Which preposition to use with iterating

in Occurrences 2%

So that she iterated in a clearer tone of protest: "You should know I dothat I do esteem you as something more than other men.

from Occurrences 1%

Doctrines and designs which a few years since could find no mouthpiece out of a bar-room, or the piratical den of a filibuster, are now clothed with power by the authentic response of the bench of our highest judicatory, and obsequiously iterated from the oracular recesses of the National Palace.

through Occurrences 1%

One simple set of fractal equations, iterated through a computer, could produce a three-dimensional image of a fern, a coastline or a cloud.

Which preposition to use with  iterating