Which preposition to use with thereby

IN Occurrences 1%

I. THE LOVE OF THE SEX REMAINS WITH EVERY MAN AFTER DEATH, ACCORDING TO ITS INTERIOR QUALITY; THAT IS, SUCH AS IT HAD BEEN IN HIS INTERIOR WILL AND THEREBY IN THE WOMAN.

OF Occurrences 1%

THEY ARE FOR THE SAKE OF HAVING BLEMISHES EXCUSED, AND THEREBY OF AVOIDING DISGRACE.

TO Occurrences 1%

" THE SEVENTH NOVEL.ISABEL OF VALOIS, BEING FORSAKEN BY ALL OTHERS, IS BEFRIENDED BY A PRIEST, WHO IN CHIEF THROUGH A CHILD'S INNOCENCE, CONTRIVES AND EXECUTES A LAUDABLE IMPOSTURE, AND WINS THEREBY TO DEATH.

Which preposition to use with  thereby