The Measurement of Fields During the Pre-sargonic Period

Lecompte, Camille

doi:10.1007/978-3-030-48389-0_8

Camille Lecompte⁶

Part of the book series: Why the Sciences of the Ancient World Matter ((WSAWM,volume 5))

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Abstract

Administrative records from the Pre-Sargonic period (approximately 24th century BCE) provide with several types of data related with field measurement (length, width and area of several plots) and show implicitly the land surveyor’s method to calculate the area of agricultural estates belonging to central institutions. The present paper investigates the mathematic procedures in use for land surveys, fields being either measured as rectangles, squares or by means of the land surveyor’s formula. As a consequence of the inaccuracy of those procedures, land surveyors used to resort to approximations and rounding. The textual evidence reveals also some of the main features of the Sumerian landscape during the third millennium, namely fields’ shape which turns out to be more diverse than generally accepted. This enquiry relies mostly on the evidence originating from Pre-Sargonic Girsu but takes into account also a more recently published corpus of tablets from Umma.

I express my gratitude to Christine Proust for the time she spent reading this paper and for her suggestions. I thank Palmiro Notizia for having shared with me the relevant information on the tablets from the Umma re6gion and for his input on several problematical and unclear lines. For the calculation of the surfaces as well as the translation of the results according to the Mesopotamian metrology, I used the MesoCalc website designed by Bapiste Mélès. http://baptiste.meles.free.fr/site/mesocalc.html, accessed 26 november 2019.

