P348768: mathematical tablet
Achaemenid Oracc
Obverse Column i
x x x# [1 _me kusz3 sag us2 en_] _he2-gid2_(!)(_sze_-)ma _he2 1_(_asz_) _gur sze-numun_
[1 _me kusz3 sag us2 en_] _he2-gid2_(!)(_sze_-)ma _he2 1_(_asz_) _gur sze-numun_ [_mu_ la3 _zu_(u2) _igi_(u2)] sza _sag a-sza3 il2_-ma [u3 _a-ra2 igi_(e)] sza# _igi-gub_(be2)-(e) _sze-numun du_(ak) u3# _sze-numun_ sza E-ka _du_-ma _us2 igi_(mar) [szum]-ma 5 am-mat-ka 8-20 1 _me kusz3 igi 8-20 7-12_ [7-12] _a-ra2 1-12 du_-ma 9 9 _a-ra2 5 du_-ma 45 45# a-na szid-du _a-sza3_-ka ta-szak-kan szum-ma 1 am-mat-ka 1-40 1 _me kusz3 igi 1-40 36 36 a-ra2 3 du_-ma 1-48 1-48# _a-ra2 5 du_-ma 9 sza 1-40 _kusz3# a-ra2_ szid-du ta-szak-kan
_a-sza3 en am3_ lu-[mah(!)(_kur_-)hir-ma _he2 1_(asz) _gur 2_(_ban2_) _sze-numun mu_ la3 _zu_(u2) _sze-numun_ sza E-ka ((E)) [A]-_ra2# igi-gub_(be2)-(e) _sze-numun# du_(ak) _am3 ti_(!)(qe2(!))-ma szi-id-du# szum-ma 5 am-mat-ka 5-20# _a-ra2 1-15_(!)(16) _du_-ma# 6-40#-_e 20_-_am3 ti_(qe2) 20 _ninda_-_am3_ tu-mah(!)(_kur_-)har szum-ma 1 am-mat-ka 5-20 _a-ra2 3 du_-ma 16-_e 4#_-_am3 ti_(qe2) 2 _me 40 kusz3_-_am3_ tu-mah(!)(_kur_-)har
_a-sza3 1_(_ban2_)# [_sze-numun_] _us2#_ u3 _sag gar-gar_-ma# [1-30] _kusz3 us2 he2-en#_ u3 _sag he2-en_-ma _mu_ la3 _zu_(u2)# [... 1/2] sza2# 1-30 _kusz3 il2_-ma 45 _kusz3 ur-a_ a-na _igi-gub_ sza# [_sze-numun_] x x 1(_ban2_)# _sze-numun_ ina lib3-bi _ti_(qe2(?))# _igi_(u2)# [sza _igi-gub_(be2)-(e)] ta-na-asz2-szam-ma _a-ra2# 45 kusz3#_ [_dah_-ma _us2_ i-na] 45 _kusz3#_ [_nim_]-ma _sag_ szum-ma 5 am-[mat-ka _us2_ u3 _sag 7-30 1_/2-sza2 3-45] _ti_(qe2) 3-45 _a-ra2 3-45#_ [_du_-ma 14-03-45] 14#-03-[45 _a-ra2_] 48# _du_-ma 11-15
_a-sza3 1_(_ban2_) 4 _sila3 sze-numun us2_ a-na _sag# 10 kusz3_ a-tar _us2 he2-en_ u3 _sag he2-en mu_ la3 _zu_(u2) mi-szil _diri# du3_-ma x _ur-a_ a-na _sze-numun_ te-((qe2))-es,-s,ip-ma [...] _sze-numun sag_ te-[... sza2] a-na _igi_-ka _e11-a_ [...] _il2_-ma 5 _kusz3 dah_-ma# _us2 igi_(mar) [... 5] _kusz3_ ta-na-asz2-szar-ma _sag igi_(mar) [szum-ma 1] am#-mat-ka 10 10 _kusz3_ mi-szil 5 _kusz3 5 a-ra2 5 du_-ma 25 [25 _a-ra2 20_] _du#_-ma 8-[20] 8-20# _tur_ a-na 16-40 _dah_-ma 16-48-20 [16-48-20 _a-ra2 3 du_-ma] 50(!)(51)25-_e 55#_-_am3 ti#_(qe2)
... 100 cubits, the length, you multiply by a kurru of seed.
You multiply 1 hundred cubits the length of the front side, so that the length is 1 kurru. You do not know the name of the seed-measure. You multiply the first line of the field by the angle of the right and the angle of the left, so that the seed-measure is visible. You multiply the length and the width of your 'path'.
