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  • BM 085200 +

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  • Old Babylonian
  • Sippar
  • mathematical
  • word-problem

BM 085200 + (MKT 1, 193) [word-problem]

Obverse
Column i
(start of column missing)
o i 1'o 1'

[...] x x IGI

(o i 1') [...] ... [...] ... [...] the procedure.

o i 2'2'

[...] BI

o i 3'3'

[... ne]--šum

o i 4'4'

[...] EN.NAM

(o i 4') [...] what? [...] ... [...] you will see. [...] Square 2. [...] Multily [3 by] 2. The height is 6. [That is] the procedure.

o i 5'5'

[...] x

o i 6'6'

[...] ta-mar

o i 7'7'

[...] 2 NIGIN

o i 8'8'

[... 3 a-na] 2 i-ši 6 SUKUD

o i 9'9'

[ki-a-am ne-]-šum


o i 10'10'

[... EN].NAM

(o i 10') [...] what? [...]

o i 11'11'

[...] x

o i 12'12'

[...] x

(6 lines missing)
o i 18'18'

[... ÚS SAG] EN.NAM

(o i 18') h1 Problem (i') [...]. What are [the length and width]?

o i 19'19'

[...] 3 ta-mar 1/2 3 ḫe- 1.30 ta-mar

(o i 19') [...] You will see 3. Break 3 in half. You will see 1;30.

o i 20'20'

[... IGI 1.30 DU₈.A] 40 ta-mar BAL SAG IGI 12 BAL BÙR DU₈.A

(o i 20') [... Release the rešiprošal of 1;30.] You will see 0;40. The ratio of the width. Release the rešiprošal of 12, the ratio of the depth.

o i 21'21'

[5 ta-mar] 5 a-na 1 i-ši 5 ta-mar a-na 40 i-ši 3.20 ta-mar

(o i 21') [You will see 0;05.] Multiply 0;05 by 1. You will see 0;05. Multiply by 0;40. You will see 0;03 20.

o i 22'22'

3.20 a-na 5 i-ši 16.40 ta-mar IGI 16.40 DU₈.A 3.36 ta-mar 3.36

(o i 22') Multiply 0;03 20 by 0;05. You will see 0;00 16 40. Find the reciprocal of 0;00 16 40. You will see 3 36. Multiply 3 36 by 1;10. You will see 4 12. The square-side is 6. Multiply 6 by 0;05. The length is 0;30. Multipy 6 by 0;03 20.

o i 23'23'

a-na 1.10 i-ši 4.12 ta-mar 6 ÍB.SI₈ 6 a-na 5 i-ši 30 ÚS 6 a-na 3 20 i-<ši>

o i 24'24'

20 SAG 6 a-na 1 i-ši 6 ta-mar BÙR ki-a-am

(o i 24') The width is 0;20. Multiply 6 by 1. You will see 6, the depth. That is the procedure.

o i 25'25'

ne--šum


o i 26'26'

.SAG ma-la ÚS BÙR-ma 1 SAḪAR-ḪI.A BA.ZI KIri ù SAḪAR-ḪI.A UL.GAR 1.10 ÚS ù SAG 50 ÚS SAG EN.NAM

(o i 26') h1 Problem (ii') An excavation. The length is equal to the depth. I removed 1, the volume. I summed my ground-area and the volume: 1;10. The (sum of the) length and width is 0;50. What are the length and width?

o i 27'27'

ZA.E 50 a-na 1 BAL i-ši 50 ta-mar 50 a-na 12 i-ši 10 ta-mar

(o i 27') You: Multiply 0;50 by 1, the ratio. You will see 0;50. Multiply 0;50 by 12. You will see 10.

o i 28'28'

10!(50) šu-tam-<ḫir> 41.40 ta-mar a-na 10 i-ši 6.56.40 ta-mar IGI-šu DU₈.A 8.38.44 ta-<mar>

(o i 28') Square 0;50. You will see 0;41 40. Multiply by 10. You will see 6;56 40. Find its reciprocal. You will see 0;08 38 44.

o i 29'29'

a-na 1.10 i-ši 10.04.48 ta-mar 36 24 42 ÍB.SI₈

(o i 29') Multiply by 1;10. You will see 0;10 04 48. The square-sides are 0;36, 0;24, 0;42.

o i 30'30'

36 a-na 50 i-ši 30 ÚS 24 a-na 50 i-ši 20 SAG 36 a-na 10 <i-ši> 6 BÙR

(o i 30') Multiply 0;36 by 0;50. The length is 0;30. Multiply 0;24 by 0;50. The width is 0;20. <Multiply> 0;36 by 10. The depth is 6. The procedure.

o i 31'31'

ne--šum


o i 32'32'

