MKT 1, 513 (P255010)

Mathematical tablet excavated in Uncertain (mod. uncertain), dated to the Old Babylonian (ca. 1900-1600 BC) period and now kept in Yale Babylonian Collection, New Haven, Connecticut, USA

Cite

Photo

Lineart

Photo (detail)

Lineart (detail)

Museum Collection(s)

Yale Babylonian Collection, New Haven, Connecticut, USA

Museum Number

YBC 04698

Period

Old Babylonian (ca. 1900-1600 BC)

Provenience

uncertain (mod. uncertain)

Artifact Type

Tablet

Material(s)

Clay

Genre / Subgenre(s)

Scholarly or scientific > Mathematical (problem text)

Language(s)

Measurements

Text

tablet
obverse
column 1
1. _sze_ a-na _1(asz) sze gur_
en: (Problem 1:) (When the principal in) grain (is) as much as 1 gur of grain,
2. _1(barig) sze_ a-na _masz2 szum2_
en: 1 barig of grain as the interest I give.
3. _sze u3 masz2 en-nam_
en: The grain and the interest are how much?
double ruling
4. _sze_ a-na _1(asz) sze gur_
en: (Problem 2:) (When the principal in) grain (is) as much as 1 gur of grain,
5. _1(barig) 4(ban2)_ a-na _masz2 szum2_
en: 1 barig 4 ban2 as the interest I give.
6. _sze u3 masz2 en-nam_
en: The grain and the interest are how much?
double ruling
7. _3(disz) sila3-ta i3 sag_
en: (Problem 3:) (Rates in-kind are) 3 sila3 of first quality oil per (gin2)
8. _1(ban2) 2(disz) sila3-ta i3-gesz_
en: (and) 1 ban2 2 sila3 of common oil per (gin2).
9. _1(disz) gin2 ku3-babbar szum2_
en: 1 gin2 of silver I gave.
10. _i3-gesz u3 i3 sag_
en: Common oil and first quality oil
11. _ib2-sa2_-ma _sa10_
en: I made equal and I bought.
double ruling
12. _1(gesz2) 3(u) dug an-bar_
en: (Problem 4:) 90 DUG of iron
13. _9(disz)? dug ku3-sig17_
en: 9? DUG of gold,
14. _1(disz) ma-na ku3-babbar szum2_
en: 1 mana silver I gave.
15. _an-bar u3 ku3-sig17_
en: The iron and gold
16. _1(disz) gin2_-ma _sa10_
en: (is) 1 gin2 and I bought.
double ruling
17. _1/2(disz) ma-na ku3-babbar szum2_
en: (Problem 5:) 1/2 mana of silver I gave.
18. _1(asz) gur-ta sa10_
en: 1 gur per (gin2) I bought.
double ruling
column 2
1. _3(u) sze gur_
en: (Problem 6:) 30 gur grain
2. _1(asz) sze gur-ta sa10-ma_
en: 1 gur of grain per (gin2) I bought,
3. _4(barig) sze-ta bur2-ra_
en: 4 barig of grain per (gin2) I sold.
4. _ku3 diri en-nam_
en: The profit in silver is how much?
5. _7(disz) 1/2(disz) gin2 ku3-babbar diri_
en: 7 1/2 gin2 of silver is the profit.
double ruling
6. _sag ku3-bi en-nam_
en: (Problem 7:) The initial price is how much?
double ruling
7. _1(asz) gur i3-gesz_
en: (Problem 8:) 1 gur of common oil.
8. _1(ban2)-ta sa10-ma_
en: 1 ban2 per (gin2) I bought and,
9. _8(disz) sila3-ta bur2-ra_
en: 8 sila3 per (gin2) I sold.
10. _ku3 diri en-nam_
en: The profit is how much?
11. _7(disz) 1/2(disz) gin2 ku3 diri_
en: 7 1/2 gin2 is the profit.
double ruling
12. _1(asz) gur i3-gesz_
en: (Problem 9:) 1 gur of common oil.
13. _i-na sa10 1(disz)! gin2_
en: When the purchase is 1! (text: 2) gin2,
14. _2(disz) sila3 szusz4_
en: 2 sila3 I cut.
15. _7(disz) 1/2(disz) gin2 ku3 diri_
en: 7 1/2 gin2 is the profit.
16. _en-nam sa10-ma_
en: How much did I buy?
17. _en-nam bur2-ra_
en: How much did I sell?
18. _1(ban2) sa10-ma_
en: 1 ban2 I bought and
19. _8(disz) sila3 bur2-ra_
en: 8 sila3 I sold.
double ruling
reverse
column 1
1. _1(asz) gur i3-gesz_
en: (Problem 10:) 1 gur of common oil.
2. _9(disz) sila3-ta sa10-ma_
en: 9 sila3 per (gin2) I bought,
3. _7(disz) 1/2(disz) sila3 bur2-ra_
en: 7 1/2 sila3 per (gin2) I sold.
4. _ku3 diri en-nam_
en: The profit is how much?
5. _6(disz) 2/3(disz) gin2 ku3 diri_
en: 6 2/3 gin2 is the profit
double ruling
