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80-565: Larsa is thought to be the source of a number of tablets involving Babylonian mathematics , including the Plimpton 322 tablet that contains patterns of Pythagorean triples . Larsa is found (as UD.UNUG) on Proto-cuneiform lexical lists from the Uruk 4 period (late 4th millennium BC). A few Proto-cuneiform tablets were also found there. Three Neolithic clay tokens, from a slightly early period, were also found at Larsa. For most of its history Larsa

160-452: A 2 + b 2 = c 2 {\displaystyle a^{2}+b^{2}=c^{2}} . The triples are too many and too large to have been obtained by brute force. Much has been written on the subject, including some speculation (perhaps anachronistic) as to whether the tablet could have served as an early trigonometrical table. Care must be exercised to see the tablet in terms of methods familiar or accessible to scribes at

240-465: A quadratic equation , the Babylonians essentially used the standard quadratic formula . They considered quadratic equations of the form: where b and c were not necessarily integers, but c was always positive. They knew that a solution to this form of equation is: and they found square roots efficiently using division and averaging. Problems of this type included finding the dimensions of

320-571: A Sumerian King List type beginning, involves Babylonian kings from Simbar-Šipak ( c. 1021–1004 BC) to Erība-Marduk ( c. 769 – 761 BC). The Chronicle of Early Kings , after an early preamble, involves kings of the First Babylonian Empire ending with the First Sealand Dynasty. The Tummal Inscription relates events from king Ishbi-Erra of Isin at the beginning of the second millennium BC. The Chronicle of

400-623: A blockade of the Assyrians. The eruption of the Thera volcano provides a possible time marker for the region. A large eruption, it would have sent a plume of ash directly over Anatolia and filled the sea in the area with floating pumice. This pumice appeared in Egypt, apparently via trade. Current excavations in the Levant may also add to the timeline. The exact date of the volcanic eruption has been

480-716: A blow to Isin, Gungunum captured the city of Ur. In his year names he recorded the defeat of the distant Anshan in Elam as well as city-states closer to Larsa such as Malgium . As the region of Larsa was the main center of trade via the Persian Gulf , Isin lost an enormously profitable trade route, as well as a city with much cultic significance. Gungunum's two successors, Abisare (c. 1905–1894 BC) and Sumuel (c. 1894–1865 BC), both took steps to cut Isin completely off from access to canals. Isin quickly lost political and economic influence. Larsa grew powerful, but never accumulated

560-642: A home in your holy court, House of Larsa, and has taken his seat upon your throne." In the Ur III empire period that ended the millennium, its first ruler Ur-Nammu recorded, in a brick inscription found at Larse, rebuilding the E-babbar temple of Utu there. The city became a political force during the Isin-Larsa period . After the Third Dynasty of Ur collapsed c. 2004 BC, Ishbi-Erra , an official of

640-485: A king's reign. Many copies of these lists have been found, with certain ambiguities. There are sometimes too many or few royal officials for the length of a king's reign, and sometimes the different versions of the eponym list disagree on a royal official, for example in the Mari Eponym Chronicle . The eponym list is considered accurate within 1 year back to 1133 BC. Before that uncertainty creeps in. There

720-401: A large territory. At its peak under king Rim-Sin I (c. 1822–1763 BC), Larsa controlled about 10–15 other city-states. In the latter half of this period the city of Mashkan-shapir acted as a second capital of the city-state. Nevertheless, huge building projects and agricultural undertakings can be detected archaeologically. After the defeat of Rim-Sin I by Hammurabi of Babylon , Larsa became

800-548: A longstanding traditional, often difficult to detect. Key documents like the Sumerian King List were repeatedly copied and redacted over generations to suit current political needs. For this and other reasons, the Sumerian King List, once regarded as an important historical source, is now only used with caution, if at all, for the period under discussion here. The translation of cuneiform documents

880-599: A minor site, though it has been suggested that it was the home of the First Sealand Dynasty of Babylon. Larsa was known to be active during the Neo-Babylonian, Achaemenid, and Hellenistic periods based on building brick inscriptions as well as a number of cuneiform texts from the Larsa temple of Samash which were found in Uruk. The E-babbar of Utu/Shamash was destroyed by fire in the 2nd century BC and

