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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク On the Equilibrium of Planes ： ウィキペディア英語版 On the Equilibrium of Planes ''On the Equilibrium of Planes'' ((ギリシア語:Περὶ ἐπιπέδων ἱσορροπιῶν)) is a treatise by Archimedes in two volumes. The first book establishes the ''Law of the Lever'', and locates the centre of gravity of the triangle and the trapezoid. According to Pappus of Alexandria, Archimedes' work on levers caused him to remark: "Give me a place to stand on, and I will move the Earth." ((ギリシア語:δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω)).〔Quoted by Pappus of Alexandria in ''Synagoge'', Book VIII〕 The second book, which contains ten propositions, examines the centres of gravity of parabolic segments.〔 == Structure of the text == Book one contains fifteen propositions with seven postulates. In proposition six Archimedes establishes the ''Law of the Lever'', concluding that "Magnitudes are in equilibrium at distances reciprocally proportional to their weights." In propositions ten and fourteen, respectively, Archimedes locates the centre of gravity of the parallelogram and the triangle. Additionally, in proposition 15, he establishes the centre of gravity of the trapezium. The second book, which contains ten propositions, studies parabolic segments exclusively. It examines these segments by substituting them with rectangles of equal area; an exchange made possible by results obtained in the Quadrature of the Parabola.〔〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「On the Equilibrium of Planes」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.