Euler E300: Proof of Bernoulli's theorem on cycloids arising from indefinitely repeated involution of a right-angled arc | English translation | OMH v1.0

English translation of Leonhard Euler's E300, Proof of Bernoulli's theorem on cycloids arising from indefinitely repeated involution of a right-angled arc. AI use and review status: OpenAI tools assisted with the translation and LaTeX. Version 1.0 is a machine draft with limited scholarly human inspection. Version 2.0 is reserved for a fully reviewed edition. Sources: Official Euler record, https://scholarlycommons.pacific.edu/euler-works/300/; Novi Commentarii Academiae Scientiarum Imperialis Petropolitanae, volume X for 1764, printed 1766, pp. 179–198 and Plate II, https://archive.org/details/novicommentariac10impe; American Museum of Natural History Library, exact BHL item 38575, https://www.biodiversitylibrary.org/item/38575.