Euler E375: First section on the state of equilibrium of fluids | English translation | OMH v1.0

English translation of “Sectio prima de statu aequilibrii fluidorum” (Eneström E375), titled “First section on the state of equilibrium of fluids.” Attribution: Leonhard Euler. This PDF includes Chapters I–V, original pp. 305–416, paragraphs 1–133, and all twenty-one figures on Plates V–VIII. Prepared for Open Math Heritage with OpenAI-assisted translation, mathematical transcription and LaTeX typesetting. OMH v1.0 is a machine-assisted draft that has undergone a full, fresh independent AI-assisted technical audit of source coverage, translation, formulas, tables and figures where present, and rendered output. This is not a claim of human scholarly review or certification of the historical mathematics. Version 2 is reserved for a fully reviewed edition. Original publication: Novi Commentarii Academiae Scientiarum Imperialis Petropolitanae, vol. XIII for 1768, printed 1769, pp. 305–416 and Plates V–VIII. Sources: https://scholarlycommons.pacific.edu/euler-works/375/; https://archive.org/details/novicommentariia13impe; https://www.biodiversitylibrary.org/page/36913707. The full-volume title establishes volume XIII, rather than the catalogue’s discrepant volume 12. The Natural History Museum Library/BHL witness supplies the omitted plates; source-specific public-domain evidence is retained, including the indexed BHL statement and corroborating historical-volume record. This does not assign rights to modern repository metadata. The historical original is public domain by age; no publication license is assigned here to the new translation or editorial notes.