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[[Old Babylonian Diyala – Mathematical Tablets]]
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   * Bruins, E. M. (1953b) ‘Three geometrical problems’, //Sumer// 9: 255-259.   * Bruins, E. M. (1953b) ‘Three geometrical problems’, //Sumer// 9: 255-259.
  
-  * Bruins, E. M.  (1954) ‘Some mathematical texts’, //Sumer// 10: 55-61.+  * Bruins, E. M.  (1954) ‘Some mathematical texts’, //Sumer// 10: 55-61.
  
   * Friberg, Jöran. (2000) ‘Mathematics at Ur in the Old Babylonian period’, //Revue d'Assyriologie// 94: 98-188.   * Friberg, Jöran. (2000) ‘Mathematics at Ur in the Old Babylonian period’, //Revue d'Assyriologie// 94: 98-188.
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   * Neugebauer, Otto and Abraham Sachs. (1945) //Mathematical Cuneiform Texts//. American Oriental Series XXIX. New Haven, Connecticut: American Oriental Society.   * Neugebauer, Otto and Abraham Sachs. (1945) //Mathematical Cuneiform Texts//. American Oriental Series XXIX. New Haven, Connecticut: American Oriental Society.
  
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 ==== Metrological Systems Present in Mathematical Tablets from the Old Babylonian Diyala ==== ==== Metrological Systems Present in Mathematical Tablets from the Old Babylonian Diyala ====
  
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 The following tables give the attested units and the numerical relationship between neighbouring units in each system of measurement: capacities, weights, surfaces and volumes and finally length. The following tables give the attested units and the numerical relationship between neighbouring units in each system of measurement: capacities, weights, surfaces and volumes and finally length.
  
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 Measurement units are presented below the way they are attested in the mathematical tablets, that is to say, phonetically or with logograms, sometimes both, according to the way they are written in the examined tablets. Measurement units are presented below the way they are attested in the mathematical tablets, that is to say, phonetically or with logograms, sometimes both, according to the way they are written in the examined tablets.
  
- + 
  
 === Units of capacity === === Units of capacity ===
  
-                                         +                                         
  
-| sila<sub>3</sub>//, qûm// | {{:image002.jpg?26x28}} | +| sila<sub>3</sub>//, qûm// | {{:Dyala002.jpg?26x28}} | 
-| **↓ × 10** || +|  **↓ × 10**  || 
-| (ban<sub>2</sub>)//, sūtum// | {{:image004.jpg?23x26}} | +| (ban<sub>2</sub>)//, sūtum// | {{:Dyala004.jpg?23x26}} | 
-| **↓ × 6** || +|  **↓ × 6**  || 
-| (barig), //parsiktum// | {{:image006.jpg?9x39}} | +| (barig), //parsiktum// | {{:Dyala006.jpg?9x39}} | 
-| **↓ × 5** || +|  **↓ × 5**  || 
-| gur | {{:image008.jpg?33x32}} |+| gur | {{:Dyala008.jpg?33x32}} |
  
- + 
  
 === Units of weight === === Units of weight ===
  
- + 
  
-| še | {{:image010.jpg?19x28}} | +| še | {{:Dyala010.jpg?19x28}} | 
-| **↓ × 180** || +|  **↓ × 180**  || 
-| gin<sub>2</sub>//, šiqlum// | {{:image012.jpg?33x28}} | +| gin<sub>2</sub>//, šiqlum// | {{:Dyala012.jpg?33x28}} | 
-| **↓ × 60** || +|  **↓ × 60**  || 
-| ma-na | {{:image014.jpg?33x31}}{{:image016.jpg?29x30}} | +| ma-na | {{:Dyala014.jpg?33x31}}{{:Dyala016.jpg?29x30}} | 
-| **↓ × 60** || +|  **↓ × 60**  || 
-| gu<sub>2</sub> | {{:image018.jpg?41x29}} |+| gu<sub>2</sub> | {{:Dyala018.jpg?41x29}} |
  
 \\ In order to express multiples of the weight measurement unit gu<sub>2</sub>, the so-called System S is employed. This is consistent with the use of System S in Southern Old Babylonian Schools, where it is additionally used to express multiples of the capacity measurement unit gur. \\ In order to express multiples of the weight measurement unit gu<sub>2</sub>, the so-called System S is employed. This is consistent with the use of System S in Southern Old Babylonian Schools, where it is additionally used to express multiples of the capacity measurement unit gur.
  
