For he mightily convinced the Jews - He did it by strong arguments; he bore down all opposition, and effectually silenced them.
And that publicly - In his public preaching in the synagogue and elsewhere.
Showing by the scriptures - Proving from the Old Testament. Showing that Jesus of Nazareth corresponded with the account of the Messiah given by the prophets. See the notes on John 5:39.
That Jesus was Christ - See the margin. That Jesus of Nazareth was the Messiah.