All 7 Uses of

establish

in

The Pathfinder by Cooper

Along both these lines of communication military posts had been established, though there existed a blank space of a hundred miles between the last fort at the head of the Mohawk and the outlet of the Oswego, which embraced most of the distance that Cap and Mabel had journeyed under the protection of Arrowhead.†
Chpt 3 (definition 1)

Lieutenant Muir, it is true, claims his right; but, being quartermaster, I do not like to break up well-established arrangements.
Chpt 10 (definition 1) *

established = long-practiced

There, sure enough, it was found that the Quartermaster's bullet had gone through the hole made by Jasper's, and that, too, so accurately as to require a minute examination to be certain of the circumstance; which, however, was soon clearly established, by discovering one bullet over the other in the stump against which the target was placed.
Chpt 11 (definition 2) *

established = demonstrated or known

Here is Sergeant Dunham's charming daughter, now, to approve of such sentiments, I'm certain; her character for discretion being already well established in the garrison, short as has been her residence among us.
Chpt 11 (definition 1)

established = set in place

It would not have been easy indeed for a person the most sensitive on the subject of circumstances to fancy that the Scud was anywhere in the vicinity of a port so long established and so well known on the frontiers as Frontenac.
Chpt 19 (definition 1)

established = settled

So unwilling, indeed, did this individual, a man of iron nerves, and one long accustomed to the dangers of the peculiar warfare in which he was engaged, appear to remain exposed to the assaults of Killdeer, whose reputation throughout all that frontier was as well established as that of Marlborough in Europe, that he did not disdain to seek a cover, insisting that his two prisoners should follow him.
Chpt 23 (definition 1)

established = set (existing firmly)

"My dearest friend," Muir commenced,—"for ye'll be dearer to us all, by seventy and sevenfold, after your late conduct than ever ye were,—ye've just established yourself in this late transaction.†
Chpt 26 (definition 1)

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)