Katerchomai describes coming or going down, chiefly in travel to a place and once of wisdom descending from above.

The attested use chiefly concerns people traveling or coming down to a destination, including descent from a mountain; James 3:15 applies the movement imagery to wisdom described as descending from above.

1. Coming or going down to a place · dominant

   The aorist forms mark completed movement down in travel: in Acts 11:27 the APB renders prophets coming from Jerusalem to Antioch, and in Acts 13:4 it renders the sent men going to Seleucia. In Luke 9:37, the genitive plural participle occurs in the clause about having come down from the mountain before the crowd meets him; Acts 18:22 likewise places the participle within a sequence of travel to Caesarea and Antioch.

   Acts 11:27Acts 13:4Acts 18:22Acts 8:5Luke 4:31Luke 9:37
2. Wisdom described as descending from above · rare

   In James 3:15, the present middle participle modifies wisdom in the contrast between wisdom descending from above and what the verse calls earthly, natural, and demonic. The APB renders the clause "This is not the wisdom descending from above."

   James 3:15

In the Anselm Project Bible: Across the travel passages, the APB uses forms such as "came down," "went down," and "descended" for the movement described in the clauses. In James 3:15 it uses "descending from above"; These renderings indicate the verse-level presentation rather than a fixed equivalent.