Euler E698: Various considerations on the area of spherical triangles | English translation | OMH v1.0

English translation of Leonhard Euler's Variae speculationes super area triangulorum sphaericorum (E698), Nova Acta Academiae Scientiarum Imperialis Petropolitanae, volume X (1797), pp. 47–62, with the six original diagrams. 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, E698, https://scholarlycommons.pacific.edu/euler-works/698/; Nova Acta Academiae Scientiarum Imperialis Petropolitanae, Tomus X (Petropoli: Typis Academiae Scientiarum, 1797), pp. 47–62 and Plate I, Figures 4–9, Natural History Museum Library, London copy, https://archive.org/details/novaactaacademia10petr.