Euler E174: On the motion of flexible bodies | English translation | OMH v1.0

English translation of “De motu corporum flexibilium” by Leonhard Euler (Eneström E174), titled “On the motion of flexible bodies.” 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: Opuscula varii argumenti, vol. 3 (Berlin, 1751), pp. 88–165, figures 1–12 on Plates IV–V. Sources: https://scholarlycommons.pacific.edu/euler-works/174/. The reproduced historical figures come from the ETH-Bibliothek Zürich witness identified with the Public Domain Mark; source assets remain distinct from the new translation. The original historical text is public domain by age; no publication license is assigned here to the new translation or editorial notes.