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''Arithmetica'' () is an Ancient Greek text on mathematics written by the mathematician Diophantus in the 3rd century AD.〔(【引用サイトリンク】url=http://www.britannica.com/EBchecked/topic/164347/Diophantus-of-Alexandria#ref704023 )〕 It is a collection of 130 algebraic problems giving numerical solutions of determinate equations (those with a unique solution) and indeterminate equations. Equations in the book are called Diophantine equations. The method for solving these equations is known as Diophantine analysis. Most of the ''Arithmetica'' problems lead to quadratic equations. It was these equations which inspired Pierre de Fermat to propose Fermat's Last Theorem, scrawled in the margins of Fermat's copy of ''Arithmetica'', which states that the equation , where , , and are non-zero integers, has no solution with greater than 2. In Book 3, Diophantus solves problems of finding values which make two linear expressions simultaneously into squares or cubes. In book 4, he finds rational powers between given numbers. He also noticed that numbers of the form cannot be the sum of two squares. Diophantus also appears to know that every number can be written as the sum of four squares. If he did know this result (in the sense of having proved it as opposed to merely conjectured it), his doing so would be truly remarkable: even Fermat, who stated the result, failed to provide a proof of it and it was not settled until Joseph Louis Lagrange proved it using results due to Leonhard Euler. ''Arithmetica'' was originally written in thirteen books, but the Greek manuscripts that survived to the present contain no more than six books. In 1968, Fuat Sezgin found four previously unknown books of ''Arithmetica'' at the shrine of Imam Rezā in the holy Islamic city of Mashhad in northeastern Iran. The four books are thought to have been translated from Greek to Arabic by Qusta ibn Luqa (820–912).〔 Norbert Schappacher has written:
''Arithmetica'' became known to mathematicians in the Islamic world in the tenth century when Abu'l-Wefa translated it into Arabic. ==See also== * Muhammad ibn Mūsā al-Khwārizmī 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「Arithmetica」の詳細全文を読む スポンサード リンク
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