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SpTU 4, 175 (P348768)

Mathematical, Hellenistic, Uruk · c. 330 BCE–141 BCE

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Designation	SpTU 4, 175
ID	P348768
Museum no.	IM —
Collection	National Museum of Iraq, Baghdad, Iraq
Language	Akkadian
Period	Hellenistic · c. 330 BCE–141 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 [0:2] o i 1'o 1'–o i 2'2'	(traces)
Obverse Column i [1:11] o i 2'2'–o i 11'11'	[The short side is 1 hundred cubits. What length should I survey be so that (the area is) 1 kurru seed-measure?
Obverse Column i [11:18] o i 12'12'–o i 18'18'	A field. How much should I make (it) square so that it is 1 kurru, 2 sūtu seed-measure?
Obverse Column i [18:33] o i 19'19'–o i 33'33'	A field of 1 sūtu [seed-measure]. I added the length and the width so that it was [1 30] cubits. How much should the length be and how much should the width be?
Obverse Column i [33:42] o i 34'34'–o i 42'42'	A field of seed-measure 1 sūtu, 4 qû. The length exceeds the width by 10 cubits. How much should the length be and how much should the width be?
Obverse Column ii [0:8] o ii 1'o 1'–o ii 8'8'	(Statement and general solution missing.)
Obverse Column ii [8:17] o ii 9'9'–o ii 17'17'	A field curved [1 pānu] seed-measure. Times 4, 1 each the quarrying (?) of [...]. How much each ... from the outer circle to the inner circle did it curve?
Obverse Column ii [17:22] o ii 18'18'–o ii 22'22'	Seed-measure of 1 thousand cubits length and 1 2/3 cubits width. Ditto.
Obverse Column ii [22:27] o ii 23'23'–o ii 27'27'	A length of 1 hundred cubits, a width of 1 hundred cubits. What should the seed-measure be?
Obverse Column ii [27:33] o ii 28'28'–o ii 33'33'	Seed-measure for a length of 1 thousand cubits, a width of 1 40 cubits. Ditto.
Obverse Column ii [33:37] o ii 34'34'–o ii 37'37'	The length is 1 hundred cubits and the width is 1 hundred cubits. [How much should the seed-measure be?]
Reverse Column i [0:5] r i 1r i 1–r i 55	(Statement of problem missing)
Reverse Column i [5:12] r i 66–r i 1212	The length is 1 hundred cubits, the width 1 hundred cubits. How much should seed-measure be?
Reverse Column i [11:16] r i 1212–r i 1616	Seed grain of a length of 1 thousand cubits, [a width of] 1 [thousand cubits]. Ditto.
Reverse Column i [16:23] r i 1717–r i 2323	[The length] is 1 hundred cubits, [the width 1 hundred cubits]. How much should the seed-grain be?
Reverse Column i [23:28] r i 2424–r i 2828	Seed-measure for 1 ikû area at 3 sūtu [by the large cubit].
Reverse Column i [28:35] r i 2929–r i 3535	The square-sides are 50 rods each. How much is the area?
Reverse Column i [35:38] r i 3636–r i 3838	Seed-measure of 1 ikû area at [3 sūtu by] the large cubit. [Because you do not understand, you multiply] the line times [ditto ...]. You multiply times 8. [...] times [...].
Reverse Column ii [0:2] r ii 1'1'–r ii 2'2'	(Statement of problem and start of solution missing.) [...] length. [You multiply] the line times the line [...]. You multiply [...] times [...]. Times 2 each.
Reverse Column ii [2:4] r ii 3'3'–r ii 4'4'	(Diagram of triangle). The length is 1 cable and the width is 1 cable. How much should the area be? 1 00 times [1 00 is 1 00 00]. Times 0;30 is 30 00. The area is 1 eblu.
Reverse Column ii [4:6] r ii 5'5'–r ii 6'6'	1 area of a triangle. The square-side <<of 8>> from which an 8th is torn out. You multiply the line times ditto and times [0;26 15].
Reverse Column ii [6:8] r ii 7'7'–r ii 8'8'	The square-sides are 1 cable each. How much should the area be? 1 00 times [1 00 is 1 00 00]. You multiply times 0;26 15 so that (you see) 26 15. [The area] is 2 eblu, 3 1/2 ikû, 25 [sar].
Reverse Column ii [8:10] r ii 9'9'–r ii 10'10'	1 area of a triangle. The square-side from which a 10th and a 30th are torn out. You multiply the line times ditto and 0;26.