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960-568: A number by 13 the Babylonians would use an approximation such as: The Babylonian clay tablet YBC 7289 ( c.  1800–1600 BC ) gives an approximation of √ 2 in four sexagesimal figures, 𒐕 𒌋𒌋𒐼 𒐐𒐕 𒌋 = 1;24,51,10, which is accurate to about six decimal digits, and is the closest possible three-place sexagesimal representation of √ 2 : As well as arithmetical calculations, Babylonian mathematicians also developed algebraic methods of solving equations . Once again, these were based on pre-calculated tables. To solve

1040-2059: A port area, all linked to the Tigris and Euphrates rivers in Old Babylonian times. In a destroyed level of the Grand Viziers residence 59 cuneiform tablets, fragments and envelopes dated to the time of Gungunum and Abisare were found. Geophysical work continued including on the 10-20 meter wide rampart wall that enclosed Larsa, with six main gates. ( Shamshi-Adad dynasty 1808–1736 BCE) (Amorites) Shamshi-Adad I Ishme-Dagan I Mut-Ashkur Rimush Asinum Ashur-dugul Ashur-apla-idi Nasir-Sin Sin-namir Ipqi-Ishtar Adad-salulu Adasi (Non-dynastic usurpers 1735–1701 BCE) Puzur-Sin Ashur-dugul Ashur-apla-idi Nasir-Sin Sin-namir Ipqi-Ishtar Adad-salulu Adasi ( Adaside dynasty 1700–722 BCE) Bel-bani Libaya Sharma-Adad I Iptar-Sin Bazaya Lullaya Shu-Ninua Sharma-Adad II Erishum III Shamshi-Adad II Ishme-Dagan II Shamshi-Adad III Ashur-nirari I Puzur-Ashur III Enlil-nasir I Nur-ili Ashur-shaduni Ashur-rabi I Ashur-nadin-ahhe I Enlil-Nasir II Ashur-nirari II Ashur-bel-nisheshu Ashur-rim-nisheshu Ashur-nadin-ahhe II Second Intermediate Period Sixteenth Dynasty Abydos Dynasty Seventeenth Dynasty (1500–1100 BCE) Kidinuid dynasty Igehalkid dynasty Untash-Napirisha Twenty-first Dynasty of Egypt Smendes Amenemnisu Psusennes I Amenemope Osorkon

1120-482: A question of using computer models to show when a given eclipse would have been visible at a site, complicated by difficulties in modeling the slowing rotation of the earth ( ΔT ) and uncertainty about the lengths of months. Most calculations for dating using eclipses have assumed the Venus Tablet of Ammisaduqa to be a legitimate source. The most notable omitted eclipses are the Mari Eponym Chronicle eclipse from

1200-409: A rectangle given its area and the amount by which the length exceeds the width. Tables of values of n  +  n were used to solve certain cubic equations . For example, consider the equation: Multiplying the equation by a and dividing by b gives: Substituting y = ax / b gives: which could now be solved by looking up the n  +  n table to find the value closest to

1280-517: A topographic survey, by drone and surface survey, to refine and correct the mapping from early excavations. Excavation was focused on a large construction of the Hellenistic period built north of the E-Babbar temple. The first season included a magnetometer survey. Excavations continued with one month seasons in 2021 and 2022. They have been able to trace a very large system of internal canals and

1360-404: Is "In month XI, 15th day, Venus in the west disappeared, 3 days in the sky it stayed away, and in month XI, 18th day, Venus in the east became visible: springs will open, Adad his rain, Ea his floods will bring, king to king messages of reconciliation will send." Using it, various scholars have proposed dates for the fall of Babylon based on the 56/64-year cycle of Venus. It has been suggested that

1440-463: Is a better metric. Some scholars discount the validity of the Venus tablet of Ammisaduqa entirely. The alternative major chronologies are defined by the date of the eighth year of the reign of Ammisaduqa , king of Babylon. The most common Venus Tablet solutions ( sack of Babylon ) The following table gives an overview of the different proposals, listing some key dates and their deviation relative to

1520-451: Is an important piece of information for archaeologists, which can be compromised by two factors. First, in ancient times old materials were often reused as building material or fill, sometimes at a great distance from the original location. Secondly, looting has disturbed archaeological sites at least back to Roman times, making the provenance of looted objects difficult or impossible to determine. Lastly, counterfeit versions of these object are

