続・アルキメデス『方法』命題11証明の復元について : 鈍角円錐状体の切片の重心の位置に関する証明

スポンサーリンク

概要

• 論文の詳細を見る

• In this article, I intend to discuss a reconstruction of the proof of Proposition 11 in Archimeses's "Method" which J. L. Heiberg discovered in 1906. Proposition 11 in "Method" discuss the volume and the center of gravity of the segment of the obtuse-angled conoid (a hyperboloid of revolution). A theorem concerning the center of gravity is expressed as follows: The center of gravity of any segment of obtuse-angled conoid is on the straight line which is the axis of the segment, and divides this straight line in such a way that the part of it adjacent to the vertex of the segment has to the remaining part the ratio which the sum of three times the axis and eight times the annex has to the sum of the axis of the segment and four times the annex. However, since the last century, the ground of the assertion about the proposition regarding the position of the center of gravity is not shown anywhere. Now, I have already demonstrated a reconstruction of the proof regarding the volume of an obtuse-angled conoid in "On Calculation-Mechanism in Archimedes's METHOD", -A Reconstruction to the Proof of Proposition 11-, KAGAKUSHI KENKYUU, JOURNAL OF HISTORY OF SCIENCE, JAPAN, Series II Vol. 32 (No. 186) Summer 1993, pp 84-90. And, as a sequel to the above article, I attempted a reconstruction of the proof regarding the position of the center of gravity of an obtuse-angled conoid. In the reconstruction of the proof of Proposition 11, the 3rd solid was a spheroid, not a cone. This was completely unexpected, and the treatment of an annex to an axis of a section of the obtuse-angled cone was complicated. Further, there was difficulty leading to the balance of a circle. The balance of the circle in the proof of the center of gravity could, in the end, be produced using the balance of the circle in the proof of volume. It is thought that the lack of this proof is caused the complexity of the proofs of Proposition 11. I divided the cylinder when Archimedes requests a position of the center of gravity. I sought the position of center of the gravity of this solid by referring to Propositions 9 and 5.

• 日本科学史学会の論文
• 1994-03-30

著者

• 林 栄治

  太田市立商業高等学校

関連論文

• 続・アルキメデス『方法』命題11証明の復元についてー鈍角円錐状体の切片の重心の位置に関する証明ー
• アルキメデス 「方法」 命題 11証明の復元の試み - 鈍角円錐状体の切片の体積について -
• 続・アルキメデス『方法』命題11証明の復元について : 鈍角円錐状体の切片の重心の位置に関する証明
• アルキメデス「方法」命題11証明の復元の試み : 鈍角円錐状体の切片の体積について

スポンサーリンク