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The analytical aspects of the "Trait\'e des \'equations" of Sharaf al-D\^inal-T\^us\^i (2nd half of the XIIth century) have been underlined by R. Rashed(1974, 1986). In the present paper, we consider again some of those aspects,when studying the "second part" of the "Trait\'e". We find out that al-T\^us\^iintroduces certain notions, develops reasonings and uses calculating proceduresthat may allow his work to be an important reference in the history of themathematical analysis. As such, one is led to examine the foundations of a J.P.Hogendijk conjecture (1989), which situates the advanced mathematics of this"2nd Part" in the only domain of Euclidian geometry. Simultaneously, we shalltry to shed some light on a passage of the "Trait\'e", made unclear byal-T\^us\^i style and expression. Our study is essentially based on the textsto confirm the originality and the importance of these XIIth centurymathematics. I would like to express my thanks to Prof. C. Houzel (Univ. ParisVII) and B. El-Mabsout (Univ. Paris VI), for reading the manuscript andproviding their precious remarks.

Aspects Analytiques Dans la Mathematique De Sharaf Al-D\^in Al-T\^US\^I