1.
Pushkin State Museum of Fine Arts
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The Pushkin State Museum of Fine Arts is the largest museum of European art in Moscow, located in Volkhonka street, just opposite the Cathedral of Christ the Saviour. The International musical festival Svyatoslav Richters December nights has been held in the Pushkin museum since 1981. The museums current name is misleading, in that it has no direct associations with the famous Russian poet Alexander Pushkin. The facility was founded by professor Ivan Tsvetaev, Tsvetaev persuaded the millionaire and philanthropist Yuriy Nechaev-Maltsov and the fashionable architect Roman Klein of the urgent need to give Moscow a fine arts museum. The Pushkin State Museum of Fine Arts building was designed by Roman Klein and Vladimir Shukhov, construction work began in 1898 and continued till 1912. Ivan Rerberg headed structural engineering effort on the site for 12 years. In 2008, President Dmitri A. Medvedev announced plans for a $177 million restoration, in 2014, Russian architect Yuri Grigoryan, and his firm Project Meganom, were chosen to take over the project. Tsvetaevs dream was realised in May 1912, when the museum opened its doors to the public, the museum was originally named after Alexander III, although the government provided only 200,000 rubles toward its construction, in comparison with over 2 million from Nechaev-Maltsev. Its first exhibits were copies of ancient statuary, thought indispensable for the education of art students, the only genuinely ancient items - Moscow Mathematical Papyrus and Story of Wenamun - had been contributed by Vladimir Golenishchev three years earlier. After the Russian capital was moved to Moscow in 1918, the Soviet government decided to transfer thousands of works from St Petersburgs Hermitage Museum to the new capital, the entire collection of Western art from the Museum Roumjantsev was added too. These paintings formed a nucleus of the Pushkin museums collections of Western art, but the most important paintings were added later from the State Museum of New Western Art. These comprised Impressionist and Post-Impressionist artwork, including top works by Van Gogh, Gauguin, Picasso, Dufrénoy, Derain, among them, Van Goghs La Vigne Rouge, apparently the only painting sold during the artists lifetime. In 1937, Pushkins name was appended to the museum, because the Soviet Union marked the centenary of the death that year. After World War II the evacuated Dresden Gallery had been stored in Moscow for 10 years, the Pushkin Museum has a numismatic collection which is unpublished. It includes archaeological material from Central Asia, such as a hoard of Kushano-Sasanian coins acquired in 2002 William Craft Brumfield
Pushkin State Museum of Fine Arts
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Pushkin Museum of Fine Arts.
Pushkin State Museum of Fine Arts
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André Derain, 1905, Le séchage des voiles (The Drying Sails), oil on canvas, 82 x 101 cm. Exhibited at the 1905 Salon d'Automne
Pushkin State Museum of Fine Arts
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Eberswalde Hoard
Pushkin State Museum of Fine Arts
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Priam's Treasure
2.
Thirteenth dynasty of Egypt
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The Thirteenth Dynasty of ancient Egypt is often combined with Dynasties XI, XII and XIV under the group title Middle Kingdom. Some writers separate it from these dynasties and join it to Dynasties XIV through XVII as part of the Second Intermediate Period, Dynasty XIII lasted from approximately 1803 BC until approximately 1649 BC, i. e. for 154 years. The 13th dynasty was a continuation of the preceding 12th dynasty. As direct heirs to the kings of the 12th dynasty, pharaohs of the 13th dynasty reigned from Memphis over Middle and Upper Egypt, all the way to the second cataract to the south. The power of the 13th dynasty waned progressively over its 150 years of existence and it came to an end with the conquest of Memphis by the Hyksos rulers of the 15th dynasty. In later texts, this dynasty is described as an era of chaos. Unfortunately, the chronology of this dynasty is difficult to determine as there are few monuments dating from the period. Many of the names are only known from odd fragmentary inscriptions or from scarabs. The names and order in the table are based on Dodson and Hilton, following these kings, the remaining rulers of the 13th Dynasty are only attested by finds from Upper Egypt. This may indicate the abandonment of the old capital Itjtawy in favor of Thebes, daphna Ben Tor believes that this event was triggered by the invasion of the eastern Delta and the Memphite region by Canaanite rulers. For some authors, this marks the end of the Middle Kingdom and this analysis is rejected by Ryholt and Baker however, who note that the stele of Seheqenre Sankhptahi, reigning toward the end of the dynasty, strongly suggests that he reigned over Memphis. Unfortunately, the stele is of unknown provenance and this is now the dominant hypothesis in Egyptology and Sobekhotep Sekhemre Khutawy is referred to as Sobekhotep I in this article. Ryholt thus credits Sekhemre Khutawy Sobkhotep I with a reign of 3 to 4 years c.1800 BC, Dodson and Hilton similarly believe that Sekhemre Khutawy Sobekhotep predated Khaankhre Sobekhotep. After allowing discipline at the forts to deteriorate, the government eventually withdrew its garrisons and, not long afterward. In the north, Lower Egypt was overrun by the Hyksos, an independent line of kings created Dynasty XIV that arose in the western Delta during later Dynasty XIII. Their regime, called Dynasty XV, was claimed to have replaced Dynasties XIII, however, recent archaeological finds at Edfu could indicate that the Hyksos 15th dynasty was already in existence at least by the mid-13th dynasty reign of king Sobekhotep IV. In a recently published paper in Egypt and the Levant, Nadine Moeller, Gregory Marouard, the preserved contexts of these seals shows that Sobekhotep IV and Khyan were most likely contemporaries of one another. Therefore, Manethos statement that the Hyksos 15th dynasty violently replaced the 13th dynasty could be a piece of later Egyptian propaganda, thus the seals of Sobekhotep IV might not indicate that he was a contemporary of Khyan
Thirteenth dynasty of Egypt
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Statue of the royal sealer and high steward Gebu, 13th dynasty, c. 1700 BC from the temple of Amun in Karnak.
3.
