Euler E422: Investigation of a particularly unusual geometrical problem | English translation | OMH v1.0

English translation of Leonhard Euler's E422, Investigation of a particularly unusual geometrical problem. 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: Euler Archive E422, https://scholarlycommons.pacific.edu/euler-works/422/; Novi Commentarii Academiae Scientiarum Imperialis Petropolitanae XVI for 1771, printed 1772, pp. 140–159 and Plate II, figures 2–3, https://archive.org/details/novicommentariac16impe; American Museum of Natural History Library / Biodiversity Heritage Library item 38594, https://www.biodiversitylibrary.org/item/38594.