III. A man who has married twice or a widow is not eligible as a priest.
Again, when each man's respectability of birth and conduct has been established, what sort of person should be associated with the ministry of the Sacred Altar we have learned both from the teaching of the Apostle and the Divine precepts and the regulations of the canons, from which we find very many of the brethren have turned aside and quite gone out of the way. For it is well known that the husbands of widows have attained to the priesthood: certain, too, who have had several wives, and have led a life given up to all licentiousness, have had all facilities put in their way, and been admitted to the Sacred Order, contrary to that utterance of the blessed Apostle, in which he proclaims and says to such, “the husband of one wife,” and contrary to that precept of the ancient law which says by way of caution: “Let the priest take a virgin to wife, not a widow, not a divorced woman.”
All such persons, therefore, who have been admitted we order to be put out of their offices in the church and from the title of priest by the authority of the Apostolic See: for they will have no claim to that for which they were not eligible, on account of the obstacle in question: and we specially claim for ourselves the duty of settling this, that if any of these irregularities have been committed, they may be corrected and may not be allowed to occur again, and that no excuse may arise from ignorance: although it has never been allowed a priest to be ignorant of what has been laid down by the rules of the canons.
These writings, therefore, we have addressed to your provinces by the hand of Innocent, Legitimus and Segetius, our brothers and fellow bishops: that the evil shoots which are known to have sprung up may be torn out by the roots, and no tares may spoil the Lord's harvest. For thus all that is genuine will bear much fruit, if that which has been wont to kill the growing crop be carefully cleared away.
Source: Letters (New Advent)