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Notes

1.
Allotte de la Fuÿe (1915) was the first scholar to attempt to understand the geometrical formulas applied by land surveyors and offered a crucial contribution to this topic. Other studies on Sumerian land surveying methods instead focused on the Ur III period, especially on field plans and round tablets: see Dunham (1986), Pettinato (1969), Quillien (2003), Damerow et al. (1993), Friberg (2009). Liverani (1990, 1996, 1997) focused on Neo-Sumerian fields in order to reconstruct the agricultural landscape during the third millennium, without considering the ED data in a systematic way.
2.
Damerow et al. (1993: 55).
3.
Chapter 9, this volume, for a discussion on the relationships between these scholastic tables and the method reflected in the administrative texts from Lagaš, see Sect. 8.4.3.
4.
Magid (2001: 313). For an overview on the history of Lagaš, see Bauer (1998: 445–495).
5.
The administration of the temple’s agricultural estate was first described by Deimel (1922); for a more recent overview, see Bauer (1998: 534–536) and Magid (1999). The bibliography on this topic goes far beyond the scope of the present article, see also Lafont (1999: VIII. 2).
6.
See the list of these texts in the Appendix 8.B: Texts Related to Land Surveying from Girsu.
7.
See the presentation of these texts below in the conclusion.
8.
Texts published in CUSAS 33, see Excursus (Appendix 8.A).
9.
On the professions in charge of field measurement, see Krecher (1973: 174–176).
10.
Gelb et al. (1991: 72–74, No. 21).
11.
Gelb et al. (1991: 69–72, iii 8 and v 11).
12.
Gelb et al. (1991: 74–80. Obv. iv 3–6).
13.
These documents record ‘the giving of pure milk and pure malt by individuals of importance in the e₂-MI₂/e₂-^dBa-U₂ (and acting as representatives of the e₂-MI₂/e₂-^dBa-U₂) to the wives of high ranking persons from other institutions’ (Prentice 2010: 181). The two individuals giving to the wife of a sa₁₂-du₅ who does not belong to the e₂-MI₂/ e₂-^dBa-U₂ are En-da-gal-di (DP 132, DP 226, VS 14, 173) and ^dBa-U₂-teš₂-mu (DP 133, TSA 5).
14.
Nik 1, 176, RTC 44, VS 14, 179. See also Prentice (2010: 198).
15.
AWL 68, III. 1 (Bauer 1972: 240).
16.
For instance, Gu-u₂, who is a ‘field surveyor’, lu₂ eš₂-gid₂, receives in HSS 3, 12. Rs. III. 5–6 barley ration. Gu-u₂ moreover receives a field in DP 584. Obv. II. 5–6.
17.
Krecher (1973: 175). Gelb, Steinkeller and Whiting (1991: 184); it is noteworthy that field surveyors are witness in the sale contract No 22-23, 88. On the attestations in Nippur, see for instance OSP 1, 36. Obv. II. 2; TMH 5, 19. Obv, 2. TMH 5, 21. Obv. III. 3. TMH 5, 56. Obv. II. 3. TMH 5, 58, etc. These texts deal with the usual administrative tasks, such as the conscription of men (TMH 5, 19 refers to 9 men under the direction of the land surveyor), or the account of oxen and workers (TMH 5, 79). An unnamed lu₂-GAN₂-gid₂ is mentioned in a document relating to field measurements, TMH 5, 57.
18.
Gelb et al. (1991: 71. Obv. iii 9, v 9, vi 5).
19.
See for instance Powell (1978: 14) about Ama-para₁₀-si, designated as SUR GU.
20.
Gelb, Steinkeller and Whiting 1991: 26.
21.
See for instance Dunham (1986: 32–37), Pettinato (1969: 13) and Quillien (2003: 10, 22).
22.
See also Powell (1987–1990: 458–475) and Chap. 9 by Proust, this volume.
23.
1 iku is therefore equal to ≈ 100 ‘ninda²’ ≈ 400 ‘gi²’. For the sake of understanding, the terms ‘gi²’ and ‘ninda²’, which do not exist in cuneiform texts, are used here in order to give a range of equivalence with the length measures.
24.
See especially the commentary on the Text 3 in the contribution of Proust, Chap. 9, this volume.
25.
Lecompte (2012).
26.
Among the numerous examples available, we can point here to DP 617, in which the ninda-DU is explicitly referred to; this document also proves that, in the corpus of land survey texts, the numerals designated as u (10) and ĝeš₂ (60) are related with the ninda (ninda-DU) and not at all with the eš, ‘rope’, as claimed by Damerow et al. (1993: 62). See for instance DP 617. Obv. I. 1. 4(u) eg₂ du₃-a ninda-DU: ‘40 ninda (length) of the dike which is built’. Numerals relating to length units in the land survey texts different from gi or 1/2 (eš₂) therefore have to be identified with the ninda (ninda-DU) and not with the eš.
27.
There are, however, some examples of the use of the numeral 1 for the eš₂ unit: DP 646, Obv. I. 1. 1(aš) eš₂ 4(diš) gi kiĝ₂-du₃-a. DP 641. Obv. III. 8. 1(aš) eš₂ Ur-du₆. Two further exceptions are VS 25, 74, and noticeably DP 568, which juxtaposes amounts of ninda-DU, implicitly expressed by the numeral ĝeš₂, and of one eš₂: Obv. I. 1. 6(ĝeš₂) 1(aš) eš₂! = 360 ninda 1 eš. The aforementioned occurrences come from texts relating to work to be done on dikes and canals, whereas the land survey texts do not seem to display a similar use of the numeral 1(aš) for the eš₂ unit.
28.
On this terminology, see Proust (2009: 7).
29.
According to our conclusion from the use of length unit (see footnote above), 1/2 is the only numeral to refer to the eš; numerals like 1(u) and 1(ĝeš₂) correspond to the ninda; for instance, in the text VS 14, 40. Obv. I. 1. 1(ĝeš₂) 1(u) 1/2 5(diš) gi us₂ sa₂ has to be interpreted as: 60 + 10 ninda + 1/2 eš 5 gi; we can therefore not follow the interpretation by Damerow et al. (1993: 62); see also AWL 4 (Bauer 1972: 74–75) for the identification of such numerals with ninda-DU.
30.
Note, however, that the tablets from Nippur express a quantity of ninda ranging from 1 to 9 by means of numerals referring to the ninda unit.
31.
See for instance Dunham (1986: 33), Allotte de la Fuÿe (1915: 137–146), Damerow et al. (1993: 55) and Proust (2007: 179).
32.
Allotte de la Fuÿe (1915: 133). Accordingly, the units used to measure the area of gardens would have been the sar and not the iku, but this is far from being certain; Allotte de la Fuÿe argues that a garden ‘à proximité de la ville avait une valeur bien plus grande’.
33.
For the representation of surface and length units, see Sect. 8.2.3.
34.
Allotte de la Fuÿe (1915: 138), see the discussion below.
35.
AWL 4,. Obv. I. 1 (Bauer 1972: 77). Against this theory, see Attinger (2008).
36.
See the edition of AWL 4 (Bauer 1972: 74–75).
37.
See also Allotte de la Fuÿe (1915: 127–128).
38.
Allotte de la Fuÿe (1915: 141–145).
39.
Friberg (1987–1990: 556). See also Friberg (1997–1998: 11), ‘quadrilateral area rule’.
40.
Allotte de la Fuÿe (1915: 138): ‘on doit donc voir dans les désignations consécutives de sak an-na, sak a-ki-ta d’une part le front ou la base supérieure, de l’autre le bas ou la base inférieure. Il semble même que dans la formation primitive de l’expression a-ki-ta, on trouve une allusion au bas de l’eau, le sak a-ki-ta serait donc bien « le bas du champ » , la partie qui reçoit l’égout de l’eau’.
41.
Marzahn (1989); FAOS 15/1, 1, Text 39 (Selz 1989: 383–384). Civil (1994: 125).
42.
Civil (1994: 125).
43.
See for instance Høyrup (2002: 43–44).
44.
See Notizia and Visicato (2016), and Excursus (Appendix 8.A).
45.
See also Quillien (2003: 17–19); the measurement of the surface of irregular quadrilaterals could only rely on three lengths and on the formula: 1/2a(b + d).
46.
Allotte de la Fuÿe (1915: 140–141). According to Allotte de la Fuÿe, the adjective sa₂ might not designate strictly two equal oppsite sides: ‘Si l’on prenait à la lettre les expressions uš DI, sak DI avec le sens de côtés égaux, les parcelles seraient des quadrilatères, dont 2 des côtés sont égaux et plus vraisemblablement des trapèzes isocèles: mais je m’étonne que cette forme, qui est en somme exceptionnelle, soit adoptée si fréquemment pour les parcelles et il me paraît probable que nous avons là des trapèzes rectangles, ce que le calcul confirme’. If the field had a shape similar to a right-angled trapezoid, the term sa₂, ‘equilateral’, would therefore refer to the side with two adjacent right angles and the formula would ignore its opposite side. The descriptions given in the tablets and the use of the adjective sa₂ seem more likely to refer to an isosceles trapezoid although fields in the Sumerian landscape may have been strips with two adjacent nearly right-angles.
47.
See for instance the method applied to calculate the area of a triangle divided into different trapezoidal strips, which is attested in mathematical texts; according to the calculation suggested by Neugebauer (1935: 253), those trapezoids forming strips inside the triangle have an area calculated as: 1/2 l₁ (b₁ + b₂), implying that one lateral side is somehow perpendicular to the bases. Compare with other school exercises, such as Neugebauer (1935: 293). The ‘surveyor’s formula’ is, on the other hand, applied in some mathematical texts too, see Proust (2007: 178–179).
48.
Pettinato (1969: 12–13); see for instance Text 3, 64. I. 7–8, where both Northern and Southern parts are equal, while there is one Eastern side (kur) and one Western side. As observed by Pettinato (1969: 12), in these cases, only Northern and Eastern sides, called mer and kur, are in fact explicitly written, whereas Southern and Western sides are implicitly given as plain numbers (the Southern and Western sides, ‘Südseite’ and ‘Westseite’ are ‘nie ausdrücklich genannt’). The situation is, on the other hand, different from the Old Sumerian field surveys, since we never find four lengths on the round tablets since every field has at least two equal sides. This can of course be due to the fact that Neo-Sumerian field surveys consisted of a method dividing the fields into a regular and an irregular part, respectively called temen and bar, which is attested for the Old Sumerian period only in DP 604 (see Allotte de la Fuÿe 1915: 145).
49.
For instance, in TCL 5, 6060, in which only three side lengths are given for the trapezoidal pieces of fields; according to the reconstruction of Damerow et al. (1993: 65), the length used for the calculation was perpendicular to one base. See also the field plans, for instance MIO 1107 and the commentary by Quillien (2003: 16); the trapezoids drawn inside the field on the board are all represented as right trapezoids.
50.
Høyrup (2002: 230): ‘the areas of trapezoidal fields were determined as the product of the length and the average width …; similarly, the frequent “repetitions” of trapezia so as to obtain rectangles show that the underlying idea is that the length and the widths are mutually perpendicular. IM 52301, by identifying the length of the statement with an “upper length” in the proof also expresses awareness that the two lengths are different but only one of them relevant (and relevant of course only in the case that the trapezium is practically right)’.
51.
Friberg (1997–1998: 8). The same author nevertheless admits: ‘This alternative interpretation, although unsupported by any known evidence, is particularly attractive because it implies that the “quadrilateral area rule” [the land surveyor’s formula] produces a correct result in this case.’ As observed below and by Friberg (1997–1998: 11), the formula applied by land surveyors is ‘approximately correct for nearly rectangular quadrilaterals, but it can be grossly incorrect in other cases’. Trapezoids of the Uruk texts are represented by Friberg (1997–1998: 12) either as isosceles or right-angle.
52.
Cf. Friberg (1997–1998: 556; 1997–1998: 11).
53.
Allotte de la Fuÿe (1915: 143, 145).
54.
We can express this difference by in iku for both surfaces: 21.8025 iku – 21.80 iku = 0.0025 iku = 1/4 sar = 15 gin (≈ 9 sq.m), which should therefore be represented as 1(u) 5(diš) gin₂.
55.
For instance in TCL 5, 6060, which uses rounding on three occasions in the range of 10 sar and one of 50 sar; see Alivernini and Lecompte (2013); other examples are given: Quillien (2003: 13–23) draws also our attention on the field plan MIO 1107, in which similar rounding is observable, like for the section MNZY, in which the area given is 10 sar bigger than the area as calculated.
56.
See the commentary by Pettinato (1969: 48, note I. 4) in his edition of the round tablets; ‘der Schreiber hat hier der Einfachheit halber eine runde Zahl als Grösse des Feldes angegeben.’ See also Alivernini and Lecompte (2013) for a presentation of the range of the rounding in these tablets. Both authors demonstrated that round tablets and field plans applied very similar rounding.
57.
This distinction is, of course, the result of a modern view.
58.
For the detail of the operation, see Appendix 8.C Fields and Calculation. Land Surveying in Lagaš.
59.
The computation can be reconstructed as follows: 5(u) 3(diš) gi us₂ sa₂: 50 ninda 3 gi (51 1/2 ninda) 5(u) 5(diš) gi saĝ an-na: 50 ninda 5 gi (52 1/2 ninda) 5(u) 1/2 la₂ 1(diš) gi saĝ a-ki-ta-ka: 50 ninda 1/2 eš minus 1 gi (54 1/2 ninda). Area: 1(bur₃) 1(eše₃) 3(iku) GAN₂ (27 iku) Accordingly, it is likely that instead of applying the “surveyor’s formula” 1/2(b + B) × 1/2(l + L), the scribe here just computed in the following way: us₂ sa₂ × saĝ an-na: 51 1/2 ninda × 52 1/2 ninda = 2703 3/4 sar, so the difference with the area given is only 3 sar 45 gin. Compare with DP 605. Field 3. However, this procedure is only attested in the former example.
60.
FAOS 15/1. In his edition of Nik 1, 34 Selz (1989: 197) comments the rounding observable in the area of the first field, which is equal to 1 1/2 iku, as follows: ‘die Feldgröße … ist etwas abgerundet’, while he thinks about the second field, for which the difference is 0.3125 iku, that ‘diese Fläche ist beträchtlich abgerundet’. Compare also with Bauer (1972: 99), who also observes that the first field shows a difference between the area calculated and the area indicated of 9.75 sar: ‘das Ergebniss ist auf 36,75 iku abgerundet’. By contrast, Firberg (1997–1998: 11) refers to the approximation produced by the type of computation applied in the Late Uruk texts.
61.
5 × 6 = 30; since 2 gi × 2 gi = 4 = 1 sar, 30 is here equal to 7 1/2 sar (30 ÷ 4 = 7.5).
62.
See the list of the mathematical texts in the contribution by Proust (Chap. 9, this volume), which includes four tablets.
63.
This method is moreover different from the procedures from the Ur III period.
64.
As suggested by Proust (Chap. 9, this volume), there is a difference between the arithmetical multiplication and the description of a field as a regular square or rectangle consisting of linear dimensions. It is, however, almost impossible to determine in most field measurements in Lagaš as to whether land surveyors calculated the area by means of the formula l ninda × w ninda or as a computation involving tables drawn up beforehand. There is as yet no evidence in the administrative documentation on the use of such tables by land surveyors.
65.
Pettinato (1969: 188, 210–211, 274) frequently comments the rounding as follows: ‘die leichte Abweichung lässt sich dadurch erklären, dass der Schreiber runde Zahlen vorgezogen’.
66.
Pettinato (1969: 150, Text 17).
67.
For instance, in CT 1, 29 (Pettinato 1969: 142, Text 16). Obv, I. 1–4. 540 ninda × 21 1/2 ninda = 11610 sar = 116.10 iku. 116.10 iku +1/2 iku bar (outer part of the field) – 1 eše 4 1/2 iku ki (part of the field not integrated within the measurement):106.10 iku = 5(bur₃) 2(eše₃) 4(iku) 10 sar. The result on the tablet as given is: 6(bur₃) 2 1/2(iku): 110 1/2 iku. The difference is accordingly 5 1/2(iku) 1(u) sar.
68.
The same observation can be applied to: DP 605, Field 5; DP 606, Field 1; DP 608, Field 3; DP 610, Field 3. However, this is far from being a rule: in many other cases, such as DP 611, Field 3, the introduction of the subtraction sign la₂ cannot be directly connected to the use of any rounding.
69.
Liverani (1990, 1996, 1997).
70.
Liverani (1996: 15; 1997: 219): ‘In the south (from the deep south around Lagash and Uruk, upwards to the Nippur area) narrow elongated strips prevail, while in the north (the Kish and the Diyala areas) “square” and irregular fields are more frequently attested’. According to Liverani, political and environmental features underlie this regional difference.
71.
Liverani (1990: 160–166, Figs. 8–14). Accordingly, the sample of fields attested among the round tablets (Pettinato 1969) shows that most of the Neo-Sumerian fields were narrow strips.
72.
Allotte de la Fuÿe (1915: 142–144).
73.
This shows that the understanding of these terms is somewhat different from later mathematics, cf. Friberg (1987–1990: 553): ‘By a tacit convention, the length is never shorter than the front’. In the documents considered in this study, also fields described as rectangles are concerned.
74.
Allotte de la Fuÿe (1915: 137).
75.
TMH 5, 58, 61, 65 and 73; these texts were edited by Westenholz (1975a: 41–43, 47).
76.
TMH 5, 58. Obv. I. 5-8: 4(u) la₂ 2(diš) (= 38 ninda) saĝ/ 1(ĝeš₂) (= 60 ninda) us₂/ aša₅-bi 1(bur₃) 1(eše₃) la₂ 1(iku) (= 23 iku), the difference is of 20 sar, the area as calculated is 2280 sar; Obv. II. 2–3: 1(ĝeš₂) 2(u) 1(aš) (= 81 ninda) saĝ/ 1(ĝeš₂) (= 60 ninda) us₂, aša₅-bi 2(bur₃) 2(eše₃) 1/2(iku) (= 48 1/2 iku) GAN₂, instead of 48.60 iku.
77.
For instance, fields surveyed in TMH 5, 58 and 73 give the most important evidence for the agricultural landscape of the Nippur countryside. 1. TMH 5, 58. Field 1. saĝ sides: 20 ninda; us₂ sides: 25 ninda; rectangular shape. Field 2. saĝ sides: 38 ninda; us₂ sides: 60 ninda; rectangular shape. Field 3. saĝ sides: 81 ninda; us₂ sides: 60 ninda; rectangular shape. Field 4. saĝ sides. 120 ninda; us₂ sides: 60 ninda; strip. Field 5. saĝ sides: 145 ninda; us₂ sides: 60 ninda; strip. Field 6. saĝ sides: [11 1/2] ninda; us₂ sides: 300 ninda; elongated strip. 2. TMH 5, 73. Field 1. saĝ sides: 180 ninda; us₂ sides: 240 ninda; rectangular shape. Field 2. saĝ sides: 85 ninda; us₂ sides: 85 ninda; square shape. In TMH 5, 61 and 65, only two fields are descibed. Field in TMH 5, 61. saĝ side 1: 40: saĝ sides 2: 110 ninda; us₂ sides: 100; irregular, trapezoidal shape. Field in TMH 5, 65. us₂ sides: 67,5 ninda; saĝ sides: 1 ninda 5 kuš 2 šudua 3 1/3 šusi; elongated strip. The proportion is accordingly as follows: 1 square shape field, 1 trapezoidal shape, 4 rectangle-like fields, 2 strips and 2 elongated strips, which seems consistent with the Ĝirsu information.
78.
As suggested to me by Chemla (2005: 132–134), ancient Chinese mathematics could also rely on the implicit distinction between the magnitude and the value produced by an algorithm, the former being its relation to the problem solved, the second the result of the computation.
79.
CUSAS 33, 175–181, 183–186, 276 and 279. The text CUSAS 33, 276, which deals with a small surface, will not be discussed here. CUSAS 33, 184 and 185 are too fragmentary to be included in the present study.
80.
Studies are furthermore hampered by the fragmentary state of these texts, since many lengths or surfaces are missing. If only one length is not well enough preserved, the whole computation cannot be reconstructed with certainty, such as is the case for the text CUSAS 33, 181.
81.
Friberg (2007: 422); cf. also Powell (1987–1990: 462).
82.
This length unit is written ninda-DU.
83.
Similarly, the area of the two fields mentioned in the text CUSAS 33, 181 is calculated by means of the product of the average length of two opposite sides.
84.
The discrepancy between the area expected from the lengths of the sides and the area indicated seems, in one instance, bigger than in the Lagaš texts: CUSAS 33, 179 Field 1 (obv. i. 1–3) mus2 sides: 244 ninda saĝ sides: 30 5/12 ninda S = 244 × 30 5/12 = 7421 2/3 sar Surface indicated: 4(bur3) 1(eše3) 1 1/2 1/4(iku) = 79 3/4 iku The difference is approximately 5 1/2 iku. On the basis of the photograph which the authors made available to me, the transliteration of the surface may be interpreted differently as 4(bur3) 3 1/2 1/4(iku), 75 3/4 iku, which represents a smaller difference with the calculated surface, although the numerals held to represent the iku unit are arranged vertically, and not in a row, as expected.
85.
Note also that, in many lines, a smaller area, which is designated by the Sumerian term u₂-rum, follows the main area. For instance, the field plot allotted to Igi-še_3tenû is associated with: 4(iku) u₂-rum. As suggested to me by Palmiro Notizia, this supplementary area is not part of the computation and is not added to the area of the field, since the results obtained by means of the product of the lengths of the sides are only equal to the ‘main area’. The meaning of this area and of the term u₂-rum, referring in Sumerian to ‘property’, is not clear in this very context.
86.
Theoretically, either the us₂ side is equal to 600 ninda or there are two us₂ sides, one being equal to 300 ninda, the other to 900. Since the latter represents a length that is too big to be plausible, and since only one common long side, us₂, is referred to regarding the plots of field allotted to the scribe and to the donkey herder, it seems unlikely that two ‘long’ sides (us₂ sig and us₂ igi-nim) were distinguished in the measurement of the other fields.
87.
The field plot is followed by: 2(iku) u₂-rum.
88.
It seems also unlikely that two lengths are missing, which would be another us₂ side and the ‘lower front’ side.
89.
According to the transliteration offered by Notizia and Visicatto and to the photographs which the authors made available to me, data are the following: rev. i. 7’. 3(ĝeš₂) 2(u) 3(aš) us₂. / ii. 1. +6(aš) [ ] / 2. 2(ĝeš₂) 3(u) 3(aš) us₂ / 3. 2(ĝeš₂) 4(u) 4(aš) us₂ / 4. 2(u) 6(aš) ninda-DU / 5. 1(bur₃) 1(eše₃) 1 1/2(iku) aša₅ / 6. 2(eše₃) 3 1/2(iku) / 7. 1(eše₃) 2(iku) saĝ-du₃. If one follows the interpretation by Notizia and Visicato, the length on the reverse, i. 7’ (203 ninda) belongs to the preceding field measurement. If one excludes the length written on rev. ii. 1 (+6), the product of the average of the two us₂ sides with the last length (likely to be the saĝ side) gives the same area as the two areas on rev. ii. 5–6: 1/2(153 ninda + 164 ninda) × 26 = 4121 sar = 41.21 iku. The addition of the aforementioned areas is: 25 1/2 + 15 1/2 = 41 iku. This might offer a preliminary interpretation to these lines.
90.
See also in the same volume the Early/Middle Sargonic tablet probably originating from Adab, CUSAS 33, 279, obv. 4–6, with saĝ sides being 40 ninda and us₂ sides 30 ninda.
91.
Allotte de la Fuÿe seems to have considered the sign NUN to have a horizontal wedge in its upper part (therefore represented as GAN₂).
92.
The field name aša₅ abgal₂ is documented in DP 596, from the second year of Iriʾinimgina lugal, which refers to a plot to be ploughed belonging to the ‘lord domain’, niĝ₂-en-na.
93.
The numerals were, however, correctly interpreted by Allotte de la Fuÿe (1915: 123, 129) as 1/2 la₂ 1(diš).
94.
Surfaces were calculated both as the result of formulas (geometrical or ‘land surveyor’ formula) represented in iku and sar, in order to present the absolute result, and by means of MesoCalc to get the conversion in Mesopotamian units. The difference toward the reconstruction of the procedures used by land surveyors mainly consists in the fact that the conversion by MesoCalc indicates directly the part of a surface represented by such small units as gin and še.
95.
Allotte de la Fuÿe (1915: 130, note 4).

