バビロニア数学粘土板A06770の再検討と新解釈の提出

抄録

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;12³ 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 "šapiltum"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 "šu-nigin" which is the weight subtracted from the initial weight"abnum" and in the remaining lines he got the "rēš abnīya" as the final answer from the šu-nigin.