Euler E848: On the construction of microscopes | English translation with redrawn figures | OMH v1.0

English translation of Leonhard Euler’s De la Construction des Microscopes (E848), article XXVI in Opera postuma mathematica et physica, Tomus alter (Petropoli, 1862), pp. 755–780, with Plate XXIV, figures 268–270. All 85 numbered paragraphs, original page markers, equations, six numerical tables, and explicit notes on source anomalies are retained. This 35-page replacement edition uses three clearly labeled independent vector schematics, preserving the historical optical point labels, order, and image orientations; lens profiles and distances are schematic, not to scale. The mathematical body is unchanged from the prior private review edition. AI use and review status: OpenAI tools assisted with the translation, LaTeX, and schematic figures. Version 1.0 is a machine draft with limited scholarly human inspection. Version 2.0 is reserved for a fully reviewed edition. Independent checks confirmed the figure geometry against paragraphs 7, 17, and 53 and the surviving plate, unchanged mathematical text, successful rebuild, and source-page extraction; these checks do not replace full human scholarly review. Sources: Euler Archive, https://scholarlycommons.pacific.edu/euler-works/848/; independent Gerstein Library, University of Toronto digitization, https://archive.org/details/operapostumamath02euleuoft. The initial textual witness was Göttingen PPN584980116. Its conflicting digitization notices have not been overridden: no Göttingen facsimile pixels are included in this replacement PDF. The Toronto scan’s Figure 270 loses the left object at the gutter; paragraph 53 expressly supplies Oo and supports its redrawn placement. Source-specific NOT_IN_COPYRIGHT and Public Domain Mark notices are documented without a universal legal guarantee. English edition: Vaibhav Shakya, Open Math Heritage.