Abbreviations

DP:: Allotte de la Fuÿe (1908–1920)
Genava 26:: Sollberger (1948)
HSS 3:: Hussey (1912)
Nik 1:: Nikolʾskij (1908)
VS 14:: Förtsch (1916)
AWL:: Bauer (1972)
FAOS 15/1:: Selz (1989)
FAOS 15/2:: Selz (1993)
OSP:: Westenholz (1975a, b)
RA 12:: Allotte de la Fuÿe (Hussey 1912)
TMH 5:: Pohl (1935)

References

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CNRS – UMR 7041 – VEPMO, MAE, 21 allée de l’Université, Nanterre Cedex, 92023, Nanterre, France
Camille Lecompte

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Camille Lecompte
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CNRS, Paris 1 Panthéon-Sorbonne, Université Paris Nanterre, Ministère de la Culture, ArScAn, UMR 7041, Nanterre, France
Cécile Michel
CNRS, Université de Paris - Paris Diderot, SPHERE, UMR 7219, Paris, France
Karine Chemla

Appendices

Appendix 8.A Excursus—Land Survey Texts from the Umma Region

Palmiro Notizia kindly provided me with his transliterations of the ED texts from the Umma region relating to land surveying before their publication and during the time I was finishing the present chapter.^{Footnote 79} Due to the lack of time to study these texts extensively, I restrain myself by offering some general considerations and a comparison with the Lagaš tablets.^{Footnote 80}

1. Length units rely on the seed cubit, kuš-numun (written kuš₃-numun) of 2 ĝiš-bad and are the same as in a mathematical text supposedly from Zabalam published by Friberg.^{Footnote 81} It includes the nikkas, written niĝ₂-ka₉ and does not use the ‘rope’ unit, eš₂.
2. The representation of field areas rarely uses small surface units, such as the sar or gin, two exceptions being: CUSAS 33, 176. obv. 3. 4(bur₃) 3(iku) la₂ 1 2/3 sar 5 gin₂-bi, and CUSAS 33, 186.
3. Method of computation: area calculated as length × width.

CUSAS 33, 178

Field 1 (obv. i.1–3)

us₂ sides: 240 ninda^{Footnote 82}
saĝ (sig) sides: 44 ninda 5 kuš-numun 1 ĝiš-bad (44 11/12 ninda)
S = 240 × 44 11/12 = 10 780 sar = 107.80 iku
Surface indicated: 6(bur₃) la₂ 3(iku) = 105 iku

Field 4 (obv. iii. 2–5)

us₂ sides: 220 ninda
saĝ sides: 44 ninda
S = 220 × 44 = 9680 sar
Surface indicated: 5(bur₃) 1(eše₃) 1(iku) = 97 iku

There are a few examples of fields, whose shape is a square:

CUSAS 33, 176

Field 1 (obv. 1–2)

86 ninda 1 nikkas sa₂: 86 1/4 ninda ‘squared’
86 1/4² = 7439,0625 sar
Surface indicated: 4(bur₃) 4(iku) = 76 iku
Surface indicated (2): 4(bur₃) 3(iku) la₂ 1 2/3 sar 5 gin₂ = 74 iku 98 sar 45 gin

Since the second surface indicated is close to the expected result, the scribe may have first given a rough approximation of the area before offering a more accurate result. Note also that, in contrast to the texts from Lagaš, the term sa₂ refers to the us₂ and saĝ sides together.