1600-563: Is around 70 ft (21 m) in height. The site of Tell es-Senkereh was first excavated, under the rudimentary archaeological standards of his day, by William Loftus in 1850 for less than a month. Loftus recovered building bricks of Nebuchadnezzar II of the Neo-Babylonian Empire which enabled the site's identification as the ancient city of Larsa. Much of the effort by Loftus was on the temple of Shamash , rebuilt by Nebuchadnezzar II. Inscriptions of Burna-Buriash II of

1680-465: Is mentioned three times. Neo-Babylonian kings are mentioned in 2 Kings 20, Hebrew : בְּרֹאדַךְ בַּלְאֲדָן , romanized :  Berodach Bal'adan , thought to be Marduk-apla-iddina II , in 2 Kings 24 Nebuchadnezzar II and in 2 Kings 25 Hebrew : אֱוִיל מְרֹדַךְ , romanized :  Evil Merodach , thought to be Amel-Marduk . In Isaiah 38 the neo-Assyrian kings Sennacherib and Esarhaddon are mentioned. Dendrochronology attempts to use

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1760-418: Is more accurate. In recent years some properly calibrated radiocarbon dates have begun to appear: Other emerging technical dating methods include rehydroxylation dating , luminescence dating , archaeomagnetic dating and the dating of lime plaster from structures. At least as far back as the reign of Thutmose I , Egypt took a strong interest in the ancient Near East. At times they occupied portions of

1840-624: Is now an Assyrian Revised Eponym List which attempts to resolve some of these issues. As often in archaeology, everyday records give the best picture of a civilization. Cuneiform tablets were constantly moving around the ancient Near East, offering alliances (sometimes including daughters for marriage), threatening war, recording shipments of mundane supplies, or settling accounts receivable. Most were tossed away after use as one today would discard unwanted receipts, but fortunately for us, clay tablets are durable enough to survive even when used as material for wall filler in new construction. A key find

1920-460: Is perhaps an unhelpful term since the earliest suggested origins date to the use of accounting devices, such as bullae and tokens , in the 5th millennium BC. The Babylonian system of mathematics was a sexagesimal (base 60) numeral system . From this we derive the modern-day usage of 60 seconds in a minute, 60 minutes in an hour, and 360 degrees in a circle. The Babylonians were able to make great advances in mathematics for two reasons. Firstly,

2000-543: Is quite difficult, especially for damaged source material. Additionally, our knowledge of the underlying languages, like Akkadian and Sumerian, has evolved over time, so a translation done now may be quite different from one done in AD 1900: there can be honest disagreement over what a document says. Worse, the majority of archaeological finds have not yet been published, much less translated. Those held in private collections may never be. Many of our important source documents, such as

2080-539: Is the mathematics developed or practiced by the people of Mesopotamia , as attested by sources mainly surviving from the Old Babylonian period (1830–1531 BC) to the Seleucid from the last three or four centuries BC. With respect to content, there is scarcely any difference between the two groups of texts. Babylonian mathematics remained constant, in character and content, for over a millennium. In contrast to

2160-477: Is widely supported. Currently the major schools of thought on the absolute dating of this period are separated by 56 or 64 years. This is because the key source for this analysis are the omen observations in the Venus tablet of King Ammisaduqa and these are multiples of the eight-year cycle of Venus visibility from Earth. More recent work by Vahe Gurzadyan has suggested that the fundamental eight-year cycle of Venus

2240-790: The Euphrates in 1854, dating from 2000 BC, give lists of the squares of numbers up to 59 and the cubes of numbers up to 32. The Babylonians used the lists of squares together with the formulae: to simplify multiplication. The Babylonians did not have an algorithm for long division . Instead they based their method on the fact that: together with a table of reciprocals . Numbers whose only prime factors are 2, 3 or 5 (known as 5- smooth or regular numbers ) have finite reciprocals in sexagesimal notation, and tables with extensive lists of these reciprocals have been found. Reciprocals such as 1/7, 1/11, 1/13, etc. do not have finite representations in sexagesimal notation. To compute 1/13 or to divide

2320-558: The First Babylonian dynasty old Babylonian period in the early second millennium BC due to the wealth of data available. There has been debate over the earliest appearance of Babylonian mathematics, with historians suggesting a range of dates between the 5th and 3rd millennia BC. Babylonian mathematics was primarily written on clay tablets in cuneiform script in the Akkadian or Sumerian languages. "Babylonian mathematics"

