Euler E245: On a method analogous to that of Diophantus in the analysis of the infinite | English translation | OMH v1.0

Abstract

English translation of “De methodo Diophanteae analoga in analysi infinitorum” by Leonhard Euler (Eneström E245), titled “On a method analogous to that of Diophantus in the analysis of the infinite.” 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: Novi Commentarii academiae scientiarum Petropolitanae, vol. 5 (printed 1760), pp. 84–144, introduction and §§1–75. Damaged pp. 89–90 were collated with an independent original-volume witness. Sources: https://scholarlycommons.pacific.edu/euler-works/245/; https://archive.org/details/novicommentariac05impe; https://archive.org/details/novicommentarii13sssrgoog. The primary historical witness is identified on Wikimedia Commons with Public Domain Mark 1.0; the independent Harvard/Google witness is catalogued NOT_IN_COPYRIGHT. These source designations do not license 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.