The Archimedes Palimpsest is a parchment codex palimpsest , originally a Byzantine Greek copy of a compilation of Archimedes and other authors. It contains two works of Archimedes that were thought to have been lost (the Ostomachion and the Method of Mechanical Theorems ) and the only surviving original Greek edition of his work On Floating Bodies . The first version of the compilation is believed to have been produced by Isidore of Miletus , the architect of the geometrically complex Hagia Sophia cathedral in Constantinople , sometime around AD 530. The copy found in the palimpsest was created from this original, also in Constantinople, during the Macedonian Renaissance (c. AD 950), a time when mathematics in the capital was being revived by the former Greek Orthodox bishop of Thessaloniki Leo the Geometer , a cousin of the Patriarch .
73-501: Following the sack of Constantinople by Western crusaders in 1204, the manuscript was taken to an isolated Greek monastery in Palestine , possibly to protect it from occupying crusaders, who often equated Greek script with heresy against their Latin church and either burned or looted many such texts (including two additional copies of Archimedes writing , at least). The complex manuscript was not appreciated at this remote monastery and
146-674: 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. The manuscript was still in the Greek Orthodox Patriarchate of Jerusalem 's library (the Metochion of the Holy Sepulchre) in Constantinople in 1920. Shortly thereafter, during a turbulent period for
219-599: A public auction, risking an ownership dispute. The ownership of the palimpsest was immediately contested in federal court in New York in the case of the Greek Orthodox Patriarchate of Jerusalem v. Christie's , Inc . The Greek church contended that the palimpsest had been stolen from its library in Constantinople in the 1920s, during a period of extreme persecution. Judge Kimba Wood decided in favor of Christie's Auction House on laches grounds, and
292-474: 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' Ostomachion immediate. Rather, the first proposition sets up a board consisting of two squares side by side (as in Tangram ). A reconciliation of
365-464: Is estimated 2,000 were killed. The Crusaders, with poor leadership, also sacked churches , monasteries and convents . The altars of these churches were smashed and torn to pieces for their gold and marble by the warriors. The Venetians stole religious relics and works of art, which they later took to Venice. It was said that the total amount looted from Constantinople was about 900,000 silver marks. The Venetians received 150,000 silver marks that
438-540: 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
511-562: Is one of the men seen in Peder Severin Krøyer 's monumental 1897 group portrait painting A Meeting in the Royal Danish Academy of Sciences and Letters . He was also painted by Harald Slott-Møller (c. 1900, Frederiksborg Museum ) and by Niels Vinding Dorph (1907, Frederiksborg Museum). He is also seen in drawings by Alfred Schmidt (Frederiksborg Museum) and Aage Roose (1924, Frederiksborg Museum). Heiberg
584-631: Is tragic that the assailants, who set out to secure free access for Christians to the Holy Land, turned against their brothers in the faith. The fact that they were Latin Christians fills Catholics with deep regret." In 2004, while Bartholomew I , Patriarch of Constantinople , was visiting the Vatican , John Paul II asked, "How can we not share, at a distance of eight centuries, the pain and disgust?" This has been regarded by some as an apology to
657-708: The Catholic and Orthodox Churches were wounded for many centuries afterwards. The Massacre of the Latins ( Italian : Massacro dei Latini ; Greek : Σφαγή τῶν Λατίνων ), a massacre of the Roman Catholic or "Latin" inhabitants of Constantinople by the usurper Andronikos Komnenos and his supporters in May 1182, affected political relations between Western Europe and the Byzantine Empire and led to
730-529: The Crusader sack of Byzantine Constantinople in 1204. There, in 1229, the Archimedes codex was unbound, scraped and washed, along with at least six other partial parchment manuscripts, including one with works of Hypereides . Their leaves were folded in half, rebound and reused for a Christian liturgical text of 177 later numbered leaves, of which 174 are extant (each older folded leaf became two leaves of
803-545: The Empire of Nicaea , which would eventually recapture Constantinople in 1261 and proclaim the reinstatement of the Empire. However, the restored Empire never managed to reclaim all its former territory or attain its earlier economic strength, and it gradually succumbed to the rising Ottoman Empire over the following two centuries. The Byzantine Empire was left poorer, smaller, and ultimately less able to defend itself against
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#1732757620582876-810: The Empire of Trebizond and the Despotate of Epirus . The sack weakened the Byzantine Empire, which allowed neighbouring groups such as the Sultanate of Rum , and later the Ottoman Turks , to gain influence (see the Byzantine–Ottoman wars ). Eight hundred years after the Fourth Crusade , Pope John Paul II twice expressed sorrow for how the events transpired. In 2001, he wrote to Christodoulos , Archbishop of Athens , saying, "It
