The headword (presumably extracted from the quotation given) is present indicative active, third person singular, of prosoudi/zw, literally 'I cause to approach the ground' (so the addition of the adverb xamai/ is somewhat redundant). See also pi 2764.
[1] Procopius, History of the Wars of Justinian 8.8.26 (web address 1); in a skirmish prior to the Battle of the Hippis River (Hippos; 550 CE, a pivotal battle during the Lazic War (541-562); cf. Barrington Atlas map 87 grid G2), a Persarmenian soldier fighting for the Romans, Artabanes (cf. PLRE IIIa s.v. Artabanes(1)), slays a Persian cavalryman; cf. Kaldellis (478) and omega 165.