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                <text>This paper is devoted to Ibn Sinān's treatise on analysis and synthesis. Ibn Sinān's text deals with two distinct, though closely related, subjects. First he considers the classification of problems, founded on the logical criteria which are the number and degree of indetermination of the solutions and (though in a less relevant way) the number of hypotheses and their possible independence. This classification does not replace the Hellenistic one, which remains relevant insofar as it purports to solve geometrical problems, but complements it and has a different frame of reference, applying principally to algebra, that new born science. Ibn Sinān's classification will be taken up and used by algebraists. Secondly, the text presents a new way of setting out analysis and synthesis, so that they become exactly reciprocal. This leads Ibn Sinān to bestow more importance on the role played by analysis in the course of the proof, the only role left to synthesis being to check that all implications involved in the course of analysis are in fact equivalences. This method will prove to be productive in algebra too, so much so that some algebraists will explicitly identify algebra with analysis., Cet article est consacré au traité d'lbn Sinān sur l'analyse et la synthèse; Ibn Sinān y aborde deux sujets distincts quoique étroitement liés:– une classification des problèmes, fondée sur les critères logiques que sont le nombre et le degré d'indetermination des solutions, ainsi que, mais de façon moins pertinente, le nombre des hypothèses et leur éventuelle indépendance. Cette classification ne se substitue pas à la classification hellénistique qui garde sa pertinence en matière de problèmes de géométrie, mais se développe à côté de celleci dans un cadre radicalement différent, et est directement applicable à l'algebre, science qui se crée aux Xe et XIe siècles. La classification d'Ibn Sinān sera reprise et utilisée par les algébristes;– une nouvelle façon d'exposer l'analyse et la synthèse d'un problème, afin qu'elles deviennent exactement inverses l'une de l'autre, ce qui conduit Ibn Sinān à accorder dans ses démonstrations une importance accrue à l'analyse, le rôle de la synthèse n'etant plus que de vérifier que toutes les implications mises en œuvre dans l'analyse sont en fait des équivalences. C'est en algèbre également que cette méthode se montrera féconde, au point que certains algébristes n'hésiteront pas à identifier l'algèbre et l'analyse.</text>
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