2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76023In this paper Euler shows how, if we have recursive functions f,g,h and an infinite sequence A,B,C,... which satisfies fA=gB+hC, f'B=g'C+h'D, f''C=g''D+h''E, f'''D=g'''E+h'''F, etc., where the primes denote an index not a derivative, then we can find a continued fraction for fA/B.17 pages, seems to be first English translation of Euler's Latin original ``De formatione fractionum continuarum'', Acta Academiae Scientarum Imperialis Petropolitinae 3 (1782), no. 1, 3-29. E522History and OverviewNumber Theory01A50; 11A55text