CUSAS 33, 180

Field 1 (obv. i. 2–5)

us₂ sides: 120 ninda
upper front side (saĝ igi-nim): 50 ninda = lower front side (saĝ sig) = 50 ninda
S = 120 × 50 = 6000 sar
Surface indicated: 3(bur₃) 1(eše₃) = 60 iku

4. Application of the ‘land surveyor’s formula’”, with three or four sides:

CUSAS 33, 177

Field 1 (obv. i. 1–ii. 1)

upper long side (us₂ igi-nim): 132 ninda
lower long side (us₂ sig): 90 ninda
upper front side (saĝ igi-nim): 61 ninda 5 kuš-numun (61 5/6 ninda)
lower front side (saĝ sig): 45 ninda
S = 1/2(132 + 90) × 1/2(61 5/6 + 45) ≈ 5929.25 sar
Surface indicated: 3(bur₃) 3 1/2(iku) = 57 1/2 iku

CUSAS 33, 180

Field 2 (obv. ii. 4–iii. 2)

lower long side (us₂ sig-ta): 126 ninda
upper long side (us₂ igi-nim): 122 ninda
upper front side (saĝ igi-nim): 60 ninda
lower front side (saĝ sig-ta): 76 ninda
S = 1/2(126 + 122) × 1/2(60 + 76) = 8432 sar

Surface indicated: 4(bur₃) 2(eše₃) = 84 iku^{Footnote 83}

5. Approximation and rounding. Since many lines are missing or are not preserved well enough to reconstruct the missing length or area, the range of approximation cannot be well understood.

Nevertheless, there are several examples of rounding and approximations similar to what has been observed in the Lagaš text:

CUSAS 33, 178

Field 4 (obv. iii. 2–5)

us₂ sides: 220 ninda
saĝ sides: 44 nindaS = 220 × 44 = 9690 sar
Surface indicated: 5(bur₃) 1(eše₃) 1(iku) = 97 iku
Difference: 20 sar

The difference can be explained as a simplification of the surface by cancelling the sar units, a procedure which is also applied in the computation of Field 2 in CUSAS 33, 180 (see above). In most of the cases, the approximations cannot be explained and do not seem to be the result of an ‘additive’ computation, such as observed in the Lagaš texts (see Sect. 8.4.3). The first field in CUSAS 33, 177 shows, for instance, the following difference between the calculated and the written surface:

S = 1/2(132 + 90) × 1/2(61 ⁵/₆ + 45) ≈ 5929.24 sar
Surface indicated: 3(bur₃) 3 1/2(iku) = 57 1/2 iku
Difference: 1.7925 iku (= 1 iku la₂ 21 sar 45 gin)

Such approximation probably represents a procedure which aims to reduce the inaccuracy of the ‘land surveyor’s formula’ but cannot be explained at present. Nevertheless, the computation of the Field 1 in CUSAS 33, 178 seems to have omitted the kuš-numun and ĝiš-bad units of the saĝ (sig) sides (44 ninda 5 kuš-numun 1 ĝiš-bad = 44 11/12 ninda): 240 × 44 = 10 560 sar, so the difference with the surface indicated on the tablet (105 iku) is only 60 sar, representing therefore a rounding. This is much smaller than the difference of 2.80 iku with the surface obtained by means of the ‘land surveyor’s formula’, which is equal to 107.80 iku.^{Footnote 84}

In the texts from Umma, the surface indicated corresponds frequently to the result expected from the product of the lengths of the sides:

CUSAS 33, 183

Field 1 (obv. i. 1–5)

long sides us₂: 180 ninda
upper front side saĝ nim: 80 ninda
lower front side saĝ sig: 95 ninda
S = 180 × 1/2(80 + 95) = 15 750 sar
Surface indicated: 8(bur₃) 2(eše₃) 1 1/2(iku) = 157 1/2 iku

6. In the documentation from the Umma region, some of the texts feature an original arrangement of information within the tablets, which can be exemplified by CUSAS 33, 175. Therein, the areas of field plots allotted to individuals are listed on the obverse of the tablet and on the first line of the reverse, while the lengths of the sides of the same fields are indicated separately on the reverse in the same order. Since a few lines are missing, the reconstruction of the computation remains uncertain. The measurement of the plots assigned to a scribe (dub-sar) and to a donkey herder (sipa anše) is nonetheless clear and relies on the product of two sides, on the one hand the ‘upper front’ side, saĝ igi-nim, specific to each field and, on the other hand, a ‘long’ side, us₂, which seems to be the same for both plots:

Surface (obv. iv. 3’–4’9).

plot of the scribe (dub-sar): 4(bur₃) 1(eše₃) = 78 iku
plot of the donkey herder (sipa anše): 2(bur₃) 3(iku) = 39 iku

Lengths (rev. i. 2–4)

saĝ side of the plot of the scribe (dub-sar): 26 ninda
saĝ side of the plot of the donkey herder: 13 ninda
common us₂ side: 300 ninda
Surface of the scribe’s plot: S = 26 × 300 = 7800 sar.

Surface indicated: 78 iku
Surface of the donkey herder’s plot: S = 13 × 300 = 3900 sar.
Surface indicated: 39 iku.

It seems therefore that the computation relies only on the ‘upper front’ side, saĝ igi-nim, but did not use the opposite front side, called ‘lower front side’, saĝ sig, which is not indicated in this section of the tablet. The same text refers to twenty other field plots, for which only the ‘upper front’ side, saĝ igi-nim, is preserved. As proven by the computation below, it is possible to reconstruct either a missing ‘common’ long side (us₂), different than the one used for the field plots of the scribe and of the donkey shepherd, or a ‘lower front’ side, saĝ sig. Therefore, I give two possible reconstructions of the surface. S(1) refers to a surface for which the common ‘long’ side us₂ is missing: as a result, the computation relies only on the ‘upper front’” side, saĝ igi-nim. By contrast, S(2) refers to a reconstruction, in which are considered the ‘upper front’ side, saĝ igi-nim, and the ‘common long’ side used for the field plots of the scribe and of the donkey shepherd, 300 ninda: therefore, I try to reconstruct a possible missing ‘lower front’ side, saĝ sig. For the sake of convenience, only 4 field plots are taken as examples:

Field plot of Igi-še_3tenû

Surface: 4(bur₃) la₂ 2(iku) = 70 iku^{Footnote 85}

‘Upper front’ side (saĝ igi-nim): 11 ninda 4 kuš-(numun) (= 11 2/3 ninda)
S(1) = 7000 ÷ 11 2/3 = 600 ninda: possible missing us₂ side.^{Footnote 86}
S(2) = 7000 ÷ 300 = 23 1/3: if we hypothesize a missing ‘lower front’ side, saĝ sig, it should be equal to: 23 1/3 = 1/2(11 2/3 + x), therefore 35 ninda. S = 1/2(11 2/3 + 35 ninda) × 300 ninda = 70 iku

Field plot of Unken-ne₂

Surface: 3(bur₃) 1(eše₃) = 60 iku

‘Upper front’ side: 10 ninda
S(1) = 6000 ÷ 10 = 600 ninda: possible missing us₂ side
S(2) = 6000 ÷ 300 = 20: if we hypothesize a missing ‘lower front’ side, it should be equal to: 20 = 1/2(10 + x), therefore 30 ninda. S = 1/2(10 + 30) × 300 ninda = 60 iku

Field plot of A-ba-mu-na-du

Surface: 3 bur₃ 1 eše₃ 1 iku = 61 iku

‘Upper front’ side: 10 ninda 1 kuš-(numun) (= 10 1/6 ninda)
S(1) = 6100 ÷ 10 1/6 = 600 ninda: possible missing us₂ side
S(2) = 6100 ÷ 300 = 20 1/3 ninda: if we hypothesize a missing ‘lower front’ side, it should be equal to: 20 1/3 = 1/2(10 1/6 + x), therefore 30 1/2 ninda. S = 1/2(10 1/6 + 30 1/2 ninda) × 300 ninda = 61 iku

Field of E₂-^dAnzu₂

Surface: 6(bur₃) 2(eše₃) 2(iku) = 122 iku^{Footnote 87}

‘Upper front’ side: 20 ninda 2 kuš-(numun) (= 20 1/3 ninda)
S(1) = 12 200 ÷ (20 1/3) = 600 ninda: possible missing us₂ side
S(2) = 12 400 ÷ 300 = 40 2/3 ninda if we hypothesize a missing ‘lower front’ side, it should be equal to: 40 2/3 = 1/2 (20 1/3 + x), therefore 61 ninda. S = 1/2(20 1/3 + 61) × 300 ninda = 122 iku

Therefore, one can suppose that a ‘common’ long side, measuring approximately 600 ninda, is missing and concerns the twenty field plots aside from those assigned to the scribe and the donkey herder. This seems more probable than the reconstruction of a missing ‘lower front’ side, saĝ sig. Since, according to the transliteration by Notizia and Visicato, only one line is missing before the measurement of the lengths of the sides of the field plot allocated to Igi-še_3tenû, it can be suggested that the missing common ‘long’ side of the field plots (aside from those of the scribe and the donkey herder) was written here (rev. ii. 1).^{Footnote 88}

It can also be noticed that the succession of five lengths of sides and of three areas on the first and second columns of CUSAS 33, 178 is somewhat puzzling.^{Footnote 89}

7. Shape of the fields. In contrast to the land survey texts from Lagaš, the fields described in the Umma documentation are almost all elongated strips, with their ‘long’ sides us₂ being at least twice as big as their ‘front’ sides saĝ. In some instances, very narrow ‘front’ sides feature the fields:

CUSAS 33, 178

Field 3 (obv. ii. 4–6)

us₂ sides: 220 ninda - saĝ sides: 25 3/4 ninda: the difference is almost in the range of the long sides being ten times longer than the front sides

CUSAS 33, 179

Field 1 (obv. i. 1–3)

us₂ sides: 244 ninda - saĝ sides: 30 5/12 ninda
‘Long’ sides of several fields nevertheless represent only two times or less the’front’ sides:

CUSAS 33, 180

Field 2 (obv. ii. 4–iii. 1)

us₂ sides: 122 and 126 ninda - saĝ sides: 60 and 76 ninda

CUSAS 33, 181

Field 1 (i. 1–ii. 1)

us₂: +60 and 100 ninda - saĝ sides: 160 ninda 10 1/4 ĝiš-bad and 97 ninda, so one saĝ side is bigger than the us₂ sides.

