BagM 21, 554-557, taf. 46-47 (P430090)
Mathematical, Old Babylonian, Uruk · c. 1900 BCE–1600 BCE
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| Designation | BagM 21, 554-557, taf. 46-47 |
|---|---|
| ID | P430090 |
| Museum no. | IM 075985 |
| Collection | National Museum of Iraq, Baghdad, Iraq |
| Language | Akkadian |
| Period | Old Babylonian · c. 1900 BCE–1600 BCE |
| Genre | Mathematical |
| Find spot | Uruk (mod. Warka) |
| Coordinates | 31.3234, 45.6395 |
English translation
By ORACC project cams/gkab · Via Open Richly Annotated Cuneiform Corpus (ORACC) · CC BY-SA 3.0 (ORACC)
| Line | English |
|---|---|
| Obverse Column i [2:3] o i 33–o i 33 | My [diameter] is 10. What is the extension of the middle? |
| Obverse Column i [8:10] o i 99–o i 1010 | 1 figure of a circle. 1 curved 1 cable. I took out the digging-out (?) 4 times, 2 rods each. What are each of the areas? |
| Obverse Column i [10:16] o i 1111–o i 1616 | [54 times] 2 is 1 48. The outer digging-out is 1 (ikû) 8 mušaru area. [42] times 2 is 1 24. The second digging-out is 1/2 (ikû) 34 mušaru area. [30] times 2 is 1 00. The third digging-out is 1/2 (ikû) 10 mušaru area. [18] times 2 is 36. The fourth digging-out is 36 mušaru. (area) [12] times 12 is 2 24. Multiply 2 24 by 0;05, so that 12. The fifth, inner digging-out is [12 mušaru (area)]. Sum them so that they are all 3 (ikû) area. |
| Obverse Column i [16:18] o i 1717–o i 1818 | [A wheel (?)] curves 1/2 rod: the shakkullu wood is 4 fingers, the fastening band is 1 finger, the rim [3 fingers], the spokes (?) 17 fingers, the hub 1/3 cubit. |
| Obverse Column ii [0:7] o ii 1o ii 1–o ii 77 | [......] The area of the shakkullu wood is [1]8 2/3 shekels. The area of the fastening band is 4 shekels and a 4th. The area of the rim is [11] shekels and 3 4ths. The area of 1 spoke (?) is 6 and 2/3 shekels. The area of 6 spokes (?) is 1/2 mina 8 shekels and a 4th. The area of the hub is 2 shekels 15 grains. Sum them so that they are all 1 mušaru 15 shekels. |
| Obverse Column ii [7:8] o ii 88–o ii 88 | Reeds, of length 1 rod(-reed), of width 1 rod(-reed) — (that is,) 1 mušaru (area). |
| Obverse Column ii [9:11] o ii 1010–o ii 1111 | <If your cubit is 1> you multiply <times ditto and times> 25. <You take> times 2 24 each. |
| Obverse Column ii [10:11] o ii 1111–o ii 1111 | The length is a chain, the width a chain. What are the mušaru (area)? |
| Obverse Column ii [12:14] o ii 1313–o ii 1414 | If your cubit is 1, there are 1 00 chains. You multiply 1 times 1 so that [1], You multiply 1 times 25, so that 25. |
| Obverse Column ii [14:15] o ii 1515–o ii 1515 | A house of 25 mušaru (area). What should the square-side be? |
| Obverse Column ii [15:17] o ii 1616–o ii 1717 | If your cubit is 1, you multiply 25 by 2 24, so that you take 1 00 00 each. <1 00>, a chain, is the square-side. |
| Obverse Column ii [17:18] o ii 1818–o ii 1818 | [The width is] 4. What length should I survey so that it is 20 mušaru (area)? |
| Obverse Column ii [19:21] o ii 2020–o ii 2121 | If your cubit is 1, a 4[8th is] 0;01 15. You multiply 0;01 15 by 2 24, so that 3. [You multiply] 3 times [20, so that 1 00]. |
| Obverse Column ii [21:22] o ii 2222–o ii 2222 | Reeds, of length 6 cubits, of width 6 cubits, (or) 1 reed. |
| Obverse Column ii [23:25] o ii 2424–o ii 2525 | If your cubit is 1, you multiply the line times [ditto] and <times> 50. Times 1 12 square-side. |
