Download A Remarkable Collection of Babylonian Mathematical Texts: by Jöran Friberg PDF

By Jöran Friberg

The ebook analyzes the mathematical pills from the non-public choice of Martin Schoyen. It contains analyses of pills that have by no means been studied earlier than. this gives new perception into Babylonian knowing of refined mathematical items. The e-book is thoroughly written and arranged. The capsules are labeled in response to mathematical content material and function, whereas drawings and images are supplied for the main fascinating capsules.

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Additional info for A Remarkable Collection of Babylonian Mathematical Texts: Manuscripts in the Schøyen Collection: Cuneiform Texts I

Example text

The answer is given directly as 28 53 20. No information is given about how this result was obtained. However, if the square side was obtained by repeated use of the square side rule, then the successive steps of the computation were (essentially) the following: 1. 2. 3. 4. 5. sq. 29 = 14 01, 13 54 = 14 01 – 7 (13 54 being the first couple of sexagesimal places in 13 54 | 34 04 | 26 40). sqs. (13 54) = sqs. (sq. 29 – 7) = appr. 29 – 7 / (2 · 29) = appr. 29 – 7 / (2 · 30) = 28;53. sq. 28 53 = 13 54 14 49, 13 54 | 34 04 = 13 54 14 49 + 19 15.

4. Counting with Sexagesimal Numbers 9 factorization method. (See the discussion in Sec. ) Interesting examples of divisions by non-regular sexagesimal numbers can be found in some of the “combined market rate exercises” in Sec. 2 below, for instance MS 2299 (Fig. 1, bottom). There, four commodities have a “combined unit price” of ;57 shekel, while the silver available is given as 16 53 20, probably meaning 16;53 20 shekels. To find out how many units of each kind can be bought for this amount of silver, one has to divide 16 53 20 by 57.

Sq. 2 (00) + 1 03 45) = appr. 2 (00) + 1 03 45/(2 · 2 (00)) = appr. 2 (00) + 15 = 2 15 sq. 2 15 = sq. (2 (00) + 15) = 4 (00 00) + 1 (00 00) + 3 45 = 5 03 45. The method works also in more complicated examples, as in MS 3049 § 5 (Sec. 1 d below). There the “inside diagonal” of a gate is computed by use of the three-dimensional diagonal rule. The last step of the solution procedure is the computation of the square side of 13 54 34 04 26 40. The answer is given directly as 28 53 20. No information is given about how this result was obtained.

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