Johann Albrecht Euler and his unpublished manuscript on the history of geometry

The article contains the scientific biography of J. A. Euler (1734-1800), the history and publication of the manuscript “History of Geometry” found by us with our comments. Johann Albrecht, the eldest son of Leonard Euler, was born in St. Petersburg, spent his youth with his father in Berlin, where he served as an inspector at the Berlin Observatory; at the age of 32, he with his family returned to St. Petersburg, where until the end of his life he was the conference secretary of the Imperial St. Petersburg Academy of Sciences. Huge administrative work and assistance to his blind father left him little time for independent scientific research. He retained meteorological and astronomical observations, as well as participation in his father's home seminars on the theory of the moon and some questions of number theory. But his manuscript on the history of geometry shows the breadth of his mathematical culture, the rigor of his criteria, and the depth of knowledge of his contemporary geometry literature. Analysis of the text of the manuscript reveals the views of Euler-father and son on the history of geometry up to the 18th century, as well as the importance they attached to the applied directions of the development of geometry (astronomy, underground geometry, fortification, geodesy, cartography, auxiliary mathematical tools). The comments provide an overview of the sources used by I.A. Euler, both on the basis of direct links, and on the basis of the list of Euler's collection and his personal contacts. For the first time, the names of many authors are introduced into the Russian historical and mathematical circulation. Despite the strong opinion that I.A. Euler, being the conference secretary of the St. Petersburg Academy of Sciences, did not have enough time for scientific work, we noted some of his important results, and also showed the range of his knowledge and scientific criteria. For us, his work is interesting because it shows the level of development of practical geometry in the 18th century.