The Greek expressions “in justice” and “in a man” mean, as the Good News Translation has indicated, with justice (see An American Translation* and New English Bible “justly”) and by means of a man. The expression fixed a day may be rendered as “has decided that on a day” or “has determined a particular day.”

Will judge the whole world must be rendered in many languages as “will judge everyone in the world.” Obviously it is not the earth itself which is to be judged, but “people on the earth.” Judge … with justice is equivalent to “judge justly,” “judge rightly,” or “judge with fairness.” Sometimes this expression is rendered in a somewhat negative fashion—for example, “judge without making a mistake” or “judge so that no one can complain.”

By means of a man indicates a secondary agency. This may be expressed as “he will cause a man to do the judging for him” or “a man whom he has chosen will do the judging.”

Given proof of this is literally “having given faith,” but most commentators understand “faith” in the present context to mean “assurance” or “proof.” It is possible, as a few have done, to understand this entire phrase to mean that God has given all men the opportunity to have faith. Has given proof of this may be equivalent to “has shown clearly that he would do this” or “has shown so well that no one can doubt.”

Quoted with permission from Newman, Barclay M. and Nida, Eugene A. A Handbook on The Acts of the Apostles. (UBS Handbook Series). New York: UBS, 1972. For this and other handbooks for translators see here .