2400-469: The Kassite dynasty of Babylon and Hammurabi of the First Babylonian dynasty were also found. Larsa was also briefly worked by Walter Andrae in 1903. The site was inspected by Edgar James Banks in 1905. He found that widespread looting by the local population was occurring there. The first modern, scientific, excavation of Senkereh occurred in 1933, with the work of André Parrot . Parrot worked at

2480-478: The Pythagorean theorem . The Babylonian tablet YBC 7289 gives an approximation of 2 {\displaystyle {\sqrt {2}}} accurate to three significant sexagesimal digits (about six significant decimal digits). Babylonian mathematics is a range of numeric and more advanced mathematical practices in the ancient Near East , written in cuneiform script . Study has historically focused on

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2560-401: The 2nd year of Tutankhamun (c. 1341–1323 BC). Assuming that the correct foreign rulers have been identified, this provides and important point of synchronization. Identification can be difficult due to the propensity for states to re-use regnal names. We have some data sources from the classical period: Berossus, a Babylonian astronomer and historian born during the time of Alexander

2640-500: The Assyrian King List, are the products of government and religious establishments, with a natural bias in favor of the king or god in charge. A king may even take credit for a battle or construction project of an earlier ruler. The Assyrians in particular have a literary tradition of putting the best possible face on history, a fact the interpreter must constantly keep in mind. Historical lists of rulers were traditional in

2720-439: The Babylonians understood and used geometry even earlier than previously thought. The Babylonians used a method for estimating the area under a curve by drawing a trapezoid underneath, a technique previously believed to have originated in 14th century Europe. This method of estimation allowed them to, for example, find the distance Jupiter had traveled in a certain amount of time. Short chronology The chronology of

2800-639: The Egyptian lunar observations. It has been suggested that lunar dates place the accession of Thutmose III , pharaoh of the Battle of Megiddo , to 1490 BC or even 1505 BC versus the current 1470 BC. A number of attempts have been made to date Kassite Kudurru stone documents by mapping the symbols to astrononomical elements, using Babylonian star catalogues such as MUL.APIN with so far very limited results. Thousands of cuneiform tablets have been found in an area running from Anatolia to Egypt. While many are

2880-789: The Elder Siamun Psusennes II Twenty-third Dynasty of Egypt Harsiese A Takelot II Pedubast I Shoshenq VI Osorkon III Takelot III Rudamun Menkheperre Ini Twenty-fourth Dynasty of Egypt Tefnakht Bakenranef ( Sargonid dynasty ) Tiglath-Pileser Shalmaneser Marduk-apla-iddina II Sargon Sennacherib Marduk-zakir-shumi II Marduk-apla-iddina II Bel-ibni Ashur-nadin-shumi Nergal-ushezib Mushezib-Marduk Esarhaddon Ashurbanipal Ashur-etil-ilani Sinsharishkun Sin-shumu-lishir Ashur-uballit II Babylonian mathematics Babylonian mathematics (also known as Assyro-Babylonian mathematics )

2960-525: The Great wrote a history of Babylon which is a lost book . Portions were preserved by other classical writers, mainly Josephus via Alexander Polyhistor . The surviving material is in chronicle form and covers the Neo-Babylonian Empire period from Nabopolassar (627–605 BC) to Nabonidus (556–539 BC). This book provides a list of kings starting with the Neo-Babylonian Empire and ending with

3040-682: The Levant and Anatolia depend significantly on the chronology of Ancient Egypt . To the extent that there are problems in the Egyptian chronology, these issues will be inherited in chronologies based on synchronisms with Ancient Egypt. There is much evidence that the Bronze Age civilization of the Indus Valley traded with the Near East, including clay seals found at Ur III and in the Persian Gulf. Seals and beads were also found at

3120-732: The Market Prices mentions various Babylonian rulers beginning from the period of Hammurabi. The Eclectic Chronicle relates events of the post-Kassite Babylonian kings. Other examples are the Religious Chronicle , and Nebuchadnezzar Chronicle , among others. The Synchronistic Chronicle, found in the library of Assurbanipal in Nineveh records the diplomacy of the Assyrian empire with the Babylonian empire. While useful,

