κατέρχομαι

Luke 4:31 κατῆλθεν He went down

Then He went down to Capernaum, a town in Galilee, and on the Sabbath He began to teach the people.

Luke 9:37 κατελθόντων when were descending

The next day, when they came down from the mountain, Jesus was met by a large crowd.

Acts 8:5 κατελθὼν having gone down

Philip went down to a city in Samaria and proclaimed the Christ to them.

Here: An aorist participle: the going-down is finished before the proclaiming starts. Jerusalem stands high in the hill country, so in Luke-Acts every trip away from it is "down." The word describes the terrain. It is not a judgment on Samaria.

Acts 9:32 κατελθεῖν descending

As Peter traveled throughout the area, he went to visit the saints in Lydda.

Acts 11:27 κατῆλθον came down

In those days some prophets came down from Jerusalem to Antioch.

Acts 12:19 κατελθὼν having gone down

After Herod had searched for him unsuccessfully, he examined the guards and ordered that they be executed. Then he went down from Judea to Caesarea and spent some time there.

Acts 13:4 κατῆλθον went down

So Barnabas and Saul, sent forth by the Holy Spirit, went down to Seleucia and sailed from there to Cyprus.

Acts 15:1 κατελθόντες having come down

Then some men came down from Judea and were teaching the brothers, “Unless you are circumcised according to the custom of Moses, you cannot be saved.”

Here: 'Having come down.' People 'went up' to Jerusalem in the hills and 'came down' from it (compare 'go up' in 15:2). The direction also carries a hint of coming from the centre of Jewish authority.

Acts 15:30 κατῆλθον went

So the men were sent off and went down to Antioch, where they assembled the congregation and delivered the letter.

Here: Jerusalem sits high in the hills and was the religious centre, so travel away from it is always described as going "down" (compare 11:27; 12:19).

Acts 18:5 κατῆλθον came down

And when Silas and Timothy came down from Macedonia, Paul devoted himself fully to the word, testifying to the Jews that Jesus is the Christ.

Here: 'They came down.' Travellers in Greek regularly 'went down' when heading south or toward the coast, and here they come south from Macedonia to Corinth. It is ordinary travel language with no religious meaning.

Acts 18:22 κατελθὼν having landed

When Paul had landed at Caesarea, he went up and greeted the church at Jerusalem. Then he went down to Antioch.

Acts 19:1 κατελθεῖν to come down

While Apollos was at Corinth, Paul passed through the interior and came to Ephesus. There he found some disciples

Acts 21:3 κατήλθομεν we disembarked

After sighting Cyprus and passing south of it, we sailed on to Syria and landed at Tyre, where the ship was to unload its cargo.

Acts 21:10 κατῆλθέν came down

After we had been there several days, a prophet named Agabus came down from Judea.

Here: 'Came down': down in height, from the Judean hill country around Jerusalem to the coast. Caesarea actually lies north-west of Jerusalem, so this is not 'down' on a map.

Acts 27:5 κατήλθομεν we came

And when we had sailed across the open sea off the coast of Cilicia and Pamphylia, we came to Myra in Lycia.

James 3:15 κατερχομένη, coming down,

Such wisdom does not come from above, but is earthly, unspiritual, demonic.

Here: Present participle of 'to come down, descend'. It pictures true wisdom as a gift that keeps coming down from God to people, not something they produce themselves.