Second Intermediate Period of Egypt
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The Second Intermediate Period marks a period when Ancient Egypt fell into disarray for a second time, between the end of the Middle Kingdom and the start of the New Kingdom. It is best known as the period when the Hyksos made their appearance in Egypt, the Twelfth Dynasty of Egypt came to an end at the end of the 19th century BC with the death of Queen Sobekneferu. Apparently she had no heirs, causing the twelfth dynasty to come to an end, and, with it. Retaining the seat of the dynasty, the thirteenth dynasty ruled from Itjtawy near Memphis and Lisht. The Thirteenth Dynasty is notable for the accession of the first formally recognised Semitic-speaking king, the Fifteenth Dynasty dates approximately from 1650 to 1550 BC. Known rulers of the Fifteenth Dynasty are as follows, Salitis Sakir-Har Khyan Apophis, 1550–1540 BC The Fifteenth Dynasty of Egypt was the first Hyksos dynasty, ruled from Avaris, without control of the entire land. The Hyksos preferred to stay in northern Egypt since they infiltrated from the north-east, the names and order of kings is uncertain. The Turin King list indicates that there were six Hyksos kings, the surviving traces on the X figure appears to give the figure 8 which suggests that the summation should be read as 6 kings ruling 108 years. Some scholars argue there were two Apophis kings named Apepi I and Apepi II, but this is due to the fact there are two known prenomens for this king, Awoserre and Aqenenre. However, the Danish Egyptologist Kim Ryholt maintains in his study of the Second Intermediate Period that these prenomens all refer to one man, Apepi and this is also supported by the fact that this king employed a third prenomen during his reign, Nebkhepeshre. Apepi likely employed several different prenomens throughout various periods of his reign and this scenario is not unprecedented, as later kings, including the famous Ramesses II and Seti II, are known to have used two different prenomens in their own reigns. The Sixteenth Dynasty ruled the Theban region in Upper Egypt for 70 years, of the two chief versions of Manethos Aegyptiaca, Dynasty XVI is described by the more reliable Africanus as shepherd kings, but by Eusebius as Theban. For this reason other scholars do not follow Ryholt and see only insufficient evidence for the interpretation of the Sixteenth Dynasty as Theban, the continuing war against Dynasty XV dominated the short-lived 16th dynasty. The armies of the 15th dynasty, winning town after town from their enemies, continually encroached on the 16th dynasty territory, eventually threatening. Famine, which had plagued Upper Egypt during the late 13th dynasty, from Ryholts reconstruction of the Turin canon,15 kings of the dynasty can now be named, five of whom appear in contemporary sources. While most likely based in Thebes itself, some may have been local rulers from other important Upper Egyptian towns, including Abydos, El Kab. By the reign of Nebiriau I, the controlled by the 16th dynasty extended at least as far north as Hu. Not listed in the Turin canon is Wepwawetemsaf, who left a stele at Abydos and was likely a local kinglet of the Abydos Dynasty, Ryholt gives the list of kings of the 16th dynasty as shown in the table below
Second Intermediate Period of Egypt
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Thebes (Luxor Temple pictured) was the capital of many of the Dynasty XVI pharaohs.
4.
Thebes, Egypt
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Thebes, known to the ancient Egyptians as Waset, was an ancient Egyptian city located east of the Nile about 800 kilometers south of the Mediterranean. Its ruins lie within the modern Egyptian city of Luxor, Thebes was the main city of the fourth Upper Egyptian nome. It was close to Nubia and the desert, with their valuable mineral resources. It was a center and the wealthiest city of ancient Egypt at its heyday. The Ancient Egyptians originally knew Thebes as Wose or Wase A was was the scepter of the pharaohs, a staff with an animals head. Thebes is the Latinized form of the Greek Thebai, the form of the Demotic Egyptian Ta-pe. This was the name not for the city itself but for the Karnak temple complex on the northern east bank of the city. As early as Homers Iliad, the Greeks distinguished the Egyptian Thebes as Thebes of the Hundred Gates, as opposed to the Thebes of the Seven Gates in Boeotia, from the end of the New Kingdom, Thebes was known in Egyptian as Niwt-Imn, the City of Amun. Amun was the chief of the Theban Triad of gods whose other members were Mut and this name appears in the Bible as the Nōʼ ʼĀmôn of the Book of Nahum and probably also as the No mentioned in Ezekiel and Jeremiah. In the interpretatio graeca, Amun was seen as a form of Zeus, the name was therefore translated into Greek as Diospolis, the City of Zeus. To distinguish it from the other cities by this name. The Greek names came into use after the conquest of Egypt by Alexander the Great. Thebes was located along the banks of the Nile River in the part of Upper Egypt about 800 km from the Delta. It was built largely on the plains of the Nile Valley which follows a great bend of the Nile. As a natural consequence, the city was laid in a northeast-southwest axis parallel to the river channel. Thebes had an area of 93 km2 which included parts of the Theban Hills in the west that culminates at the sacred 420-meter al-Qurn, in the east lies the mountainous Eastern Desert with its wadis draining into the valley. Significant of these wadis is Wadi Hammamat near Thebes and it was used as an overland trade route going to the Red Sea coast. In the fourth Upper Egyptian nome, Thebes was found to have neighboring towns such as Per-Hathor, Madu, Djerty, Iuny, Sumenu, according to George Modelski, Thebes had about 40,000 inhabitants in 2000 BC
Thebes, Egypt
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Egypt - Temple of Seti, east entrance, Thebes. Brooklyn Museum Archives, Goodyear Archival Collection
Thebes, Egypt
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Luxor Temple
Thebes, Egypt
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The Theban Necropolis
5.
Hieratic
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Hieratic is a cursive writing system used in the provenance of the pharaohs in Egypt and Nubia. It developed alongside cursive hieroglyphs, from which it is separate yet intimately related and it was primarily written in ink with a reed brush on papyrus, allowing scribes to write quickly without resorting to the time-consuming hieroglyphs. In the 2nd century AD, the term hieratic was first used by Saint Clement of Alexandria. It derives from the Greek phrase γράμματα ἱερατικά, as at time, hieratic was used only for religious texts, as had been the case for the previous eight. Hieratic can also be an adjective meaning f or associated with sacred persons or offices, in the Proto-Dynastic Period of Egypt, hieratic first appeared and developed alongside the more formal hieroglyphic script. It is an error to view hieratic as a derivative of hieroglyphic writing, indeed, the earliest texts from Egypt are produced with ink and brush, with no indication their signs are descendants of hieroglyphs. True monumental hieroglyphs carved in stone did not appear until the 1st Dynasty, the two writing systems, therefore, are related, parallel developments, rather than a single linear one. Hieratic was used throughout the period and into the Graeco-Roman Period. Around 660 BC, the Demotic script replaced hieratic in most secular writing, through most of its long history, hieratic was used for writing administrative documents, accounts, legal texts, and letters, as well as mathematical, medical, literary, and religious texts. During the Græco-Roman period, when Demotic had become the chief administrative script, in general, hieratic was much more important than hieroglyphs throughout Egypts history, being the script used in daily life. It was also the system first taught to students, knowledge of hieroglyphs being limited to a small minority who were given additional training. In fact, it is possible to detect errors in hieroglyphic texts that came about due to a misunderstanding of an original hieratic text. Most often, hieratic script was written in ink with a brush on papyrus, wood. Thousands of limestone ostraca have been found at the site of Deir al-Madinah, besides papyrus, stone, ceramic shards, and wood, there are hieratic texts on leather rolls, though few have survived. There are also hieratic texts written on cloth, especially on linen used in mummification, there are some hieratic texts inscribed on stone, a variety known as lapidary hieratic, these are particularly common on stelae from the 22nd Dynasty. During the late 6th Dynasty, hieratic was sometimes incised into mud tablets with a stylus, similar to cuneiform. About five hundred of these tablets have been discovered in the palace at Ayn Asil. At the time the tablets were made, Dakhla was located far from centers of papyrus production and these tablets record inventories, name lists, accounts, and approximately fifty letters
Hieratic
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One of four official letters to vizier Khay copied onto fragments of limestone (an ostracon).
