Euler E120: Investigations into the question of the inequalities in the motion of Saturn and Jupiter | English translation | OMH v1.0

English translation of “Recherches sur la question des inégalités du mouvement de Saturne et de Jupiter” (Eneström E120), titled “Investigations into the question of the inequalities in the motion of Saturn and Jupiter.” Attribution: Leonhard Euler. This PDF includes all original pp. 1–123, the supplement, both foldout observation tables and the two-figure diagram 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: 1749 publication of the Paris Academy prize essay for 1748, pp. 1–123, two foldout tables and a diagram plate. Sources: https://scholarlycommons.pacific.edu/euler-works/120/; https://doi.org/10.3931/e-rara-49411. The Zentralbibliothek Zürich witness, NE 663,2, carries the Public Domain Mark. The far-right formula tail on p. 60 is clipped in both available scans; the supplied cos p factor is explicitly an editorial completion, not a reading of an invisible glyph. Historical numerical discrepancies and blank table cells are retained. The historical original is public domain by age; no publication license is assigned here to the new translation or editorial notes.