By Jöran Friberg
The ebook analyzes the mathematical capsules from the personal number of Martin Schoyen. It comprises analyses of pills that have by no means been studied earlier than. this offers new perception into Babylonian knowing of refined mathematical items. The ebook is thoroughly written and arranged. The pills are categorised in response to mathematical content material and goal, whereas drawings and images are supplied for the main attention-grabbing drugs.
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Extra info for A Remarkable Collection of Babylonian Mathematical Texts: Manuscripts in the Schøyen Collection: Cuneiform Texts I
4 f. Number Signs for Sexagesimal Numbers With and Without Place Value Notation When writing sexagesimal numbers in place value notation, the only numbers signs needed are signs for the ‘ones’ from 1 to 9, and for the ‘tens’ from 10 to 50. The normal Babylonian forms of the cuneiform signs for the ones and tens are displayed in Fig. 1 below. 1. Babylonian cuneiform number signs in place value notation. Note that since there are special cuneiform signs for the tens, it is appropriate to call those signs for instance 1º, 2º, 3º, 4º, and 5º, as here, rather than 10, 20, 30, 40, and 50.
Empty 5˚ 11˚ 5˚ 5 5˚ 5 MS 2728. Three similarly consecutive multiplication exercises. obv. 2˚5 7 1˚ 7 3˚ 1˚7 3˚ 2˚6 4˚ 8 rev. empty 1˚ 8 2˚ 7 8 1˚9 3˚ 1˚8 3˚ MS 3944. Three multiplication exercises with gradually increasing data. Fig. 1. Three hand tablets with intricately constructed multiplication exercises. 1. Old Babylonian Multiplication Exercises 15 35 40 30 Whether this geometric interpretation is correct or not, it is clear that the three exercises on MS 2728 constitute a “continuation” of the three exercises on MS 2729.
45 = 1 1 30 + 33 45 3 03 45 (The modern formulation of this result, with anachronistically inserted zeros, is that sq. 1 45 = sq. ) The incorrect result in the text corresponds to the following careless addition (a “telescoping error”): sq. 1 45 = sq. (1 + 45) = sq. 1 + 2 · 1 · 45 + sq. 45 = 1 1 30 + 33 45 2 30 33 45 obv. 1 4˚ 5 1 4˚ 5 1 5˚ 4 1 5˚ 4 2 2 2 3˚ 3 3˚ 3˚ 3 4˚ 5 6 3˚ 6 4 3˚ 2 3 4˚ 5 4 3˚ 5 4 3˚ 5 rev. 2˚1 2˚5 2˚1 2˚5 3 cm Fig. 2. MS 3946, four squaring exercises with a puzzling choice of data and an interesting error.