Hieratic
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Hieratic
Hieratic
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Exercise tablet with hieratic excerpt from The Instructions of Amenemhat. Dynasty XVIII, reign of Amenhotep I, c. 1514–1493 BC. Text reads: "Be on your guard against all who are subordinate to you... Trust no brother, know no friend, make no intimates."
6.
Egyptian mathematics
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Ancient Egyptian mathematics is the mathematics that was developed and used in Ancient Egypt c.3000 to c.300 BC. Written evidence of the use of mathematics dates back to at least 3000 BC with the ivory labels found in Tomb U-j at Abydos and these labels appear to have been used as tags for grave goods and some are inscribed with numbers. Further evidence of the use of the base 10 number system can be found on the Narmer Macehead which depicts offerings of 400,000 oxen,1,422,000 goats and 120,000 prisoners. The evidence of the use of mathematics in the Old Kingdom is scarce, the lines in the diagram are spaced at a distance of one cubit and show the use of that unit of measurement. The earliest true mathematical documents date to the 12th dynasty, the Rhind Mathematical Papyrus which dates to the Second Intermediate Period is said to be based on an older mathematical text from the 12th dynasty. The Moscow Mathematical Papyrus and Rhind Mathematical Papyrus are so-called mathematical problem texts and they consist of a collection of problems with solutions. These texts may have been written by a teacher or a student engaged in solving typical mathematics problems, an interesting feature of Ancient Egyptian mathematics is the use of unit fractions. Scribes used tables to help work with these fractions. The Egyptian Mathematical Leather Roll for instance is a table of unit fractions which are expressed as sums of unit fractions. The Rhind Mathematical Papyrus and some of the other texts contain 2 n tables and these tables allowed the scribes to rewrite any fraction of the form 1 n as a sum of unit fractions. During the New Kingdom mathematical problems are mentioned in the literary Papyrus Anastasi I, in the workers village of Deir el-Medina several ostraca have been found that record volumes of dirt removed while quarrying the tombs. Our understanding of ancient Egyptian mathematics is impeded by the paucity of available sources. The Reisner Papyrus dates to the early Twelfth dynasty of Egypt and was found in Nag el-Deir, the Rhind Mathematical Papyrus dates from the Second Intermediate Period, but its author, Ahmes, identifies it as a copy of a now lost Middle Kingdom papyrus. The RMP is the largest mathematical text, from the New Kingdom we have a handful of mathematical texts and inscription related to computations, The Papyrus Anastasi I is a literary text from the New Kingdom. It is written as a written by a scribe named Hori. A segment of the letter describes several mathematical problems, ostracon Senmut 153 is a text written in hieratic. Ostracon Turin 57170 is a written in hieratic. Ostraca from Deir el-Medina contain computations, ostracon IFAO1206 for instance shows the calculations of volumes, presumably related to the quarrying of a tomb
Egyptian mathematics
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Slab stela of Old Kingdom princess Neferetiabet (dated 2590–2565 BC) from her tomb at Giza, painting on limestone, now in the Louvre.
Egyptian mathematics
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Image of Problem 14 from the Moscow Mathematical Papyrus. The problem includes a diagram indicating the dimensions of the truncated pyramid.
7.
Egyptologist
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A practitioner of the discipline is an Egyptologist. In Europe, particularly on the Continent, Egyptology is primarily regarded as being a philological discipline, the first explorers were the ancient Egyptians themselves. Thutmose IV restored the Sphinx and had the dream that inspired his restoration carved on the famous Dream Stele, less than two centuries later, Prince Khaemweset, fourth son of Ramesses II, is famed for identifying and restoring historic buildings, tombs and temples including the pyramid. The Ptolemies were much interested in the work of the ancient Egyptians, the Romans too carried out restoration work in this most ancient of lands. A number of their accounts have survived and offer insights as to conditions in their time periods. Abdul Latif al-Baghdadi, a teacher at Cairos Al-Azhar University in the 13th century, similarly, the 15th-century Egyptian historian al-Maqrizi wrote detailed accounts of Egyptian antiquities. In the early 17th century, John Greaves measured the pyramids, having inspected the broken Obelisk of Domitian in Rome, then destined for the Earl of Arundels collection in London. In the late 18th century, with Napoleons scholars recording of Egyptian flora, fauna and history, the British captured Egypt from the French and gained the Rosetta Stone. Modern Egyptology is generally perceived as beginning about 1822, egyptologys modern history begins with the invasion of Egypt by Napoleon Bonaparte. The subsequent publication of Description de lÉgypte between 1809 and 1829 made numerous ancient Egyptian source materials available to Europeans for the first time, jean-François Champollion, Thomas Young and Ippolito Rosellini were some of the first Egyptologists of wide acclaim. The German Karl Richard Lepsius was a participant in the investigations of Egypt, mapping, excavating. Champollion announced his general decipherment of the system of Egyptian hieroglyphics for the first time, the Stones decipherment was a very important development of Egyptology. Egyptology became more professional via work of William Matthew Flinders Petrie, Petrie introduced techniques of field preservation, recording, and excavating. Howard Carters expedition brought much acclaim to the field of Egyptology, a tradition of collecting objets-orientales Egyptologists Electronic Forum, version 64. List shows Egyptology societies and Institutes Egyptology at DMOZ Egyptology Books, the University of Memphis Institute of Egyptian Art and Archaeology. Hawass, Zahi, Brock, Lyla Pinch, eds, Egyptology at the Dawn of the Twenty-First Century Proceedings of the Eighth International Congress of Egyptologists. Rare Books and Special Collections Digital Library Underwood & Underwood Egypt Stereoviews Collection, czech Institute of Egyptology, Faculty of Arts, Charles University in Prague
Egyptologist
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The Great Sphinx of Giza against Khafre's Pyramid at the Giza pyramid complex
Egyptologist
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Hieroglyphs and depictions transcribed by Ippolito Rosellini in 1832
Egyptologist
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A section of the Papyrus of Ani showing cursive hieroglyphs
8.