3200-552: The accession of Hammurabi as either 1848, 1792, or 1736 BC, known as the "high" ("long"), " middle ", and "short (or low) chronology" . A record of the movements of Venus over roughly a 16-day period during the reign of a king, believed to be Ammisaduqa of the First Babylonian Dynasty, has been preserved on a tablet called Venus tablet of Ammisaduqa ( Enuma Anu Enlil 63). Twenty copies and fragments have been recovered, all Neo-Assyrian and later. An example entry

3280-409: The ancient Near East is a framework of dates for various events, rulers and dynasties. Historical inscriptions and texts customarily record events in terms of a succession of officials or rulers: "in the year X of king Y". Comparing many records pieces together a relative chronology relating dates in cities over a wide area. For the 3rd and 2nd millennia BC, this correlation is less certain but

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3360-602: The ancient Near East. Covers rulers of Mesopotamia from a time "before the flood " to the fall of the Isin Dynasty , depending on the version. Its use for pre-Akkadian rulers is limited to none. It continues to have value for the Akkadian period and later. The Sumerian King List omits any mention of Lagash , even though it was clearly a major power during the period covered by the list. The Royal Chronicle of Lagash appears to be an attempt to remedy that omission, listing

3440-580: The ancient equivalent of grocery receipts, these tablets, along with inscriptions on buildings and public monuments, provide the major source of chronological information for the ancient Middle East. While there are some relatively pristine display-quality objects, the vast majority of recovered tablets and inscriptions are damaged. They have been broken with only portions found, intentionally defaced, and damaged by weather or soil. Many tablets were not even baked and have to be carefully handled until they can be hardened by heating. The site of an item's recovery

3520-1488: The area re-used for poorly built private homes. The entire site was abandoned by the 1st century BC. The following list should not be considered complete: r.  c. 1961 – c. 1940 BC ( SC ) r.  c. 1940 – c. 1912 BC (SC) r.  c. 1912 – c. 1877 BC (SC) r.  c. 1877 – c. 1868 BC (SC) r.  c. 1868 – c. 1841 BC (SC) (29 years) r.  c. 1841 – c. 1830 BC (SC) (11 years) r.  c. 1830 – c. 1801 BC (SC) (27 years) r.  c. 1801 – c. 1785 BC (SC) (15 years) r.  c. 1785 – c. 1778 BC (SC) (7 years) r.  c. 1778 – c. 1776 BC (SC) (2 years) r.  c. 1776 – c. 1771 BC (SC) (5 years) r.  c. 1771 – c. 1770 BC (SC) (less than 1 year) r.  c. 1770 – c. 1754 BC (SC) r.  c. 1770 – c. 1758 BC (SC) (12 years) r.  c. 1758 – c. 1699 BC (SC) (60 years) r.  c. 1699 – c. 1686 BC (SC) r.  c. 1686 – c. 1678 BC (SC) r.  c. 1678 – c. 1674 BC (SC) The remains of Larsa cover an area of about 200 hectares. The highest point

3600-417: The calibration method. There have also been issues with dating for charcoal samples, which may reflect much older wood the charcoal was made from. There are also calibration issues with annual and regional C14 variations. A further problem is that earlier archaeological dates used traditional radiocarbon dating while newer results sometimes come from Accelerator mass spectrometry (AMS) radiocarbon dating which

3680-589: The chronology. His research has recently been included in the Oxford History of the Ancient Near East and has been cited widely in the recent academic literature. A new method has been developed to combine dendrochronology with Miyake events to extend the range to other areas. As in Egypt and the eastern Mediterranean, radiocarbon dates run one or two centuries earlier than the dates proposed by archaeologists. Recently, radiocarbon dates from

3760-419: The circumference of a circle as three times the diameter and the area as one-twelfth the square of the circumference, which would be correct if π is estimated as 3. They were aware that this was an approximation, and one Old Babylonian mathematical tablet excavated near Susa in 1936 (dated to between the 19th and 17th centuries BC) gives a better approximation of π as 25/8 = 3.125, about 0.5 percent below

