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S, and A = u · s. Therefore, the purpose of El. 7 may have been, essentially, to demonstrate that any quadratic-linear system of equations of type B2b: sq. u + sq. s = S, u–s=p is equivalent to a rectangular-linear system of equations of type B1b: u · s = A, u – s = q u p A where A = (S – sq. q)/2. s u q sq. s s s A sq. s s A sq. q sq. u A q u El. 4 : El. 7 : sq. (u + s) = sq. u + sq. s + 2 u · s sq. u + sq. s = 2 u · s + sq. (u – s) B2a : B2b : sq. u + sq. s = S, u + s = p sq. u + sq. s = S, u – s = q ‰ u · s = A = (sq.

If 10 each it is equalsided, the expansion is what? 28 Amazing Traces of a Babylonian Origin in Greek Mathematics 4. If A is the field, the arc is what? 5. To the field of the arc c (times) the length I added, P. From the field of the arc c (times) the length I tore off, Q. 6. The fields of 2 arcs I joined, S. Arc over arc 10 beyond. 7. The field of the arc, the transversal of the arc, the go-around of the arc I joined, S. ) For various reasons, it is advisable to use literal translations of Babylonian mathematical texts.

H, u + s = p. What does this result have to do with El. 14, where Euclid shows how to “construct a square equal to a given rectilineal figure”? The proposition is illustrated by the diagram in Fig. 1, right. Euclid begins by constructing a rectangle equal to the given figure (which is a paraphrase for a rectangle of given area A) by use of El. 45. How he then continues can be explained as follows: He lets u (BE) and s (ED) be the sides of the rectangle with the given area A, and constructs a semicircle with the diameter p = u + s (BF).

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