949-602: The Hippodrome were sent back to adorn the façade of St Mark's Basilica in Venice, where they remain. As well as being seized, works of considerable artistic value were destroyed for their material value. One of the most precious works to suffer such a fate was a large bronze statue of Hercules , created by the legendary Lysippos , court sculptor of Alexander the Great . Like so many other considerable artworks made of bronze,
1022-744: The Kingdom of Thessalonica , a vassal state of the new Latin Empire. The Venetians also founded the Duchy of the Archipelago in the Aegean Sea. Most of the Byzantine aristocracy fled the city. Amongst the ordinary people of the former empire there was no sympathy for the Byzantine elite, who were seen as having ruled the empire with increasing incompetence. The contemporary Byzantine historian and eyewitness Nicetas Choniates closed his account of
1095-501: 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
1168-568: The Rochester Institute of Technology , Dr. William A. Christens-Barry from Equipoise Imaging, and Dr. Keith Knox (then with Boeing LTS, now retired from the 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 that of Archimedes. After imaging and digitally processing
1241-572: The Seljuk and Ottoman conquests that followed. The actions of the Crusaders, therefore, accelerated the collapse of Christendom in the east, and in the long run helped facilitate the later Ottoman conquests of southeastern Europe. The sack of Constantinople is considered a turning point in medieval history . Reports of Crusader looting and brutality horrified the Orthodox world; relations between
1314-759: The Stanford Linear Accelerator Center in Menlo Park, California, were used by Drs. Uwe Bergmann 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
1387-422: 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 involving volume , Archimedes used a form of Cavalieri's principle , that two volume with equal-area cross-sections are equal;
1460-450: 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
1533-563: The sack of Thessalonica by Normans. Although regular trade agreements were soon resumed between Byzantine and Latin States, some Westerners sought some form of revenge. Following the siege of Constantinople in 1203 , on 1 August 1203 the pro-Crusader Alexios Angelos was crowned Emperor Alexios IV of the Byzantine Empire. He attempted to pacify the city, but riots between anti-Crusader Greeks and pro-Crusader Latins broke out later that month and lasted until November, during which time most of
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#17327576205821606-550: The 1840s, and, intrigued by the Greek mathematics visible on the palimpsest he found in a Greek Orthodox library, removed a leaf of it (which is now in the Cambridge University Library). In 1899, the Greek scholar Papadopoulos-Kerameus produced a catalog of the library's manuscripts and included a transcription of several lines of the partially visible underlying text. Upon seeing these lines Johan Heiberg ,
1679-546: The Crusaders for a withdrawal from Byzantine territory without payment, but they refused in order to avenge Alexios IV and receive the money that was promised. In March 1204, the Crusader and Venetian leadership decided on the outright conquest of Constantinople in order to settle debts, and drew up a formal agreement to divide the Byzantine Empire between them. By the end of March, the combined Crusader armies were besieging Constantinople as Emperor Alexios V began to strengthen
1752-601: The Greek Orthodox Church for the slaughter perpetrated by the warriors of the Fourth Crusade. In April 2004, in a speech on the 800th anniversary of the capture of the city, Ecumenical Patriarch Bartholomew I formally accepted the apology. "The spirit of reconciliation is stronger than hatred," he said during a liturgy attended by Roman Catholic Archbishop Philippe Barbarin of Lyon, France. "We receive with gratitude and respect your cordial gesture for
1825-780: The Greek community in Turkey that saw a Turkish victory in the Greco-Turkish War (1919–22) along with the Greek genocide and the forced population exchange between Greece and Turkey , the palimpsest disappeared from the Greek church's library in Istanbul. Sometime between 1923 and 1930, the palimpsest was acquired by Marie Louis Sirieix, a "businessman and traveler to the Orient who lived in Paris." Though Sirieix claimed to have bought
1898-454: The Holy Land (1095–1291) Later Crusades (1291–1717) Northern (1147–1410) Against Christians (1209–1588) Popular (1096–1320) The sack of Constantinople occurred in April 1204 and marked the culmination of the Fourth Crusade . Crusaders sacked and destroyed most of Constantinople , the capital of the Byzantine Empire . After the capture of
1971-465: The Holy Sepulchre at Istanbul in 1906, and realized that it contained mathematical works by Archimedes that were unknown to scholars at the time. Heiberg was permitted by the Greek Orthodox Church to take photographs of the palimpsest's pages, and from these he produced transcriptions, published between 1910 and 1915 in a complete works of Archimedes. Heiberg's examination of the manuscript