.SAG ma-la ÚS BÙR-ma 1 SAḪAR-ḪI.A BA.ZI KIri ù SAḪAR-ḪI.A UL.<GAR> 1.10 ÚS UGU SAG 10 DIRI

(o i 32') h1 Problem (iii') An excavation. The depth is as much as the length. I removed 1, the volume. I summed my ground-area and volume: 1;10. The length exceeded the width by 0;10.

o i 33'33'

ZA.E 1 ù 12 BAL GAR.RA 10 DIRI a-na 1 i-ši 10 ta-mar a-na 12 i-ši 2 ta-mar

(o i 33') You: Put down 1 and 12, the ratios. Multiply 0;10, the excess, by 1. You will see 0;10. Multiply by 12. You will see 2.

o i 34'34'

10 šu-tam-<ḫir> 1.40 ta-mar a-na 2 i-ši 3.20 ta-mar IGI 3.20 DU₈.A 18 ta-mar

(o i 34') Square 0;10. You will see 0;01 40. Multiply by 2. You will see 0;03 20. Find the reciprocal of 0;03 20. You will see 18.

o i 35'35'

a-na 1.10 i-ši 21 ta-mar 3 2 21 ÍB.SI₈ [10 a-na 3] i-ši 30 ÚS

(o i 35') Multiply by 1;10. You will see 21. The square-sides are 3, 2, 21. Multiply [0;10 by 3]. The length is 0;30.

o i 36'36'

10 a-na 2 i-ši 20 SAG 3 a-na 2 i-ši 6 ta-mar [6] BÙR

(o i 36') Multiply 0;10 by 2. The width is 0;20. Multiply 3 by 2. You will see 6. The depth is [6]. The procedure.

o i 37'37'

ne--šum


o i 38'38'

.SAG ma-la ÚS BÙR-ma SAḪAR-ḪI.A BA.ZI KIri ù SAḪAR-ḪI.A UL.GAR-ma 1.10 30 ÚS SAG EN.[NAM]

(o i 38') h1 Problem (iv') An excavation. The length is as much as the depth. I removed a volume.I summed my ground-area and the volume: 1;10. The length is 0;30. What is the width?

o i 39'39'

ZA.E 30 ÚS a-na 12 i-ši 6 ta-mar BÙR 1 a-na 6 DAḪ.ḪA 7 ta-mar

(o i 39') You: multiply 0;30, the length, by 12. You will see 6, the depth. Add 1 to 6. You will see 7.

o i 40'40'

IGI 7 NU DU₈.A EN.NAM a-na 7 GAR.RA ša 1.10 SUM.MU 10 GAR.RA IGI 30 ÚS DU₈.A

(o i 40') The reciprocal of 7 cannot be found. What should I put to 7 that will give me 1;10? Put 0;10. Solve the reciprocal of 0;30, the length.

o i 41'41'

2 ta-mar 10 a-na 2 i-ši 20 SAG ta-mar

(o i 41') You will see 2. Multiply 0;10 by 2. You will see 0;20, the width. The procedure.

o i 42'42'

ne--šum


o i 43'43'

.SAG ma-la ÚS BÙR-ma SAḪAR-ḪI.A BA.ZI KIri ù SAḪAR-ḪI.A UL.GAR-ma 1.10 20 SAG ÚS <EN.NAM>

(o i 43') h1 Problem (v') An excavation. The length is as much as the depth. I removed a volume. I summed my ground-area and the volume: 1;10. The width is 0;20. <What is> the length?

o i 44'44'

ZA.E 20 a-na 12 i-ši 4 ta-mar 4 a-na 1.10 i-ši 4.40 ta-mar

(o i 44') You: multiply 0;20 by 12. You will see 4. Multiply 4 by 1;10. You will see 4;40.

o i 45'45'

1/2 20 SAG ḫe- 10 ta-mar 10 šu-tam-ḫir 1.40 ta-mar a-na 4.40 DAḪ.ḪA

(o i 45') Break in 1/2 0;20, the width. You will see 0;10. Square 0;10. You will see 0;01 40. Add to 4;40.

o i 46'46'

4.41.40 ta-mar 2.10 ÍB.SI₈ 10 ša Ì.GU₇.GU₇ BA.ZI-ma

(o i 46') You will see 4;41 40. The square-side is 2;10. Subtract 0;10 that you squared and you will see 2. Find the reciprocal of 4. you will 0;15. Multiply by 2.

o i 47'47'

2 ta-mar IGI 4 DU₈.A 15 ta-mar a-na 2 i-ši

o i 48'48'

30 ta-mar ÚS

(o i 48') You will see 30, the length. The procedure.

o i 49'49'

ne--šum


Column ii
(start of column missing)
o ii 1'o 1'

[...] DAḪ.ḪA [...]

