バビロニア数学における平方根の近似計算 : VAT 6598 Rs. II. 1-4の解釈について

概要

論文の詳細を見る
In 1931 Neugebauer made clear that the arithmetic mean and the harmonic mean were used in approximation of square roots in Babylonian mathematics. This fact was later reconfirmed by the important tablet YBC 7289 and tablet YBC 7243. But his interpretation of VAT 6598 Rs. II. 1-4 is doubtful. If we denote the arithmetic mean and the harmonic mean of h and (h^2+w^2)/h in the text by d_1 and d_2 respectively, we get the following expressions d_1=h+(w^2)/(2h), d_2=h+2w^2h (h=0;40, w=0;10) I regard the numeral 2 of d_2 not as a constant coefficient but as a mistaken value for 1/(2h^2+w^2). That is 1/(2h^2+w^2)=1/(2・0;26,40+0;1,40)=1/(0;1,40)・1/((1+1/0;1,40)・0;28,20) (2・0;26,40=0;28,20 is mistaken)=36・1/(1+17)=2 ∴ d_2=h+(w^2h)/(2h^2+w^2)=h+2w^2h As a result of this mistake the text gives a wrong relation between d_1, d_2 and √<h^2+w^2>; √<h^2+w^2><d_1<d_2 though the right one is d_2<√<h^2+w^2><d_1.
日本科学史学会の論文
1986-05-15