καθ
Strong's 2596 (κατά)
about, according as (to), after, against, (when they were) X alone, among, and, X apart, (even, like) as (concerning, pertaining to touching), X aside, at, before, beyond, by, to the charge of, (charita-)bly, concerning, + covered, (dai-)ly, down, every, (+ far more) exceeding, X more excellent, for, from … to, godly, in(-asmuch, divers, every, -to, respect of), … by, after the manner of, + by any means, beyond (out of) measure, X mightily, more, X natural, of (up-)on (X part), out (of every), over against, (+ your) X own, + particularly, so, through(-oughout, -oughout every), thus, (un-)to(-gether, -ward), X uttermost, where(-by), with
(prepositionally) down (in place or time), in varied relations (according to the case (genitive, dative or accusative) with which it is joined)
a primary particle;