3840-586: The citizens of Uruk, Larsa, and Pa-tibira ... He restored (the second) to the god Utu’s control in Larsa ...". Larsa is attested in the Akkadian Empire in the Temple Hymns of Enheduanna , daughter of Sargon of Akkad . "... Your lord is the soaring sunlight, the ruler ... righteous voice. He lights up the horizon, he lights up the zenith of heaven. Utu, lord of the Shining House,has built

3920-571: The consensus is that this chronicle should not be considered reliable. Chronicle P provides the same type of information as the Assyrian Synchronistic Chronicle, but from the Babylonian point of view. Rulers in the ancient Near East liked to take credit for public works. Temples, buildings and statues are likely to identify their royal patron. Kings also publicly recorded major deeds such as battles won, titles acquired, and gods appeased. These are very useful in tracking

4000-426: The earliest Hellenistic floor, was dated to the reign of Philip Arrhidaeus (320 BC). Soundings showed that the Neo-Babylonian temple followed that plan of the prior Kassite and earlier temples. Numerous inscriptions and cuneiform tablets were found representing the reigns of numerous rulers, from Ur-Nammu to Hammurabi all the way up to Nebuchadnezzar II. In 2019 excavations were resumed. The first season began with

4080-543: The early Roman Emperors. The entries relevant to the ancient Near East run from Nabonassar (747–734 BC) to the Macedonian king Alexander IV (323–309 BC). Though mostly accepted as accurate there are known issues with the Canon. Some rulers are omitted, there are times for which no ruler is listed, and the early dates have been converted from the lunar calendar used by the Babylonians to the Egyptian solar calendar. Not having

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4160-454: The exact value. The volume of a cylinder was taken as the product of the base and the height, however, the volume of the frustum of a cone or a square pyramid was incorrectly taken as the product of the height and half the sum of the bases. The Pythagorean rule was also known to the Babylonians. The "Babylonian mile" was a measure of distance equal to about 11.3 km (or about seven modern miles). This measurement for distances eventually

4240-405: The exercise "Given an interest rate of 1/60 per month (no compounding), compute the doubling time." This yields an annual interest rate of 12/60 = 20%, and hence a doubling time of 100% growth/20% growth per year = 5 years. The Plimpton 322 tablet contains a list of " Pythagorean triples ", i.e., integers ( a , b , c ) {\displaystyle (a,b,c)} such that

4320-404: The final destruction of Ebla have been shown to definitely favour the middle chronology (with the fall of Babylon and Aleppo at c. 1595 BC), and seem to discount the ultra-low chronology (same event at c. 1499 BC), although it is emphasized that this is not presented as a decisive argument. Radiocarbon dates in literature should be discounted if they do not include the raw C14 date and

4400-586: The following periods can be distinguished: Due to the sparsity of sources throughout the "Dark Age", the history of the Near Eastern Middle Bronze Age down to the end of the First Babylonian Dynasty is founded on a floating or relative chronology. There have been attempts to anchor the chronology using records of eclipses and other methods such as dendrochronology and radiocarbon dating , but none of those dates

4480-434: The fundamental 8-year cycle of Venus is a better metric, leading to the proposal of an "ultra-low" chronology. Other researchers have declared the data to be too noisy for any use in fixing the chronology. A number of lunar and solar eclipses have been suggested for use in dating the ancient Near East. Many suffer from the vagueness of the original tablets in showing that an actual eclipse occurred. At that point, it becomes

4560-654: The kings of Lagash in the form of a chronicle though some scholars believe the Lagash chronicle to be either a parody of the Sumerian King List or a complete fabrication. This list deals only with the rulers of Babylon. It has been found in two versions, denoted A and B both written in Neo-Babylonian times. The later dynasties in the list document the Kassite and Sealand periods though a number of Kassite rulers are damaged. Ruler names largely match other records but

4640-568: The last king of the Third Dynasty of Ur, Ibbi-Sin , relocated to Isin and set up a government which purported to be the successor to the Third Dynasty of Ur. From there, Ishbi-Erra recaptured Ur as well as the cities of Uruk and Lagash, which Larsa was subject to. Subsequent rulers of Isin appointed governors to rule over Larsa; one such governor was an Amorite named Gungunum . He eventually broke with Isin and established an independent dynasty in Larsa. To legitimize his rule and deliver