| Obverse Column ii [25:26] o ii 2626–o ii 2626 | [The length is 2 1/2 rods], the width [2 1/2 rods]. What should the reeds be? |
| Obverse Column ii [28:30] o ii 2929–o ii 3030 | [If] your [cubit is 1], 30 each. You multiply 30 times 30, so that 15 00. You multiply [15 00 times 0;00 50], so that 12;30. |
| Obverse Column ii [30:31] o ii 3131–o ii 3131 | [The width is 2. What length] should I survey so that it is 20 reeds? |
| Obverse Column ii [33:35] o ii 3434–o ii 3535 | If your cubit is [0;05], 2 rods is 2. The reciprocal of 2 is 0;30. You multiply 0;30 times 0;30, [so that 0;15]. You multiply [0;15 times] 10, so that 2 30. You survey 2 1/2 rods. |
| Obverse Column ii [35:38] o ii 3636–o ii 3838 | [If] your [cubit is 1], 2 rods is 24. A 24th is [0;02 30]. You multiply [0;02 30] times 1 12, so that 3. [You multiply] 3 times [10, so that] 30. You survey 2 1/2 rods. |
| Obverse Column ii [38:39] o ii 3939–o ii 3939 | A house ... so that it is 1 hundred reeds? |
| Obverse Column ii [39:40] o ii 4040–o ii 4040 | Because you do not understand, you multiply reeds times the reciprocal of the constant [of] reeds, and then [you take] each (square-side). |
| Obverse Column ii [40:44] o ii 4141–o ii 4444 | If [your cubit] is 0;05, you multiply 50 times 0;30, so that [25. You take each (square-side)]. The square-side [is a chain]. |
| Obverse Column ii [44:56] o ii 4545– | (Too fragmentary to translate) |
| Reverse Column i [3:4] r i 44–r i 44 | The square-side of a house is sixty cubits. [I bought] a square-side of 3 cubits for [1/2 shekel]. What did I buy the total house for? |
| Reverse Column i [4:7] r i 55–r i 77 | Since [you] do not [understand, ...] you multiply the line which is sixty cubits [times ditto, times the reciprocal of ] the line [which is] 3 cubits times [ditto and times 30], so that you see. |
| Reverse Column i [7:10] r i 88–r i 1010 | If your cubit <is 0;05>, [the sixty cubits] are 5, the 3 cubits [are 0;15]. [5] times 5 is 25. [You multiply] 0;15 <times> «you multiply» [0;15, so that 0;03 45]. the reciprocal of 0;03 45 is 16. 16 times 25 is 6 40. You multiply 6 40 by 0;30, [so that] 3 20. |
| Reverse Column i [10:14] r i 1111–r i 1414 | If your cubit is 1 [the sixty cubits are 1 00], the 3 cubits are 3. 1 00 times <1 00 is 1 00 00> «3». 3 times 3 is 9. [A 9th is 0;06 40.] 0;06 40 times 1 00 00 is 6 40. You multiply 6 40 times 0;30, so that 3 20. You buy the total house for 3 1/3 mina. |
| Reverse Column i [14:15] r i 1515–r i 1515 | Ditto. <I bought> a square-side of sixty cubits for 3 <1/3> «2/3» mina. What <did I buy> [a square-side of] 3 cubits for? |
| Reverse Column i [15:18] r i 1616–r i 1818 | Because you do not understand, you multiply times the line [of 3 cubits] times the reciprocal of times the line of [sixty cubits], and you multiply times 3 <1/3> «2/3» mina, so that [you see]. |
| Reverse Column i [18:19] r i 1919–r i 1919 | If your [cubit] is 0;05, a 25th is 0;02 24. [0;02 24] times 0;03 45 is 0;00 09. You multiply 0;00 09 times 3 20, so that 0;30. |
| Reverse Column i [19:22] r i 2020–r i 2222 | [If] your cubit is 1, a 1 00 00th is 0;00 01. [You multiply] 0;00 01 times 9, [so that 0;00 09]. You multiply [0;00 09] times 3 20, so that 0;30. <You buy> a square-side of 3 cubits for 1/2 [shekel] silver. |
| Reverse Column i [22:24] r i 2323–r i 2424 | Ditto. For [3] <1/3> «2/3» mina silver I bought a square-side of 1 sixty cubits. What square-side could I buy for 1/2 shekel of silver? |