(o ii 1') h1 Problem (vi') [...] add [...] 4;30, 53;20, 1;45 ... [...]

o ii 2'2'

4.30 53.20 1.45 x [...]

o ii 3'3'

30 ÚS 22.30 a-na 53.20 i-ši 20 SAG [...]

(o ii 3') The length is 0;30. Multiply 0;22 30 by 0;53 20. The width is 0;20. [...] The procedure.

o ii 4'4'

ne--šum


o ii 5'5'

.SAG ma-la ÚS BÙR-ma SAḪAR-ḪI.A BA.ZI KIri ù SAḪAR-ḪI.A UL.[GAR]

(o ii 5') An excavation. The length is as much as the depth. I removed a volume. I summed my ground-area and the volume.

o ii 6'6'

IGI 7-GÁL él- a-na KIri DAḪ.ḪA-ma 20-E 30 [ÚS SAG EN.NAM]

(o ii 6') I took a 7th. I added (it) to my ground-area and it was 0;20. [The length is] 0;30. [What is the width?]

o ii 7'7'

ZA.E 30 a-na 12 i-ši 6 ta-mar BÙR 1 a-na 6 [DAḪ.ḪA]

(o ii 7') You: multiply 0;30 by 12. You will see 6, the depth. [Add] 1 to 6.

o ii 8'8'

7 ta-mar IGI 7-GÁL le- 1 ta-mar 1 ù 1 UL.[GAR]

(o ii 8') You will see 7. Take a 7th. You will see 1. Sum 1 and 1.

o ii 9'9'

2 ta-mar IGI 2 DU₈.A 30 ta-mar 30 a-na 20 UL.GAR i-[ši]

(o ii 9') You will see 2. Find the reciprocal of 2. You will see 0;30. Multiply 0;30 by 0;20, the sum.

o ii 10'10'

10 ta-mar IGI 30 ÚS DU₈.A 2 ta-mar 2 a-na 10 i-ši [20 SAG]

(o ii 10') You will see 0;10. Find the reciprocal of 0;30, the length. You will see 2. Multiply 2 by 0;10. [The width is 0;20.] The procedure.

o ii 11'11'

ne--šum


o ii 12'12'

.SAG ma-la ÚS BÙR-ma SAḪAR-ḪI.A BA.ZI --ri ù SAḪAR-ḪI.A UL.[GAR]

(o ii 12') h1 Problem (vii') An excavation. The length is as much as the depth. I removed a volume. I summed my ground-area and the volume: 1;10 I took a 7th of it. I added (it) to my ground-area: 0;20. The width was 20.

o ii 13'13'

1.10 IGI 7-GÁL-šu él- a-na KIri DAḪ 20 20 SAG

o ii 14'14'

ZA.E 20 a-na 7 i-ši 2.20 ta-mar 20 SAG a-na 12 i-ši

(o ii 14') You: multiply 0;20 by 7. You will see 2;20. Multiply 0;20, the width, by 12.

o ii 15'15'

4 ta-mar 4 a-na 2.20 i-ši 9.20 ta-mar a-na 7 1 DAḪ.ḪA

(o ii 15') You will see 4. Multiply 4 by 2;20. You will see 9;20. Add 1 to 7.

o ii 16'16'

8 ta-mar 20 a-na 8 i-ši 2.40 ta-mar 1/2 2.40 ḫe- [šu-<tam-ḫir>]

(o ii 16') You will see 8. Multiply 8 by 0;20. You will see 2;40. Break 1/2 of 2;40. [Square (it).]

o ii 17'17'

1.46.40 ta-mar a-na 9.20 DAḪ.ḪA 11.06.40 ta-[mar]

(o ii 17') You will see 1;46 10. Add to 9;20. You will see 11;06 40.

o ii 18'18'

3.20 ÍB.SI₈ 1.20 ša Ì.GU₇.GU₇ BA.ZI 2 ta-[mar]

(o ii 18') The square-side is 3;20. Subtract the 1;20 that you squared. You will see 2.

o ii 19'19'

IGI 4 DU₈.A 15 ta-mar 15 a-na 2 i-ši 30 [ÚS]

(o ii 19') Find the riciprocal of 4. You will see 0;15. Multiply 0;15 by 2. [The length is] 0;20. The procedure.

o ii 20'20'

ne--šum


o ii 21'21'

.SAG ma-la IGI ÚS ma-la IGI.BI SAG ma-la <ša> IGI UGU IGI.BI DIRI

(o ii 21') h1 Problem (viii') An excavation. The length is as much as a reciprocal. The width is as much as its reciprocal pair. The depth is as much as that by which the the reciprocal exceeds its reciprocal pair. I removed [a volume] of 16. What are the length, width, and depth?

o ii 22'22'

