The Area and the Side I Added: Some old Babylonian Geometry
[La surface et le côté que j'ai ajouté : un problème de géométrie babylonienne]
Revue d'histoire des mathématiques, Tome 11 (2005) no. 1, pp. 7-21.

Il y avait en Mésopotamie un procédé standard pour résoudre des problèmes quadratiques impliquant des longueurs et des surfaces de carrés. Nous montrons, sur un exemple de Suse, que des constantes géométriques ont été employées pour ramener des problèmes concernant d'autres figures au format standard.

There was a standard procedure in Mesopotamia for solving quadratic problems involving lengths and areas of squares. In this paper, we show, by means of an example from Susa, how area constants were used to reduce problems involving other geometrical figures to the standard form.

Keywords: old Babylonian, Susa, area constants, apsamikkum
Mot clés : Mésopotamie, Suse, constantes géométriques, apsamikkum 
@article{RHM_2005__11_1_7_0,
     author = {J. Melville, Duncan},
     title = {The {Area} and the {Side} {I} {Added:} {Some} old {Babylonian} {Geometry}},
     journal = {Revue d'histoire des math\'ematiques},
     pages = {7--21},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {11},
     number = {1},
     year = {2005},
     zbl = {1082.01002},
     language = {en},
     url = {http://archive.numdam.org/item/RHM_2005__11_1_7_0/}
}
TY  - JOUR
AU  - J. Melville, Duncan
TI  - The Area and the Side I Added: Some old Babylonian Geometry
JO  - Revue d'histoire des mathématiques
PY  - 2005
SP  - 7
EP  - 21
VL  - 11
IS  - 1
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/RHM_2005__11_1_7_0/
LA  - en
ID  - RHM_2005__11_1_7_0
ER  - 
%0 Journal Article
%A J. Melville, Duncan
%T The Area and the Side I Added: Some old Babylonian Geometry
%J Revue d'histoire des mathématiques
%D 2005
%P 7-21
%V 11
%N 1
%I Société mathématique de France
%U http://archive.numdam.org/item/RHM_2005__11_1_7_0/
%G en
%F RHM_2005__11_1_7_0
J. Melville, Duncan. The Area and the Side I Added: Some old Babylonian Geometry. Revue d'histoire des mathématiques, Tome 11 (2005) no. 1, pp. 7-21. http://archive.numdam.org/item/RHM_2005__11_1_7_0/

[1] E. M. Bruins & M. Rutten, Textes mathématiques de Suse, Mémoires de la Délégation en Perse 34, 1961 | MR | Zbl

[2] D. H. Fowler & E. Robson, “Square root approximations in Old Babylonian mathematics: YBC7289 in context”, Historia Mathematica 25 (1998), p. 366-378 | MR | Zbl

[3] J. Friberg, “Methods and traditions of Babylonian mathematics II: an Old Babylonian catalogue text with equations for squares and circles”, J. Cuneiform Studies 33 (1981), p. 57-64 | MR | Zbl

[4] J. Friberg, “Seed and Reeds continued: Another metro-mathematical topic text from Late Babylonian Uruk”, Baghdader Mitteilungen 28 (1997), p. 251-365

[5] J. Høyrup, The Old Babylonian Square texts. BM13901 and YBC4714: Retranslation and analysis, in: Changing Views on Ancient Near Eastern Mathematics (JensHøyrupPeterDamerow ed.), Dietrich Reimer Verlag, Berlin, 2001, p. 155-218

[6] J. Høyrup, Lengths, Widths, Surfaces: A portrait of Old Babylonian Algebra and its Kin, Springer, 2002 | MR | Zbl

[7] A. Imhausen, The algorithmic structure of the Egyptian mathematical problem texts, in: Under One Sky: Astronomy and Mathematics in the Ancient Near East (JohnSteeleAnetteImhausen ed.), Ugarit-Verlag, Münster, 2002, p. 147-166 | Zbl

[8] A. Imhausen, Ägyptische Algorithmen : eine Untersuchung zu den mittelägyptischen mathematischen Aufgabentexten, Harrassowitz, 2003 | MR | Zbl

[9] D. E. Knuth, “Ancient Babylonian algorithms”, Communications for the Association of Computing Machinery 15 (1972), p. 671-677 | MR | Zbl

[10] K. Muroi, “Quadratic equations in the Susa mathematical text no. 21”, SCIAMVS 1 (2000), p. 3-10 | MR | Zbl

[11] K. Muroi, “Expressions of multiplication in Babylonian mathematics”, Historia Sci. (2) 12 (2002), p. 115-120 | MR | Zbl

[12] K. Muroi, “Extraction of square roots in Babylonian mathematics”, Historia Sci. (2) 9 (1999), p. 127-133 | MR | Zbl

[13] O. Neugebauer, Mathematische Keilschrifttexte, I-III, Springer, 1935/37 | JFM | Zbl

[14] O. Neugebauer & A. Sachs, Mathematical Cuneiform Texts, American Oriental Series 29, American Oriental Society, 1945, reprinted in 1986 | MR | Zbl

[15] J. Ritter, Babylon -1800, in: A History of Scientific Thought (MichelSerres ed.), Blackwell, Oxford, 1995, p. 17-43

[16] J. Ritter, Measure for measure: Mathematics in Egypt and Mesopotamia, in: A History of Scientific Thought (MichelSerres ed.), Blackwell, Oxford, 1995, p. 44-72

[17] J. Ritter, Reading Strasbourg 368: A Thrice-Told Tale, 1998 | Zbl

[18] E. Robson, “Three Old Babylonian methods for dealing with ‘Pythagorean' triangles”, J. Cuneiform Studies 49 (1997), p. 51-72

[19] E. Robson, Mesopotamian Mathematics, 2100-1600 BC. Technical Constants in Bureaucracy and Education, Oxford Editions of Cuneiform Texts 14, Clarendon Press, 1999 | MR | Zbl

[20] F. Thureau-Dangin, “L'équation du deuxième degré dans la mathématique babylonienne d'après une tablette inédite du British Museum”, Revue d'Assyriologie 33 (1936), p. 27-48 | JFM