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

By Jöran Friberg

The e-book analyzes the mathematical drugs from the non-public selection of Martin Schoyen. It comprises analyses of drugs that have by no means been studied prior to. this gives new perception into Babylonian knowing of refined mathematical gadgets. The e-book is punctiliously written and arranged. The capsules are categorised in response to mathematical content material and objective, whereas drawings and photographs are supplied for the main fascinating drugs.

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

Example text

3. 4. 5. 6. 7. 8. [10] 10 10 10 [10] 10 10 [10 2]0 20 [10 10] 10 [10] 10 10 10 10 20 20 · · · · · · · · 8 9 [9] 30 [9] 40 [8] 9 9 30 9 40 = = = = = = = = 1 21 20 1 31 30 1 36 36 35 1 39 56 [33 20] [1 21 20] [1 31 30] 1 36 36 [3]5 1 39 56 33 20 The three first exercises in this text are examples of what happens when a one-place sexagesimal number like 8, 9, or a two-place sexagesimal number like 9 30 is multiplied by a “funny” sexagesimal number like 10 10 or 10 10 10. 1. Old Babylonian Multiplication Exercises 17 Once the student has understood the principle, he can carry out computations like these in his head.

1 (00) · 55 = 55 (00) (2,250) (2,750) (3,300) The three computations are consecutive in the same way as the computations on MS 2729, with the short side in exercise # 2 equal to the long side in exercise # 1, and the short side in exercise # 3 equal to the long side in exercise # 2. Thus, in MS 2729 just as in MS 2728 the three exercises can be interpreted as computations of the areas of three rectangles, chained together pairwise. See the second diagram in Fig. 2. In addition, since the long side of a rectangle in MS 2729 is equal to the short side of a rectangle in MS 2728, the three rectangles in the former text can be linked to the three rectangles in the latter text as shown in the third diagram in Fig.

Apparently the author of VAT 5457 computed the product incorrectly, in the following way, by use of a multiplication table with the head number 7 30: 52 44 03 45 · 7 30 = 6 30 5 30 22 30 + 5 37 30 6 35 58 07 30 The correct value, however, is computed as follows: 52 44 03 45 · 7 30 = 6 30 5 30 22 30 + 5 37 30 6 35 30 28 07 30 (It is almost impossible to avoid “positional errors” of this kind without the use of final zeros. ) MS 2699 (Fig. 3, bottom) is a square tablet inscribed with two lines of numbers near the upper edge of the obverse and one or two additional lines of numbers near the lower edge.

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