Euler E777: On solving the equation 0 = a + bx + cy + dx^2 + exy + fy^2 + gx^2y + hxy^2 + ix^2y^2 in rational numbers | English Translation | OMH v1.0

English translation of Leonhard Euler’s “De resolutione hujus aequationis 0 = a + bx + cy + dxx + exy + fyy + gxxy + hxyy + ixxyy per numeros rationales” (E777). 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, https://scholarlycommons.pacific.edu/euler-works/777/; facsimile, https://archive.org/details/mmoiresdelacad11impe.