4720-455: The list was first constructed in the time of Ashur-uballit I (1365–1330 BC). The king list is considered to be roughly correct from that point on, less so for earlier entries which have numerous inconsistencies. Its purpose is to create a narrative of continuity and legitimacy for Assyrian kingship, blending in the kings of Amorite origin. The existing source consists of 3 mostly complete tables and 2 small fragments. There are differences between

4800-590: The location again in 1967. In 1969 and 1970, Larsa was excavated by Jean-Claude Margueron. Between 1976 and 1991, an expedition of the Delegation Archaeologic Francaise en Irak led by J-L. Huot excavated at Tell es-Senereh for 13 seasons. The primary focus of the excavation was the Neo-Babylonian E-Babbar temple of Utu/Shamash. Floors and wall repairs showed its continued use in the Hellenistic period. A tablet, found on

4880-474: The middle chronology, omitting the Supershort Chronology (sack of Babylon in 1466 BC): In the series, the conjunction of the rise of Venus with the new moon provides a point of reference, or rather three points, for the conjunction is a periodic occurrence. Identifying a conjunction during the reign of king Ammisaduqa with one of these calculated conjunctions will therefore fix, for example,

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4960-607: The number 60 is a superior highly composite number , having factors of 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 (including those that are themselves composite), facilitating calculations with fractions . Additionally, unlike the Egyptians and Romans, the Babylonians had a true place-value system, where digits written in the left column represented larger values (much as, in our base ten system, 734 = 7×100 + 3×10 + 4×1). The Babylonians used pre-calculated tables to assist with arithmetic . For example, two tablets found at Senkerah on

5040-443: The observations occurred (Memphis is usually assumed), c) what day the observations were taken (two are known to be the 1st lunar day), and d) the Egyptian calendar for this period is not fully known, especially how intercalary months were handled. Since the Assyrian eponym list is accurate to one year only back to 1132 BC, ancient Near East chronology for the preceding century or so is anchored to Ramsesses II, based on synchronisms and

5120-599: The region, a favor returned later by the Assyrians. Some key synchronisms: There are problems with using Egyptian chronology. Besides some minor issues of regnal lengths and overlaps, there are three long periods of poorly documented chaos in the history of ancient Egypt, the First , Second , and Third Intermediate Periods , whose lengths are doubtful. This means the Egyptian Chronology actually comprises three floating chronologies. The chronologies of Mesopotamia,

5200-543: The regnal lengths are more problematic. There is also a Babylonian King List of the Hellenistic Period in later part of the 1st millennium. The Assyrian King List extends back to the reign of Shamshi Adad I (1809 – c. 1776 BC), an Amorite who conquered Assur while creating a new kingdom in Upper Mesopotamia. The list extends to the reign of Shalmaneser V (727–722 BC). It is believed that

5280-400: The reign of a ruler. Unlike current calendars, most ancient calendars were based on the accession of the current ruler, as in "the 5th year in the reign of Hammurabi". Each royal year was also given a title reflecting a deed of the ruler, like "the year Ur was defeated". The compilation of these years are called date lists. In Assyria, a royal official or limmū was selected in every year of

5360-411: The right-hand side. The Babylonians accomplished this without algebraic notation, showing a remarkable depth of understanding. However, they did not have a method for solving the general cubic equation. Babylonians modeled exponential growth, constrained growth (via a form of sigmoid functions ), and doubling time , the latter in the context of interest on loans. Clay tablets from c. 2000 BC include

5440-500: The scarcity of sources in Egyptian mathematics , knowledge of Babylonian mathematics is derived from hundreds of clay tablets unearthed since the 1850s. Written in cuneiform , tablets were inscribed while the clay was moist, and baked hard in an oven or by the heat of the sun. The majority of recovered clay tablets date from 1800 to 1600 BC, and cover topics that include fractions , algebra , quadratic and cubic equations and

5520-627: The site of Esnunna . In addition, if the land of Meluhha does indeed refer to the Indus Valley, then there are extensive trade records ranging from the Akkadian Empire until the Babylonian Dynasty I. Goods from Greece made their way into the ancient Near East, directly in Anatolia and via the island of Cyprus in the rest of the region and Egypt. A Hittite king, Tudhaliya IV, even captured Cyprus as part of an attempt to enforce