As seen above, there is also an example of a field described as a square (CUSAS 33, 176, Field 1).

Only a few fields seem to feature saĝ sides bigger than us₂ sides:

CUSAS 33, 181

Field 1 (obv. i. 1–ii. 1)

us₂ sides (igi-nim and sig): 60 + and 100 ninda
saĝ sides (igi-nim and sig) 160 ninda 5 kuš-numun 1/4 (ĝiš-bad) and 97 ninda^{Footnote 90}

Furthermore, most of the fields described in the texts originating from the Umma region are probably ‘subsistence fields’, šuku, allotted to individuals. This supports Liverani’s hypothesis of a Sumerian landscape in which narrow elongated strips prevail, but also the idea expressed above that a tie might exist between the shape of the fields and social status, since the ‘lord domain’ fields described in the texts of Lagaš exhibit a bigger variety in shape.

Appendix 8.B: Texts Related to Land Surveying from Girsu

On the occasion of a stay in the Louvre Museum, I collated the relevant tablets edited by Allotte de La Fuÿe in his magisterial Documents présargoniques (abbreviated DP). I express my gratitude to Béatrice André-Salvini for having given me the authorization to work on these tablets. The few details I corrected are given here.

CT 50, 40

Copy: Sollberger.
Transliteration, photograph: CDLI P221677
Date: Iriʾinimgina x

VS 14, 40

Copy: Förtsch
Edition: Bauer, AWL 4, pp. 74–84.
New copy, commentary: Damerow et al. (1993: 62, Fig. 55). Transliteration, photograph: CDLI P020054
Date: Iriʾinimgina ensi₂ (?) 4

VS 14, 156

Copy: Förtsch.
Edition: AWL 6 (Bauer 1972: 97–103)
Transliteration, photograph: CDLI P020169
Date: Lugalanda +1

VS 25, 76

Copy: Marzahn. T
ransliteration, photograph: CDLI P020282
Date: Iriʾinimgina ensi₂/lugal? 2

Nik 1, 34

Copy: Nikolskij
Edition:FAOS 15/1, 34 (Selz 1989: p. 196–197)
Transliteration, photograph: CDLI P221741
Date: Lugalanda 4

Nik 1, 37

Copy: Nikolskij.
Edition: FAOS 15/1 p. (Selz 1989: 201–202)
Transliteration, photograph: CDLI P221744
Date: Lugalanda? 1

Genava 26, 4

Copy and edition: Genava 26 (Sollberger 1948: 55–56).

Transliteration, photograph: CDLI P225845
Date: Iriʾinimgina (?) 5
Collation, according to the photograph available on the website CDLI: Obv. II. 1. aša₅-bi 1(bur₃) 2(eše₃) Ur-dam, instead of 3(bur₃).

DP 604

Copy: Allotte de La Fuÿe
Edition: RA 12 (Allotte de la Fuÿe 1912: 124–125)
Transliteration: CDLI P221254
Date: Iriʾinimgina ensi₂ 1.
I suggest reading Obv. IV. 1. as 1(ĝeš₂) 1(u) 3 (diš) gi instead of 6(u) 3(diš) gi, which is impossible since 60 is only expressed in the sexagesimal system as 1(ĝeš₂)

DP 605

Copy: Allotte de la Fuÿe
Edition: RA 12 (Allotte de la Fuÿe 1912: 125–126)
Transliteration: CDLI P221255
Date: Iriʾinimgina ensi₂ (?) 1

DP 606

Copy: Allotte de la Fuÿe
Edition: RA 12(Allotte de Fuÿe 1912: 127)Transliteration: CDLI P221256
Date: Iriʾinimgina ensi₂ (?) 1

DP 607

Copy: Allotte de la Fuÿe
Edition: RA 12 (Allote de la Fuÿe 1912: 127–128)
Transliteration: CDLI P221257
Date: Iriʾinimgina lugal 2
Collation: Rs. II. 5. abgal₂ (NUN.ME.KA × GAN₂tenû) instead of GAN₂ ME.KA × GAN₂tenû^{Footnote 91}
So far, the term abgal₂ is attested in several texts, especially in connection with the goddess Nanše, abgal₂-^dNanše, which shows that it designated a cultic function.^{Footnote 92} The abgal₂ who is said to have rented a plot field of 1 bur₃ in DP 607, may be the same person as the abgal-^dNanše who is allotted another smaller plot of 1 eše₃ 3 iku according to VS 25, 78, O0202.

DP 608

Copy: Allotte de la Fuÿe
Edition: RA 12 (Allotte de la Fuÿe 1912: 128–130)
Transliteration: CDLI P221258
Date: Iriʾinimgina?
Collation: Rs. II. 6. 1/2 la₂ 1(diš) gi saĝ instead of 1/2 la₂ 2(diš) gi^{Footnote 93}

DP 609

Copy: Allotte de la Fuÿe
Edition: RA 12 (Allotte de la Fuÿe 1912: 130).
Date: Iriʾinimgina?

DP 610

Copy: Allotte de la Fuÿe
Edition: Allotte de la Fuÿe, RA 12, pp. 130–131
Transliteration: CDLI P221260
Date: Iriʾinimgina?
Collation: Obv. III. 2. kiri₆ E₂-ku₄-kam (kam forgotten in the copy)

DP 611

Copy: Allotte de la Fuÿe
Transliteration, photograph: CDLI P221261
Date: Iriʾinimgina?

Appendix 8.C: Fields and Area Calculation. Land Surveying in Lagaš

The following tables consist of: the lengths and surfaces as given in the tablets in the upper part, with their conversion in a number of ninda and iku respectively; the area calculation according to the given length compared with the surface indicated in the lower part, wherever numerals are well enough preserved: the result is given according to the same codes as for the transliteration of values.^{Footnote 94} Tables are therefore presented as follows (Table 8.6):

Table 8.6 Presentation of calculation in this appendix

Full size table

Since most of the Sumerian expressions given here in transliteration are the same, only the difficult passages will be translated. The usual terms are:

us₂: ‘flank side’, ‘length’

saĝ: ‘front side’, ‘width’

sa₂: ‘equal, equilateral’: us₂ sa₂/ saĝ sa₂: ‘equal length’,’equal width’

2 kam: ‘this is the second’, applied to unequal sides

saĝ a-ki-ta/ an-na: ‘lower/upper front side’

aša₅-bi n GAN₂: ‘this field (has an area of)’

CT 50, 40

1. Field 1

x us₂ x us₂ 2 kam-ma 3(u) 3(diš) gi saĝ (31 1/2 ninda) 3(u) 7(diš) gi saĝ 2 kam-ma (33 1/2 ninda)	aša₅-bi 2(bur₃) 3 1/4(iku) GAN₂ (21 1/4 iku)

2. Field 2

2(ĝeš₂) 4(diš) gi us₂ sa₂ (122 ninda) 1(ĝeš₂) 3(u) saĝ (90 ninda) x saĝ 2(diš) kam-ma	aša₅-bi 6(bur₃) 4 1/2 1/4(iku) GAN₂ (112 3/4 iku)

3. Field 3

2(ĝeš₂) 120 4(diš) gi us₂ (122 ninda) 1(ĝeš₂) 5(u) 4(diš) gi us₂ 2(diš) kam-ma (112 ninda) 1(ĝeš₂) 4(u) saĝ (100 ninda) 1(ĝeš₂) 1(u) 1/2 4(diš) gi saĝ 2(diš) kam-ma (77 ninda)	aša₅-bi 5(bur₃) 2(eše₃) 1 1/2(iku) GAN₂ (103 1/2 iku)
1/2(122 + 112) ninda × 1/2(100 + 77) ninda	5 bur 2 eše 1 1/2 iku 4 sar 30 gin (103 iku 54 1/2 sar) difference: –4 1/2 sar

Difference by omission of the product of gi unit: 1/2(4 + 4) gi × 4 gi = 4 sar

VS 14, 40

4. Field 1

1(ĝeš₂) 1(u) 1/2 5(diš) gi us₂ sa₂ (77 1/2 ninda) 3(u) 6(diš) gi saĝ sa₂ (33 ninda)	aša₅-bi 1(bur₃) 1(eše₃) 1 1/2(iku) tug_x-si-ga-kam (25,5 iku)
77 1/2 ninda × 33 ninda	1 bur 1 eše 1 1/2 iku 7 sar 30 gin (25 iku 57 1/2 sar) difference: –7 1/2 sar

Difference: 5 gi × 6 gi = 30 gi² = 7 1/2 sar

5. Field 2

1(ĝeš₂) 3(u) saĝ sa₂ (90 ninda) 1(ĝeš₂) 1(u) 1/2 5(diš) gi us₂ sa₂ (77 1/2 ninda)	aša₅-bi 4(bur₃) la₂ 2 ¼(iku) GAN₂ (69 ¾ iku)
90 ninda × 77 1/2 ninda	4 bur minus 2 1/4 iku (69 3/4 iku)