2044-532: 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
2117-541: The Suter board with this Codex board was published by Richard Dixon Oldham , FRS, in Nature in March, 1926, sparking an Ostomachion 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
2190-557: The assault forces were driven back when the troops that landed came under heavy archery fire in open ground between Constantinople's fortifications and the shore. On 12 April 1204 weather conditions finally favoured the Crusaders as the weather cleared and a second assault on the city was ordered. A strong north wind aided the Venetian ships near the Golden Horn to come close to the city wall, which enabled attackers to seize some of
2263-460: The book in order to increase its sales value, further damaging the text. These forged gold leaf portraits nearly obliterated the text underneath them, and x-ray fluorescence imaging at the Stanford Linear Accelerator Center would later be required to reveal it. Sirieix died in 1956, and, in 1970, his daughter began attempting quietly to sell the valuable manuscript. Unable to sell it privately, in 1998, she finally turned to Christie's to sell it in
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2336-467: The businessman's daughter risked a public auction in New York contested by the Greek church; the U.S. court ruled for the auction, and the manuscript was purchased by an anonymous buyer (rumored to be Jeff Bezos ). The texts under the forged pictures, as well as previously unreadable texts, were revealed by analyzing images produced by ultraviolet , infrared , visible and raking light , and X-ray . All images and transcriptions are now freely available on
2409-593: The city in the northwest and used it as a base to attack the rest of the city, but while attempting to defend themselves with a wall of fire they ended up burning down even more of the city. Emperor Alexios V fled from the city that night through the Polyandriou (Rhegium) Gate and escaped into the countryside to the west. The Crusaders looted , pillaged, and vandalized Constantinople for three days, during which many ancient and medieval Roman and Greek works were either seized or destroyed. The famous bronze horses from
2482-485: The city's defences while conducting more active operations outside the city. By the first week of April, the Crusaders had begun their siege from their encampment in the town of Galata across the Golden Horn from Constantinople. On 9 April 1204, the Crusader and Venetian forces began an assault on the Golden Horn fortifications by crossing the waterway to the northwest wall of the city, but, because of bad weather,
2555-713: The city, the Latin Empire (known to the Byzantines as the Frankokratia , or the Latin occupation ) was established and Baldwin of Flanders crowned as Emperor Baldwin I of Constantinople in Hagia Sophia . After the city's sacking, most of the Byzantine Empire's territories were divided up among the Crusaders. Byzantine aristocrats also established a number of small independent splinter states—one of them being
2628-423: 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
2701-549: The fall of the city with the following description of a column of aristocratic refugees, including the Patriarch, making their way to Selymbria : The peasants and common riff-raff jeered at those of us from Byzantium and were thick-headed enough to call our miserable poverty and nakedness equality...Many were only too happy to accept this outrage, saying "Blessed be the Lord that we have grown rich", and buying up for next to nothing
2774-495: 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 viewed plane figures as made out of infinitely many lines as in
2847-525: 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 Ostomachion , 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
2920-404: 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, a commentary on Aristotle 's Categories running to some 9 000 words. Most of this text was recovered in early 2009 by applying principal component analysis to
2993-465: The later method of indivisibles , and balanced each line, or 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 the figures are equal. Once he shows that each slice of one figure balances each slice of
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3066-532: The liturgical book). The palimpsest remained near Jerusalem through at least the 16th century at the isolated Greek Orthodox monastery of Mar Saba . At some point before 1840 the palimpsest was brought back by the Greek Orthodox Patriarchate of Jerusalem to its library (the Metochion of the Holy Sepulcher) in Constantinople. The Biblical scholar Constantin von Tischendorf visited Constantinople in
3139-525: The manuscript from a monk, who would not in any case have had the authority to sell it, Sirieix had no receipt or documentation for a sale of the valuable manuscript. Stored secretly for years by Sirieix in his cellar, the palimpsest suffered damage from water and mold. In addition, after its disappearance from the Greek Orthodox Patriarchate's library, a forger added copies of medieval evangelical portraits in gold leaf onto four pages in