Vladimir Golenishchev
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Vladimir Semyonovich Golenishchev was one of the first and most accomplished Russian Egyptologists. Golenishchev, the son of a merchant, was educated at the Saint Petersburg University. In 1884–85 he organized and financed excavations in Wadi Hammamat, followed by the research at Tell el-Maskhuta in 1888–89 and he also published the so-called Hermitage papyri, including the Prophecy of Neferti, now stored in the Hermitage Museum. Having sold his collection to the Moscow Museum of Fine Arts in 1909, following the Russian Revolution of 1917, he never returned to Russia, residing in Nice and Cairo. In Egypt, he established and held the chair in Egyptology at the University of Cairo from 1924 to 1929 and he was also employed by the Egyptian Museum in Cairo, where he catalogued hieratic papyri. Golenishchev died in Nice aged 90 and his papers are held at the Pushkin Museum, at the Centre Wl. Golenischeff, Paris and also in the Griffith Institute, Oxford, a memorial to famous egyptologists by the Egyptian Museum since 2006 features a bust of Vladimir Golenishchev. Egyptian Collection of the Hermitage Museum Oscar Eduardovich Lemm Boris Turayev Centre Wl, golenischeff, Paris Bibliography of Vladimir Golenishchev
Vladimir Golenishchev
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Vladimir Golenishchev
9.
Palaeography
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Palaeography or paleography is the study of ancient and historical handwriting. The discipline is important for understanding, authenticating, and dating ancient texts, however, it cannot in general be used to pinpoint dates with high precision. Palaeography can be a skill for historians and philologists, as it tackles two main difficulties. First, since the style of an alphabet in each given language has evolved constantly. Second, scribes often used many abbreviations, usually so as to more quickly and sometimes to save space. Knowledge of individual letter-forms, ligatures, punctuation, and abbreviations enables the palaeographer to read, the palaeographer must know, first, the language of the text, and second, the historical usages of various styles of handwriting, common writing customs, and scribal or notarial abbreviations. Philological knowledge of the language, vocabulary, and grammar generally used at a time or place can help palaeographers identify ancient or more recent forgeries versus authentic documents. Knowledge of writing materials is essential to the study of handwriting. Palaeography can be used to provide information about the date at which a document was written, scholars also tend to oversimplify diachronic development, assuming models of simplicity rather than complexity. It spread from the Mediterranean coast to the borders of India, becoming popular and being adopted by many people. The Aramaic script was written in a form with a direction from right to left. One innovation in Aramaic is the matres lectionis system to indicate certain vowels, Early Phoenician-derived scripts did not have letters for vowels, and so most texts recorded just consonants. Most likely as a consequence of changes in North Semitic languages. The letter aleph was employed to write /ā/, he for /ō/, yod for /ī/, Aramaic writing and language supplanted Babylonian cuneiform and Akkadian language, even in their homeland in Mesopotamia. The wide diffusion of Aramaic letters led to its writing being used not only in monumental inscriptions, Aramaic papyri have been found in large numbers in Egypt, especially at Elephantine – among them are official and private documents of the Jewish military settlement in 5 BC. In the Aramaic papyri and potsherds, words are separated usually by a small gap, at the turn of the 3rd to 2nd centuries BC, the heretofore uniform Aramaic letters developed new forms, as a result of dialectal and political fragmentation in several subgroups. The most important of these is the so-called square Hebrew block script, followed by Palmyrene, Nabataean, Aramaic is usually divided into three main parts, Old Aramaic Middle Aramaic, and Modern Aramaic of the present day. Old Aramaic appeared in the 11th century BC as the language of the first Aramaean states
Palaeography
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William Shakespeare's will, written in secretary hand: a script difficult for modern readers to interpret
Palaeography
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Table showing the Mandaic alphabet (Abagada) with some of the mysteries represented by the letters
Palaeography
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Detail of the Berlin papyrus 9875 showing the 5th column of Timotheus' Persae, with a coronis symbol to mark the end.
Palaeography
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The Derveni Papyrus, a Greek Macedonian philosophical text dating around 340 BC, considered Europe's oldest manuscript
10.
Soviet Union
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The Soviet Union, officially the Union of Soviet Socialist Republics was a socialist state in Eurasia that existed from 1922 to 1991. It was nominally a union of national republics, but its government. The Soviet Union had its roots in the October Revolution of 1917 and this established the Russian Socialist Federative Soviet Republic and started the Russian Civil War between the revolutionary Reds and the counter-revolutionary Whites. In 1922, the communists were victorious, forming the Soviet Union with the unification of the Russian, Transcaucasian, Ukrainian, following Lenins death in 1924, a collective leadership and a brief power struggle, Joseph Stalin came to power in the mid-1920s. Stalin suppressed all opposition to his rule, committed the state ideology to Marxism–Leninism. As a result, the country underwent a period of rapid industrialization and collectivization which laid the foundation for its victory in World War II and postwar dominance of Eastern Europe. Shortly before World War II, Stalin signed the Molotov–Ribbentrop Pact agreeing to non-aggression with Nazi Germany, in June 1941, the Germans invaded the Soviet Union, opening the largest and bloodiest theater of war in history. Soviet war casualties accounted for the highest proportion of the conflict in the effort of acquiring the upper hand over Axis forces at battles such as Stalingrad. Soviet forces eventually captured Berlin in 1945, the territory overtaken by the Red Army became satellite states of the Eastern Bloc. The Cold War emerged by 1947 as the Soviet bloc confronted the Western states that united in the North Atlantic Treaty Organization in 1949. Following Stalins death in 1953, a period of political and economic liberalization, known as de-Stalinization and Khrushchevs Thaw, the country developed rapidly, as millions of peasants were moved into industrialized cities. The USSR took a lead in the Space Race with Sputnik 1, the first ever satellite, and Vostok 1. In the 1970s, there was a brief détente of relations with the United States, the war drained economic resources and was matched by an escalation of American military aid to Mujahideen fighters. In the mid-1980s, the last Soviet leader, Mikhail Gorbachev, sought to reform and liberalize the economy through his policies of glasnost. The goal was to preserve the Communist Party while reversing the economic stagnation, the Cold War ended during his tenure, and in 1989 Soviet satellite countries in Eastern Europe overthrew their respective communist regimes. This led to the rise of strong nationalist and separatist movements inside the USSR as well, in August 1991, a coup détat was attempted by Communist Party hardliners. It failed, with Russian President Boris Yeltsin playing a role in facing down the coup. On 25 December 1991, Gorbachev resigned and the twelve constituent republics emerged from the dissolution of the Soviet Union as independent post-Soviet states
Soviet Union
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Vladimir Lenin addressing a crowd with Trotsky, 1920
Soviet Union
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Flag
Soviet Union
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Stalin and Nikolai Yezhov, head of the NKVD. After Yezhov was executed, he was edited out of the image.
Soviet Union
11.
