バビロニア数学粘土板AO 6770の再検討と新解釈の提出

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AO 6770 is a very important text which treats the calculation of a compound interest among others. Many scholars have tried to make clear the mathematical meaning of the text, but in my opinion none have completely succeeded in doing so. I reexamined the text philologically and mathematically, and have arrived at the following conclusions. 1. The line 1 of the problem No. 1 reads "Length and width. One (ma-la) iku. Be it (sag) a square number." The Babylonian solved this problem by transforming a square the sides of which are 10 ninda into a rectangle retaining the same area the width of which is 4 ninda. He presupposed that the answer would be 4, and confirmed it by demonstrating that the length was given in an integer through the calculation of 0;15 ・1, 40. 2. Thureau-Dangin and Neugebauer's interpretation of the problem No. 2 is fundamentally right. It is certain that the transformation of units in the answer was carried out, so to speak, automatically, because the rate of the compound interest was 20%. And also in the lines 13-17 we can see the special form of division which is generally used when the divisor is a so-called "irregular number", though the divisor 1; 12^3 in this case is not an irregular number. 3. The problem No. 3 treats a linear equation which is formulated correctly by Thureau-Dangin (though his explanation of the process of the calculation is erroneous). I translate "sapillum" as "a result of a calculation", that is, I translate it in the line 7 as 0; 55 which is one result of an addition but not its sum, and in the line 9 as 6 which is a result of a subtracion, namely a remainder. In the lines 6, 7 the Babylonian conducted a complicated calculation of "su-nigin" which is the weight subtracted from the initial weight"abnum" and in the remaining lines he got the "res abniya" as the final answer from the su-nigin.
日本科学史学会の論文
1987-10-30

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室井和男
文理予備校

バビロニア数学粘土板AO 6770の再検討と新解釈の提出

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