[1] Both the headword (extracted from the quotation given) and its gloss are accusative singular.
[2] Aristophanes, Frogs 566. The present gloss is that of the scholia there, and occurs also in other lexica: Hesychius s.v. kath=liy and meso/dmh; Photius s.v. kath=liy; and Pollux 7. 123. It denotes a horizontal construction in the upper part (roof) of a house or a ship (e.g, a storage shelf supported by a beam; see Dover 1993). *kath=liy occurs again in Lucian, Lexiphanes 8.5. meso/dmh is more common (for the designation of a part in the house, see e.g also Homer, Odyssey 19.37 (with scholion), 20.354; Quintus Smyrnaeus 13.451. For its use in the context of ships, see e.g. Homer, Odyssey 2.424 (with scholion), 15.289; Apollonius Rhodius, Argonautica 1.563 and scholion; Lycophron, Alexandra 751 and scholion; Nonnus, Dionysiaca 36.407, 39.316, 45.142). In the Suda (mu 666) meso/dmh is defined as referring to the middle.