Le processus d'expertise preparatoire a l'amenagement de rivieres etait comparativement plus lent et plus decentralise dans la France du XVIII^e siecle que daps d'autres parties de l'Europe telle l'Angleterre ou l'Italie. Au milieu du siecle, ce manque de structure decisive au sein de l'administration permet a l'Academie royale des sciences de Paris de s'imposer progressivement sur ces questions, en jouant un role consultatif aupres du gouvernement sur differents projets de canaux. Cet article examinera deux de ces projets-celui du canal de Picardie et celui du canal de l'Yvette, jamais etudie pour lui-meme en histoire sociales des sciences. Tout d'abord, ces projets permettent d'observer une dynamique de concurrence entre les academiciens pour determiner la personne qui dirigera l'expertise. Ensuite, cette rivalite, qui s'explique par des milieux socio-professionnels d'origines differentes, bat son plein dans les annees 1770 notamment entre, d'une part, des personnes dotees d'un savoir-faire technique avere par leur arriere-plan institutionnel tel J.-R. Perronet du corps des Ponts et Chaussees et, d'autre part, des savants theoriciens tels D'Alembert et Condorcet. Chacun adopte une approche differente du probleme: une tentative mathematiquement plus elementaire mais plus pratique et qui permettra la decouverte de la formule de Chezy pour les techniciens, ou bien une combinaison entre analyse et experimentation hydraulique pour les mathematiciens. Mais au-dela d'une simple opposition binaire, on montrera comment le cas du projet du canal de l'Yvette correspond plutot a l'apparition d'une nouvelle division du travail entre les savants theoriciens et techniciens dans les annees 1780.

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This paper clarifies Cauchy's and Weierstrass's contributions to the construction of differential calculus represented in terms of epsilonics. In the eighteenth century the limit concept had a geometrical image that is typically represented in >indefinitely approaching to a fixed value>. In 1820s Cauchy described this concept in terms of inequalities and defined the limit. Since his new calculus theory was based on this concept, he could transform previous results from calculus to his new theory developed only by algebraic techniques. He also defined his original concept of infinitesimals based on the limit concept. The relations between the infinitesimals and infinitely large numbers or infinitesimally small changes can be represented in term of epsilon-delta inequalities. Although Cauchy occasionally used the term of infinitesimals in the usual sense, he substantially developed his calculus theory in epsilonics using his infinitesimals. Weierstrass noted the differential calculus needs to apply neither Cauchy's limit nor infinitesimals, but the relations that involve them. Neither isolated limits nor infinitesimals can be written in terms of epsilon-delta inequalities, but their relations can. Weierstrass began his 1861 lectures on the differential calculus by defining the fundamental concepts in terms of epsilon-delta inequalities. His original limit concept was also defined in terms of these, without any geometrical image. In contrast to Cauchy, Weierstrass's theory was pure algebraic and had no geometrical background. Although both mathematicians basically developed their differential calculus in epsilonics, the essential difference between their approaches lies in this point.

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