Oriental studies
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European study of the region formerly known as the Orient had primarily religious origins, which has remained an important motivation until recent times. Learning from Arabic medicine and philosophy, and the Greek translations from Arabic, was an important factor in the Middle Ages. Linguistic knowledge preceded a wider study of cultures and history, and as Europe began to encroach upon the region, political, from the late 18th century archaeology became a link from the discipline to a wide European public, as treasures brought back filled new European museums. In the last century, scholars from the region itself have participated on equal terms in the discipline, the classical world had initimate knowledge of their Ancient Persian neighbours, but very imprecise knowledge of most of the world further East, including the Seres. However, there was substantial direct Roman trade with India in the Imperial period, the rise of Islam and Muslim conquests in the 7th century established a sharp opposition, or even a sense of polarity, between medieval European Christendom and the medieval Islamic world. During the Middle Ages, Muslims and Jews were considered the enemies of Christendom. The earliest translation of the Quran into Latin was completed in 1143, although little use was made of it until it was printed in 1543, gerard of Cremona and others based themselves in Al-Andaluz to take advantage of the Arabic libraries and scholars there. Later, with the Christian Reconquista in full progress, such contacts became rarer in Spain, chairs of Hebrew, Arabic and Aramaic were briefly established at Oxford, and four other universities following the Council of Vienne. There was vague but increasing knowledge of the civilizations in China and India. From the Age of Exploration, European interest in mapping Asia, University Oriental studies became systematic during the Renaissance, with the linguistic and religious aspects initially continuing to dominate. There was also a political dimension, as translations for diplomatic purposes were needed, a landmark was the publication in Spain in 1514 of the first Polyglot Bible, containing the complete existing texts in Hebrew and Aramaic, in addition to Greek and Latin. At Cambridge University there has been a Regius Professor of Hebrew since 1540, Oxford followed for Hebrew in 1546. The University of Salamanca had Professors of Oriental Languages from at least the 1570s, Study of the Far East was pioneered by missionaries, especially Matteo Ricci and others in the Jesuit China missions, and missionary motives were to remain important, at least in linguistic studies. The end of the saw the beginnings in the great increase in study of the archaeology of the period. Egyptology led the way, and as many other ancient cultures, provided the linguists with new material for decipherment. Some of these occurred in the context of Franco–British rivalry for control of India. Liberal economists, such as James Mill, denigrated Eastern civilizations as static, karl Marx, himself of Jewish origin, characterized the Asiatic mode of production as unchanging, because of the economic narrowness of village economies and the States role in production. Oriental despotism was generally regarded in Europe as a factor in the relative failure of progress of Eastern societies
Oriental studies
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Ancient Assyrian antiquities in the British Museum. In the 19th century the placing of spectacular antiquities in the new museums brought unusual interest from the general public to Oriental studies.
Oriental studies
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Hayton of Corycus remitting his report on the Mongols, to Pope Clement V, in 1307.
Oriental studies
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Matteo Ricci (left) and Xu Guangqi (徐光啟) (right) in the Chinese edition of Euclid's Elements (幾何原本) published in 1607.
Oriental studies
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The old building of the Asiatic Society in Calcutta, founded by William Jones in 1784.
12.
Rhind Mathematical Papyrus
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The Rhind Mathematical Papyrus is one of the best known examples of Egyptian mathematics. It is named after Alexander Henry Rhind, a Scottish antiquarian and it dates to around 1550 BC. It is one of the two well-known Mathematical Papyri along with the Moscow Mathematical Papyrus, the Rhind Papyrus is larger than the Moscow Mathematical Papyrus, while the latter is older than the former. The Rhind Mathematical Papyrus dates to the Second Intermediate Period of Egypt and it was copied by the scribe Ahmes, from a now-lost text from the reign of king Amenemhat III. Written in the script, this Egyptian manuscript is 33 cm tall. The papyrus began to be transliterated and mathematically translated in the late 19th century, the mathematical translation aspect remains incomplete in several respects. The document is dated to Year 33 of the Hyksos king Apophis and also contains a separate later historical note on its verso likely dating from the period of his successor, Khamudi. In the opening paragraphs of the papyrus, Ahmes presents the papyrus as giving Accurate reckoning for inquiring into things, the scribe Ahmose writes this copy. Several books and articles about the Rhind Mathematical Papyrus have been published, a more recent overview of the Rhind Papyrus was published in 1987 by Robins and Shute. The first part of the Rhind papyrus consists of reference tables, the problems start out with simple fractional expressions, followed by completion problems and more involved linear equations. The first part of the papyrus is taken up by the 2/n table, the fractions 2/n for odd n ranging from 3 to 101 are expressed as sums of unit fractions. For example,2 /15 =1 /10 +1 /30. The decomposition of 2/n into unit fractions is never more than 4 terms long as in for example 2 /101 =1 /101 +1 /202 +1 /303 +1 /606. This table is followed by a smaller, tiny table of fractional expressions for the numbers 1 through 9 divided by 10. Problems 1-7, 7B and 8-40 are concerned with arithmetic and elementary algebra, problems 1–6 compute divisions of a certain number of loaves of bread by 10 men and record the outcome in unit fractions. Problems 7–20 show how to multiply the expressions 1 + 1/2 + 1/4 = 7/4 and 1 + 2/3 + 1/3 =2 by different fractions, problems 21–23 are problems in completion, which in modern notation are simply subtraction problems. Problems 24–34 are ‘’aha’’ problems, these are linear equations, problem 32 for instance corresponds to solving x + 1/3 x + 1/4 x =2 for x. Problems 35–38 involve divisions of the heqat, which is an ancient Egyptian unit of volume, problems 39 and 40 compute the division of loaves and use arithmetic progressions
Rhind Mathematical Papyrus
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A portion of the Rhind Papyrus
Rhind Mathematical Papyrus
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Building
13.
Frustum
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In geometry, a frustum is the portion of a solid that lies between one or two parallel planes cutting it. A right frustum is a truncation of a right pyramid. The term is used in computer graphics to describe the viewing frustum. It is formed by a pyramid, in particular, frustum culling is a method of hidden surface determination. In the aerospace industry, frustum is the term for the fairing between two stages of a multistage rocket, which is shaped like a truncated cone. Each plane section is a floor or base of the frustum and its axis if any, is that of the original cone or pyramid. A frustum is circular if it has circular bases, it is if the axis is perpendicular to both bases, and oblique otherwise. The height of a frustum is the distance between the planes of the two bases. Cones and pyramids can be viewed as degenerate cases of frusta, the pyramidal frusta are a subclass of the prismatoids. Two frusta joined at their bases make a bifrustum, the Egyptians knew the correct formula for obtaining the volume of a truncated square pyramid, but no proof of this equation is given in the Moscow papyrus. V = h 1 a h 12 − h 2 a h 223 = a 3 By factoring the difference of two cubes we get h1−h2 = h, the height of the frustum, and α/3. Distributing α and substituting from its definition, the Heronian mean of areas B1, the alternative formula is therefore V = h 3 Heron of Alexandria is noted for deriving this formula and with it encountering the imaginary number, the square root of negative one. In particular, the volume of a circular cone frustum is V = π h 3 where π is 3.14159265. and R1, R2 are the radii of the two bases. The volume of a frustum whose bases are n-sided regular polygons is V = n h 12 cot π n where a1. The surface area of a frustum whose bases are similar regular n-sided polygons is A = n 4 where a1. On the back of a United States one-dollar bill, a pyramidal frustum appears on the reverse of the Great Seal of the United States, certain ancient Native American mounds also form the frustum of a pyramid. The John Hancock Center in Chicago, Illinois is a frustum whose bases are rectangles, the Washington Monument is a narrow square-based pyramidal frustum topped by a small pyramid. The viewing frustum in 3D computer graphics is a photographic or video cameras usable field of view modeled as a pyramidal frustum
Frustum
14.