You multiply the field by a single kurru and 2 sutu of seed. You do not know the name of the seed that you have cultivated. You multiply the seed by a single kurru and you multiply it by a single kurru. You take and you measure the barley. If your cubit is 5 and you multiply it 5 times 1 15 and 16 times, so that 6 40. You take 20 nindanu. You take 20 nindanu. If your cubit is 5 20 times 3 times, so that 16 is 4 you take 2 40 cubits.
You multiply the length and width by 0;01 30 cubits, the width, and the height, and you do not know the name. ... 1/2 cubit, the width, and 0;01 30 cubits, you multiply, and you multiply 0;45 cubits. You multiply by 0;01 30 cubits, the height, and the width, and you multiply by 0;01 45 cubits, the height of 0;01 30. You multiply by 0;01 45 cubits, the width of 0;01 45 cubits, and you multiply by 0;01 45 cubits, and the width. If your 5 lines are 0;01 30 1/2 cubits, you multiply 0;01 30. You multiply 0;01 30. You multiply 0;01 30. You multiply 0;01 30. You multiply 0;01 30. You multiply 0;01 30. You multiply 0;01 30. You multiply 0;01 30. You multiply 0;01 15. You multiply 0;11 15.
You multiply the field by 1 sutu 4 qû. You multiply the length by 10 cubits, the width, and the height. You do not know how much the length is, but you multiply half a stele and you ... the stele to the seed-corn. You take and ... the seed-corn at the top ... which is before you ... and you multiply 5 cubits, so that the width is visible. You multiply 5 cubits, so that the width is visible. If your first measurement is 1 cubit 10 cubits, half a cubit 5 cubits, so that 25 cubits, so that 25 cubits, so that 8 cubits, so that 8 cubits, so that 16 40 cubits, so that 16 48-20 cubits, so that 5/5 of a cubit, you take.
The short side is 1 hundred cubits. What length should I survey be so that the area is 1 kurru seed-measure?
A field. How much should I make it square so that it is 1 kurru, 2 sutu seed-measure?
A field of 1 sutu 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?
A field of seed-measure 1 sutu, 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
[szum-ma 5 am-mat-ka 50 10 _kusz3 igi 50 il2_-ma 1-12] 1-12 _a-ra2 1-15 du_-ma 1-30# [1-30 _a-ra2 10 1_(_ban2_) _il2_-ma 15] 15 4-szu2 _il2_-ma 3-45 50# [i-na 3-45 _nim_-ma] 2-55 re-e-hi 2 1/2 _ninda_ ((_asz_)) 5 _kusz3_ [_ur-a_] szum-ma# 1 am-mat#-ka 10 10 _kusz3 igi 10 il2_-ma# 6 _a-ra2 3 du#_-ma ((1))-18 18 _a-ra2 10 1_(_ban2_) _il2_-ma 3 [4-szu2] _il2_-ma ((x)) 45 10 i-na 45 _nim_-ma 35 re-e-hi 35 _kusz3 ur-a_ x _sag_
_a-sza3_ [1 _pi_] _sze-numun# gur2_(up) _a-ra2 4 1_-_ta-am3_ na-pal [...]-_a en am3_ x x x x isz-tu [kip-pat] _ka2_-a-ni-ti a-di kip-(pat) _gur2_(up)# _e2_-a-ni-ti _mu_ la3 _zu_(u2) 1 _a-ra2 6 du_-ma 6 6 i-na# 30 _nim_-ma 24 _du3_ kip-pat# sza2-ni-ti 6 i-na 24 _nim_-ma 18 _du3 18 gur2_ sza2-lul-ti 6 i-na 18 _nim_-ma 12 x 12 kip-pat# re-bi-ti 6 i-na 12 _nim_-ma 6 _du3 6_ kip-pat# ha-usz-ti 6 (gana2)kip-pat _e2_-a-ni#-ti i-ta-pal
_sze-numun_ sza2 1 lim ((x x)) _kusz3 us2_ u3 1 2/3 _kusz3 sag ki-min#_((_he2-en_)) _sze-numun_ szum-ma 5 am-mat-ka mi-hi-il-ti _a-ra2 ki-min_((mi-hi-il-ti)) u3 43-12 _du_(ak) _a-ra2 1-23-20 ib-sa_ szum-ma 1 am-mat-ka mi-hi-il-ti _a-ra2 ki-min_((mi-hi-il-ti)) u3 _a-ra2 18 du_-ma _a-ra2 3-20 ib-sa_
