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Rhind Papyrus
The Rhind Mathematical Papyrus (RMP; also designated as papyrus British Museum 10057 and pBM 10058) is one of the best known examples of ancient Egyptian mathematics. It is named after Alexander Henry Rhind, a Scottish antiquarian, who purchased the papyrus in 1858 in Luxor, Egypt; it was apparently found during illegal excavations in or near the Ramesseum. It dates to around 1550 BC. The British Museum, where the majority of the papyrus is now kept, acquired it in 1865 along with the Egyptian Mathematical Leather Roll, also owned by Henry Rhind. There are a few small fragments held by the Brooklyn Museum in New York City and an central section is missing. 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. The Rhind Mathematical Papyrus dates to the Second Intermediate Period of Egypt. It was copied by the scribe Ahmes (i.e., Ahmose; ''Ahmes' ...
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British Museum
The British Museum is a public museum dedicated to human history, art and culture located in the Bloomsbury area of London. Its permanent collection of eight million works is among the largest and most comprehensive in existence. It documents the story of human culture from its beginnings to the present.Among the national museums in London, sculpture and decorative and applied art are in the Victoria and Albert Museum; the British Museum houses earlier art, non-Western art, prints and drawings. The National Gallery holds the national collection of Western European art to about 1900, while art of the 20th century on is at Tate Modern. Tate Britain holds British Art from 1500 onwards. Books, manuscripts and many works on paper are in the British Library. There are significant overlaps between the coverage of the various collections. The British Museum was the first public national museum to cover all fields of knowledge. The museum was established in 1753, largely b ...
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Ahmes
Ahmes ( egy, jꜥḥ-ms “, a common Egyptian name also transliterated Ahmose) was an ancient Egyptian scribe who lived towards the end of the Fifteenth Dynasty (and of the Second Intermediate Period) and the beginning of the Eighteenth Dynasty (and of the New Kingdom). He transcribed the Rhind Mathematical Papyrus, a work of ancient Egyptian mathematics that dates to approximately 1550 BC; he is the earliest contributor to mathematics whose name is known. He's also the first mathematician to use fractions A fraction (from la, fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight .... Ahmes claimed not to be the writer of the work but rather just the scribe. He claimed the material came from an even older document from around 2000 B.C. See also * List of ancient Egyptian scribes References Extern ...
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Egyptian Fraction
An Egyptian fraction is a finite sum of distinct unit fractions, such as \frac+\frac+\frac. That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from each other. The value of an expression of this type is a positive rational number \tfrac; for instance the Egyptian fraction above sums to \tfrac. Every positive rational number can be represented by an Egyptian fraction. Sums of this type, and similar sums also including \tfrac and \tfrac as summands, were used as a serious notation for rational numbers by the ancient Egyptians, and continued to be used by other civilizations into medieval times. In modern mathematical notation, Egyptian fractions have been superseded by vulgar fractions and decimal notation. However, Egyptian fractions continue to be an object of study in modern number theory and recreational mathematics, as well as in modern historical studies of ancient mathematics. ...
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Rhind Mathematical Papyrus 2/n Table
The Rhind Mathematical Papyrus, an ancient Egyptian mathematical work, includes a mathematical table for converting rational numbers of the form 2/''n'' into Egyptian fractions (sums of distinct unit fractions), the form the Egyptians used to write fractional numbers. The text describes the representation of 50 rational numbers. It was written during the Second Intermediate Period of Egypt (approximately 1650–1550 BCE) by Ahmes, the first writer of mathematics whose name is known. Aspects of the document may have been copied from an unknown 1850 BCE text. Table The following table gives the expansions listed in the papyrus. This part of the Rhind Mathematical Papyrus was spread over nine sheets of papyrus. Explanations Any rational number has infinitely many different possible expansions as a sum of unit fractions, and since the discovery of the Rhind Mathematical Papyrus mathematicians have struggled to understand how the ancient Egyptians might have calculated th ...
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Season Of The Inundation
The Season of the Inundation or Flood ( egy, Ꜣḫt) was the first season of the lunar and civil Egyptian calendars. It fell after the intercalary month of Days over the Year ('). and before the Season of the Emergence ('). In the modern Coptic Calendar, this season lasts from Paoni 12 to Paopi 9. Names The pronunciation of the ancient Egyptian name for the Season of the Inundation is uncertain as the hieroglyphs do not record its vowels. It is conventionally transliterated Akhet. The name refers to the annual flooding of the Nile. Lunar calendar In the lunar calendar, the intercalary month was added as needed to maintain the heliacal rising of Sirius in the fourth month of the season of the Harvest. This meant that the Season of the Inundation usually lasted from September to January. Because the precise timing of the flood varied, the months of "Inundation" no longer precisely reflected the state of the river but the season was usually the time of the annual floodin ...
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Khamudi
Khamudi (also known as Khamudy) was the last Hyksos ruler of the Fifteenth Dynasty of Egypt. Khamudi came to power in 1534 BC or 1541 BC, ruling the northern portion of Egypt from his capital Avaris. His ultimate defeat at the hands of Ahmose I, after a short reign, marks the end of the Second Intermediate Period. Attestations Khamudi is listed on the Turin canon, column 10, line 28 ( Gardiner entry 10.20) as the last Hyksos king. Beyond this, only two scarab seals are firmly attributed to him, both from Jericho. Additionally, a cylinder seal of unknown provenance but possibly from ByblosFlinders Petrie: ''Scarabs and cylinders with names : illustrated by the Egyptian collection in University College, London (1917)'available online see pl. XIX, seal under the name "Khondy". is inscribed with a cartouche which may read "Khamudi". This reading is contested by the egyptologist Kim Ryholt who proposed that the cartouche reads "Kandy" instead and refers to an hitherto unknown king. In ...