6. Field 3

1(ĝeš₂) us₂ sa₂ (60 ninda) 3(u) saĝ sa₂ (30 ninda)	aša₅-bi 1(bur₃) GAN₂ (18 iku)
60 ninda × 30 ninda	1 bur (18 iku)

7. Field 4

1(ĝeš₂) 1(u) 1/2 3(diš) gi us₂ sa₂ (76 1/2 ninda) 7(diš) gi saĝ sa₂ (3 1/2 ninda)	aša₅-bi 2 1/2 1/8 (iku) GAN₂ (2 iku 62 1/2 sar)
76 ½ ninda × 3 ½ ninda	2 1/2 iku 17 sar 45 gin (2 iku 67 3/4 sar) difference: –5 1/4 sar

Difference by omission of the gi unit: 3 gi × 7 gi = 5 1/4 sar

VS 14, 156

8. Field 1

1(ĝeš₂) 1(u) us₂ (70 ninda) 1(ĝeš₂) 1(u) 1/2 la₂ 1(diš) gi us₂ 2(diš) kam-ma (74 1/2 ninda) 5(u) saĝ (50 ninda) 5(u) 4(diš) gi saĝ 2(diš) kam-ma (52 ninda)	aša₅-bi 2(bur₃) 1/2 1/4(iku) GAN₂ (36 3/4 iku)
1/2(70 + 74 1/2) ninda × 1/2(50 + 52) ninda	2 bur 1/2 iku 34 sar 45 gin (36 iku 84 3/4 sar) difference: –9 3/4 sar

9. Field 2

5(u) us₂ sa₂ (50 ninda) 1(u) 4(diš) gi saĝ sa₂ (12 ninda)	aša₅-bi 1(eše₃) (6 iku)
50 ninda × 12 ninda	1 eše (6 iku)

VS 25, 76

10. Field 1

2(u) us₂ (20 ninda) 1(u) 1/2 5(diš) gi us₂ 2(diš) kam-ma (17 1/2 ninda) 1(u) 1/2 5(diš) gi saĝ (17 1/2 ninda) 1(u) 3(diš) gi saĝ 2(diš) kam-ma (11 1/2 ninda)	aša₅-bi 2 1/2 1/4(iku) GAN₂ (2 3/4 iku)
1/2(20 + 17 1/2) ninda × 1/2(17 1/2 + 11 1/2) ninda	2 1/2 iku 21 sar 52 gin 63 še (2 iku 71.875 sar) difference: + 3 sar 7 1/2 gin

11. Field 2

3(u) 1(diš) gi us₂ sa₂ (30 1/2 ninda) 1(u) 7(diš) gi saĝ (13 1/2 ninda) 1/2 4(diš) saĝ 2(diš) kam-ma (7 ninda)	aša₅-bi 3(iku) GAN₂ [x] SAR? (3 iku)
30 1/2 ninda × 1/2(13 1/2 + 7) ninda	3 iku 12 sar 63 še (3 iku 12.625 sar) difference:?

12. Field 3

1/2 5(diš) [gi] us₂ [sa₂] (7 1/2 ninda) 1/2 2(diš) < gi > saĝ s[a₂] (6 ninda)	aša₅-bi 4(u) 5(diš) sar (45 sar)
7 1/2 ninda × 6 ninda	45 sar

Nik 1, 34

13. Field 1

2(ĝeš₂) 1/2 5(diš) gi us₂ sa₂ (127 1/2 ninda) 1(ĝeš₂) saĝ sa₂ (60 ninda)	aša₅-bi 4(bur₃) 3(iku) GAN₂ tug_x-si-ga (75 iku)
127 1/2 ninda × 60 ninda	4 bur 4 1/2 iku (76 1/2 iku) difference: –1 1/2 iku

Difference by omission of the gi unit: 125 ninda × 60 ninda = 7500 sar = 75 iku

14. Field 2

2(ĝeš₂) 1/2 us₂ sa₂ (125 ninda) 1(u) 1/2 2(diš) gi kuš₃ 3(diš) saĝ sa₂ (16 1/4 ninda)	aša₅-bi 1(bur₃) 2(iku) GAN₂ ki-ĝal₂ (‘fallow’) (20 iku)
125 ninda × 16 1/4 ninda	1 bur 2 iku 31 sar 15 gin (20 iku 31.25 sar) difference: –31 sar 15 gin

Difference by omission of the gi unit: 125 ninda × 16 ninda = 2000 sar = 20 iku: 1(bur₃) 2(iku)

Nik 1, 37

15. Field 1

2(u) 1/2 3(diš) gi kuš₃ 3(diš) saĝ sa₂ (26 3/4 ninda) 1(ĝeš₂) 3(u) 1/2 5(diš) gi us₂ sa₂ (97 1/2 ninda)	aša₅-bi 1(bur₃) 1(eše₃) 2(iku) (26 iku)
26 3/4 ninda × 97 1/2 ninda	1 bur 1 eše 2 iku 8 sar 7 gin 63 še (26 iku 8.125 sar) difference: –8 sar 7 1/2 gin 20 še

Genava 26, 4

16. Field 1

1(ĝeš₂) 3(u) 1/2 3(diš) gi us₂ (96 1/2 ninda) 1(ĝeš₂) 1(u) us₂ 2(diš) kam-ma (70 ninda) 4(u) saĝ (40 ninda) 3(u) 5(diš) gi saĝ 2(diš) kam-ma (32 1/2 ninda)	aša₅-bi 1(bur₃) 2(eše₃)* Ur-dam (30 iku)
1/2 (96 1/2 + 70) ninda × 1/2(40 + 32 1/2) ninda	1 bur 2 eše 17 sar 48 gin 15 še (30 iku 17.8125 sar) difference: –17 sar 48 3/4 gin

According to Sollberger, the surface should be: 3(bur₃), 54 iku. However, the discrepancy with the surface, such as it can be measured by the way of the land-surveyor formula, would be too big. Furthermore, on the photograph available on CDLI, the two last numerals interpreted as 2(bur₃) have a wedge on the left which brings to mind the numeral eše₃, as it is drawn for instance in the tablets published in HSS 3.

17. Field 2

5(u) 8(diš) gi us₂ sa₂ (54 ninda) 1(u) 1/2 2(diš) gi saĝ (16 ninda) 4(diš) gi saĝ 2(diš) kam-ma (2 ninda)	aša₅-bi 5(iku) gi gissu (‘shady reed’)
54 ninda × 1/2(16 + 2) ninda	4 1/2 iku 36 sar (4iku 86 sar) difference: + 14 sar

18. Field 3

4(u) 1/2 la₂ 1(diš) gi us₂ eg₂ x (44 1/2 ninda) 4(u) ½ 2(diš) gi us₂ murgu₂ ki-duru₅ us₂-sa (46 ninda) 3(u) 5(diš) gi saĝ an-[na] (32 ½ ninda) 5(u) 8(diš) gi saĝ a-ki-ta-ka (54 ninda)	aša₅-bi 1(bur₃) GAN₂ tug_x-si-ga
1/2(44 1/2 + 46) ninda × 1/2(32 1/2 + 54) ninda	1 bur 1 1/2 iku 7 sar 3 gin 135 še (19 iku 57.0625 sar) difference: bigger than – 1 1/2 iku!

Translation of this text is somewhat difficult:

40 ninda 1/2 (eš) minus 1 gi: length of the dike (?) x

40 ninda 1/2 (eš) 2 gi: length on the ‘shoulder’ along the ‘wet land’

30 ninda 5 gi: upper width

50 ninda 8 gi: ‘lower’ width

this field: 1 bur, ploughed

19. Field 4

2(u) 1/2 7(diš) gi kuš₃ 2(diš) us₂ sa₂ (28 4/6 ninda) 1(u) 1/2 saĝ sa₂ (15 ninda)	aša₅-bi 4 1/4(iku) GAN₂
28 4/6 ninda × 15 ninda	4 iku 30 sar (≈ 4.30 iku) difference: –0.175 iku

Difference by omission of the kuš unit: 28 1/2 ninda × 15 ninda = 427 1/2 sar = 4.275 iku, which is close to 4 1/4 iku as indicated on the tablet

DP 604

20. Field 1

1(ĝeš₂) us₂ sa₂ (60 ninda) 1(ĝeš₂) 1(u) 8(diš) gi saĝ sa₂ (74 ninda)	aša₅-bi 2(bur₃) 1(eše₃) 2 1/2(iku) GAN₂ (44 1/2 iku)
60 ninda × 74 ninda	2 bur 1 eše 2 iku 40 sar (44 iku 40 sar) difference: + 10 sar

21. Field 2

4(u) 3(diš) gi us₂ sa₂ (= 41 1/2 ninda) 3(u) 1/2 5(diš) < gi > saĝ sa₂ (= 37 1/2 ninda)	aša₅-bi 2(eše₃) 3 1/2(iku) GAN₂ (15 1/2 iku)
41 1/2 ninda × 37 1/2 ninda	2 eše 3 1/2 iku 6 sar 15 gin (15 1/2 iku 6 1/4 sar) difference: –6 sar 15 gin

22. Field 3

1(ĝeš₂) us₂ sa₂ (60 ninda) 1(ĝeš₂) 2(u) 7(diš) gi saĝ (83 1/2 ninda) 1(ĝeš₂) 1(u)* 3(diš) gi/ saĝ 2(diš) kam-ma (71 1/2 ninda)	aša₅-bi 2(bur₃) 1(eše₃) 4 1/2(iku) (46 1/2 iku)
60 ninda × 1/2(83 1/2 + 71 1/2) ninda	2 bur 1 eše 4 1/2 iku (46 1/2 iku)