6. _1(asz) gur i3-gesz_
en: (Problem 11:) 1 gur of common oil.
7. i-na _sa10 1(disz) gin2 1(disz) 1/2(disz) sila3 szusz4_
en: When the purchase is 1 gin2, 1 1/2 sila3 I cut.
8. _6(disz) 2/3(disz) gin2 ku3 diri_
en: 6 2/3 gin2 is the profit.
9. _en-nam sa10-ma en-nam bur2-ra_
en: How much did I buy? How much did I sell?
10. _9(disz) sila3 sa10-ma 7(disz) 1/2(disz) sila3 bur2-ra_
en: 9 sila3 I bought, and 7 1/2 sila3 is sold.
double ruling
11. _7(disz) ma-na u3 1(u) 1(disz) ma-na siki gesz?_
en: (Problem 12:) (Per) 7 mana and 11 mana of ... wool
12. _1(disz) gin2 ku3 szum2 ib2-sa2_-ma _sa10-ma_
en: 1(disz) gin2 I paid. I made equal and I bought.
13. _4(disz) 1(u) 6(disz) 4(u) sa10_
en: 4.16.40 I bought.
double ruling
14. _7(disz) sila3-ta i3-gesz_
en: (Problem 13:) Per 7 sila3 of common oil
15. _1(ban2) 2(disz) sila3-ta i3-szah2_
en: per 1 ban2 2 sila3 of lard,
16. _1(disz) gin2 szum2 ib2-sa2_-ma _sa10 2(ban2) 3(disz) 1/3(disz) sila3_
en: 1 gin2 I gave. I made equal and I bought: 2 ban2 3 1/3 sila3.
double ruling
17. _ganba_ a-na _1(disz) 2(disz) 3(disz) 4(disz) 5(disz)_
en: (Problem 14:) (When) rates (in-kind are) as much as 1 2 3 4 5
18. _6(disz) 7(disz) 8(disz) 9(disz) ganba_
en: 6 7 8 9, the rate (in grain)
19. _1(barig) sze szum2 sze he2-e3_
en: 1 barig I give. Let the grain rise
20. _u3 he2-e11_-ma
en: or fall so that
21. _ganba ib2-sa2_
en: the rates in-kind are equal.
double ruling
column 2
1. _ganba 3(disz) ku6-a 5(disz) sila3_
en: (Problem 15:) Rate in-kind for 3 fish, 5 sila3
2. _5(disz) ku6-a ku6 x-x_
en: for 5 fish, fish ...
3. _sze gar-gar_-ma _4(asz) 1(barig) 4(ban2) 5(disz)? <sila3>_
en: The grain I added: 4 (gur) 1 barig 4 ban2 5 (2?) (sila3)
4. _ku6-a gar-gar_-ma _ku6_
en: The fish I added. Let the fish
5. _sze he2-e3 u3 he2-e11_-ma
en: and the grain rise or fall
6. _ku6-a ib2-sa2_
en: so that the fish are equal.
double ruling
7. ma-la _ganba hi-a nagga_
en: (Problem 16:) As much as the rates in-kind of the lead
8. _ku3 i3?-la2_-ma
en: silver I weighed and
9. _nagga sa10_
en: lead I bought.
10. _ku3 u3 nagga gar-gar_-ma
en: The silver and the lead I added:
11. _7(disz) ma-na ku3 u3 nagga_
en: 7 mana. The silver and the lead
12. _en-nam_
en: are how much?
double ruling
13. _na4 szu-ti-a_-ma
en: (Problem 17:) Stones I received and
14. _ki-la2-bi nu-zu_
en: their weight I don’t know.
15. _6(disz)-ta sa10_
en: 6 (stones) per (gin2) I bought.
16. _6(disz)-ta ku3-sig17 gar-ra_
en: 6 gold inlaid (stones) per (gin2 I bought).
17. _ku3-sig17 gar-ra_
en: Gold inlaid (stones),
18. a-na _6(disz)-ta sa10_
en: as much as 6 (stones) per (gin2) I bought.
19. _na4 ku3-babbar en-nam_
en: The stone, the silver how much
20. _gar-gar_-ma _1/2(disz) ma-na 1(disz) 1/2(disz) gin2_
en: did I add? 1/2 mana 1 1/2 gin2
21. _x ma na? gar-gar_-ma
en: ... I added and
22. _1(disz) ma-na 3(disz) gin2_
en: 1 mana 3 gin2.
double ruling
23. ($ blank space $) _dub 3(disz)-kam-ma_
en: 3rd tablet.
blank space is erasure

Consult previous versions and their differences
Consult sign list of Old Babylonian (ca. 1900-1600 BC)
Consult word list of Old Babylonian (ca. 1900-1600 BC)

Text content

Genre(s)	Scholarly or scientific > Mathematical (problem text)
Language(s)

Chronology

Period	Old Babylonian (ca. 1900-1600 BC)
Dates Referenced
Accounting Period

Record

CDLI number	P255010
LOD URI	https://cdli.network/entity/P255010

Physical information

Artifact type	Tablet
Dimensions
Weight
Material(s)	Clay
Preservation

Provenance

Provenience	uncertain (mod. uncertain)
Written In
Archive
Excavation Number
Findspot
Stratigraphic Level
Elevation

