Abstract
What follows is a general exposition of the principles that guide Chap. 4, where the texts of the mathematical tablets are presented and commented. Section 3.1 deals with the general rules for transliteration, transcription and translation. Section 3.2 exposes some special, problematic cases pertaining to the mathematical language and the solutions that were adopted here.
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Notes
- 1.
I followed Borger’s practical guidelines for transliteration (MesZL, pages 242–243). For the rules governing the transliteration (as well as transcription and translation) of numbers, see Chap. 2, under the heading Floating Point Arithmetic and Orders of Magnitude.
- 2.
Here too grammar does not enable us to distinguish this sentence from “that your head holds”.
- 3.
The tablet is indeed badly published. The numbering of the lines is inconsistent and, without being able to check the reading, it is not possible to be sure of the unusual a.ša and ib.si.e that Bruins writes instead of the more common a.ša3 and ib2.si.e. Here I use the latter forms, but collation is necessary.
- 4.
Here I simplify the issue of the orders of magnitude, for my purpose is to deal with the vocabulary of square and cube roots. In the text of the problem, we have the abstract number 26.15. The writing 26, 0, 15, 0 = 26 × 603 + 0 × 602+15 × 60 + 0 is only a possible interpretation for it. Although there was no notation for 0 in Old Babylonian mathematics, scribes were able to tackle empty sexagesimal positions.
- 5.
Which is similar to the thought that “transforms a ‘Euclidean line’ in a ‘broad line’” (Høyrup 2002, 51), by interpreting a given line l as a rectangle of sides l and 1.
- 6.
This is not the place to enter into details about Sumerian pronunciation, but the reader should be reminded that a same cuneiform sign may be employed with different phonetic values. In particular, the sign ak, that corresponds to the Sumerian verb “to do”, may be read ak, aga, a5, but also, ki3, ke3 and kid3. For more about the Sumerian verb ak, “to do”, see Powell (1982) and Attinger (2005).
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Gonçalves, C. (2015). Conventions. In: Mathematical Tablets from Tell Harmal. Sources and Studies in the History of Mathematics and Physical Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-22524-1_3
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