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Verso
'''' is the "right" or "front" side and ''verso'' is the "left" or "back" side when text is written or printed on a leaf of paper () in a bound item such as a codex, book, broadsheet, or pamphlet. Etymology The terms are shortened from Latin: and ' (which translate as "on the right side of the leaf" and "on the back side of the leaf"). The two opposite pages themselves are called ' and ' in Latin, and the ablative ', ' already imply that the text on the page (and not the physical page itself) are referred to. Usage In codicology, each physical sheet (', abbreviated ''fol.'' or ''f.'') of a manuscript is numbered, and the sides are referred to as ' and ', abbreviated as ''r'' and ''v'' respectively. Editions of manuscripts will thus mark the position of text in the original manuscript in the form ''fol. 1r'', sometimes with the ''r'' and ''v'' in superscript, as in ''1r'', or with a superscript ''o'' indicating the ablative ', ', as in ''1ro''. This terminology has been sta ...
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Apepi I
Apepi (also Ipepi; Egyptian language '), Apophis ( gr, Ἄποφις); regnal names Neb-khepesh-Re, A-qenen-Re and A-user-Re) was a Hyksos ruler of Lower Egypt during the Fifteenth Dynasty and the end of the Second Intermediate Period. According to the Turin Canon of Kings, he reigned over the northern portion of Egypt for forty years during the early half of the 16th century BCE. Although officially only in control of the Lower Kingdom, Apepi in practice dominated the majority of Egypt during the early portion of his reign. He outlived his southern rival, Kamose, but not Ahmose I.Grimal, p.189 While Apepi exerted suzerainty over and maintained peaceful trade relations with the native Theban Seventeenth Dynasty to the south, the other kingdom eventually regained control. The Hyksos were driven out of Egypt no more than fifteen years after his death. Kamose, the last king of the Seventeenth Dynasty, refers to Apepi as a "Chieftain of Retjenu" in a stela that implies a Canaanit ...
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Hyksos
Hyksos (; Egyptian '' ḥqꜣ(w)- ḫꜣswt'', Egyptological pronunciation: ''hekau khasut'', "ruler(s) of foreign lands") is a term which, in modern Egyptology, designates the kings of the Fifteenth Dynasty of Egypt (fl. c. 1650–1550 BC). The seat of power of these kings was the city of Avaris in the Nile delta, from where they ruled over Lower and Middle Egypt up to Cusae. In the ''Aegyptiaca'', a history of Egypt written by the Greco-Egyptian priest and historian Manetho in the 3rd century BC, the term Hyksos is used ethnically to designate people of probable West Semitic, Levantine origin. While Manetho portrayed the Hyksos as invaders and oppressors, this interpretation is questioned in modern Egyptology. Instead, Hyksos rule might have been preceded by groups of Canaanite peoples who gradually settled in the Nile delta from the end of the Twelfth Dynasty onwards and who may have seceded from the crumbling and unstable Egyptian control at some point during the Thirteent ...
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Manuscript
A manuscript (abbreviated MS for singular and MSS for plural) was, traditionally, any document written by hand – or, once practical typewriters became available, typewritten – as opposed to mechanically printed or reproduced in some indirect or automated way. More recently, the term has come to be understood to further include ''any'' written, typed, or word-processed copy of an author's work, as distinguished from the rendition as a printed version of the same. Before the arrival of printing, all documents and books were manuscripts. Manuscripts are not defined by their contents, which may combine writing with mathematical calculations, maps, music notation, explanatory figures, or illustrations. Terminology The study of the writing in surviving manuscripts, the "hand", is termed palaeography (or paleography). The traditional abbreviations are MS for manuscript and MSS for manuscripts, while the forms MS., ms or ms. for singular, and MSS., mss or mss. for pl ...
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Hieratic
Hieratic (; grc, ἱερατικά, hieratiká, priestly) is the name given to a cursive writing system used for Ancient Egyptian and the principal script used to write that language from its development in the third millennium BC until the rise of Demotic in the mid-first millennium BC. It was primarily written in ink with a reed pen on papyrus. Etymology In the second century, the term ''hieratic'' was used for the first time to describe this Ancient Egyptian writing system by the Greek scholar Clement of Alexandria. The term derives from the Greek for "priestly writing" ( grc-koi, γράμματα ἱερατικά) because at that time, for more than eight and a half centuries, hieratic had been used traditionally only for religious texts and literature. ''Hieratic'' can also be an adjective meaning " or associated with sacred persons or offices; sacerdotal." Development Hieratic developed as a cursive form of hieroglyphic script in the Naqada III period of Ancient E ...
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Twelfth Dynasty Of Egypt
The Twelfth Dynasty of ancient Egypt (Dynasty XII) is considered to be the apex of the Middle Kingdom by Egyptologists. It often is combined with the Eleventh, Thirteenth, and Fourteenth dynasties under the group title, Middle Kingdom. Some scholars only consider the 11th and 12th dynasties to be part of the Middle Kingdom. History The chronology of the Twelfth Dynasty is the most stable of any period before the New Kingdom. The Turin Royal Canon gives 213 years (1991–1778 BC). Manetho stated that it was based in Thebes, but from contemporary records it is clear that the first king of this dynasty, Amenemhat I, moved its capital to a new city named "Amenemhat-itj-tawy" ("Amenemhat the Seizer of the Two Lands"), more simply called, Itjtawy. The location of Itjtawy has not been discovered yet, but is thought to be near the Fayyum, probably near the royal graveyards at el-Lisht. The order of its rulers of the Twelfth Dynasty is well known from several sources: two lists ...
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