| Reverse Column i [24:27] r i 2525–r i 2727 | Because you do not understand, you multiply the reciprocal of 3 <1/3> «5/6» times 0;30, and then you multiply that which came up for you to see times the line [of sixty] cubits, and then you take each (square-side). The reciprocal of 3 20 is 0;00 18. You multiply times 0;30, so that 0;00 09. |
| Reverse Column i [27:29] r i 2828–r i 2929 | If your cubit is 0;05, you multiply 0;00 09 by 25, so that 0;03 45. You take 0;15, each (square-side). |
| Reverse Column i [29:31] r i 3030–r i 3131 | If your cubit is 1, 0;00 09 times 1 00 00 is 9. <You take> 3, each <square-side>. For 1/2 shekel silver <you buy> a square-side of 3 cubits each. |
| Reverse Column i [31:33] r i 3232–r i 3333 | Ditto. For 1/2 shekel of silver I bought a square-side of 3 cubits. What square-side could I buy for 3 <1/3> «5/6» mina of silver? |
| Reverse Column i [33:36] r i 3434–r i 3636 | Because you do not understand, you multiply the reciprocal of 1/2 shekel times 3 <1/3> «5/6» mina, and then you take each <square-side>, and then you multiply times 3 cubits, so that you see. A 30th is 2. You multiply by 3 20, and then you take 20, each (square-side) of 6 40. |
| Reverse Column i [36:38] r i 3737–r i 3838 | If your cubit is <0;05>, you multiply 20 times 0;15, so that the square-side of the house is 5, a chain. |
| Reverse Column i [38:40] r i 3939–r i 4040 | If your cubit is 1, you multiply 20 by 3, so that 1 00. The square-side of the house is sixty cubits. |
| Reverse Column i [40:41] r i 4141–r i 4141 | The square-side of a courtyard is 20 cubits. The square-side of a baked brick for paving is <2/3> «5/6» cubit. What is the number of bricks that are in the courtyard? |
| Reverse Column i [41:44] r i 4242–r i 4444 | Because you do not know, you multiply the constant of line of the courtyard times the reciprocal of the constant of the line of the baked brick, so that you see the number of the bricks. |
| Reverse Column i [44:46] r i 4545–r i 4646 | If your cubit is 0;05, 1;40 times 1 ;40 is 2;46 40. You multiply [0;03 20] times 0;03 20, so that 0;00 <1>1 16 40. The reciprocal of 0;00 11 16 40 is 5 24. You multiply 5 24 [times] 2;46 40, so that 15 00. |
| Reverse Column i [46:49] r i 4747–r i 4949 | If your cubit is 1, 20 times [20 is 6 40. 0;40] times 0;40 is 0;26 40. The reciprocal of 0;26 40 is 2;15. [You multiply] 2;15 [times 6 40], so that 15 00, (or) 9 hundred. There are 9 hundred baked bricks. |
| Reverse Column ii [0:4] r ii 1r ii 1–r ii 44 | [...] 3 cubits square-side [...] breadth [...] livestock [...] multiply, so that the total sheepfold is 1 40. |
| Reverse Column ii [4:8] r ii 55–r ii 88 | [10 times 10 is 1 40, (or) 1 ikû.] 7;30 times 7;30 is 56;15, (or) [56 mušaru, 15 shekels. 5 times 5 is 25, (or) 25 mušaru]. 2;30 times 2;30 is 6;15, (or) [6 mušaru 15 shekels]. [6;15 times 30 is 3] 07;30. The reciprocal of 3 07;30 is 0;00 19 12. 0;00 19 12 [times 1 40 is 0;32 ...]. 3x600 lengths, square-side of the livestock (??). |
| Reverse Column ii [8:13] r ii 99–r ii 1313 | [0;32 times 1 40] is 53;20. The [...] area is 1/2 ikû 3 <1/3> «2/3» mušaru. You multiply 0;32 times 56;15, so that 30. [The ... area is] 30 mušaru. You multiply [0;32] times 25, so that 13;20. [The ... area] is 13 1/3 mušaru. You multiply [0;32] times 6;15, so that 3;20. [The ... area] is 3 1/3 mušaru. Sum them all, so that the total courtyard is 1 40, (or) 1 ikû. |