Cubit
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The cubit is an ancient unit based on the forearm length from the middle finger tip to the elbow bottom. Cubits of various lengths were employed in many parts of the world in antiquity, during the Middle Ages, the term is still used in hedge laying, the length of the forearm being frequently used to determine the interval between stakes placed within the hedge. The English word cubit comes from the Latin noun cubitus elbow, from the verb cubo, cubare, cubui, cubitum to lie down, the ancient Egyptian royal cubit is the earliest attested standard measure. Cubit rods were used for the measurement of length, a number of these rods have survived, two are known from the tomb of Maya, the treasurer of the 18th dynasty pharaoh Tutankhamun, in Saqqara, another was found in the tomb of Kha in Thebes. Fourteen such rods, including one double cubit rod, were described and compared by Lepsius in 1865. These cubit rods range from 523.5 to 529.2 mm in length, and are divided into seven palms, each palm is divided into four fingers and the fingers are further subdivided. Use of the royal cubit is also known from Old Kingdom architecture, in 1916, during the last years of the Ottoman Empire and in the middle of World War I, the German assyriologist Eckhard Unger found a copper-alloy bar while excavating at Nippur. The bar dates from c.2650 BC and Unger claimed it was used as a measurement standard and this irregularly formed and irregularly marked graduated rule supposedly defined the Sumerian cubit as about 518.6 mm. The Near Eastern or Biblical cubit is usually estimated as approximately 457.2 mm, in ancient Greek units of measurement, the standard forearm cubit measured approximately 0.46 m. The short forearm cubit, from the wrist to the elbow, in ancient Rome, according to Vitruvius, a cubit was equal to 1 1⁄2 Roman feet or 6 palm widths. Other measurements based on the length of the forearm include some lengths of ell, the Chinese chi, the Japanese shaku, the Indian hasta, the Thai sok, the Tamil, the Telugu, a cubit arm in heraldry may be dexter or sinister. It may be vested and may be shown in positions, most commonly erect. It is most often used erect as a crest, for example by the families of Poyntz of Iron Acton, Rolle of Stevenstone, the Encyclopaedia of Ancient Egyptian Architecture. The Cubit, A History and Measurement Commentary, Journal of Anthropology doi,10. 1155/2014/489757,2014 Media related to Cubit arms at Wikimedia Commons The dictionary definition of cubit at Wiktionary
Cubit
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Egyptian cubit rod in the Liverpool World Museum
Cubit
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Cubit rod of Maya, 1336-1327 BC (Eighteenth Dynasty)
Cubit
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Cubit rod from the Turin Museum.
Cubit
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The Nippur cubit-rod in the Archeological Museum of Istanbul, Turkey
15.
Egyptian hieroglyphs
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Egyptian hieroglyphs were the formal writing system used in Ancient Egypt. It combined logographic, syllabic and alphabetic elements, with a total of some 1,000 distinct characters, cursive hieroglyphs were used for religious literature on papyrus and wood. The later hieratic and demotic Egyptian scripts are derived from hieroglyphic writing, the writing system continued to be used throughout the Late Period, as well as the Persian and Ptolemaic periods. Late survivals of hieroglyphic use are found well into the Roman period, with the closing of pagan temples in the 5th century, knowledge of hieroglyphic writing was lost, and the script remained undeciphered throughout the medieval and early modern period. The decipherment of hieroglyphs would only be solved in the 1820s by Jean-François Champollion, the word hieroglyph comes from the Greek adjective ἱερογλυφικός, a compound of ἱερός and γλύφω, supposedly a calque of an Egyptian phrase mdw·w-nṯr gods words. The glyphs themselves were called τὰ ἱερογλυφικὰ γράμματα the sacred engraved letters, the word hieroglyph has become a noun in English, standing for an individual hieroglyphic character. As used in the sentence, the word hieroglyphic is an adjective. Hieroglyphs emerged from the artistic traditions of Egypt. For example, symbols on Gerzean pottery from c.4000 BC have been argued to resemble hieroglyphic writing, proto-hieroglyphic symbol systems develop in the second half of the 4th millennium BC, such as the clay labels of a Predynastic ruler called Scorpion I recovered at Abydos in 1998. The first full sentence written in hieroglyphs so far discovered was found on a seal found in the tomb of Seth-Peribsen at Umm el-Qaab. There are around 800 hieroglyphs dating back to the Old Kingdom, Middle Kingdom, by the Greco-Roman period, there are more than 5,000. However, given the lack of evidence, no definitive determination has been made as to the origin of hieroglyphics in ancient Egypt. Since the 1990s, and discoveries such as the Abydos glyphs, as writing developed and became more widespread among the Egyptian people, simplified glyph forms developed, resulting in the hieratic and demotic scripts. These variants were more suited than hieroglyphs for use on papyrus. Hieroglyphic writing was not, however, eclipsed, but existed alongside the other forms, especially in monumental, the Rosetta Stone contains three parallel scripts – hieroglyphic, demotic, and Greek. Hieroglyphs continued to be used under Persian rule, and after Alexander the Greats conquest of Egypt, during the ensuing Ptolemaic and Roman periods. It appears that the quality of comments from Greek and Roman writers about hieroglyphs came about, at least in part. Some believed that hieroglyphs may have functioned as a way to distinguish true Egyptians from some of the foreign conquerors, another reason may be the refusal to tackle a foreign culture on its own terms, which characterized Greco-Roman approaches to Egyptian culture generally
Egyptian hieroglyphs
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A section of the Papyrus of Ani showing cursive hieroglyphs.
Egyptian hieroglyphs
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Hieroglyphs on a funerary stela in Manchester Museum
Egyptian hieroglyphs
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The Rosetta Stone in the British Museum
Egyptian hieroglyphs
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Hieroglyphs typical of the Graeco-Roman period
16.
