Euler E806: Arithmetical fragments taken from the mathematical notebooks | English translation | OMH v1.0

English translation of “Fragmenta arithmetica ex Adversariis mathematicis depromta” (Eneström E806), titled “Arithmetical fragments taken from the mathematical notebooks.” Attribution: the Leonhard Euler collection, with individual contributors’ attributions preserved. This PDF includes all 110 original numbered pages, pp. 157–266, including Latin, French and German passages, original tables, corrections and failed arguments, and the one figure assigned to p. 229. Individual fragments are not all attributed to Leonhard Euler. 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: Opera postuma mathematica et physica, vol. I (1862), pp. 157–266. Sources: https://scholarlycommons.pacific.edu/euler-works/806/; https://archive.org/details/operapostumamath01euleuoft; https://commons.wikimedia.org/wiki/File:Opera_postuma_mathematica_et_physica_-_Leonhard_Euler_-_vol._1,_1862_(IA_operapostumamath01euleuoft).pdf. This is a multi-contributor collection, not a sole-authored Euler text; printed credits include J. A. Euler, Lexell, N. Fuss I, Golovin, Krafft and W. L. Krafft. The historical-volume Commons record identifies public-domain status. Missing pp. 184–185 in the main scan are supplied from Pacific part A; overlapping part boundaries are reconciled. Plate figure 1 is an editable schematic redrawing; unrelated figures are excluded. The historical original is public domain by age; no publication license is assigned here to the new translation or editorial notes.