Reverse Column ii [10:11] r ii 11'11'–r ii 11'11'	[...] 1 00 times 1 00 is 1 00 00. Times [...]

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)
o i
1'	⸢x x x⸣
2'	1 ME KUŠ₃ SAG US₂ EN] HE₂.GID₂(ŠE-)ma HE₂ 1(AŠ) GUR ŠE.NUMUN
3'	[MU la₃ ZU{u₂} IGI{u₂]} ša SAG A.ŠA₃ IL₂-ma
4'	[u₃ A.RA₂ IGI{e]} ⸢ša⸣ IGI.GUB{be₂-e} ŠE.NUMUN DU{ak}
5'	⸢u₃⸣ ŠE.NUMUN ša E-ka DU-ma US₂ IGI{mar}
6'	[šum]-ma 5 am-mat-ka 8.20 1 ME KUŠ₃ IGI 8.20 7.12
7'	7.12 A.RA₂ 1.12 DU-ma 9 9 A.RA₂ 5 DU-ma 45
8'	45 a-na šid-du A.ŠA₃-ka ta-šak-kan
9'	šum-ma 1 am-mat-ka 1.40 1 ME KUŠ₃ IGI 1.40 36
10'	36 A.RA₂ 3 DU-ma 1.48 1.48 A.RA₂ 5 DU-ma 9
11'	ša 1.40 ⸢KUŠ₃⸣ A.RA₂ šid-du ta-šak-kan
12'	A.ŠA₃ EN AM₃ lu-[mah(KUR-)hir-ma HE₂ 1(aš) GUR 2(BAN₂) ŠE.NUMUN
13'	MU la₃ ZU{u₂} ŠE.NUMUN ša E-ka
14'	[A].⸢RA₂⸣ IGI.GUB{be₂-e} ŠE.⸢NUMUN⸣ DU{ak} ⸢AM₃ TI{qe₂}ma ši-id-du⸣
15'	šum-ma 5 am-mat-ka 5.20 A.RA₂ 1.15(16) DU-⸢ma⸣ 6.40-E
16'	20-AM₃ TI{qe₂} 20 NINDA-AM₃ tu-mah(KUR-)har
17'	šum-ma 1 am-mat-ka 5.20 A.RA₂ 3 DU-ma 16-E
18'	4-AM₃ TI{qe₂} 2 ME 40 KUŠ₃-AM₃ tu-mah(KUR-)har
19'	A.ŠA₃ 1(BAN₂) [ŠE.NUMUN] ⸢US₂⸣ u₃ SAG GAR.GAR-⸢ma⸣ 1.30 ⸢KUŠ₃ US₂ HE₂.EN⸣
20'	u₃ SAG HE₂.EN-ma ⸢MU la₃ ZU{u₂⸣} [... 1/2 ⸢ša₂⸣ 1.30 KUŠ₃ IL₂-ma
21'	45 KUŠ₃ UR.A a-⸢na IGI.GUB ša⸣ [ŠE.NUMUN] x x 1(BAN₂) ŠE.NUMUN
22'	ina lib₃-bi ⸢TI{qe₂⸣} IGI{⸢u₂⸣} [ša IGI.GUB{be₂-e]} ta-na-aš₂-šam-ma
23'	A.⸢RA₂⸣ 45 ⸢KUŠ₃⸣ [DAH-ma US₂ i-na] 45 KUŠ₃⸣ [NIM]-ma SAG šum-ma
24'	5 am-[mat-ka US₂ u₃ SAG 7.30 1/2-ša₂ 3.45 TI{qe₂} 3.45 A.RA₂
25'	3.45 [DU-ma 14.03.45 14.03.45 A.RA₂] 48 DU-ma 11.15
26'	1.07.30 {giš}BAN 1(BAN₂) 10 i-na 11.15 ⸢NIM⸣-ma 1.15 re-e-hu
27'	1.15 A.RA₂] 1.15 <DU-ma> 1.33.45-[E] 1.15-AM₃ TI{qe₂}
28'	1.15 a]-na 3.45 DAH-ma 5 NINDA US₂] u₃ 1.15 i-na 3.45
29'	[NIM-ma] 2.30 [NINDA SAG šum-ma 1 am-mat]-⸢ka⸣ 1.30 KUŠ₃ 1/2-ša₂ 45 TI
30'	45 A.RA₂] 45 DU⸣-ma 33.45 33.45 A.RA₂ 20 DU-ma
