottfried Leibniz, working independently. 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. Contrary to exaggerations found in some 20th century calculus textbooks, he did not use anything like Riemann sums, either in the work embodied in this palimpsest or in any of his other works. For explicit details of the method used, see how Archimedes used infinitesimals. This article deals with the concept of an integral in calculus. ... (16th century - 17th century - 18th century - more centuries) As a means of recording the passage of time, the 17th century was that century which lasted from 1601-1700. ... Sir Isaac Newton, (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist, regarded by many as the greatest figure in the history of science. ... Gottfried Leibniz Gottfried Wilhelm von Leibniz (July 1, 1646 in Leipzig - November 14, 1716 in Hannover) was a German philosopher, scientist, mathematician, diplomat, librarian, and lawyer of Sorb descent. ... This article or section may contain original research or unverified claims. ... A sphere is a perfectly symmetrical geometrical object. ... A frustum is the portion of a solid â€“ normally a cone or pyramid â€“ which lies between two parallel planes cutting the solid. ... Paraboloid of revolution Hyperbolic paraboloid In mathematics, a paraboloid is a quadric, a type of surface in three dimensions, described by the equation: (elliptic paraboloid), or (hyperbolic paraboloid). ... A parabola A graph showing the reflective property, the directrix (light blue), and the lines connecting the focus and directrix to the parabola (blue) In mathematics, the parabola (from the Greek: παραβολή) (IPA pronunciation: ) is a conic section generated by the intersection of a right circular conical surface and a plane... Secant is a term in mathematics. ... (19th century - 20th century - 21st century - more centuries) Decades: 1900s 1910s 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s As a means of recording the passage of time, the 20th century was that century which lasted from 1901–2000 in the sense of the Gregorian calendar (1900–1999... In mathematics, a Riemann sum is a method for approximating the values of integrals. ... The ancient Greek mathematician, physicist, and engineer Archimedes of Syracuse was the first mathematician to make explicit use of infinitesimals. ...

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. Johannes Kepler (December 27, 1571 – November 15, 1630) was a German Lutheran mathematician, astronomer and astrologer, and a key figure in the 17th century astronomical revolution. ...

Some pages of the Method remained unused by the author of the Palimpsest and thus they are still—probably forever—lost. Between them, an announced result concerned the volume of the intersection of two cylinders, a figure that Apostol and Mnatsakian 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, a problem treated in the Palimpsest that appears to deal with a children's puzzle. Reviel Netz of Stanford University has shown that Archimedes found that the number of ways to solve the puzzle is 17,152. This is perhaps the most sophisticated work in the field of combinatorics in classical antiquity. The Leland Stanford Junior University, commonly known as Stanford University (or simply Stanford), is a private university located approximately 37 miles (60 kilometers) southeast of San Francisco and approximately 20 miles northwest of San José in an unincorporated area of Santa Clara County. ... Combinatorics is a branch of pure mathematics concerning the study of discrete (and usually finite) objects. ...

Modern history

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 versus 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 information technology person. The 1920s is a decade sometimes referred to as the Jazz Age or the Roaring Twenties, usually applied to America. ... 1998 (MCMXCVIII) was a common year starting on Thursday of the Gregorian calendar, and was designated the International Year of the Ocean [1]. // Coated in ice, power and telephone lines sag and often break, resulting in power outages. ... The Orthodox Patriarch of Jerusalem is the head bishop of the Orthodox Church of Jerusalem, ranking fourth of nine patriarchs in the Eastern Orthodox Church. ... Christies Auction Room in London circa 1808. ... Mar Saba seen from the view point Mar Saba seen from the bottom of the gorge Mar Saba in the 19th century Mar Saba is a Greek Orthodox monastery located near Bethlehem, Israel (Palestine), and overlooks the Kidron River. ... Kimba Wood (born 1944) is a U.S. federal judge. ... Laches is an equitable defense, or doctrine, in an action at law. ...

The palimpsest is now at the Walters Art Museum in Baltimore, where conservation continues (as it had suffered considerably from mold). A more accurate edition of the manuscript, including its drawn geometrical figures, is expected, possibly in 2007. The Walters Art Museum in Baltimore, Maryland is one of the finest small privately-formed art collections open to the public in the United States. ... Nickname: Monument City, Charm City, Mob Town[1][2], B-more Motto: The Greatest City in America,[3] Get in on it. ... It has been suggested that Toxic mold be merged into this article or section. ...

A team of imaging scientists from the Rochester Institute of Technology and Johns Hopkins University has used computer processing of digital images from various spectral bands, including ultraviolet and visible light, to reveal more of Archimedes' text. Dr. Reviel Netz [2] of Stanford University has been trying to fill in gaps in Heiberg's account with these images. Rochester Institute of Technology (RIT) is a private higher education institute, emphasizing career preparation, located in the township of Henrietta, outside of Rochester, New York. ... The Leland Stanford Junior University, commonly known as Stanford University (or simply Stanford), is a private university located approximately 37 miles (60 kilometers) southeast of San Francisco and approximately 20 miles northwest of San José in an unincorporated area of Santa Clara County. ...

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 rendered the underlying text forever illegible. Then, in May 2005, highly-focused X-rays produced at the Stanford Linear Accelerator Center in Menlo Park, California were used to begin deciphering the parts of the 174-page text that have 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." [3] In the NATO phonetic alphabet, X-ray represents the letter X. An X-ray picture (radiograph) taken by Röntgen An X-ray is a form of electromagnetic radiation with a wavelength approximately in the range of 5 pm to 10 nanometers (corresponding to frequencies in the range 30 PHz... The Stanford Linear Accelerator Center (SLAC) is a United States Department of Energy National Laboratory operated by Stanford University under the programmatic direction of the U.S. Department of Energy Office of Science. ... Fluorescence induced by exposure to ultraviolet light in vials containing various sized Cadmium selenide (CdSe) quantum dots. ... Synchrotron radiation emerging from a beam port. ...

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. This was likely written by Alexander of Aphrodisias. Doctor William Noel, the curator of manuscripts at the Walters Art Museum, 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 4th century BC, which has also been found within the palimpsest. [4] Aristotle (Greek: Aristotélēs) (384 BC – March 7, 322 BC) was a Greek philosopher, a student of Plato and teacher of Alexander the Great. ... Alexander of Aphrodisias, a pupil of Aristocles of Messene, was the most celebrated of the Greek commentators on the writings of Aristotle. ... The Walters Art Museum in Baltimore, Maryland is one of the finest small privately-formed art collections open to the public in the United States. ... Hypereides (c. ... For other uses, see Athens (disambiguation). ... (2nd millennium BC - 1st millennium BC - 1st millennium) The 4th century BC started on January 1, 400 BC and ended on December 31, 301 BC. // Overview Events Bust of Alexander the Great in the British Museum. ...

References

• Reviel Netz, The Archimedes Codex, Weidenfeld & Nicolson, 2007[5]

External links

• The Archimedes Palimpsest Project Web Page
• The Archimedes Palimpsest web pages at the Walters Art Museum
• The Nova Program outlined
• The Nova Program teacher's version
• Did Isaac Barrow read it?
• May 2005 Stanford Report: Heather Rock Woods, "Archimedes manuscript yields secrets under X-ray gaze" May 19, 2005
• The Greek Orthodox Patriarchate of Jerusalem v. Christies’s Inc., 1999 U.S. Dist. LEXIS 13257 (S.D. N.Y. 1999)