Collections

Collection(s)	Yale Babylonian Collection, New Haven, Connecticut, USA
Museum Number	YBC 04698
Accession Number

External resources

External Resource	Identifiers
Yale Babylonian Collection (YBC)	BC-018763
Electronic Babylonian Library (eBL)	YBC.4698

References

primary: MKT 1, 513

[Neugebauer1935MKT1] Neugebauer, Otto E. 1935. Mathematische Keilschrift-Texte. Erster Teil: Texte. Quellen Und Studien Zur Geschichte Der Mathematik, Astronomie Und Physik, Abteilung A: Quellen 3. Berlin: Verlag von Julius Springer.
history: New MCT, §11.1 YBC 04698

[Friberg2016NewMCT] Friberg, Jöran, and Farouk N. H. al-Rawi. 2016. New Mathematical Cuneiform Texts. Sources and Studies in the History of Mathematics and Physical Sciences. Cham : Springer.
history: MKT 3, 042, TMB 214

[Neugebauer1935-1937MKT3] Neugebauer, Otto E. 1935-1937. Mathematische Keilschrifttexte Vol. 3. Berlin, Springer.
history: Middeke-Conlin, Robert & Proust, Christine, CDLJ 2014/003

[sec46942] N.d.

Revisions and credits

Created	Creator	Type	Authors	Project	Reviewer	Status
2024-08-28 at 10:09:45	Firth, Richard	Artifact metadata, Other metadata	Firth, Richard		Firth, Richard	Approved
2024-08-28 at 10:07:33	Firth, Richard	Artifact metadata, Other metadata	Firth, Richard		Firth, Richard	Approved
2023-01-19 at 10:20:17	Pagé-Perron, Émilie	Artifact metadata	Földi, Zsombor J.; Jiménez, Enrique; Pagé-Perron, Émilie	Electronic Babylonian Library	Pagé-Perron, Émilie	Approved
2014-01-20 at 14:12:56	Englund, Robert K.	Transliteration	Englund, Robert K.		CDLI, CDLI	Approved
2014-01-20 at 14:07:28	Englund, Robert K.	Transliteration	Englund, Robert K.		CDLI, CDLI	Approved
2014-01-20 at 13:54:07	Englund, Robert K.	Transliteration	Englund, Robert K.		CDLI, CDLI	Approved
2014-01-20 at 11:12:52	Englund, Robert K.	Transliteration	Englund, Robert K.		CDLI, CDLI	Approved
2005-02-01 at 00:00:00	CDLI, CDLI	Artifact metadata	Friberg, Jöran; Guerra, Dylan; Middeke-Conlin, Robert; Peterson, Jeremiah		CDLI, CDLI	Approved

Cite this Artifact

“MKT 1, 513 Artifact Entry.” (2005) 2024. Cuneiform Digital Library Initiative (CDLI). August 28, 2024. https://cdli.earth/P255010.

MKT 1, 513 artifact entry (No. P255010). (2024, August 28). Cuneiform Digital Library Initiative (CDLI). https://cdli.earth/P255010 (Original work published 2005)

MKT 1, 513 artifact entry (2024) Cuneiform Digital Library Initiative (CDLI). Available at: https://cdli.earth/P255010 (Accessed: November 6, 2026).

@misc{2024MKT,
	note = {[Online; accessed 2026-11-06]},
	year = {2024},
	month = {aug 28},
	title = {MKT 1, 513 artifact entry},
	url = {https://cdli.earth/P255010},
	howpublished = {https://cdli.earth/P255010},
}

TY  - ELEC
DA  - 2024/8/28/
PY  - 2024
ID  - P255010
LB  - CDLI:P255010
M1  - 2026/11/6/
TI  - MKT 1, 513 artifact entry
UR  - https://cdli.earth/P255010
ER  -

Cite this Artifact

“MKT 1, 513 Artifact Entry.” (2005) 2024. Cuneiform Digital Library Initiative (CDLI). August 28, 2024. https://cdli.earth/P255010.

MKT 1, 513 artifact entry (No. P255010). (2024, August 28). Cuneiform Digital Library Initiative (CDLI). https://cdli.earth/P255010 (Original work published 2005)

MKT 1, 513 artifact entry (2024) Cuneiform Digital Library Initiative (CDLI). Available at: https://cdli.earth/P255010 (Accessed: November 6, 2026).

@misc{2024MKT,
	note = {[Online; accessed 2026-11-06]},
	year = {2024},
	month = {aug 28},
	title = {MKT 1, 513 artifact entry},
	url = {https://cdli.earth/P255010},
	howpublished = {https://cdli.earth/P255010},
}

TY  - ELEC
DA  - 2024/8/28/
PY  - 2024
ID  - P255010
LB  - CDLI:P255010
M1  - 2026/11/6/
TI  - MKT 1, 513 artifact entry
UR  - https://cdli.earth/P255010
ER  -