バビロニアの幾何学 : 2, 3の未解決問題について

概要

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Many investigations, especially that of Neugebauer, have thrown light upon Babylonian mathematics. But some problems still remain unsettled and I will attempt to interpret some of them. 1. I conjecture that the triangle in MLC 1950 was originally a right-angled one and the area-formula for a trapezoid was obtained by using what is called "Gnomon". 2. Problems which deal with the segment of a circle in BM 85194, MLC 1354 have similar contents; the arrow of the segment is 1/4 (igi-gub-ba) of a diameter and the area of it is replaced approximately with an area of a trapezoid whose height is 2/3 of the arrow. But this approximation is not a good one. The quadratic equation in MLC 1354 is solved by the same procedure in BM 13901. 3. I am sure that a correct volume-formula was used in BM 85194 for a frustum of a pyramid. In the text we find for 1, 13・18 the value 22, 30 instead of 21, 54. One may explain this mistake as the result of error 1, 15・18, for standard multiplication tables involve 1, 15・n (n=1, 2, …, 19, 20, 30, 40, 50) but not 1, 13・n. Moreover we can get the formula V={((a+b)/2)^2+1/3((a-b)/2)^2}h by dividing a frustum of a pyramid into one rectangular parallelopiped and four triangular cones.
日本科学史学会の論文
1986-02-14