- + 
  
 -System S -System S
  
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 | Transliteration | Sign | Value | | Transliteration | Sign | Value |
-| 1(aš) | {{:image020.jpg?21x38}} | 1 | +| 1(aš) | {{:Dyala020.jpg?21x38}} | 1 | 
-| 1(u) | {{:image022.jpg?12x35}} | 10 |+| 1(u) | {{:Dyala022.jpg?12x35}} | 10 |
  
- + 
  
 Example: Example:
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 1(u) 2(aš) gu<sub>2</sub> of silver, meaning 12 gu<sub>2</sub> of silver, as in [[http://www.cdli.ucla.edu/P225113|IM 067330]] 1(u) 2(aš) gu<sub>2</sub> of silver, meaning 12 gu<sub>2</sub> of silver, as in [[http://www.cdli.ucla.edu/P225113|IM 067330]]
  
- + 
  
- + 
  
 === Units of surface and volume === === Units of surface and volume ===
  
- + 
  
-| sar//, mušarum// | {{:image024.jpg?42x37}} | +| sar//, mušarum// | {{:Dyala024.jpg?42x37}} | 
-| **↓ × 100** || +|  **↓ × 100**  || 
-| gan<sub>2</sub> | {{:image026.jpg?38x36}} |+| gan<sub>2</sub> | {{:Dyala026.jpg?38x36}} |
  
- + 
  
 In order to express multiples of the surface (and volume) measurement unit gan<sub>2</sub>, the so-called System G is employed. In order to express multiples of the surface (and volume) measurement unit gan<sub>2</sub>, the so-called System G is employed.
  
- + 
  
 -System G -System G
  
- + 
  
-| Transliteration | Signs | Value | +| Transliteration         | Signs                                           | Value      | 
-|   | {{:image028.jpg?26x36}} | 1/4 iku | +|                         | {{:Dyala028.jpg?26x36}}                         | 1/4 iku    | 
-| **↓ × 2** ||   | +|  **↓ × 2**                                                                           ||| 
-| 1(ubu) | {{:image030.jpg?19x40}} | ½ iku | +| 1(ubu)                  | {{:Dyala030.jpg?19x40}}                         | ½ iku      | 
-| **↓ × 2** || ** ** | +|  **↓ × 2**                                                                           ||| 
-| 1(iku) | {{:image020.jpg?21x38}} | 1 iku | +| 1(iku)                  | {{:Dyala020.jpg?21x38}}                         | 1 iku      | 
-| **↓ × 6** || ** ** | +|  **↓ × 6**                                                                           ||| 
-| 1(eše<sub>3</sub>) | {{O:image032.jpg?30x44}} | 6 iku | +| 1(eše<sub>3</sub>)      | {{Dyala032.jpg?30x44}}                          | 6 iku      | 
-| **↓ × 3** || ** ** | +|  **↓ × 3**                                                                           ||| 
-| 1(bur<sub>3</sub>) | {{:image033.jpg?12x35}} | 18 iku | +| 1(bur<sub>3</sub>)      | {{:Dyala033.jpg?12x35}}                         | 18 iku     | 
-| **↓ × 10** || ** ** | +|  **↓ × 10**                                                                          ||| 
-| 1(bur’u) | {{:image035.jpg?14x35}} | 180 iku | +| 1(bur’u)                | {{:Dyala035.jpg?14x35}}                         | 180 iku    | 
-| **↓ × 6** || ** ** | +|  **↓ × 6**                                                                           ||| 
-| 1(šar<sub>2</sub>) | {{:image037.jpg?22x35}} | 1080 iku | +| 1(šar<sub>2</sub>)      | {{:Dyala037.jpg?22x35}}                         | 1080 iku   | 
-| **↓ × 10** || ** ** | +|  **↓ × 10**                                                                          ||| 
-| 1(šar’u) | {{O:image039.jpg?22x35}} | 10800 iku | +| 1(šar’u)                | {{:Dyala039.jpg?22x35}}                         | 10800 iku  | 
-| **↓ × 6** || ** ** | +|  **↓ × 6**                                                                           ||| 
-| 1(šar<sub>2</sub>) gal | {{:image040.jpg?22x35}}{{:image042.jpg?26x34}} | 34800 iku |+| 1(šar<sub>2</sub>) gal  | {{:Dyala040.jpg?22x35}}{{:Dyala042.jpg?26x34}}  | 34800 iku  |
  
