Euler E414: An investigation of the perturbations affecting the motions of the planets through their mutual action | English translation | OMH v1.0

English translation of “Investigatio perturbationum quibus motus planetarum afficitur mutua eorum actione” (Eneström E414), titled “An investigation of the perturbations affecting the motions of the planets through their mutual action.” Attribution: Leonhard Euler. This PDF includes the complete historical title, preface and mathematical text through original p. 138, and the two-figure plate. 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 independent 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: Recueil des pièces qui ont remporté les prix de l’Académie royale des sciences, vol. 8 (Paris, 1771), pp. 1–138 and one plate; doubled prize of 1756. Sources: https://scholarlycommons.pacific.edu/euler-works/414/; https://archive.org/details/recueildespdes08acad. The complete Natural History Museum Library/BHL witness supplies pp. 114–138 and the plate omitted by the Pacific download. Its item-specific metadata describes the historical work as public domain. Unclear marks on p. 124 and the plate engraver’s name remain uncertain. Modern Opera Omnia readings are not silently substituted. The historical original is public domain by age; no publication license is assigned here to the new translation or editorial notes.