Euler E384: Research on the inequalities of Jupiter and Saturn | English translation | OMH v1.0

Abstract

English translation of “Recherches sur les inégalités de Jupiter et de Saturne” by Leonhard Euler (Eneström E384), titled “Research on the inequalities of Jupiter and Saturn.” The publication-title and prize-title variants are distinguished. 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: Recueil des pièces qui ont remporté les prix de l’Académie royale des sciences, vol. 7 (Paris: Panckoucke, 1769), preceding publication title leaf and pp. 1–84. The sole geometric figure is on the publication title leaf. The prize essay is for 1752; its prize title uses “irrégularités du mouvement,” while the publication title uses “inégalités.” Sources: https://scholarlycommons.pacific.edu/euler-works/384/; https://archive.org/details/recueildespdes07acad. The NHM/BHL repository describes the historical volume as public domain; no new translation license is asserted. The original historical text is public domain by age; no publication license is assigned here to the new translation or editorial notes.