Euler E711: A new and easy method for expressing the roots of all algebraic equations and any powers of them by elegant series | English translation | OMH v1.0

English translation of Leonhard Euler's E711, A new and easy method for expressing the roots of all algebraic equations and any powers of them by elegant series. 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, E711, https://scholarlycommons.pacific.edu/euler-works/711/ ; Nova Acta Academiae Scientiarum Imperialis Petropolitanae, XII (Academy history through 1794; printed 1801), pp. 71–90, https://archive.org/details/novaactaacademia12impe ; American Museum of Natural History Library / Biodiversity Heritage Library, item 38591, https://www.biodiversitylibrary.org/item/38591 .