- + 
  
 Examples: Examples:
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 1(bur<sub>3</sub>) 2(eše<sub>3</sub>) gan<sub>2</sub>, meaning 18 + 2 x 6 gan<sub>2</sub> = 30 gan<sub>2</sub>, as in [[http://www.cdli.ucla.edu/P368229|A21948]] 1(bur<sub>3</sub>) 2(eše<sub>3</sub>) gan<sub>2</sub>, meaning 18 + 2 x 6 gan<sub>2</sub> = 30 gan<sub>2</sub>, as in [[http://www.cdli.ucla.edu/P368229|A21948]]
  
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 === Units of length === === Units of length ===
  
-// // 
  
-| //ubānum// || 
-| **↓ × 30** || 
-| kuš<sub>3</sub>//, ammatum// | {{:image044.jpg?23x34}} | 
-| **↓ × 3** || 
-| //nikkassum// || 
-| **↓ × 3** || 
-| //qanûm// || 
-| **↓ × 2** || 
-| ninda | {{:image046.jpg?18x34}} | 
-| **↓ × 5** || 
-| //ṣuppum// || 
-| **↓ × 2** || 
-| //ašlum// || 
  
- +|  //ubānum//                                                || 
 +|  **↓ × 30**                                                || 
 +|  kuš<sub>3</sub>//, ammatum// {{:Dyala044.jpg?23x34}}      || 
 +|  **↓ × 3**                                                 || 
 +|  //nikkassum//                                             || 
 +|  **↓ × 3**                                                 || 
 +|  //qanûm//                                                 || 
 +|  **↓ × 2**                                                 || 
 +|  ninda {{:Dyala046.jpg?18x34}}                             || 
 +|  **↓ × 5**                                                 || 
 +|  //ṣuppum//                                                || 
 +|  **↓ × 2**                                                 || 
 +|  //ašlum//                                                 ||
  
- + 
  
-=== Bridges ===+ 
  
- +=== Bridges ===
  
 The relation between units of length and units and surface is that: The relation between units of length and units and surface is that:
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 ==== Metrological Volume and Capacities ==== ==== Metrological Volume and Capacities ====
- 
-  
  
 In the evidence from the Diyala, one finds two different equivalencies between volume given in sar and capacities. In the evidence from the Diyala, one finds two different equivalencies between volume given in sar and capacities.
  
- + 
  
 For clay: For clay:
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 1 sar of volume is equivalent to 60 gur of capacity (Haddad 104, problems #7-#8). 1 sar of volume is equivalent to 60 gur of capacity (Haddad 104, problems #7-#8).
  
- + 
  
 For grain: For grain:
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 1 sar of volume is equivalent to 72 gur of capacity (Haddad 104, problems #1-#5). 1 sar of volume is equivalent to 72 gur of capacity (Haddad 104, problems #1-#5).
  
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 ==== Fractions ==== ==== Fractions ====
  
- +|  1/3  | {{:Dyala048.jpg?26x40}}  | 
 +|  1/2  | {{:Dyala050.jpg?18x34}}  | 
 +|  2/3  | {{:Dyala052.jpg?23x36}}  | 
 +|  5/6  | {{:Dyala054.jpg?23x35}}  |
  
-| 1/3 | {{:image048.jpg?26x40}} | + 
-| 1/2 | {{:image050.jpg?18x34}} | +
-| 2/3 | {{:image052.jpg?23x36}} | +
-| 5/6 | {{:image054.jpg?23x35}} | +
- +
- +
  
 All of these fractions occur in [[http://www.cdli.ucla.edu/P368229|A 21948]] All of these fractions occur in [[http://www.cdli.ucla.edu/P368229|A 21948]]
  
 See also, for 1/3, 1/2 and 5/6, [[http://www.cdli.ucla.edu/P225105|IM 063106]] See also, for 1/3, 1/2 and 5/6, [[http://www.cdli.ucla.edu/P225105|IM 063106]]
 +
 +
 +
 +//
 +//
 +Page prepared by Carlos Gonçalves (digital version prepared by BG)
old_babylonian_dyala.1453844287.txt.gz · Last modified: 2016/01/26 21:38 (external edit)
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