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By Jöran Friberg

The booklet analyzes the mathematical capsules from the personal number of Martin Schoyen. It comprises analyses of capsules that have by no means been studied prior to. this gives new perception into Babylonian realizing of refined mathematical items. The publication is thoroughly written and arranged. The drugs are categorised in line with mathematical content material and function, whereas drawings and photographs are supplied for the main fascinating capsules.

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Extra resources for A Remarkable Collection of Babylonian Mathematical Texts: Manuscripts in the Schøyen Collection: Cuneiform Texts I

Example text

Bi 3˚ 9 3˚ 8 4˚ 8 3˚ 8 2˚ 8 3˚ 5˚ 7 7 4˚ 2 8 6 4˚ 3 2˚ 7 5˚ 3 5 1˚1 4˚ 9 6 4˚ 3 1˚ 5 4˚ The reciprocal of the 7-place sexagesimal number in line 3 is an 18-place number beginning in line 4 of the obverse with 5 sexagesimal places and continuing with 13 additional places, written on the edge and in two lines on the reverse. An interesting mistake was made in the computation of the first reciprocal. Fig. 5. MS 3264. Two many-place regular sexagesimal numbers and their reciprocals. The two pairs of numbers on MS 3264 can be transliterated as 1.

R* – 12 00 ninda · r* = 1 00 00 sq. $à lul ‘false area’, and where 1 00 00 sq. ninda is twice the ‘true area’. The quadratic equation is solved by use of a routine application of metric algebra (cf. Friberg, op. cit. Sec. 7c). In one of the last steps of the solution algorithm, the problem has been reduced to a linear equation: 6 14 24 · r* = 2 36 (00) ninda. The division of 2 36 (00) by 6 14 24 is not explicitly given, but was possibly achieved as follows: 6 14 24 15 36 26 13 2 30 1 40 30 2 36 6 30 10 50 5 25 Thus, the removal of all regular factors in 6 14 24 shows that the equation 6 14 24 · r* = 2 36 (00) ninda can be simplified to 13 (00) · r* = 5 25 ninda.

Obv. 1 2˚ 6 1˚ 3 2˚ 4 4˚ 5 1˚1 6 4˚ igi 4˚ 1 4˚ 2 4˚ 9 2˚ 2 2˚ 1 1˚2 3˚ 9 2˚ 2 rev. empty 3˚ MS 2894. The regular sexagesimal number 2 05 doubled 29 times and its reciprocal, 41 42 49 22 21 12 39 22 30. The number in the first line is incorrect, [1 2]6 13 24 45 11 06 40 instead of 1 26 18 09 11 06 40. obv. rev. empty 1 4˚ 9 2 1˚3 2˚ 2 4˚ 2˚ 2 1˚4 5˚ 1˚ 9 1˚ 5 5˚ 5 1˚8 4˚ 5 3˚ 2˚2 2 3˚ 2˚ 9 3˚ 5 2˚8 4˚ 5 1 2˚ 4 2˚ MS 2699. The regular sexagesimal number 2 41 49 02 13 20 (2 05 doubled 24 times) and its reciprocal.

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