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Cet article applique les notions de texte et d'\'enonc\'e inaugural \`a laTh\'eorie analytique de la chaleur de Fourier et \`a la controverse des cordesvibrantes. Il \'etablit que seul le livre de Fourier est un texte inaugural. Ilpropose en outre une analyse s\'emiotique des modes d'expression de lag\'en\'eralit\'e qui permet dans chaque cas de clarifier les conditionsd'introduction de la possibilit\'e de repr\'esenter une fonction arbitraire pardes s\'eries trigonom\'etriques. (The inauguration of trigonometrical series inFourier's Th\'eorie analytique de la chaleur and in the vibrating stringscontroversy) This paper applies the notions of inaugural text and statement toFourier's Th\'eorie analytique de la chaleur and to the vibrating stringscontroversy. It establishes that only Fourier's book is an inaugural text. Itpresents also a semiotic analysis of the expression modes of generality whichallows to clarify in both cases the conditions of introducing of thepossibility to represent an arbitrary function by trigonometrical series.

L'inauguration des s\'eries trigonom\'etriques dans la Th\'eorie analytique de la chaleur de Fourier et dans la controverse des cordes vibrantes