31'	⸢ŠE.NUMUN⸣ 11.15 1(BAN₂) 10 ⸢i⸣-na 11.15 NIM-ma 1.15 re-e-hu 1.15
32'	A.RA₂ 3 ⸢DU⸣-[ma] 3.45-E 15-AM₃ TI
33'	15 A.RA₂ 45 DAH-ma 1 ŠU KUŠ₃ ⸢US₂⸣ i-na 45 NIM-ma 30 KUŠ₃ SAG
34'	A.ŠA₃ 1(BAN₂) 4 SILA₃ ŠE.NUMUN US₂ a-na ⸢SAG⸣ 10 KUŠ₃ a-tar US₂ HE₂.EN u₃ SAG HE₂.EN
35'	MU la₃ ZU{u₂} mi-šil ⸢DIRI⸣ DU₃-ma x UR.A a-na ŠE.NUMUN te-<<qe₂>>-eṣ-ṣip-ma
36'	[...] ŠE.NUMUN SAG te-[... ša₂] a-na IGI-ka E₁₁.A
37'	[...] IL₂-ma 5 KUŠ₃ ⸢DAH-ma⸣ US₂ IGI{mar}
38'	[... 5 KUŠ₃ ta-na-aš₂-šar-ma SAG IGI{mar}
39'	[šum-ma 1 ⸢am⸣-mat-ka 10 10 KUŠ₃ mi-šil 5 KUŠ₃ 5 A.RA₂ 5 DU-ma 25
40'	25 A.RA₂ 20 ⸢DU⸣-ma 8.20 8.20 TUR a-na 16.40 DAH-ma 16.48.20
41'	16.48.20 A.RA₂ 3 DU-ma] 50(51).25-E 55-AM₃ ⸢TI⸣{qe₂}
42'	55 a-na 5 DAH-ma 1 ŠU KUŠ₃ US₂ 5 ⸢ta⸣-na-aš₂-šar-ma 50(1/3) KUŠ₃(KI) SAG
o ii
1'	[šum-ma 5 am-mat-ka 50 10 KUŠ₃ IGI 50 IL₂-ma 1.12
2'	1.12 A.RA₂ 1.15 DU-ma 1.30 1.30 A.RA₂ 10 1(BAN₂) IL₂-ma 15
3'	15 4-šu₂ IL₂-ma 3.45 50 [i-na 3.45 NIM-ma]
4'	2.55 re-e-hi 2 1/2 NINDA 5 KUŠ₃ [UR.A]
5'	šum-⸢ma⸣ 1 am-⸢mat⸣-ka 10 10 KUŠ₃ IGI 10 IL₂-ma⸣
6'	6 A.RA₂ 3 DU⸣-ma 1.18 18 A.RA₂ 10 1(BAN₂) IL₂-ma
7'	3 4-šu₂] IL₂-ma 45 10 i-na 45 NIM-ma
8'	35 re-e-hi 35 KUŠ₃ UR.A x SAG
9'	A.ŠA₃ 1 PI] ⸢ŠE.NUMUN⸣ GUR₂{up} A.RA₂ 4 1-TA.AM₃ na-pal
10'	[...].A EN AM₃ x x x x iš-tu [kip-pat]
11'	KA₂-a-ni-ti a-di kip-<pat> GUR₂{⸢up⸣} E₂-a-ni-ti MU la₃ ZU{u₂}
12'	1 A.RA₂ 6 DU-ma 6 6 i-⸢na⸣ 30
13'	NIM-ma 24 DU₃ kip-⸢pat⸣ ša₂-ni-ti
14'	6 i-na 24 NIM-ma 18 DU₃ 18 GUR₂ ša₂-lul-ti
15'	6 i-na 18 NIM-ma 12 x 12 ⸢kip-pat⸣ re-bi-ti
16'	6 i-na 12 NIM-ma 6 DU₃ 6 ⸢kip-pat⸣ ha-uš-ti
17'	6 {gana₂}kip-pat E₂-a-⸢ni⸣-ti i-ta-pal
18'	ŠE.NUMUN ša₂ 1 lim KUŠ₃ US₂ u₃ 1 2/3 KUŠ₃ SAG {<\|KI.MIN\|(HE₂.EN)>} ŠE.NUMUN
19'	šum-ma 5 am-mat-ka mi-hi-il-ti A.RA₂ {<\|KI.MIN\|(mi-hi-il-ti)>} u₃
20'	43.12 DU{ak} A.RA₂ 1.23.20 IB.SA šum-ma
21'	1 am-mat-ka mi-hi-il-ti A.RA₂ {<\|KI.MIN\|(mi-hi-il-ti)>}