3212-472: 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 one finds two sequences U and L, and U is 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
3285-526: 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. Sometime after 1938, a forger placed four Byzantine-style religious images in the manuscript in an effort to increase its sales value. It appeared that these had rendered the underlying text forever illegible. However, in May 2005, highly focused X-rays produced at
3358-444: 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
3431-459: 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. Sack of Constantinople In
3504-632: The palimpsest was bought for $ 2 million by an anonymous American buyer. The lawyer 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 . 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 while in Sirieix's cellar). This
3577-756: The palimpsest. It is from his speech Against Diondas , and was published in 2008 in the academic journal 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 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 Doug Emery of Emery IT. On October 29, 2008 (the tenth anniversary of
3650-433: The populace began to turn against him. On 25 January 1204, the death of co-Emperor Isaac II set off rioting in Constantinople in which the people deposed Alexios IV . He turned to the Crusaders for help, but was imprisoned by the imperial chamberlain, Alexios Doukas , who declared himself Emperor on 5 February before executing Alexios IV on 8 February by strangulation. Emperor Alexios V then attempted to negotiate with
3723-547: The preservation of digital data, Swiss scientists encoded text from the Archimedes Palimpsest into DNA. Thanks to its deciphering, some mathematicians suggest it is possible that Archimedes may have invented integration . Source: The palimpsest contains the only known copy of The Method of Mechanical Theorems . In his other works, Archimedes often proves the equality of two areas or volumes with Eudoxus ' method of exhaustion , an ancient Greek counterpart of
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#17327576205823796-469: The property that their fellow-countrymen were forced to offer for sale, for they had not yet had much to do with the beef-eating Latins and they did not know that they served a wine as pure and unmixed as unadulterated bile, nor that they would treat the Byzantines with utter contempt. Byzantine aristocratic refugees founded their own successor states , the most notable of these being the Empire of Nicaea under Theodore Laskaris (a relative of Alexius III),
3869-499: 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 , and processed images of the palimpsest in original page order were posted as a Google Book. In 2011, it was the subject of the Walters Art Museum exhibit "Lost and Found: The Secrets of Archimedes". In 2015, in an experiment into
3942-543: The same principle forms the basis of 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. But there are two essential differences between Archimedes' method and 19th-century methods: A problem solved exclusively in
4015-491: 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
4088-559: The statue was melted down for its content by the Crusaders for surplus profit. Despite their oaths and the threat of excommunication, the Crusaders systematically assaulted the city's holy sanctuaries, destroying or seizing all that was deemed remotely of value; little was spared, and the tombs of the emperors inside the Church of the Holy Apostles fell victim to such looting as well. Of the civilian population of Constantinople, it
4161-578: The then Byzantine Greek capital city of Constantinople. A copy of Isidorus' edition of Archimedes was made around AD 950 by an anonymous scribe, again in the Byzantine Empire, in a period during which the study of Archimedes flourished in Constantinople in a school founded by the mathematician, engineer, and former Greek Orthodox archbishop of Thessaloniki, Leo the Geometer , a cousin to the patriarch . This medieval Byzantine manuscript then traveled from Constantinople to Jerusalem , likely sometime after
4234-442: 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
4307-462: 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
4380-586: The towers along the wall. After a short battle approximately 70 Crusaders managed to enter the city. Some Crusaders were eventually able to knock holes in the walls large enough for a few knights at a time to crawl through; the Venetians were also successful at scaling the walls from the sea, although there was extremely bloody fighting with the Varangians . The Crusaders captured the Blachernae section of
4453-499: The tragic events of the Fourth Crusade. It is a fact that a crime was committed here in the city 800 years ago." Bartholomew said his acceptance came in the spirit of Pascha . "The spirit of reconciliation of the resurrection... incites us toward reconciliation of our churches." 41°01′00″N 28°58′37″E / 41.0167°N 28.9769°E / 41.0167; 28.9769 Johan Ludvig Heiberg (historian) Johan Ludvig Heiberg (27 November 1854 – 4 January 1928)
