By Joran Friberg

A sequel to unforeseen hyperlinks among Egyptian and Babylonian arithmetic (World medical, 2005), this ebook is predicated at the writer s in depth and floor breaking reviews of the lengthy heritage of Mesopotamian arithmetic, from the past due 4th to the overdue 1st millennium BC. it's argued within the booklet that a number of of the main recognized Greek mathematicians seem to have been accustomed to a variety of features of Babylonian metric algebra, a handy identify for an complicated blend of geometry, metrology, and quadratic equations that's recognized from either Babylonian and pre-Babylonian mathematical clay drugs. The e-book s use of metric algebra diagrams within the Babylonian type, the place the part lengths and parts of geometric figures are explicitly indicated, rather than fully summary lettered diagrams within the Greek variety, is vital for a more robust realizing of many attention-grabbing propositions and structures in Greek mathematical works. the writer s comparisons with Babylonian arithmetic additionally result in new solutions to a few vital open questions within the background of Greek arithmetic

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**Example text**

U = S/2 – sq. s when sq. p + sq. q = S, p = u + s and q = u – s. In LWS (2002), 67-70, Figs. 10-12, Høyrup presents three different possible configurations in terms of squares and rectangles which the OB mathematicians may have used to prove identities like the ones mentioned above. There is, however, a fourth possible, and perhaps more plausible, configuration, which Høyrup did not consider in this connection (but which he did consider elsewhere, op. , 259, Fig. 67). or q s q d d u s p u s s p (sq.

Two possible interpretations of the diagram in El. 3. According to the interpretation in Fig. 3, right, the statement in El. 3 can be reformulated as a quadratic equation of type B4c: p · u – sq. u = A, where A = u · s. Alternatively, the same statement can be reformulated as a rectangularlinear system of equations of type B1a: u · s = A, u + s = p. Therefore, another purpose of El. 3 may have been to demonstrate that any quadratic equation of type B4c: p · u – sq. u = A is equivalent to a rectangular-linear system of equations of type B1a: u · s = A, u + s = p.

M – sq. q and m – q given given given sq. m – sq. q = ? p, m, q = ? p, m, q = ? 1 problem 1 problem 2 values for c 1 problem 1 problem 1 problem Note: In 9b-c it is tacitly assumed that p – q = q – r. In §§ 1-4 of TMS 5, the given values of the coefficient c are allowed to vary in the same way as the given values of the coefficient c in § 5 of BM 80209 (Sec. 10 above), but much more extensively. 11. A Large Old Babylonian Catalog Text of a Similar Kind c s c s c s 1 2 3 4 3" 2' 3' 4 3' 4 1 3" 1 2' 1 3' 14 1 3' 4 2 2' 3 3' 44 30 1 7 27 17 127 7 1/7 7 2 1/7 1 77 277 177 1277 1 11 2 11 35 1 11 11 2 11 11 1 11 7 2 11 7 1 3" 2' 3' 11 7 2 3" 2' 3' 11 7 10 05 4 05 33 35 = 5 · 7 4 05 = 5 · 7 · 7 6 25 55 = 5 · 11 12 50 10 05 = 5 · 11 · 11 6 25 = 5 · 7 · 11 12 50 = 2 · 5 · 7 · 11 55 Probably in order to save space, the values given for c in this text make use of some otherwise undocumented notations for fractions.