Abstract
Chapter 4 represents the most important part of the book. In it, the 12 selected tablets are presented and analysed. Each tablet receives initially a transliteration and a transcription:
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• A transliteration of the cuneiform signs identifies the signs by their conventional names and tries to respect their isolated pronunciation.
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• A transcription renders morphological and syntactical aspects of the original text (see also Chap. 3 for the details and conventions governing each of these parts).
The tablets are then translated and commented. The only exception is IM54010, whose bad state of conservation prevents a complete understanding.
Transliteration and transcription are directed to specialists in cuneiform mathematics or to readers who possess at least a basic command of the Akkadian and a desire to improve their understanding of the original texts. Translation and commentary, on the other hand, were designed to satisfy the readers’ appetite for the mathematical ideas and techniques that these texts bear.
Besides, in this chapter, I also offer some philological remarks and a mathematical analysis for each tablet.
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- 1.
I am indebted to Hermann Hunger for allowing me to have access to these photos.
- 2.
For the benefit of the mathematically minded reader, it should be said that these equivalence classes would not be the usual ones obtained in the modulus-60 arithmetics. Instead, two numbers are equivalent here if one is the other multiplied by a power of 60. So it is not true that 62 and 2 are equivalent in this floating point system. But 2,0 (that is to say, 120) and 2 are indeed equivalent (Proust 2013).
- 3.
Here too, I am indebted to Hermann Hunger for the access to the photos.
- 4.
The first three lines on the edge seem to have been written in two columns. This produces, for each line, an initial and a final segment. The separation is marked by double slashes.
- 5.
The concept of unorthographic writing serves to explain deviations from expected writings. In the present example, dug4 is the expected way a scribe writes the verb to say, but as the phonetic values of the sign tug include the pronunciation “dug”, this sign can be used instead, constituting an unexpected or unorthographic writing.
- 6.
See mathematical commentary for the order of magnitude.
- 7.
Following Friberg’s (2000, 118) interpretation.
- 8.
The second segments of lines E1, E2 and E3 on the edge are marked with double slashes: E1//, E2// and E3//.
- 9.
That is to say, Text 14 of Bruins and Rutten’s TMS.
- 10.
The metrological table of surfaces was used for volumes too.
- 11.
See also the commentary to IM54478, where the strategy of positing a second figure, similar to that of the problem, might have been in action too.
- 12.
See again IM54478, where a similar computation of a linear ratio from the ratio of volumes might have been present.
- 13.
- 14.
However, Hussein (2009, 92) states that this tablet also comes from room 252.
- 15.
Which contained perhaps a mistyping. I propose “On two times the length (3 × the width) add 10; on the width, add 10”.
- 16.
The occurrences of this word are registered under ellum in the vocabulary.
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Gonçalves, C. (2015). Mathematical Tablets. 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_4
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