Euler E078: Dissertation on the best construction of the capstan | English translation | OMH v1.0

English translation of “Dissertation sur la meilleure construction du cabestan” by Leonhard Euler (Eneström E078), titled “Dissertation on the best construction of the capstan.” The French original was anonymous; the edition preserves the Euler Archive’s attribution to Euler. 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 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: Pièces qui ont remporté le prix de l’Académie royale des sciences, prize volume for 1741 (Paris, printed 1745), pp. 29–87, Plates IV–VI. The missing p. 87 in the Archive extract was recovered and collated from complete-volume witnesses. Sources: https://scholarlycommons.pacific.edu/euler-works/78/; https://archive.org/details/A077240121. The reproduced plate assets come from the University of Seville witness, whose repository record carries Public Domain Mark 1.0; this source designation is separate from translation rights. The original historical text is public domain by age; no publication license is assigned here to the new translation or editorial notes.