John Calvin Commentary Acts 13:42

"And as they went out, they besought that these words might be spoken to them the next sabbath." — Acts 13:42 (ASV)

When they had gone out of the synagogue. This may also be read as, "out of the synagogue of the Jews," and perhaps more fittingly. For it is likely that they had gone out before the multitude dispersed; this is gathered from the text because Luke says shortly after, that when the synagogue gathering ended, certain of the Jews followed Paul and Barnabas. Therefore, the meaning is that Paul and Barnabas went out while the Jews were still assembled, and that they were then requested by the Gentiles to devote some effort to them in the meantime.

Afterward, certain of the Jews and proselytes came to Paul, desiring both to learn and also to profess their faith. When the old interpreter and Erasmus translated it as the Sabbath following, they did not understand Luke’s meaning. For since he is speaking in this place of the Gentiles, I do not think that they would choose a Sabbath on which to hear Paul and Barnabas. For that day was appointed for the Jews, but the Gentiles had no less opportunity on other days. Therefore, for what purpose should they defer their desire and prayers until the eighth day? Indeed, they eagerly desired to hear Paul while he was at leisure and not occupied in teaching the Jews. So the Lord does not allow them to be idle until the Sabbath comes, offering them subject matter among the Gentiles, in which they could engage themselves.

They would speak words. I have translated it as it is in Luke, though the article τα may be taken for τα αυτα, as in some other places. Then the meaning would be that they were requested to speak about the same things before the Gentiles that week. Furthermore, while the Gentiles greedily seize every first opportunity, the Jews, remaining quiet, neglect what is set before them; only certain of them join themselves to Paul and Barnabas. Luke mentions the proselytes by name, who, since they had embraced the doctrine of the law and worshiped the God of Israel, were not puffed up with that pride which hindered the Jews, who boasted of their long lineage and ancestry.