By Czedli G.

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21 22 Friberg, 2007, p. 247. See Høyrup, 2002, pp. 362–385 and Robson, 2008, pp. 123–124 for more details. 32 Chapter 2 ************* The extant papyri and tablets containing Egyptian and Mesopotamian mathematics were generally teaching documents used to transmit knowledge from one scribe to another and, frequently, from a senior scribe to an apprentice. In the Mesopotamian case, in particular, long lists of quadratic problems were given as “real-world’’ problems, although they are, in fact, just as contrived as problems found in most current algebra texts.

9. 10. Euclid’s Elements VI-28 (although labeled VI-26) from f. 58 of the Plimpton MS 165 (ca. 1294), courtesy of the Rare Book and Manuscript Library, Columbia University. Note that the parallelogram is drawn as a rectangle. To simplify matters, and to show why we can think of Euclid’s constructions as solving quadratic equations, assume, as in the figures, that the given parallelogram in each case is a square, that is, that the defect or the excess will itself be a square. This implies that the constructed parallelograms are rectangles.

12. B S 48 Chapter 3 As before, Euclid dealt only with geometric figures and never actually wrote out rules like these. However, while his formulation of the problem—in terms of finding two lengths satisfying certain conditions— was nearly identical to the Mesopotamian formulation, it nevertheless enabled him to generalize the Mesopotamian problem from rectangles to parallelograms. 28 in the Elements). Since the notion of application of areas is important in the definition of the conic sections and since Euclid is credited with a book on that subject, it is not surprising that he explored these ideas in the Elements.

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Categories: Algebra