BÙR-ma 16 [SAḪAR-ḪI.A BA].ZI ÚS SAG ù BÙR EN.NAM

o ii 23'23'

ZA.E IGI 12 DU₈.[A 5] ta-mar 5 [a-na] 16 i-ši [1].20 ta-<mar>

(o ii 23') You: find the reciprocal of 12. You will see [0;05]. Multiply 0;05 by 16. You will see [1];20.

o ii 24'24'

1.20 IGI IGI 1.20 [DU₈.A 45 ta]-mar 45!(40) IGI.BI [16] BÙR

(o ii 24') The reciprocal is 1;20. [Find] the reciprocal of 1;20. You will see [0;45]. Its recipocal pair is 0;45. The depth is [16]. The procedure.

o ii 25'25'

ne-[]-šum


o ii 26'26'

.SAG ma-la IGI ÚS ma-[la IGI.BI] SAG ma-la ša IGI UGU IGI.BI DIRI <BÙR-ma>

(o ii 26') h1 Problem (ix') An excavation. The length is as much as a reciprocal. The width is as much as [its reciprocal pair]. <The depth is> as much as that by which the reciprocal exceeds its reciprocal pair.

o ii 27'27'

36 SAḪAR-ḪI.A BA.ZI IGI [IGI.BI ù BÙR] EN.NAM

(o ii 27') I removed a volume of 26. What are the reciprocal, [its reciprocal pair, and the depth]?

o ii 28'28'

ZA.E IGI 12 DU₈.A [5 ta-mar] 36 a-na 5 <<a-na 36⸣>> i-<ši>

(o ii 28') You: solve the reciprocal of 12. You will see 0;05. Multiply 36 by 0;05 <<by 36>>.

o ii 29'29'

3 ta-mar 1/2 3 ḫe-[ 1.30 ta-mar] 1.30 IGI 40 IGI.[BI] 36 BÙR

(o ii 29') You will see 3. Break 3 in 1/2. [You will see 1;30.] The recriprocal is 1;30. Its reciprocal pair is 0;40. The depth is 36. The procedure.

o ii 30'30'

ne--šum


o ii 31'31'

.SAG ma-la IGI ÚS ma-la [IGI.BI SAG] ma-la NIGIN IGI ù IGI.BI BÙR-ma

(o ii 31') h1 Problem (x') An excavation. The length is as much as a reciprocal. [The width is as much as its reciprocal pair]. The depth is as much as the total of the reciprocal and its reciprocal pair.

o ii 32'32'

26 SAḪAR-ḪI.A BA.ZI IGI IGI.BI ù BÙR EN.NAM

(o ii 32') I removed a volume of 26. What are the reciprocal, its reciprocal pair, and the depth?

o ii 33'33'

ZA.E IGI 12 DU₈.A 5 ta-mar 5 a-na 26 i-ši

(o ii 33') You: find the reciprocal of 12. You will see 0;05. Multiply 0;05 by 26.

o ii 34'34'

2.10 ta-mar 1/2 2.10 ḫe- šu-tam-<ḫir> 1.10.25 ta-mar <1 i-na 1.10.25 BA.ZI 10.25 ta-mar>

(o ii 34') You will see 2;10. Break 2;10 in 1/2. Square (it). You wil see 1;10 25. <Subtract 1 from 1;10 25. You will see 0;10 25.>

o ii 35'35'

25 ÍB.SI₈ a-na <1>.05 DAḪ ù BA.ZI 1.30 ù!(IGI) 40 ta-[mar]

(o ii 35') The square-side is 0;25. Add and subtract (it) to <1>;05. You will see 1;30 and 0;40.

o ii 36'36'

1.30 IGI 40 IGI.BI 26 BÙR

(o ii 36') The reciprocal is 1;30. Its reciprocal pair is 0;40. The depth is 26. The procedure.

o ii 37'37'

ne--šum


o ii 38'38'

.SAG ma-la IGI ÚS ma-la IGI.BI SAG ma-la ša IGI UGU IGI.BI DIRI

(o ii 38') h1 Problem (xi') An excavation. The length is as much as a reciprocal. The width is as much as its reciprocal pair. The depth is as much as that by which the reciprocal exceeds its reciprocal pair, subtracted from the reciprocal. I removed a volume of 6. [What are] the reciprocal and its reciprocal pair?

o ii 39'39'

i-na IGI BA.ZI BÙR-ma 6 SAḪAR-ḪI.A BA.ZI IGI ù IGI.BI [EN.NAM]

o ii 40'40'

ZA.E IGI 12 DU₈.A 5 ta-mar a-na 6 i-ši 30 ta-mar

(o ii 40') You: find the reciprocal of 12. You will see 0;05. Multiply by 6. You will see 0;30.

o ii 41'41'