Sphere
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A sphere is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball. This distance r is the radius of the ball, and the point is the center of the mathematical ball. The longest straight line through the ball, connecting two points of the sphere, passes through the center and its length is twice the radius. While outside mathematics the terms sphere and ball are used interchangeably. The ball and the share the same radius, diameter. The surface area of a sphere is, A =4 π r 2, at any given radius r, the incremental volume equals the product of the surface area at radius r and the thickness of a shell, δ V ≈ A ⋅ δ r. The total volume is the summation of all volumes, V ≈ ∑ A ⋅ δ r. In the limit as δr approaches zero this equation becomes, V = ∫0 r A d r ′, substitute V,43 π r 3 = ∫0 r A d r ′. Differentiating both sides of equation with respect to r yields A as a function of r,4 π r 2 = A. Which is generally abbreviated as, A =4 π r 2, alternatively, the area element on the sphere is given in spherical coordinates by dA = r2 sin θ dθ dφ. In Cartesian coordinates, the element is d S = r r 2 − ∑ i ≠ k x i 2 ∏ i ≠ k d x i, ∀ k. For more generality, see area element, the total area can thus be obtained by integration, A = ∫02 π ∫0 π r 2 sin θ d θ d φ =4 π r 2. In three dimensions, the volume inside a sphere is derived to be V =43 π r 3 where r is the radius of the sphere, archimedes first derived this formula, which shows that the volume inside a sphere is 2/3 that of a circumscribed cylinder. In modern mathematics, this formula can be derived using integral calculus, at any given x, the incremental volume equals the product of the cross-sectional area of the disk at x and its thickness, δ V ≈ π y 2 ⋅ δ x. The total volume is the summation of all volumes, V ≈ ∑ π y 2 ⋅ δ x. In the limit as δx approaches zero this equation becomes, V = ∫ − r r π y 2 d x. At any given x, a right-angled triangle connects x, y and r to the origin, hence, applying the Pythagorean theorem yields, thus, substituting y with a function of x gives, V = ∫ − r r π d x. Which can now be evaluated as follows, V = π − r r = π − π =43 π r 3
Sphere
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Circumscribed cylinder to a sphere
Sphere
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A two-dimensional perspective projection of a sphere
Sphere
Sphere
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Deck of playing cards illustrating engineering instruments, England, 1702. King of spades: Spheres
17.
Volume
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Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance or shape occupies or contains. Volume is often quantified numerically using the SI derived unit, the cubic metre, three dimensional mathematical shapes are also assigned volumes. Volumes of some simple shapes, such as regular, straight-edged, volumes of a complicated shape can be calculated by integral calculus if a formula exists for the shapes boundary. Where a variance in shape and volume occurs, such as those that exist between different human beings, these can be calculated using techniques such as the Body Volume Index. One-dimensional figures and two-dimensional shapes are assigned zero volume in the three-dimensional space, the volume of a solid can be determined by fluid displacement. Displacement of liquid can also be used to determine the volume of a gas, the combined volume of two substances is usually greater than the volume of one of the substances. However, sometimes one substance dissolves in the other and the volume is not additive. In differential geometry, volume is expressed by means of the volume form, in thermodynamics, volume is a fundamental parameter, and is a conjugate variable to pressure. Any unit of length gives a unit of volume, the volume of a cube whose sides have the given length. For example, a cubic centimetre is the volume of a cube whose sides are one centimetre in length, in the International System of Units, the standard unit of volume is the cubic metre. The metric system also includes the litre as a unit of volume, thus 1 litre =3 =1000 cubic centimetres =0.001 cubic metres, so 1 cubic metre =1000 litres. Small amounts of liquid are often measured in millilitres, where 1 millilitre =0.001 litres =1 cubic centimetre. Capacity is defined by the Oxford English Dictionary as the applied to the content of a vessel, and to liquids, grain, or the like. Capacity is not identical in meaning to volume, though closely related, Units of capacity are the SI litre and its derived units, and Imperial units such as gill, pint, gallon, and others. Units of volume are the cubes of units of length, in SI the units of volume and capacity are closely related, one litre is exactly 1 cubic decimetre, the capacity of a cube with a 10 cm side. In other systems the conversion is not trivial, the capacity of a fuel tank is rarely stated in cubic feet, for example. The density of an object is defined as the ratio of the mass to the volume, the inverse of density is specific volume which is defined as volume divided by mass. Specific volume is an important in thermodynamics where the volume of a working fluid is often an important parameter of a system being studied
Volume
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A measuring cup can be used to measure volumes of liquids. This cup measures volume in units of cups, fluid ounces, and millilitres.
18.
Berlin Papyrus 6619
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The Berlin Papyrus 6619, simply called the Berlin Papyrus when the context makes it clear, is an ancient Egyptian papyrus document from the Middle Kingdom, second half of the 12th or 13th dynasty. The two readable fragments were published by Hans Schack-Schackenburg in 1900 and 1902, the papyrus is one of the primary sources of ancient Egyptian mathematics. The Berlin Papyrus contains two problems, the first stated as the area of a square of 100 is equal to that of two smaller squares, the side of one is ½ + ¼ the side of the other. The interest in the question may suggest some knowledge of the Pythagorean theorem, though the papyrus only shows a straightforward solution to a single second degree equation in one unknown. In modern terms, the simultaneous equations x2 + y2 =100 and x = y reduce to the equation in y,2 + y2 =100. Papyrology Timeline of mathematics Egyptian fraction Simultaneous equation examples from the Berlin papyrus Two algebra problems compared to RMP algebra Two suggested solutions
Berlin Papyrus 6619
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Berlin Papyrus 6619, as reproduced in 1900 by Schack-Schackenburg
19.
Boris Turaev
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Boris Alexandrovich Turayev was a Russian scholar who studied the Ancient Near East. He was admitted into the Russian Academy of Sciences in 1918, after graduating from the University of St Petersburg Turayev studied under Gaston Maspero and Adolf Erman and worked in museums of Berlin, Paris and London. Since 1896, he delivered lectures at the University of St Petersburg and he was an ordinary professor of this university since 1911. After the establishment of the Moscow Museum of Fine Arts, Turayev persuaded Vladimir Golenishchev to sell his collection of ancient Egyptian statuary, for a time he lived in the museum building, preparing the collection for exhibition. His own collection of Egyptian antiquities went to the State Hermitage, Boris Turayevs magnum opus, History of Ancient East, quite unprecedented in its scope, brought him recognition throughout Europe. It was the first comprehensive study that analyzed the whole history and he also wrote books about Egyptian literature and mythology. Complete Bibliography of Boris Turayev Turaevs History of the Ancient East online
Boris Turaev
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Boris Turayev.
20.