1 _me kusz3 us2 1 me kusz3 sag he2-en sze-numun_ szum-ma 5 am-mat-ka 8-20 1 _me kusz3 8-20 a-ra2 8-20 1-09-28-40 1-09-28-40 a-ra2 43-12 du_-ma 5(U) (_gur_) 5(_ban2_) _sze-numun_ szum-ma (1) am-mat-ka 1-40 1 _me kusz3 1-40 a-ra2 1-40 2-46-20 2-46-40 a-ra2 18 du_-ma 50 (_gur_) 5(_ban2_)(!)(_bi_) _sze-numun_
_sze-numun_ sza2 1 lim _kusz3 us2_ u3 1-40 _kusz3 sag ki-min#_(([_he2-en_)) _sze-numun_] szum-ma 5 am-mat-ka mi-hi-il-ti _a-ra2 ki-min_(([mi-hi-il-ti])) u3 _a-ra2 51-50-24 du_ u3 1-09-26-[40 _ib-sa_] szum-ma 1 am-mat-ka mi-hi-il-ti [_a-ra2 ki-min_((mi-hi-il-ti)) u3 _a-ra2_] 21-36 _du_(ak) _a-ra2 2-46#_-[40 _ib-sa_ szum-ma] 36 am-mat-ka mi-hi-il-[ti _a-ra2 ki-min_((mi-hi-il-ti)) u3 _a-ra2 1 du_]
1 _me kusz3 us2_ u3 1 _me kusz3 sag_ [_he2-en sze-numun_] szum-[ma 5 am-mat-ka] 8-20 1 _me kusz3#_ [8-20 _a-ra2_] 8(!)(9)[20 1-09-26-40 _a-ra2 51-50-24 du_-ma 1 1 _pi sze-numun_] szum-ma# [1 am-mat-ka 1-40 1 _me kusz3 1-40 a-ra2 1-40_]
If your cubit is 5 and your cubit is 10 cubits, you multiply 50 times 50, so that 1 12 00. You multiply 1 12 00 times 1 15 so that 1 30. You multiply 1 30 times 10 1 sutu, so that 15. You multiply 15 times 4 so that 3 45. You multiply 50 times 3 45, so that 2 55 is the left. You multiply 2 1/2 nindanu. You multiply 5 cubits. If your cubit is 1: 10 00. You multiply 10 times 10 times 10 and you multiply 6 times 10 so that 18 is 18 times 10 1 sutu. You multiply 3 times 4 times 45. You multiply 10 times 45 so that 35 is the left. You multiply x cubits.
The area is 1 panu. The seed-measure is 1 panu. The length is 4 times 0;01, the width 0;00. Until ... from the gate of the gate to the gate of the house is not known.
Seed-measure of 1 thousand cubits length and 1 2/3 cubits width ditto.
If your cubit is 1 hundred cubits, the length is 100 cubits, the width is 50 cubits. You multiply 5 times 8 20. You multiply 1 hundred cubits 8 20 times 8 20. You multiply 1 09 28 40 times 43 12. You multiply 5 sutu, so that 50 kurru 5 sutu of seed. If your cubit is 1 40, you multiply 1 40 times 1 40. You multiply 2 46 20 times 18 so that 50 kurru 5 sutu of seed.
Seed-measure of 1 thousand cubits length and 1 40 cubits width ditto.
The length is 100 cubits, the width 100 cubits. You multiply by 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00. You multiply 0;00.
Statement and general solution missing.
A field curved 1 panu seed-measure. Times 4, 1 each the quarrying ? of .... How much each ... from the outer circle to the inner circle did it curve?
Seed-measure of 1 thousand cubits length and 1 2/3 cubits width. Ditto.
A length of 1 hundred cubits, a width of 1 hundred cubits. What should the seed-measure be?
Seed-measure for a length of 1 thousand cubits, a width of 1 40 cubits. Ditto.
The length is 1 hundred cubits and the width is 1 hundred cubits. How much should the seed-measure be?
Reverse Column i
[...] szum-[ma 5 am-mat-ka mi-hi-il-ti _a-ra2 ki-min_((mi-hi-il-ti])) u3 _a#_-[_ra2_ ...] _du_[(ak) _a-ra2 ... du_-ma ...] szum-ma (1) am-mat#-[ka] mi-hi-il-ti _a#_-[_ra2 ki-min_((mi-hi-il-ti)) u3 _a-ra2_] 24 _du_(!)#(ak) _a-ra2 2-30_ [_du_-ma ...]
