All 5 Uses

establish
in
Abraham Lincoln and the Self-Made Myth
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There was another Lincoln who had a lawyer-like feeling for the niceties of established rules and a nationalist's reverence for constitutional sanction.
Subsection 3 *

established = firmly set in place
Notice that while it is politically on the radical or "popular" side of the fight, it is historically conservative: it aims to preserve a long-established order that has well served the common man in the past.
Subsection 5

established = existing
So general was this sentiment that when the aged John J. Crittenden of Kentucky introduced into Congress on the day after Bull Run a resolution declaring that the war was not being waged for conquest or subjugation nor to interfere with "the established institutions" of the seceded states, even Republicans of Jacobin leanings were afraid to vote against it.
Subsection 6

established = set in place
Such popular government has often been called an experiment, he went on, but two phases of the experiment have already been successfully concluded: the establishing and administering of it.†
Subsection 5
Bring the South back, save the Union, restore orderly government, establish the principle that force cannot win out, and do it with the least cost in lives and travail—there is the Lincoln program.†
Subsection 5

Definitions:

(1) (establish as in: establish a positive tone)
create, start, or set in [a] place
(2) (establish as in: establish that there is a need)
show or determine (cause to be recognized or figure out)
(3) (meaning too rare to warrant focus)