Between 9th and 11th centuries, the geometrical transformations gave to the mathematicians a method more and more fertile, leading them to modify their modes of apprehension of the geometrical figures. This article aims to highlight al-Sijzī’s contribution to this change by setting two tasks: first, to precisely understand what al-Sijzī means by transformation (he is one of the first to recognize explicitly a method in their use); and secondly, to give an account of his research on geometrical invariants, obtained by a variation of some elements of a figure. The use of transformations and the search for invariants seem to be the two faces of the same tendency, that to break with an Euclidean manner to consider the figures in a way isolated and static for better exploiting the common properties which can link them. The article is completed by the edition and the translation of a small treatise devoted to invariants.
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