1 _me kusz3# us2_ u3 1 _me kusz3 sag he2-en sze_-[_numun_] szum-ma 5 am-mat-ka 8-20 1 _me kusz3 8-20 a-ra2 8-20_ [1]-09-26-40 1-09-26-40 _a-ra2 57-36 du_-[ma] [1]-06-40 1 _pi 4 sila3 sze_-[_numun_] szum-ma 1 am-mat-ka (1)-40-1 _me kusz3_ [1]-40 _a-ra2 1_-[40] 2-46-40 2-46#-40 _a-ra2 24# du_-ma 1-06-40 _sze-numun_ sza2 1 lim _kusz3 us2 1_ [lim _kusz3 sag_] _ki-min#_((_he2-en_)) _sze-numun_ szum-ma [5]
_sze-numun_ sza2 1 lim _kusz3 us2 1_ [lim _kusz3 sag_] _ki-min#_((_he2-en_)) _sze-numun_ szum-ma [5] am-mat-ka# [mi-hi]-il#-ti [A]-_ra2# ki-min_((mi-hi-il-ti)) u3 1-26#-[24 _du_-ma] [2-46-40] _a-ra2_ x 45 [... szum-ma 1 am-mat-ka] mi-hi#-il-tu2 _a-ra2 ki-min#_((mi-hi-il-ti)) [u 36 _du_-ma 2-46-40 ...] szum-ma 6# am-[mat]-ka mi-hi-il-tu _du_-ma [...]
1 _me kusz3#_ [_us2 1 me kusz3 sag_] _he2-en# sze-numun#_ szum-ma 5 am-mat#-[ka 8]-20 1 _me kusz3 8_-[20 A]-_ra2 8-20#_ [1]-09-26-40# 1-[09-26-40] ((A)) _a-ra2_ (1)-26-24# _du_-[ma] 1-40 szum-ma 1 am-mat-ka 1-40 1 _me kusz3#_ [1-40] _a-ra2 1-40 2-46-40 2-46#_-[40 _a-ra2 36_] _du_-ma# 1-40 szum-ma 6 am-mat-(ka) 10 1 _me kusz3 10_ [_a-ra2 10 1-40_] sza 1 _me kusz3 ur-a 1 pi 4_(_ban2_) _sze#_-[_numun_]
_sze-numun_ sza 1(iku)(!)(_me_)(gana2) 3(_ban2_)# [ina _kusz3 gal_](ti)# [szum-ma] 5 am-mat-ka mi-hi-il-ti [_a-ra2_] _ki-min#_((mi-hi-il-ti)) u3 _a-ra2 18 du_(ak) [_a-ra2 3-20_ ...] szum-ma 1 am-mat-ka mi#-[hi-il]-ti# _a-ra2 ki-min#_((mi-hi-il-ti)) u3 _a-ra2 7-30 du_-ma A(!)-[_ra2 8_ ...]
50 _ninda_-(_am3_) ((_a-ra2_)) _ur-a en# gana2_ [...] _mu_ la3 _zu_[(u2)] szum-ma 5 am-mat-ka 50# [50 _ninda 50 a-ra2_] 50 _du_-ma x 1(_bur_'U) 1(_esze3_) u3 1(_iku_)(gana2)# [...] 1(_bur_'U) 1(_esze3_) u3 1(_iku_)(gana2)# 1(_iku_)(gana2) [...] _sze-numun 41-40 a_(!)-_ra2 18 du_(ak) 12#-30 [...] szum-ma 1 am-mat-ka 10-((1))-50(!)(10) _kusz3_ [10 _a-ra2 10 1-40 a-ra2 7-30_] _du_-ma 12-[30] _sze_-[_numun_]
_sze-numun_ sza2 1(_iku_)(gana2) [3(_ban2_) ina] _kusz3 gal_(ti) [_mu_ la3 _zu_(u2)] mi-hi-il-ti _a-ra2_ [_ki-min_((mi-hi-il-ti)) ...] [... A]-_ra2 8 du_(ak) _a-ra2#_ [...]
... If your cubit is 5 and you multiply the cubits by ditto and by ..., and then you multiply by ..., and then .... If your cubit is 1 and you multiply the cubits by ditto and by 24 times, and then you multiply by 2 30 .
