These are both superlatives of the first glossing term μέσος "middle".
The extension from "middlemost" to "high" comes from using "middlemost" to refer to hills in the middle of a plain, as in Josephus, Jewish Wars 2.511 ("that mountain which lies in the very middle of Galilee": web address 1), or structures tall in the middle, as in Josephus, Jewish Antiquities 15.393 ("but the middlemost [stone of the Temple] was much higher": web address 2).
Both words are also used in the scholia to Homer, Odyssey 1.426, to gloss περισκέπτῳ "conspicuous".