Lewis & Short

Alphēus (trisyl.) or Alphēŏs, i, m., = Ἀλφειός, the chief river in the Peloponnesus, now Rufia. It rises in the southern part of Arcadia, not far from Asea, unites with the Eurotas, and then losing itself under ground, makes its appearance again in Megalopolis. It afterwards flows, in a north-west direction, through Arcadia to Elis, and then turns west from Olympia, and falls into the Ionian Sea. At its mouth there was a grove consecrated to Diana or Alphiusa (Mann. Greece, 467 sq. 503). Its disappearance under ground gives occasion for the fable that it flows under the sea, and appearing again in Sicily, mingles with the waters of Arethusa.
Hence personified as the lover of the nymph Arethusa, Ov. M. 2, 250; 5, 599; id. Am. 3, 6, 29 (cf. Verg. E. 10, 1 sqq.).
Hence. Alphēus, a, um. adj., = Ἀλφεῖος, of or pertaining to the Alpheus: Alpheae Pisae, founded by a colony from Pisa, in Elis, on the river Alpheus, Verg. A. 10, 179: Alpheae ripae, Claud. B. Get. 575.