The length is 1 hundred cubits, the width 1 hundred cubits. The height is 1 hundred cubits. The area is 1 hundred cubits. The length is 1 hundred cubits. The width is 8-20. The length is 1 hundred cubits. The width is 1 hundred cubits. The length is 1 hundred cubits. The width is 1 hundred cubits. The length is 1 hundred cubits. The width is 1 hundred cubits. The length is 1 hundred cubits. The width is 1 hundred cubits. The width is 1 hundred cubits. The width is 1 hundred cubits. The width is 1 hundred cubits. The width is 1 hundred cubits. The width is 1 hundred cubits. The width is 1 hundred cubits. The width is 1 hundred cubits. The width is 1 hundred cubits. The width is 1 hundred cubits. The width is 1 hundred cubits. The width is 1 hundred cubits. The width is 1 hundred cubits.
Seed-measure of 1 thousand cubits length and 1 thousand cubits width. Ditto.
The length is 100 cubits, the width 100 cubits. The height is a ... of seed. If your cubit is 5 cubits, the length is 1 hundred cubits. The width is 8 20 cubits. The length is 8 20 cubits. The width is 1 09 26-40. The length is 1 09 26-40. The length is 1 09 26-40. You multiply 1 40 by 1 40. If your cubit is 1 40, you multiply 1 40 by 2 46 40. You multiply 2 46 40 times 36. You multiply 1 40 times 6 times 10. You multiply 1 40 times 10 — the width is 1 40. The width is 1 panu 4 sutu. The grain is 1 panu 4 sutu.
Seed-measure of 1 ikû field, 3 sutu, in large cubits.
50 nindanu per ura, the area of the field ... ... is not known. If your cubit is 5 and you multiply 50 nindanu by 50, so that ... 1 bur'u 1 eshe3 and 1 iku ... 1 bur'u 1 eshe3 and 1 iku ... the seed-measure: 41 40 times 18 you multiply. 12 30 ... If your cubit is 1 iku, 10 times 10 is 1 40, so that 7 30 you multiply, so that 12 30 seed-measure
The seed-measure of 1 ikû field is 3 sutu, measured by the large cubit. If you do not know, multiply the times ditto ... times 8 .
Statement of problem missing
The length is 1 hundred cubits, the width 1 hundred cubits. How much should seed-measure be?
Seed grain of a length of 1 thousand cubits, a width of 1 thousand cubits. Ditto.
The length is 1 hundred cubits, the width 1 hundred cubits. How much should the seed-grain be?
Seed-measure for 1 ikû area at 3 sutu by the large cubit.
The square-sides are 50 rods each. How much is the area?
Seed-measure of 1 ikû area at 3 sutu by the large cubit. Because you do not understand, you multiply the line times ditto .... You multiply times 8. ... times ....
Reverse Column ii
[...] _us2_ mi-hi-il-ti _a-ra2_ mi-hi-il#-[ti] [_du_ ...] _a-ra2_ [x] _du_(ak) _a-ra2 2_-_am3_
1 _usz_(!)(_gana2_) _us2_ u3 1 _us2 sag he2-en gana2_(ki)-_hi-a 1 a-ra2#_ [1 1] _a-ra2 30 30 1_(_esze3_) _gana2_(ki)-_hi-a_
1 (gana2)_sag-kak ur-a_ ((sza 8(!)(5) sza 8-szu na-as-hu mi-hi-il-tu2 _a-ra2 ki-min_((mi-hi-il-ti)) u3 _a-ra2_ [26-15] _du_
1 _usz_-_am3 ur-a he2-en gana2_(ki)-_hi-a 1 a_-[_ra2 1 1_] _a#_-[_ra2_] 26#-15 _du_-ma 26-15 1(_esze3_) 1(_esze3_) 3(_iku_)(gana2) 1/2(_iku_)(gana2) 25# [_sar gana2_(ki)-_hi_]-_a#_
1(!)(4) (gana2)_sag-kak ur-a_ sza 10-szu u3 30-szu na-as-hu mi#-hi-il-tu2 _a-ra2 ki-min_((mi-hi-il-ti)) u3# 26 _du#_(ak)
[...] _a 1 a-ra2 1 1 a-ra2_
... the length of the mihiltu-strength, the length of the mihiltu-strength ... the length ... you go. The length of the 2nd time.
If the length is 1 utah and the width is 1 utah: the area of the fields will increase.
1 saggakku-field, the 'foot' of 8 x
If the length is 1 utam3: the land will be scattered.
If you go one sagkakku-field, you multiply the square-side of the lion by 10, and the square-side of the snake by 0;26.
... 1 times 1 1 times
Statement of problem and start of solution missing. ... length. You multiply the line times the line .... You multiply ... times .... Times 2 each.
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.
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.
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.
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.
... 1 00 times 1 00 is 1 00 00. Times ...