IGI 30 DU₈.A 2 ta-mar 2 IGI 30 IGI.BI 6 BÙR

(o ii 41') Find the reciprocal of 0;30. You will see 2. The reciprocal is 0;30, its reciprocal pair 2, the depth 6. The procedure.

o ii 42'42'

ne--šum


o ii 43'43'

.SAG ma-la IGI ÚS ma-la IGI.BI SAG ma-la NIGIN IGI IGI.BI [BÙR]-ma 30 SAḪAR-[ḪI.A BA.ZI]

(o ii 43') h1 Problem (xii') An excavation. The length is as much as a reciprocal. The width is as much as its reciprocal pair. The [depth] is as much as the total of the reciprocal and its recriproal pair. [I removed] a volume of 30.

o ii 44'44'

ZA.E IGI 12 DU₈.A 5 ta-mar 5 a-na 30 SAḪAR-ḪI.A i-ši

(o ii 44') You: find the reciprocal of 12. You will see 0;05. Multiply 0;05 by 30, the volume.

o ii 45'45'

2.30 ta-mar 1/2 2.30 ḫe- šu-[tam-ḫir 1.33].45 ta-[mar]

(o ii 45') You will see 2;30. Break 2;30 in 1/2. Square (it). You will see [1;33] 45.

o ii 46'46'

1 i-na 1.33.45 BA.ZI 33.45 ta-mar 45 ÍB.SI₈

(o ii 46') Subtract 1 from 1;33 45. You will see 0;33 45. The square-side is 0;45.

o ii 47'47'

a-na 1.45 DAḪ.ḪA ù BA.ZI 2 ù 30 ta-mar

(o ii 47') Add and subtract from 1;45. You will see 2 and 0;30. The procedure.

o ii 48'48'

ne--šum


o ii 49'49'

.SAG ma-la IGI ÚS ma-la IGI.BI SAG ma-la IGI.BI BÙR-ma

(o ii 49') h1 Problem (xiii') An excavation. The length is as much as a reciprocal. The width is as much as its reciprocal pair. The depth is as much as the reciprocal pair.

o ii 50'50'

20 SAḪAR-ḪI.A BA.<ZI> IGI IGI.BI ù BÙR EN.NAM

(o ii 50') I removed a volume of 20. What are the reciprocal, its reciprocal pair, and the depth?

o ii 51'51'

ZA.E IGI 12 DU₈.A a-na 20 i-ši 1.40 ta-mar

(o ii 51') You: find the reciprocal of 12. Multiply by 20. You will see 1;40.

o ii 52'52'

1.40 IGI 36 IGI.BI 20 BÙR

(o ii 52') The reciprocal is 1;40. Its reciprocal pair is 0;36. The depth is 20. The procedure.

o ii 53'53'

ne--šum

Reverse
Column i
r i 1r i 1

.SAG ma-la -tam-<ḫir> ù 7 KÙŠ BÙR-ma 3.20 SAḪAR-ḪI.A BA.ZI

(r i 1) h1 Problem (xiv') An excavation. The depth is as much as I squared and 7 cubits. I removed 3 20, the volume.

r i 22

ÚS SAG ù BÙR EN.NAM

(r i 2) What are the length, width, and depth?

r i 33

ZA.E IGI 7-GÁL 7 le- 1 ta-mar IGI 12 DU₈.A 5 ta-mar

(r i 3) You: take a 7th of 7. You will see 1. Find the reciprocal of 12. You will see 0;05.

r i 44

5 a-na 1 i-ši 5 ta-mar 5 a-na 12 i-ši 1 ta-mar

(r i 4) Multiply 0;05 by 1. You will see 0;05. Multiply 0;05 by 12. You will see 1.

r i 55

5 šu-tam-<ḫir> 25 a-na 1 i-ši 25 ta-mar IGI 25 DU₈.A 2.24

(r i 5) Square 0;05. Multiply 0;00 25 by 1. You will see 0;00 25. Find the reciprocal of 0;00 25. You will see 2 24. Multiply 2 24 by 3 20, the volume. You will see 8 00 00. (With)what does it square itself?

r i 66

ta-mar 2.24 a-na 3.20 SAḪAR-ḪI.A i-ši 8 ta-mar EN.NAM ÍB.<SI₈>

r i 77

1 1 8 ÍB.SI₈ 5 a-na 1 i-ši 5 ta-mar 5 KÙŠ ÚS

(r i 7) It squares itself (with sides of) 1 00, 1 00, 8. Multiply 0;05 by 1 00. You will see 5. The length is 5 cubits.

r i 88

8 a-na 1 i-ši 8 KÙŠ BÙR

(r i 8) Multiply 8 by 1. The depth is 8 cubits. The procedure.

