108 Or “vehemently.” εὐτόνως has “vigorously, vehemently … εὐ. διακατελέγχεσθαί τινι refute someone vigorously Ac 18:28.”
109 L&N 33.442 translates the phrase τοῖς Ἰουδαίοις διακατηλέγχετο δημοσίᾳ (tois Ioudaiois diakatēlencheto dēmosia) as “he defeated the Jews in public debate.” On this use of the term δημόσιος (dēmosios) see 2.
110 Or “Messiah”; both “Christ” (Greek) and “Messiah” (Hebrew and Aramaic) mean “one who has been anointed.” Again the issue is identifying the Christ as Jesus (see 5:42; 8:5; 9:22; 18:5). See the note on Christ in .
111 Although many English translations have here “that Jesus was the Christ,” in the case of two accusatives following a copulative infinitive, the first would normally be the subject and the second the predicate nominative. Additionally, the first accusative here (τὸν χριστόν, ton christon) has the article, a further indication that it should be regarded as subject of the infinitive.

In other versions

for he powerfully refuted the Jews in public, showing by the Scriptures that the Christ was Jesus.

For he vigorously refuted his Jewish opponents in public debate, proving from the Scriptures that Jesus was the Messiah.

For he vigorously refuted the Jews in public, demonstrating through the Scriptures that Jesus is the Messiah.

He refuted the Jews with powerful arguments in public debate. Using the Scriptures, he explained to them that Jesus was the Messiah.

For he was vigorously refuting the Jews in public, demonstrating through the scriptures that the Christ was Jesus.

For he mightily convinced the Jews, and that publickly, shewing by the scriptures that Jesus was Christ.

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