Euler E646: On two or more algebraic curves whose equal arcs cut off from fixed endpoints have amplitudes in a given ratio | English translation | OMH v1.0

English translation of Leonhard Euler’s E646, "De duabus pluribusve curvis algebraicis, in quibus, si a terminis fixis aequales arcus abscindantur, eorum amplitudines datam inter se teneant rationem". 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/646/; original volume facsimile, https://archive.org/details/novaactaacademia06impe; Biodiversity Heritage Library, https://www.biodiversitylibrary.org/item/38598.