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By Asger Aaboe

Professor Aaboe supplies the following the reader a sense for the universality of vital arithmetic, placing each one selected subject into its right environment, hence bringing out the continuity and cumulative nature of mathematical wisdom. the fabric he selects is mathematically basic, but shows the intensity that's attribute of really nice concept styles in every age. The luck of this exposition is because of the author's new angle to his topic. He correctly refrains from making an attempt a basic survey of arithmetic in antiquity, yet selects, in its place, a couple of consultant goods that he can deal with intimately. He describes Babylonian arithmetic as published from cuneiform texts stumbled on only in the near past, in addition to extra ordinary themes constructed through the Greeks. even though every one bankruptcy will be learn as a separate unit, there are lots of connecting threads. Aaboe remains as as regards to the unique texts as is cozy for a contemporary reader, and the bibliography allows the scholar to delve extra deeply into any element of historic arithmetic that catches his or her fancy.

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If we remove either the two segments I or segment I1 from the semicircle, we must end up with the same area; for, in either case we have removed the same amount. lb) and in the second the crescent or lune ABC (Figure 2 . The triangle and the lune must therefore have the same area. So we are able to square the lune. (To square a plane figure means to find a square of area equal to that of the given figure. ) Hippocrates gives two other examples of squarable lunes; in one the outer arc is less and in the other greater than a semicircle.

Even special third degree equations of the form 2(2 + 1) = a were solved. The problems are often worded in such a way that, when 30 EPISODES they are translated into modem algebraic letter-notation, extremely complicated expressions arise, with parentheses within parentheses, and one cannot help feeling most impressed with the skill of the Babylonians who were able to reduce such expressions to standard forms of equations without the aid of our algebraic techniques. Incidentally, we iind several instances of problem texts in each of which the different problems always yield the same answer; this is a parallel to the modem habit of giving answers in the back of the book.

The procedure is, in crude outline, as follows: We compare maxiuscripts X and Y. If Y has all the errors and peculiarities of X and in addition some of its own, it is a fair assumption that t There are, however, some snippets of Greek papyri from the first centuries AD. containing parts of the Elements; they are so few and so small that they cannot give any idea of the work as a whole, but they provide valuable spot checks. 35 36 EPISODES Y is a copy, or a copy of a copy, of X. If X and Y have a number of errors in common and each some of its own, they are probably both derived from a common archetype 2, which may be lost but reconstructible.

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