22'	u₃ A.RA₂ 18 DU-ma A.RA₂ 3.20 IB.SA
23'	1 ME KUŠ₃ US₂ 1 ME KUŠ₃ SAG HE₂.EN ŠE.NUMUN šum-ma 5 am-mat-ka
24'	8.20 1 ME KUŠ₃ 8.20 A.RA₂ 8.20 1.09.28.40 1.09.28.40
25'	A.RA₂ 43.12 DU-ma 5(U) <GUR> 5(BAN₂) ŠE.NUMUN šum-ma 1 am-mat-ka
26'	1.40 1 ME KUŠ₃ 1.40 A.RA₂ 1.40 2.46.20 2.46.40
27'	A.RA₂ 18 DU-ma 50 <GUR> 5(BAN₂)(BI) ŠE.NUMUN
28'	ŠE.NUMUN ša₂ 1 lim KUŠ₃ US₂ u₃ 1.40 KUŠ₃ SAG {<\|KI.MIN\|([HE₂.EN)>} ŠE.NUMUN]
29'	šum-ma 5 am-mat-ka mi-hi-il-ti A.RA₂ {<\|KI.MIN\|([mi-hi-il-ti])>} u₃
30'	A.RA₂ 51.50.24 DU u₃ 1.09.26.40 IB.SA]
31'	šum-ma 1 am-mat-ka mi-hi-il-ti [A.RA₂ {<\|KI.MIN\|(mi-hi-il-ti)>} u₃ A.RA₂]
32'	21.36 DU{ak} A.RA₂ 2.46.40 IB.SA šum-ma]
33'	36 am-mat-ka mi-hi-il-[ti A.RA₂ {<\|KI.MIN\|(mi-hi-il-ti)>} u₃ A.RA₂ 1 DU]
34'	1 ME KUŠ₃ US₂ u₃ 1 ME KUŠ₃ SAG [HE₂.EN ŠE.NUMUN]
35'	šum-[ma 5 am-mat-ka] 8.20 1 ME ⸢KUŠ₃⸣ 8.20 A.RA₂]
36'	8(9).20 1.09.26.40 A.RA₂ 51.50.24 DU-ma 1 1 PI ŠE.NUMUN]
37'	šum-⸢ma⸣ 1 am-mat-ka 1.40 1 ME KUŠ₃ 1.40 A.RA₂ 1.40
r i
1	[...]
2	šum-[ma 5 am-mat-ka mi-hi-il-ti A.RA₂ {<\|KI.MIN\|(mi-hi-il-ti])>}
3	u₃ ⸢A⸣.[RA₂ ...] DU{[ak} A.RA₂ ... DU-ma ...]
4	šum-ma 1 am-⸢mat⸣-[ka] mi-hi-il-ti ⸢A⸣.[RA₂ {<\|KI.MIN\|(mi-hi-il-ti)>} u₃ A.RA₂]
5	24 ⸢DU⸣{ak} A.RA₂ 2.30 [DU-ma ...]
6	1 ME ⸢KUŠ₃⸣ US₂ u₃ 1 ME KUŠ₃ SAG HE₂.EN ŠE.[NUMUN]
7	šum-ma 5 am-mat-ka 8.20 1 ME KUŠ₃ 8.20 A.RA₂ 8.20
8	1.09.26.40 1.09.26.40 A.RA₂ 57.36 DU-[ma]
9	1.06.40 1 PI 4 SILA₃ ŠE.[NUMUN]
10	šum-ma 1 am-mat-ka 1.40.1 ME KUŠ₃ 1.40 A.RA₂ 1.40
11	2.46.40 2.46.40 ⸢A.RA₂ 24 DU-ma 1.06.40
12	ŠE.NUMUN ša₂ 1 lim KUŠ₃ US₂ 1 [lim KUŠ₃ SAG] {<\|KI.MIN\|(HE₂.EN)>} ŠE.NUMUN šum-ma 5
13	⸢am-mat-ka⸣ [mi-hi]-⸢il⸣-ti [A].⸢RA₂⸣ {<\|KI.MIN\|(mi-hi-il-ti)>} u₃ 1.26.24 DU-ma]
14	2.46.40 A.RA₂ x 45 [... šum-ma 1 am-mat-ka]
15	⸢mi-hi⸣-il-tu₂ ⸢A.RA₂ {<\|KI.MIN\|(mi-hi-il-ti)>} [u 36 DU-ma 2.46.40 ...]
16	šum-ma 6 am-[mat]-ka mi-hi-il-tu DU-ma [...]
