Which preposition to use with averments

of Occurrences 3%

My readers, therefore, will not be surprised to learn, by a plain averment of the simple truth, that not one of all the score of ladies, whose names had been coupled with his own, would Doctor Bugbee have married, if he could, and that to none of them had he ever given any good reason for believing that she stood especially high in his esteem.

in Occurrences 1%

But with the first echo from abroad of its earliest announcements here came the most positive averments in the English papers, with scarcely a single exception, that the knell of this Union had struck.

Which preposition to use with  averments