r i 99

ne--šum


r i 1010

.SAG ma-la -tam-ḫir ù 7 KÙŠ BÙR-ma <<13>> <3.15> SAḪAR-<ḪI.A> BA.ZI

(r i 10) h1 Problem (xv') An excavation. The depth is as much as I squared and 7 cubits. I removed a volume of <3 15> <<13>>.

r i 1111

ÚS SAG ù BÙR EN.NAM

(r i 11) What are the length, width, and depth?

r i 1212

ZA.E ki-ma maḫ-ri-ma e-pu- 7!(4)48 EN.NAM ÍB.SI₈

(r i 12) You: do as before. (W)ith what does 7 48 square itself?

r i 1313

6 6 13 ÍB.SI₈ 6 im-<ta-ḫar> 13 BÙR

(r i 13) Its square-sides are 6, 6, and 13. It squares itself (with a side of) 6. The depth is 13. The procedure.

r i 1414

ne--šum


r i 1515

.SAG ma-la -tam-ḫir BÙR-ma 1.30 SAḪAR-ḪI.A BA.ZI ÚS SAG ù BÙR <EN.NAM>

(r i 15) h1 Problem (xvi') An excavation. The depth is as much as I made square. I removed a volume of 1;30. <What are> the length, width, and depth?

r i 1616

ZA.E IGI 12 DU₈.A 5 ta-mar 5 a-na 1.30 i-ši 7.30 <ta-mar>

(r i 16) You: find the reciprocal of 12. You will see 0;05. Multiply 0;05 by 1;30. <You will see> 0;07 30.

r i 1717

30 ÍB.SI₈ 30 a-na 1 i-ši 30 im-ta-ḫar 30 a-na 12 i-<ši> 6 BÙR

(r i 17) The square-side is 0;30. Multiply 0;30 by 1. It squares itself (with a side of) 0;30. Multilpy 0;30 by 12. The depth is 6. The procedure.

r i 1818

ne--šum


r i 1919

.SAG ma-la -tam-ḫir ù 1 KÙŠ DIRI BÙR-ma 1.45 SAḪAR-ḪI.A BA.ZI

(r i 19) h1 Problem (xvii') An excavation. The depth is as much as I made square and 1 cubit excess. I removed a volume of 1;45.

r i 2020

ZA.E 5 DIRI a-na 1 BAL i-ši 5 ta-mar a-na 12 i-ši 1 ta-mar

(r i 20) You: Multiply 0;05, the excess by 1, the ratio. You will see 0;05. Muliply by 12. You will see 1.

r i 2121

5 šu-tam-<ḫir> 25 ta-mar 25 a-na 1 i-ši 25 ta-mar IGI 25 [DU₈.A]

(r i 21) Square 0;05. You will se 0;00 25. Multiply 0;00 25 by 1. You will see 0;00 25. [Find] the reciprocal of 0;00 25.

r i 2222

2.24 ta-mar 2.24 a-na 1.45 i-ši 4.12 [ta-mar]

(r i 22) You will see 2 24. Multiply 2 24 by 1;45. [You will see] 4 12.

r i 2323

i-na ÍB.SI₈ 1 DAḪ.ḪA 6 1 ÍB.SI₈ 6 a-[na] 5 i-ši 30 ta-<mar 6> im-<ta-ḫar> 6 BÙR

(r i 23) In the square-side, 1 added, the square-sides are 6 (and) 1. Multiply 6 by 0;05. You will see 0;30. It squares itself (with a side of) <0;30>. The depth is 7!(6). The procedure.

r i 2424

ne--šum


r i 2525

.SAG 3.20 BÙR-ma 27.46.40 SAḪAR-ḪI.A BA.ZI ÚS UGU SAG 50 DIRI

(r i 25) h1 Problem (xviii') An excavation. The depth is 3;20. I removed a volume of 27;46 40. The length exceeds the width by 0;50.

r i 2626

ZA.E IGI 3.20 BÙR DU₈.A 18 ta-mar a-na 27.46.40 SAḪAR-ḪI.<A> i-ši

(r i 26) You: find the reciprocal of 3;20, the depth. You will see 0;18. Multiply by 27;46 40, the volume.

r i 2727

8.20 ta-mar 1/2 50 ḫe- šu-tam-<ḫir> 10.25 ta-mar

(r i 27) You will see 8;20. Break 50 in 1/2. Square (it). You will see 0;10 25.

r i 2828

a-na 8.20 DAḪ.ḪA 8.30.25 ta-mar

(r i 28) Add to 8;20. You will see 8;30 25.

r i 2929

2.55 ÍB.SI₈ a-di [2 GAR.RA] a-na 1 DAḪ.ḪA i-na 1 BA.ZI

(r i 29) The square-side is 2;55. [Put it down] twice. Add to 1, subtract from 1.