Great Soviet Encyclopedia
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The Great Soviet Encyclopedia is one of the largest Russian-language encyclopedias. Published by the Soviet state from 1926 to 1990, and again since 2002 by Russia, the GSE claimed to be the first Marxist-Leninist general-purpose encyclopedia. The idea of the Great Soviet Encyclopedia emerged in 1923 on the initiative of Otto Schmidt, also involved was Anatoly Lunacharsky, Commissar of Enlightenment, who had previously been involved with a proposal by Alexander Bogdanov and Maxim Gorky to produce a Workers Encyclopedia. The first edition of 65 volumes was published during 1926–1947, the editor being Otto Schmidt. The second edition of 50 volumes was published in 1950–1958, chief editors, Sergei Vavilov and Boris Vvedensky, the third edition of 1969–1978 contains 30 volumes. Volume 24 is in two books, one being a book about the USSR, all with about 21 million words. In the third edition, much attention was paid to the problems of natural sciences, physical and chemical sciences. From 1957 to 1990, the Yearbook of the Great Soviet Encyclopedia was released annually with up-to-date articles about the Soviet Union, the first online edition, an exact replica of text and graphics of the third edition, was published by Rubricon. com in 2000. With exhaustive completeness it must show the superiority of socialist culture over the culture of the capitalist world, operating on Marxist-Leninist theory, the encyclopedia should give a party criticism of contemporary bourgeois tendencies in various provinces of science and technics. The third edition of the GSE subsequently expanded on the role of education, Education is essential to preparing for life and it is the basic means by which people come to know and acquire culture, and it is the foundation of cultures development. A. Vvedensky stating their compliance with the 1949 decree of the Council of Ministers and they are working under a government directive that orders them to orient their encyclopedia as sharply as a political tract. The encyclopedia was planned to provide the intellectual underpinning for the Soviet world offensive in the duel for mens minds. The Soviet government ordered it as a propaganda weapon. And the government attaches such importance to its political role that its board of editors is chosen by and is only to the high Council of Ministers itself. The third edition was translated and published into English in 31 volumes between 1974 and 1983 by Macmillan Publishers, not all entries were translated into English, these are indicated in the index. Articles from the English edition are available online by TheFreeDictionary. com. The third edition was translated into Greek and published in 34 volumes between 1977 and 1983, all articles that were related to Greece or Greek history, culture and society were expanded and hundreds of new ones were written especially for the Greek edition. Thus the encyclopedia contains, for example, both the Russian entry on Greece as well as a larger one prepared by Greek contributors
Great Soviet Encyclopedia
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Большая советская энциклопедия
Great Soviet Encyclopedia
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Complete set of an English-language version of the Great Soviet Encyclopedia
21.
JSTOR
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JSTOR is a digital library founded in 1995. Originally containing digitized back issues of journals, it now also includes books and primary sources. It provides full-text searches of almost 2,000 journals, more than 8,000 institutions in more than 160 countries have access to JSTOR, most access is by subscription, but some older public domain content is freely available to anyone. William G. Bowen, president of Princeton University from 1972 to 1988, JSTOR originally was conceived as a solution to one of the problems faced by libraries, especially research and university libraries, due to the increasing number of academic journals in existence. Most libraries found it prohibitively expensive in terms of cost and space to maintain a collection of journals. By digitizing many journal titles, JSTOR allowed libraries to outsource the storage of journals with the confidence that they would remain available long-term, online access and full-text search ability improved access dramatically. Bowen initially considered using CD-ROMs for distribution, JSTOR was initiated in 1995 at seven different library sites, and originally encompassed ten economics and history journals. JSTOR access improved based on feedback from its sites. Special software was put in place to make pictures and graphs clear, with the success of this limited project, Bowen and Kevin Guthrie, then-president of JSTOR, wanted to expand the number of participating journals. They met with representatives of the Royal Society of London and an agreement was made to digitize the Philosophical Transactions of the Royal Society dating from its beginning in 1665, the work of adding these volumes to JSTOR was completed by December 2000. The Andrew W. Mellon Foundation funded JSTOR initially, until January 2009 JSTOR operated as an independent, self-sustaining nonprofit organization with offices in New York City and in Ann Arbor, Michigan. JSTOR content is provided by more than 900 publishers, the database contains more than 1,900 journal titles, in more than 50 disciplines. Each object is identified by an integer value, starting at 1. In addition to the site, the JSTOR labs group operates an open service that allows access to the contents of the archives for the purposes of corpus analysis at its Data for Research service. This site offers a facility with graphical indication of the article coverage. Users may create focused sets of articles and then request a dataset containing word and n-gram frequencies and they are notified when the dataset is ready and may download it in either XML or CSV formats. The service does not offer full-text, although academics may request that from JSTOR, JSTOR Plant Science is available in addition to the main site. The materials on JSTOR Plant Science are contributed through the Global Plants Initiative and are only to JSTOR
JSTOR
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The JSTOR front page
22.
Moscow Mathematical Papyrus
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Golenishchev bought the papyrus in 1892 or 1893 in Thebes. It later entered the collection of the Pushkin State Museum of Fine Arts in Moscow, approximately 5½ m long and varying between 3.8 and 7.6 cm wide, its format was divided into 25 problems with solutions by the Soviet Orientalist Vasily Vasilievich Struve in 1930. It is a well-known mathematical papyrus along with the Rhind Mathematical Papyrus, the Moscow Mathematical Papyrus is older than the Rhind Mathematical Papyrus, while the latter is the larger of the two. The problems in the Moscow Papyrus follow no particular order, the papyrus is well known for some of its geometry problems. Problems 10 and 14 compute a surface area and the volume of a frustum respectively, the remaining problems are more common in nature. Problems 2 and 3 are ships part problems, one of the problems calculates the length of a ships rudder and the other computes the length of a ships mast given that it is 1/3 + 1/5 of the length of a cedar log originally 30 cubits long. Aha problems involve finding unknown quantities if the sum of the quantity, the Rhind Mathematical Papyrus also contains four of these type of problems. Problems 1,19, and 25 of the Moscow Papyrus are Aha problems, for instance problem 19 asks one to calculate a quantity taken 1 and ½ times and added to 4 to make 10. In other words, in mathematical notation one is asked to solve 3 /2 × x +4 =10 Most of the problems are pefsu problems,10 of the 25 problems. A pefsu measures the strength of the beer made from a heqat of grain pefsu = number loaves of bread number of heqats of grain A higher pefsu number means weaker bread or beer, the pefsu number is mentioned in many offering lists. Then reckon what you need for a des-jug of beer like the beer called 1/2 1/4 malt-date beer The result is 1/2 of the heqat measure needed for des-jug of beer made from Upper-Egyptian grain. Calculate 1/2 of 5 heqat, the result will be 2 1/2 Take this 2 1/2 four times The result is 10, then you say to him, Behold. The beer quantity is found to be correct, problems 11 and 23 are Baku problems. These calculate the output of workers, problem 11 asks if someone brings in 100 logs measuring 5 by 5, then how many logs measuring 4 by 4 does this correspond to. Problem 23 finds the output of a given that he has to cut. Seven of the problems are geometry problems and range from computing areas of triangles, to finding the surface area of a hemisphere. The 10th problem of the Moscow Mathematical Papyrus asks for a calculation of the area of a hemisphere or possibly the area of a semi-cylinder. Below we assume that the problem refers to the area of a hemisphere, the text of problem 10 runs like this, Example of calculating a basket
Moscow Mathematical Papyrus
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14th problem of the Moscow Mathematical Papyrus (V. Struve, 1930)
Moscow Mathematical Papyrus
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