Euler E705: Investigation of series for approximating the ratio of a circle's circumference to its diameter | English translation | OMH v1.0

English translation of Leonhard Euler's E705, Investigation of series for approximating the ratio of a circle's circumference to its diameter. 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 E705 (https://scholarlycommons.pacific.edu/euler-works/705/); Nova Acta Academiae Scientiarum Imperialis Petropolitanae, volume XI, for 1793 (printed 1798), pp. 133–149; digitized volume https://archive.org/details/novaactaacademia11petr; BHL item https://www.biodiversitylibrary.org/item/113775.