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#17327576205824526-723: The web at the Archimedes Digital Palimpsest under the Creative Commons License CC BY . Archimedes lived in the 3rd century BC and wrote his proofs as letters in Doric Greek addressed to contemporaries, including scholars at the Great Library of Alexandria . These letters were first compiled into a comprehensive text by Isidorus of Miletus , the architect of the Hagia Sophia patriarchal church, sometime around AD 530 in
4599-404: The works of Archimedes (1880 and 1912), Euclid (with Heinrich Menge) (1883–1916), Apollonius of Perga (1891–93), Serenus of Antinouplis (1896), Ptolemy (1898/1903), and Hero of Alexandria (1899). Many of his editions are still in use today. The Archimedes Palimpsest is a 10th-century parchment codex palimpsest. Heiberg inspected the vellum manuscript in the library of The Church of
4672-415: The world's authority on Archimedes, realized that the work was by Archimedes. When Heiberg studied the palimpsest in Constantinople in 1906, he confirmed that the palimpsest included works by Archimedes thought to have been lost. Heiberg was permitted by the Greek Orthodox Church to take careful photographs of the palimpsest's pages, and from these he produced transcriptions, published between 1910 and 1915, in
4745-440: 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. He also published an edition of Ptolemy's Almagest . Heiberg was born in Aalborg , the son of medical doctor Emil Theodor Heiberg (1820–93) and Johanne (Hanne) Henriette Jacoba Schmidt (1821–83). He
4818-469: 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. The target audiences for the digitisation are Greek scholars, math historians, people building applications, libraries, archives, and scientists interested in the production of the images. A team of imaging scientists including Dr. Roger L. Easton, Jr. from
4891-464: Was not elected as the new emperor, although the citizens seemed to consider him as such; the Venetians thought he had too many connections with the former empire because of his brother, Renier of Montferrat , who had been married to Maria Comnena , daughter and for a time heir-apparent of Manuel I. Instead they placed Baldwin of Flanders on the throne. He was crowned Emperor in the Hagia Sophia as Baldwin I of Constantinople. Boniface went on to found
4964-439: Was principal of Borgerdyd School in Østerbro . Heiberg was Professor of Classical Philology at the University of Copenhagen from 1896 until 1924 and Professor of Archeology from 1896 until 1911. He became a member of the Royal Danish Academy of Sciences and Letters in 1893 and served as its editor in 1902–13. He was president of Rask-Ørstedfondet from 1919 until his death. Among his more than 200 publications were translations of
5037-562: Was related to 19th-century Danish poet Johan Ludvig Heiberg (1791–1860). His sister, Johanne Louise Heiberg (1860–1934), married biochemist Max Henius (1859–1935). Heiberg matriculated from Aalborg Cathedral School in 1871. He acquired a degree in classical philology from the University of Copenhagen in 1876 and spent the next few years teaching. He acquired a doctorate degree with the dissertation Quæstiones Archimedeæ in 1879. From 1884 to 1896, alongside first Søren Georg Møller (1834–1890) and then Søren Ludvig Tuxen (1850–1919), he
5110-416: Was soon overwritten (1229) with a religious text. In 1899, nine hundred years after it was written, the manuscript was still in the possession of the Greek church, and back in Istanbul, where it was catalogued by the Greek scholar Papadopoulos-Kerameus , attracting the attention of Johan Heiberg . Heiberg visited the church library and was allowed to make detailed photographs in 1906. Most of the original text
5183-419: Was still visible, and Heiberg published it in 1915. In 1922, the manuscript went missing in the midst of the evacuation of the Greek Orthodox library in Istanbul, during a tumultuous period following World War I . A Western businessman concealed the book for over 70 years, and at some point forged pictures were painted on top of some of the text to increase resale value. Unable to sell the book privately, in 1998,
5256-410: Was their due and the Crusaders received 50,000 silver marks. A further 100,000 silver marks were divided evenly between the Crusaders and Venetians. The remaining 500,000 silver marks were secretly kept back by many Crusader knights. According to a prearranged treaty the empire was apportioned between Venice and the crusade's leaders, and the Latin Empire of Constantinople was established. Boniface
5329-581: Was with the naked eye only, while modern analysis of the texts has employed x-ray and ultraviolet light . The Archimedes Palimpsest is currently stored at the Walters Art Museum in Baltimore , Maryland . On 6 April 1879, he was married to Cathrine Asmussen (7 October 1856 - 25 August 1929), daughter of first lieutenant and later captain Michael Overgaard Asmussen (1827–92) and Laura Nicoline Margrethe Johnsen (1830–92). Heiberg
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