5600-684: The stability of buried clay tablets, the records of the Hebrews have a great deal of ancient editorial work to sift through when used as a source for chronology. However, the Hebrew kingdoms lay at the crossroads of Babylon, Assyria, Egypt and the Hittites, making them spectators and often victims of actions in the area during the 1st millennium. Mostly concerned with regional events in the Levant, in 2 Kings 23 Hebrew : פַרְעֹה נְכֹה , romanized :  Phare'oh Necho , thought to be pharaoh Necho II ,

5680-541: The subject of strong debate, with dates ranging between 1628 and 1520 BC. These dates are based on radiocarbon samples, dendrochronology, ice cores, and archaeological remains. Archaeological remains date the eruption toward the end of the Late Minoan IA period (c. 1636–1527 BC) roughly comparable to the beginning of the New Kingdom in Egypt. Radiocarbon dating has placed it at between 1627 BC and 1600 BC with

5760-502: The tablets involving regnal lengths, names, and in one case a king being left out entirely. Not surprising given that they are noted as being copies of earlier tablets. Many chronicles have been recovered in the ancient Near East, most fragmentary, with a political slant, and sometimes contradictory; but when combined with other sources, they provide a rich source of chronological data. Most available chronicles stem from later Babylonian and Assyrian sources. The Dynastic Chronicle , after

5840-649: The time of Shamshi-Adad I and the Sargon of Akkad eclipse (from the Legends of the Kings of Akkad and a liver omen). Some important examples: There are thirteen Egyptian New Kingdom lunar observations which are used to pin the chronology in that period by locking down the accession year of Ramsesses II to 1279 BC. There are a number of issues with this including a) the regnal lengths for Neferneferuaten , Seti I , and Horemheb are actually not known with accuracy, b) where

5920-400: The time. [...] the question "how was the tablet calculated?" does not have to have the same answer as the question "what problems does the tablet set?" The first can be answered most satisfactorily by reciprocal pairs, as first suggested half a century ago, and the second by some sort of right-triangle problems. Babylonians knew the common rules for measuring volumes and areas. They measured

6000-468: The variable growth pattern of trees, expressed in their rings, to build up a chronological timeline. At present there are no continuous chronologies for the Near East, and a floating chronology has been developed using trees in Anatolia for the Bronze and Iron Ages. Professor of archaeology at Cornell, Sturt Manning, has spearheaded efforts to use this floating chronology with radiocarbon wiggle-match to anchor

6080-456: Was a number of cuneiform tablets from Amarna in Egypt, the city of the pharaoh Akhenaten . Mostly in Akkadian, the diplomatic language of the time, a number of them name foreign rulers including kings of Assyria and Babylon as well as Tushratta king of Mitanni and rulers of small states in the Levant. The letters date from the later stages of the reign of Amenhotep III (c. 1386–1349 BC) to

6160-517: Was converted to a "time-mile" used for measuring the travel of the Sun, therefore, representing time. The Babylonian astronomers kept detailed records of the rising and setting of stars , the motion of the planets , and the solar and lunar eclipses , all of which required familiarity with angular distances measured on the celestial sphere . They also used a form of Fourier analysis to compute an ephemeris (table of astronomical positions), which

6240-552: Was discovered in the 1950s by Otto Neugebauer . To make calculations of the movements of celestial bodies, the Babylonians used basic arithmetic and a coordinate system based on the ecliptic , the part of the heavens that the sun and planets travel through. Tablets kept in the British Museum provide evidence that the Babylonians even went so far as to have a concept of objects in an abstract mathematical space. The tablets date from between 350 and 50 B.C.E., revealing that

6320-583: Was primarily a cult site for the god Utu. In the early part of the 2nd millennium BC the First Dynasty of Lagash made it a major power for perhaps two centuries. The last known occupation was in the Hellenistic period. The historical "Larsa" was already in existence as early as the reign of Early Dynastic ruler Eannatum of Lagash (circa 2500–2400 BC), who annexed it to his empire. In a large victory stele found at Girsu he wrote: "... E-anatum

6400-416: Was very clever indeed and he made up the eyes of two doves with kohl , and adorned their heads with cedar (resin). For the god Utu, master of vegetation, in the E-babbar at Larsa, he had them offered as sacrificial bulls." A later ruler, Entemena , nephew of Eannatum, is recorded on a foundation cone found at nearby Bad-Tibira as cancelling the debts of the citizens of Larsa "He cancelled [oblig]ations for

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