Although the numerals in the third line are broken, we could observe, during the collation of this tablet, that only two numerals may have been written, 1(ĝeš₂) 1(u) = 70. Moreover, the numerals copied by Allotte de la Fuÿe, 6(u), should refer to 60 nindan, though this is quite impossible since one would expect here: 1(ĝeš₂) for 60

23. Field 4

1(ĝeš₂) us₂ (60 ninda) 1(ĝeš₂) 1/2 us₂ 2(diš) kam-ma (65 ninda) 5(u) saĝ sa₂ (50 ninda)	aša₅-bi 1(bur₃) 2(eše₃) 1 1/4(iku) (31 1/4 iku)
1/2(60 + 65) ninda × 50 ninda	1 bur 2 eše 1 1/4 iku (31 1/4 iku)

24. Field 5

1(ĝeš₂) 1/2 us₂ (65 ninda) 4(u) us₂ 2(diš) kam-ma (40 ninda) 4(u) 4(diš) gi saĝ an-na (42 ninda) 2(u) 8(diš) gi saĝ a-ki-ta-ka (24 ninda)	aša₅-bi 1(bur₃) la₂ 1/2 1/4(iku) GAN₂ (17 1/4 iku)
1/2(65 + 40) ninda × 1/2(42 + 24) ninda	2 eše 5 iku 32 sar 30 gin (17 iku 32 1/2 sar) difference: –7 1/2 sar

DP 605

25. Field 1

1(ĝeš₂) us₂ sa₂ (60 ninda) 1(ĝeš₂) saĝ an-na (60 ninda) 1(ĝeš₂) 2(u) saĝ a-ki-ta-ka (80 ninda)	aša₅-bi 2(bur₃) 1(eše₃) GAN₂ (42 iku)
60 ninda × 1/2(60 + 80) ninda	2 bur 1 eše (42 iku)

26. Field 2

1(ĝeš₂) us₂ sa₂ (60 ninda) 1(ĝeš₂) saĝ sa₂ (60 ninda)	aša5-bi 2(bur3) GAN2 (36 iku)
60² ninda	2 bur (36 iku)

27. Field 3

1(ĝeš₂) us₂ (60 ninda) 5(u) 1/2 2(diš) gi us₂ 2(diš) kam-ma (56 ninda) 3(u) 7(diš) gi saĝ an-na (33 1/2 ninda) 3(u) 3(diš) gi saĝ a-ki-ta-ka (31 1/2 ninda)	aša₅-bi 1(bur₃) 1/2 1/4(iku) GAN₂ (18 3/4 iku)
1/2(60 + 56) ninda × 1/2(33 1/2 + 31 1/2) ninda	1 bur 1/2 1/4 iku 10 sar (18 iku 85 sar) difference: –10 sar = 0.10 iku

Here, the product of the smaller long side by the side called saĝ an-na is close to the area indicated on the tablet:

us₂ 2 kam × saĝ an-na: 56 ninda × 33, 1/2 ninda = 1876 sar = 18.76 iku

28. Field 4

2(u) 1/2 5(diš) gi us₂ sa₂ (27 1/2 ninda) 2(u) 6(diš) gi saĝ sa₂ (23 ninda)	aša₅-bi 1(eše₃) GAN₂ (6 iku)
27 1/2 ninda × 23 ninda	1 eše 32 sar 30 gin (6 iku 32 sar) difference: –1/4 iku 7 sar

Difference by omission of the gi unit: 20 ninda × 20 ninda = 400 sar

20 ninda × 3 ninda = 60 sar

5 ninda × 20 ninda = 100 sar

= 610 sar

29. Field 5

1(ĝeš₂) us₂ (60 ninda) 5(u) 1/2 3(diš) gi us₂ 2(diš) kam-ma (56 1/2 ninda) 1(ĝeš₂) 2(u) saĝ an-na (80 ninda) 1(ĝeš₂) 4(u) saĝ a-ki-ta-ka (100 ninda)	aša₅-bi 3(bur₃) la₂ 2(iku) GAN₂ (52 iku)
1/2(60 + 56 1/2) ninda × 1/2(80 + 100) ninda	2 bur 2 eše 4 iku 42 sar 30 gin (52 iku 42 1/2 sar) difference: –1/4/81/8 iku 5 sar

30. Field 6

5(u) 3(diš) gi us₂ sa₂ (51 1/2 ninda) 5(u) 5(diš) gi saĝ an-na (52 1/2 ninda) 5(u) 1/2 la₂ 1(diš) gi saĝ a-ki-ta-ka (54 1/2 ninda)	aša₅-bi 1(bur₃) 1(eše₃) 3(iku) GAN₂ (27 iku)
51 1/2 ninda × 1/2(52 1/2 + 54 1/2) ninda	1 bur 1 eše 3 1/2 iku 5 sar 15 gin (27 1/2 iku 5 1/4 sar) difference: –1/2 iku 5 sar 15 gin

If we apply a formula us₂ sa₂ × saĝ an-na: 51 1/2 × 52 1/2 = 2703 3/4 sar, the difference is only 3 sar 45 gin

31. Field 7

5(u) 4(diš) gi us₂ sa₂ (52 ninda) 1(ĝeš₂) saĝ sa₂ (60 ninda)	aša₅-bi 1(bur₃) 2(eše₃) 1(iku) GAN₂ (31 iku)
52 ninda × 60 ninda	1 bur 2 eše 1 iku 20 sar (31 iku 20 sar) difference: –20 sar

32. Field 8

4(u) us₂ sa₂ (40 ninda) 4(u) saĝ sa₂ (40 ninda)	aša₅-bi 2(eše₃) 4(iku) GAN₂ (16 iku)
40² ninda	2 eše 4 iku (16 iku)

DP 606

33. Field 1

1(ĝeš₂) 3(u) < <gi > > us₂ sa₂ (90 ninda) 1(ĝeš₂) 1(u) 1/2 4(diš) gi saĝ (77 ninda) 1(ĝeš₂) 2(u) la₂ 2(diš) gi saĝ 2(diš) kam-ma-am₆ (79 ninda)	aša₅-bi 4(bur₃) la₂ 2(iku) GAN₂ (70 iku)
90 ninda × 1/2(77 + 79) ninda	3 bur 2 eše 4 iku 20 sar (70 iku 20 sar) difference: –20 sar

34. Field 2

2(u) 1/2 la₂ 1(diš) gi saĝ (24 1/2 ninda) 2(u) 1/2 3(diš) gi saĝ 2(diš) kam-ma (26 1/2 ninda) 1(ĝeš₂) 2(u) 1/2 6(diš) gi us₂ (88 ninda) 1(ĝeš₂) 2(u) 6(diš) gi saĝ 2(diš) kam-ma (83 ninda)	aša₅-bi 1(bur₃) 3 1/2(iku) 3(u) sar (21.80 iku)
1/2(24 1/2 + 26 1/2) ninda × 1/2(88 + 83) ninda	1 bur 3 1/2 1/4 iku 5 sar 15 gin (21 iku 80 1/4 sar) difference: –15 gin

DP 607

35. Field 1

1(ĝeš₂) 5/u) 7(diš) gi us₂ sa₂ (113 1/2 ninda) 1(u) 2(diš) gi saĝ sa₂ (11 ninda)	aša₅-bi 2(eše₃) GAN₂ (12 iku)
113 1/2 ninda × 11 ninda	2 eše 48 sar 30 gin (12 iku 48 1/2 sar) difference: –48 1/2 sar

Difference by omission of the gi unit: 110 ninda × 10 ninda = 1100 sar

110 ninda × 2 gi = 110 ninda

= 1210 sar

36. Field 2

1(ĝeš₂) 5(u) la₂ 2(diš) gi us₂ sa₂ (109 ninda) 1(u) 2(diš) gi saĝ sa₂ (11 ninda)	aša₅-bi 2(eše₃) GAN₂ (12 iku)
109 ninda × 11 ninda	1 eše 5 1/2 1/4 iku 14 sar (11 iku 99 sar) difference: + 1 sar

The result can be represented as: 2(eše₃) la₂ 1(diš) sar, whereby the scribe did merely not take into account the small amount to be subtracted

Difference by the omission of the gi unit: 110 ninda × 11 ninda = 1210 sar

Or 2 gi × 2 gi = 4 gi² = 1 sar

37. Field 3

1(ĝeš₂) 4(u) 4 (diš)gi us₂ sa₂ (102 ninda) 1(u) 5(diš) gi saĝ sa₂ (12 1/2 ninda)	aša₅-bi 2(eše₃) 1/2 1/4(iku) GAN₂ (12 3/4 iku)
102 ninda × 12 1/2 ninda	2 eše 1/2 1/4 iku (12 3/4 iku)

DP 608

38. Field 1

+1(u) 6(diš) gi us₂ (? ninda) [+ 1(ĝeš₂] x(diš) gi us₂ 2(diš) kam-ma (? ninda) 3(u) 1/2 6(diš) gi saĝ sa₂ (38 ninda)	aša₅-bi (bur₃) 1 1/2 1/4(iku) (19 3/4 iku)
1/2 (x + x) ninda × 38 ninda

According to the surface of the field, the average of both us₂ sides should be approximately equal to 51 nindan

39. Field 2

1(ĝeš₂) 3(diš) gi us₂ (61 1/2 ninda) 1(ĝeš₂) 2(u) 3(diš) gi us₂ 2(diš) kam-ma (81 1/2 ninda) 2(u) 1/2 4(diš) gi saĝ sa₂ (27 ninda)	aša₅-bi 1(bur₃) 1(iku) (19 iku)
1/2 (61 1/2 + 81 1/2) ninda × 27 ninda	1 bur 1 iku 30 sar 30 gin (19 iku 30 1/2 sar) difference: –30 1/2 sar