r i 3030

3.20 ÚS 2.30 SAG ta-mar

(r i 30) You will see 3;20, the length, (and) 2;30, the width. The procedure.

r i 3131

ne--šum


r i 3232

.SAG 3.20 BÙR-ma 27.46.40 [SAḪAR-ḪI.A BA.ZI ÚS ù SAG UL.GAR] 5.50

(r i 32) h1 Problem (xix') An excavation. The depth is 3;20. [I removed a volume of] 27;46 40. [I summed the length and width:] 5;50.

r i 3333

ZA.E IGI 3.20 BÙR DU₈.A 18 ta-mar a-[na 27.46.40 i-ši]

(r i 33) You: find the reciprocal of 3;20. You will see 0;18. [Multiply (it)] by [27;46 40].

r i 3434

8.20 ta-mar 1/2 5.50 ḫe- šu-tam-<ḫir> 8.[30.25 ta-mar]

(r i 34) You will see 8;20. Break 1/2 of 5;50. Square (it). [You will see] 8;[30 25].

r i 3535

8.20 i-na ŠÀ-BA BA.ZI 10.25 [ta-mar 25 ÍB.SI₈]

(r i 35) Subtract 8;20 from inside it. [You will see] 0;10 25. [The square-side is 0;25.]

r i 3636

a-na 2.55 DAḪ.ḪA ù BA.ZI 3.20 [ÚS 2.30 SAG]

(r i 36) Add and subtract from 2;55. [The length is] 3;20. [The width is 2;30.] The procedure.

r i 3737

ne--[šum]


r i 3838

.SAG 3.20 BÙR-ma 27.46.40 SAḪAR-ḪI.A [BA.ZI SAG UGU BÙR DIRI ma-la 2/3 ÚS]

(r i 38) h1 Problem (xx') An excavation. The depth is 3;20. [I removed] a volume of 27;46 40. [The width exceeds the depth by as much as 2/3 of the length.]

r i 3939

ZA.E IGI 3.20 DU₈.A 18 ta-mar a-na 27.[46.40 i-ši]

(r i 39) You: find the reciprocal of 3;20. You will see 0;18. [Multiply (it)] by 27;[46 40].

r i 4040

8.20 ta-mar 8.20 a-na 40 i-ši 5.33.[20 ta-mar 3.20 BÙR a-na 5 i-ši 16.40]

(r i 40) You will see 8;20. Multiply 8;20 by 0;40. [You will see] 5;33 [20. Multiply 3;20, the depth, by 0;05: 0;16 40.]

r i 4141

NÍGIN.NA 1/2 16.40 ḫe- 8.20 ta-mar šu-tam-<ḫir> [1.09.26.40 a-na 5.33.20 DAḪ.ḪA]

(r i 41) Start again. Break 1/2 of 0;16 40. You will see 0;08 20. Square (it). [Add 0;01 09 26 40 to 5;33 20.]

r i 4242

EN.NAM ÍB.SI₈ 2.21!(31)40 a-di 2 GAR.RA 8.20 [DAḪ.ḪA ù BA.ZI]

(r i 42) (With) what does it square itself? Put down 2;21 40 twice. [Add and subtract] 0;08 20.

r i 4343

2.30 SAG 2.13.20 ta-mar IGI 40 DU₈.A 1.30 ta-mar [a-na 2.13.20 i-ši]

(r i 43) You will see 2;30, the width (and) 2;13 20. Release the reciprocal of 0;40. You will see 1;30. [Multiply by 2;13 20.] you will see 3;20, the length. The procedure.

r i 4444

3.20 ÚS ta-mar

r i 4545

ne--šum


r i 4646

.SAG 1.40 ÚS IGI 7-GÁL ša ÚS UGU SAG DIRI BÙR-ma 1.40 SAḪAR-[ḪI.A BA.ZI]

(r i 46)

r i 4747

<<ÚS>> SAG ù BÙR EN.[NAM]

r i 4848

ZA.E 1.40 ÚS a-na 12 BAL BÙR i-ši 20 ta-[mar]

(r i 48) You: multiply 1;40, the length, by 12, the ratio of the depth. You will see 20.

r i 4949

IGI 20 DU₈.A 3 ta-mar 3 a-na 1.40 SAḪAR-[ḪI.A i-ši 5 ta-mar]

(r i 49) Release the reciprocal of 20. You will see 0;03. [Multiply] 0;03 by 1;40, the volume. [You will see 0;05.]

r i 5050

7 a-na 5 i-ši 35 ta-[mar 1/2 1.40 ḫe- šu-tam-ḫir 41.40]

(r i 50) Multiply 7 by 0;05. You will see 0;35. [Break in half 1;40. Square (it). 0;41 40.]

