Complex sentence: With the dominance of the Neo-Platonism and Peripatetic School philosophy (and later Christianity) Epicureanism' declined until by the late third century A.D. there was very little trace of its existence.
Split into simpler sentences: With the dominance of the Neo-Platonism and Peripatetic School philosophy (and later Christianity), Epicureanism declined. By the late third century AD, there was very little trace of its existence.