40. Field 3

1(ĝeš₂) 1(u) 3(diš) gi us₂ (71 1/2 ninda) 1(ĝeš₂) 2(u) 1/2 la₂ 1(diš) gi us₂ 2(diš) kam-ma (84 1/2 ninda) 2(u) 2(diš) gi saĝ an-na (21 ninda) 4(u) 1/2 saĝ a-ki-ta-ka (45 ninda)	aša₅-bi 1(bur₃) 1(eše₃) 2(iku) GAN₂ (26 iku)
1/2(71 1/2 + 84 1/2) ninda × 1/2(21 + 45) ninda	1 bur 1 eše 1 1/2 1/4 iku minus 1 sar (25 iku 74 sar) difference: + 1/4 iku 1 sar

41. Field 4

3(u) us₂ sa₂ (30 ninda) 1(u) saĝ sa₂ (10 ninda)	aša₅-bi 3(iku) GAN₂
10 ninda × 30 ninda	3 iku

42. Field 5

1(u) 2(diš) gi us₂ sa₂ (11 ninda) 1(u) 4(diš) gi saĝ (12 ninda) 1/2 3(diš) gi saĝ 2(diš) kam-ma (6 1/2 ninda)	aša₅-bi 1(iku) GAN₂
11 ninda × 1/2(12 + 6 1/2) ninda	1 iku 1 sar 45 gin (1 iku 1 1/4 sar) difference: –1 sar 45 gin

43. Field 6

4(u) us₂ sa₂ (40 ninda) 1/2 la₂ 1(diš) gi saĝ (4 1/2 ninda) 1/2 3(diš) gi saĝ 2(diš) kam-ma (6 1/2 ninda*)	aša₅-bi 2(iku) 2(u) sar (2.20 iku)
40 × 1/2(4,5 + 6.5)	2 iku 20 sar (2.20 iku)

44. Field 7

2(u) 1(diš) gi us₂ (20 1/2 ninda) 1(u) 1/2 3(diš) gi us₂ 2(diš) kam-ma (16 1/2 ninda) 1/2 5(diš) gi saĝ (7 1/2 ninda) 1(u) 2(diš) gi saĝ 2(diš) kam-ma (11 ninda)	aša₅-bi 1 1/2 1/4(iku) (1 3/4 iku)
1/2(20 1/2 + 16 1/2) ninda × 1/2(7 1/2 + 11) ninda	1 1/2 iku 21 sar 7 gin 90 še (1 iku 71.125 sar) difference: + 3 sar 52 gin 90 še

DP 609

45. Field 1

1/2 6(diš) gi kuš₃ 3(diš) us₂ sa₂ (8 1/4 ninda) 1/2 3(diš) gi saĝ sa₂ (6 1/2 ninda)	aša₅-bi 1/2(iku) 4(diš) sar GAN₂ (0.54 iku)
8 1/4 ninda × 6 1/2 ninda	1/2 iku 3 sar 37 gin 90 še (53.625 sar) difference: + 22 1/2 gin

46. Field 2

1/2 5(diš) gi us₂ sa₂ (7 1/2 ninda) 1/2 5(diš) gi saĝ sa₂ (7 1/2 ninda)	aša₅-bi ½(iku) 6 ½(diš) sar (0.565 iku)
7 1/2² ninda	1/2 iku 6 sar 15 gin (56 1/4 sar) difference: + 15 gin

47. Field 1

1/2 eš₂ 3(diš) saĝ (6 1/2 ninda) 1/2 6 (diš) kuš₃ 3(diš) us₂ (8 1/4 ninda)	3(u) 4(diš) sar (30:04 sar = 54 sar) (1/2 iku + 4 sar = 54 sar)
8 1/4 ninda × 6 1/2 ninda	1/2 iku 37 gin 90 še (53.625 sar) difference: + 22 1/2 gin

Use of sexagesimal system? The indication of the area as 3(u) 4(diš) sar is not, as suggested by Allotte de la Fuÿe,^{Footnote 95} a mistake , but is surely another expression of the area of the Field 1: accordingly, 1/2(iku), corresponding to 50 sar, was here expressed as 30/60 and not 50/100. It could be a further clue on the computation, probably made with the gi unit in some cases. It is also noteworthy that the way of writing is similar to the unusual notation of length on the Reverse of VS 14, 100.

DP 610

48. Field 1

2(u) us₂ sa₂ (20 ninda) 1/2 3(diš) gi saĝ sa₂ (6 1/2 ninda)	aša₅-bi 1(iku) GAN₂ 3(u) sar (1.3 iku)
20 × 6 1/2	1 1/4 iku 5 sar (1 iku 30 sar)

49. Field 2

2(u) us₂ sa₂ (20 ninda) 6(diš) gi kuš₃ 3(diš) saĝ sa₂ (3 1/4 ninda)	aša₅-bi 1/2 (iku) 15 sar (0.65 iku)
20 × 3 1/4	1/2 iku 15 sar (65 sar)

50. Field 3

2(u) 4 gi us₂ sa₂ (22 ninda) 1/2 7(diš) gi kuš₃ 3(diš) saĝ sa₂ (8 3/4 ninda)	aša₅-bi 2(iku) GAN₂ la₂ 7 1/2(diš) sar (1.925 iku)
22 × 8.75	2 iku minus 7 1/2 sar (192 1/2 sar = 1 iku 92 1/2 sar)

DP 611

51. Field 1

1(ĝeš₂) us₂ sa₂ (60 ninda) 1(ĝeš₂) saĝ sa₂ (60 ninda)	aša₅-bi 2(bur₃) ziz₂ (36 iku)
60² ninda	2 bur (36 iku)

52. Field 2

2(u) us₂ (20 ninda) 1(u) 1/2 us₂ 2(diš) kam-ma (15 ninda) 4(u) 1/2 saĝ (45 ninda) […] saĝ 2(diš) kam-ma	aša₅-bi < … > GAN₂ še saĝ-an-na-bi
1/2(20 + 15) ninda × 1/2(45 + x) ninda

In this text, Fields 2 and 4 seem to correspond to the ‘lower’ and ‘superior’ limits of an agricultural unit. Following terms are indicated: GAN₂ še saĝ-an-na-bi, ‘barley field, its upper front part’; numun ĝar-ra-am₆, ‘(field,) which is sowed’; tug_x-si-ga-am₆ ki-su₇ za₃-bi a-ki-ta-kam, ‘field, which was deeply ploughed, its side is the threshing floor, this is the lower (part)’

53. Field 3

1(ĝeš₂) us₂ sa₂ (60 ninda) 2(u) 1/2 saĝ sa₂ (25 ninda)	aša₅-bi 1(bur₃) la₂ 3(iku) numun ĝar-ra-am₆ (15 iku)
60 ninda × 25 ninda	2 eše 3 iku (15 iku)

54. Field 4

1(ĝeš₂) us₂ sa₂ (60 ninda) 3(u) 7(diš) gi saĝ sa₂ (33 1/2 ninda)	aša₅-bi 1(bur₃) 2(iku) tug_x-si-ga-am₆ ki-su₇ za₃-bi a-ki-ta-kam (20 iku)
60 ninda × 33 1/2 ninda	1 bur 2 iku 10 sar (20 iku 10 sar) difference: –10 sar

Appendix 8.D: Data Related to the Fields in Girsu

See Tables 8.7 and 8.8.

Table 8.7 Abbreviations and terminology used in this appendix

Full size table

Table 8.8 Data related to the fields

Full size table

Appendix 8.E: Chronology

	Period
2600	Early Dynastic IIIa = Fāra	Texts from Fāra and Abu Ṣalābīḫ
2550	Early Dynastic IIIb	First Dynasty of Lagaš Lagaš (city) . Ur-Nanše
2500		Eannatum Enannatum I
2450		Enmetena
2400		Lugalanda – Iriʾinimgina: archives from Girsu. Land survey texts.
2350	Sargonic period	Lugalzagesi of Umma–end of the Lagaš dynasty. Land survey texts from Nippur– Sargon of Akkad
2300

Appendix 8.F: Fields’ Shapes

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Lecompte, C. (2020). The Measurement of Fields During the Pre-sargonic Period. In: Michel, C., Chemla, K. (eds) Mathematics, Administrative and Economic Activities in Ancient Worlds. Why the Sciences of the Ancient World Matter, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-030-48389-0_8

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DOI: https://doi.org/10.1007/978-3-030-48389-0_8
Published: 30 September 2020
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-48388-3
Online ISBN: 978-3-030-48389-0
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The Measurement of Fields During the Pre-sargonic Period

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The spatial form of traditional villages in Fuzhou area of Jiangxi Province determined via GIS methods

The Topographic Survey of the Netherlands East Indies, Batavia 1864–1950

The Challenge of Digitized Survey Data

Notes

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Appendices

Appendix 8.A Excursus—Land Survey Texts from the Umma Region

Appendix 8.B: Texts Related to Land Surveying from Girsu

Appendix 8.C: Fields and Area Calculation. Land Surveying in Lagaš

Appendix 8.D: Data Related to the Fields in Girsu

Appendix 8.E: Chronology

Appendix 8.F: Fields’ Shapes

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The Measurement of Fields During the Pre-sargonic Period

Abstract

Access this chapter

Similar content being viewed by others

The spatial form of traditional villages in Fuzhou area of Jiangxi Province determined via GIS methods

The Topographic Survey of the Netherlands East Indies, Batavia 1864–1950

The Challenge of Digitized Survey Data

Notes

Abbreviations

References

Author information

Authors and Affiliations

Corresponding author

Editor information

Editors and Affiliations

Appendices

Appendix 8.A Excursus—Land Survey Texts from the Umma Region

Appendix 8.B: Texts Related to Land Surveying from Girsu

Appendix 8.C: Fields and Area Calculation. Land Surveying in Lagaš

Appendix 8.D: Data Related to the Fields in Girsu

Appendix 8.E: Chronology

Appendix 8.F: Fields’ Shapes

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