History of Science and Engineering Annotation << Back Of a history of becoming of differential geometry of plane curves in XVIII century: about L. Euler’s one research on the theory evolutes and evolvents I.V. Ignatushina There is a clever presentation of L. Euler’s research of one question of the theory evolutes and evolvents. Considerably, that the decision of this private problem of geometry has led Euler to construction of the theory of the linear homogeneous differential equations with constant factors. The submitted material is an illustration of process of formation of differential geometry in XVIII century. Key words: differential geometry; Leonhard Euler; the theory evolutes and evolvents; history of mathematics. E-mail: streleec@yandex.ru