17	1 ME ⸢KUŠ₃⸣ [US₂ 1 ME KUŠ₃ SAG] HE₂.⸢EN⸣ ŠE.⸢NUMUN⸣
18	šum-ma 5 ⸢am-mat⸣-[ka 8.20 1 ME KUŠ₃ 8.20 A].⸢RA₂ 8.20
19	1.09.26.40 1.09.26.40 A.RA₂ 1.26.24 DU-[ma]
20	1.40 šum-ma 1 am-mat-ka 1.40 1 ME ⸢KUŠ₃⸣ 1.40
21	A.RA₂ 1.40 2.46.40 2.46.40 A.RA₂ 36 ⸢DU-ma⸣
22	1.40 šum-ma 6 am-mat-<ka> 10 1 ME KUŠ₃ 10 [A.RA₂ 10 1.40
23	ša 1 ME KUŠ₃ UR.A 1 ⸢PI 4(BAN₂) ŠE⸣.[NUMUN]
24	ŠE.NUMUN ša 1(iku)(ME){gana₂} 3(BAN₂) [ina KUŠ₃ GAL]{⸢ti⸣} [šum-ma]
25	5 am-mat-ka mi-hi-il-ti [A.RA₂] {<\|KI.MIN\|(mi-hi-il-ti)>}
26	u₃ A.RA₂ 18 DU{ak} [A.RA₂ 3.20 ...]
27	šum-ma 1 am-mat-⸢ka mi⸣-[hi-il]-⸢ti⸣ A.RA₂ {<\|KI.MIN\|(mi-hi-il-ti)>}
28	u₃ A.RA₂ 7.30 DU-ma A.[RA₂ 8 ...]
29	50 NINDA-<AM₃> UR.A ⸢EN⸣ GANA₂ [...] MU la₃ ZU{[u₂]}
30	šum-ma 5 am-mat-ka 50 50 NINDA 50 A.RA₂] 50 DU-ma
31	x 1(BURʾU) 1(EŠE₃) u₃ 1(IKU){⸢gana₂⸣} [...]
32	1(BURʾU) 1(EŠE₃) u₃ 1(IKU){⸢gana₂⸣} 1(IKU){gana₂} [...]
33	ŠE.NUMUN 41.40 A.RA₂ 18 DU{⸢ak} 12.30 [...]
34	šum-ma 1 am-mat-ka 10.1.50(10) KUŠ₃ 10 A.RA₂ 10 1.40 A.RA₂ 7.30
35	DU-ma 12.30 ŠE.[NUMUN]
36	ŠE.NUMUN ša₂ 1(IKU){gana₂} 3(BAN₂) ina] KUŠ₃ GAL{ti} [MU la₃ ZU{u₂]}
37	mi-hi-il-ti A.RA₂ {<\|KI.MIN\|(mi-hi-il-ti)>} ...]
38	[... A].RA₂ 8 DU{ak} A.⸢RA₂⸣ [...]
r ii
1'	[...] US₂ mi-hi-il-ti A.RA₂ mi-hi-⸢il⸣-[ti]
2'	[DU ...] A.RA₂ [x] DU{ak} A.RA₂ 2-AM₃
3'	1 UŠ(GANA₂) US₂ u₃ 1 US₂ SAG HE₂.EN GANA₂{ki}HI.A 1 A.⸢RA₂⸣ 1 1
4'	A.RA₂ 30 30 1(EŠE₃) GANA₂{ki}HI.A
5'	1 {gana₂}SAG.KAK UR.A ša 8-šu na-as-hu mi-hi-il-tu₂
6'	A.RA₂ {<\|KI.MIN\|(mi-hi-il-ti)>} u₃ A.RA₂ 26.15 DU
7'	1 UŠ-AM₃ UR.A HE₂.EN GANA₂{ki}HI.A 1 A.[RA₂ 1 1 ⸢A⸣.[RA₂]
8'	26.15 DU-ma 26.15 1(EŠE₃) 1(EŠE₃) 3(IKU){gana₂} 1/2(IKU){gana₂} 25 [SAR GANA₂{ki}HI].⸢A⸣
9'	1(4) {gana₂}SAG.KAK UR.A ša 10-šu u₃ 30-šu na-as-hu
10'	⸢mi⸣-hi-il-tu₂ A.RA₂ {<\|KI.MIN\|(mi-hi-il-ti)>} ⸢u₃⸣ 26 ⸢DU⸣{ak}
11'	[...] A 1 A.RA₂ 1 1 A.RA₂

Sources & licences

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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)

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