In this paper, I examine the opposition between direct proof and proof per impossibile, introduced by al-Sijzī (second half of the 10th century) in his treatise entitled The side is not commensurable with the diagonal. From this example he gives to illustrate this opposition, al-Sijzī argues the superiority of the direct proof. In this paper, I also give the editio princeps of his treatise, as well as its first translation.

中文翻译：

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DÉMONSTRATION PAR L'ABSURDE OU DÉMONSTRATION DIRECTE: AL-SIJZĪ, SUR L'INCOMMENSURABILITÉ DE LA DIAGONALE AVEC LE CÔTÉ

在本文中，我研究了直接证明和证明之间的对立不可能的，由 al-Sijzī（10 世纪下半叶）在其题为“边与对角线不可公度. 从他给出的这个例子来说明这种对立，al-Sijzī 论证了直接证明的优越性。在本文中，我还给出了王子版他的论文，以及它的第一个翻译。