ESV Luke 22:
For the Son of Man goes as it has been determined, but woe to that man by whom he is betrayed!".
Strong's 2596: A primary particle; down, in varied relations (genitive, dative or accusative) with which it is joined).
it has been determined,
Verb - Perfect Participle Middle or Passive - Accusative Neuter Singular
Strong's 3724: From horion; to mark out or bound, i.e. to appoint, decree, specify.
In this case, κατὰ is followed by an accusative verb.
Thayer's Greek Lexicon:
I. With the genitive
II. With the accusative
- of place;
- of Time
- it denotes reference, relation, proportion, of various sorts;
c. according to, agreeably to; in reference to agreement or conformity to a standard
My paraphrase of Luke 22:22a:
The Son of Man will go as it has been agreed upon.
New International Version
The Son of Man will go as it has been decreed.
The grammatical pattern in Matthew 19:3 is similar:
And Pharisees came up to him and tested him by asking, “Is it lawful to divorce one’s wife for [κατὰ] any [accusative] cause [accusative]?”
Is it lawful to divorce one’s wife for any cause according to the standard agreement?
OP: If something were decreed to happen would not all the circumstances that led up to it happening fall under that decree? kata, down.
Yes, in some English sense of down. The Greek sense is slightly different,
Usage: gen: against, down from, throughout, by;
acc: over against, among, daily, day-by-day, each day, according to, by way of.