| Reverse Column ii [13:16] r ii 1414–r ii 1616 | [Reed measure, of which] the length is 7 cubits, the width 7 cubits, is 1 reed (area), by the small cubit (?). You multiply the line times ditto and 1 12, and then you double that which came up for you to see [...] number of reeds and small cubits. The square-side is 1 10 cubits. What should the reed measure be? |
| Reverse Column ii [16:19] r ii 1717–r ii 1919 | 1 10 times 1 10 is 1 21 40. 1 21 40 times 0;01 12 (is 1 38). 1 38 reeds and 1 38 small cubits, or 2 reeds. You double 2 reeds to 1 38, so that the reeds are 1 hundred. |
| Reverse Column ii [19:22] r ii 2020–r ii 2222 | 1 reed times 1 reed is 1 reed. 1 reed times 1 cubit is 1 cubit. 1 reed times 1 finger is 1 finger. 1 cubit times 1 reed is 1 cubit. [1] cubit times 1 cubit is 1 small cubit. 1 cubit times 1 finger is 1 grain. |
| Reverse Column ii [22:26] r ii 2323–r ii 2626 | [1] finger <times> 1 reed is 1 finger. 1 finger times 1 cubit is 1 [grain]. [1] finger times <1 finger is> 1 small finger. 24 small fingers are [1] grain. 7 grains are 1 finger. 24 fingers are 1 cubit. 7 cubits are 1 reed. 3 fingers and 3 grains are 1 small cubit. 7 small cubits are 1 cubit. |
| Reverse Column ii [26:27] r ii 2727–r ii 2727 | 3 qû in seed-measure. What should the reed-measure be? |
| Reverse Column ii [29:32] r ii 3030–r ii 3232 | [The reciprocal of] 48 is 0;01 15. 0;01 15 times 2 is 0;02 30. 0;02 30 times 5 is 0;12 30. The reed-measure is 25. Ditto. The reciprocal of 0;20 is 3. You multiply 3 times 50, so that 2 30. |
| Reverse Column ii [32:33] r ii 3333–r ii 3333 | 25 reeds. What should the seed-measure be? |
| Reverse Column ii [34:37] r ii 3535–r ii 3737 | The reciprocal of 2 is 0;30. 0;30 times 0;00 48 is 0;00 24. You multiply 0;00 24 times 12;30 so that 0;05. The seed-measure is 3 qû. Ditto. The reciprocal of 50 is 0;01 12. 0;01 12 times <0;20> is 0;00 24. |
| Reverse Column ii [37:38] r ii 3838–r ii 3838 | I enlarged a courtyard with 9 hundred baked bricks of <2/3> «5/6» cubits each (square-side). What is the square-side of the courtyard? |
| Reverse Column ii [38:40] r ii 3939–r ii 4040 | You multiply each (square-side) of the baked bricks times 0;40. You take 30, each (square-side) of 15 00. You multiply 30 times 0;40, so that 20. The square-side of the courtyard is 20 cubits. |
| Reverse Column ii [40:45] r ii 4141–r ii 4545 | Seed-measure and reed-measure, finished. Copy of a wooden writing-board, written and collated according to its original. Tablet of Šamaš-iddina, son of Nadinu, descendant of Šangû-Ninurta, incantation-priest, Urukian. |
Transliteration (ATF)
From Open Richly Annotated Cuneiform Corpus (ORACC) · CC BY-SA 3.0 (ORACC default); per-file JSON license fields say: This data is released under the CC0 license (133618)
| Line | ATF | Machine English (draft) |
|---|---|---|
| r ii | ||
| 45 | {lu₂}⸢MAŠ⸣.MAŠ LU₂ qaq-qar {d}a-nu{ki}u₂ | |
Sources & licences
- Cuneiform Digital Library Initiative · CDLI: reuse of catalogue/transliteration data with citation of CDLI; images restricted (not fetched) · Cuneiform Digital Library Initiative (CDLI), https://cdli.earth/ ; cite CDLI and the P-number
- Open Richly Annotated Cuneiform Corpus (ORACC) · CC BY-SA 3.0 (ORACC default); per-file JSON license fields say: This data is released under the CC0 license (133618) · ORACC project editions, https://oracc.museum.upenn.edu/ ; cite the individual project (see texts.extra_json.project)
Cite the original edition and translator. Page generated by Unread Atlas from the public corpus export of 2026-10-11.