r i 5151

35 i-na ŠÀ-[BA BA.ZI 6.40 ta-mar 20 ÍB.SI₈]

(r i 51) [Subtract] 0;35 from it. [You will see 0;06 40. The square-side is 0;20.]

r i 5252

a-[na 50 DAḪ.ḪA ù BA.ZI 1.10 ù 30 SAG ... IGI 7-GÁL 1.10 le- 10 BÙR]

(r i 52) [Add and subtract] to [0;50. 1;10 and 0;30, the width. ... Take one-seventh of 1;10. The depth is 0;10. The procedure.]

r i 5353

[ne--šum]

Column ii
r ii 1r ii 1

.SAG 1.40 ÚS IGI 7-<GÁL> ša ÚS UGU SAG DIRI ù 2 KÙŠ BÙR-ma 3.20 SAḪAR-ḪI.<A BA.ZI>

(r ii 1)

r ii 22

SAG ù BÙR EN.NAM

r ii 33

ZA.E 1.40 ÚS a-na 12 BAL BÙR i-ši 20 ta-mar IGI 20 DU₈.A 3 ta-mar

(r ii 3) You: multiply 1;40, the length, by 12, the ratio of the depth. You will see 20. Release the reciprocal of 20. You will see 0;03.

r ii 44

3 a-na 3.20 i-ši 10 ta-mar <<10 a-na 7 i-ši 1.10 ta-mar>> 10 DIRI a-na 7 i-ši 1.[10] ta-mar

(r ii 4) Multiply 0;03 by 3;20. You will see 0;00 10. Multiply 0;10, the excess, by 7. You will see 1;10.

r ii 55

1.40 ÚS a-na 1.10 DAḪ.ḪA 2.50 ta-mar 1/2 2.50 ḫe- šu-tam-ḫir

(r ii 5) Add 1;40, the length, to 1;10. You will see 2;50. Break in half 2;50. Square (it).

r ii 66

2.oo.25 ta-mar i-na 2.oo.25 1.10 BA.ZI 50.25 ta-mar

(r ii 6) You will see 2;00 25. Subtract 1;10 from 2;00 25. You will see 0;50 25.

r ii 77

55 ÍB.SI₈ a-na 1.25 DAḪ.ḪA ù BA.ZI-ma

(r ii 7) Add and subtract 0;55, the square-side, to 1;25 and you will see 2;20 and 0;30, the width. Take one-seventh of 2;20. The depth is 0;20. The procedure.

r ii 88

2.20 ù 30 SAG ta-mar IGI 7-GÁL 2.20 le-[] 20 BÙR

r ii 99

ne--šum


r ii 1010

.SAG 1.40 ÚS IGI 7-GÁL ša ÚS UGU SAG DIRI ù 1 KÙŠ BA. BÙR-ma

(r ii 10)

r ii 1111

50 SAḪAR-ḪI.A BA.ZI SAG ù BÙR EN.NAM

r ii 1212

ZA.E 1.40 ÚS a-na 12 BAL BÙR i-ši 20 ta-mar IGI 20 DU₈.A 3 ta-<mar>

(r ii 12) You: Multiply 1;40, the length, by 12, the ratio of the depth. You will see 20. Release the reciprocal of 20. You will see 0;03.

r ii 1313

3 a-na 50 i-ši 2.30 ta-mar 2.30 a-na 7 i-ši 17.30 ta-[mar]

(r ii 13) Multiply 0;03 by 0;50. You will see 0;02 30. Multiply 0;02 30 by 7. You will see 0;17 30.

r ii 1414

7 a-na 5 1 KÙŠ i-ši 35 ta-mar 35 i-na 1.40 ÚS BA.ZI

(r ii 14) Multiply 7 by 0;05, 1 cubit. You will see 0;35. Subtract 0;35 from 1;40, the length.

r ii 1515

1.05 ta-mar 1/2 1.05 ḫe- 32.30 šu-tam-<ḫir> 17.36.15 ta-<mar>

(r ii 15) You will see 1;05. Break in half 1;05. Square 0;32 20. You will see 0;17 36 15.

r ii 1616

i-na ŠÀ-BI 17.30 BA.ZI 6.15 ta-mar 2.30 ÍB.SI₈

(r ii 16) Subtract 0;17 30 from it. You will see 0;00 06 15. Its square-side is 0;02 30.

r ii 1717

a-na 32.30 DAḪ.ḪA ù BA.ZI 35 ù 30 SAG ta-mar <IGI> 7-<GÁL> 35 5 BÙR

(r ii 17) Add and subtract to 0;32 30. You will see 0;35 and 0;30, the width. One-seventh of 0;35 is 0;05, the depth. The procedure.

r ii 1818

ne--šum


r ii 1919

30 ki-ib-su

(r ii 19) 30 procedures.

(rest of column missing)