All 6 Uses

establish
in
The American, by Henry James
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He established himself in some rooms selected for him by Tom Tristram, in accordance with the latter's estimate of what he called his social position.
Chpt 6 *

established = settled
Newman refused a cigar, but he established himself upon one of the divans, while the marquis puffed his own weed before the fire-place, and Valentin sat looking through the light fumes of a cigarette from one to the other.
Chpt 12
It is said that all women love a lover, and Mrs. Bread's sense of the pre-established harmony which kept servants in their "place," even as planets in their orbits (not that Mrs. Bread had ever consciously likened herself to a planet), barely availed to temper the maternal melancholy with which she leaned her head on one side and gazed at her new employer.
Chpt 23

pre-established = previously created
Even say we firmly established by medical evidence the presumption of a mind disordered by fever, ...
Chpt 24 *

established = proved
During the next three weeks Newman saw Bellegarde several times, and without formally swearing an eternal friendship the two men established a sort of comradeship.†
Chpt 7
He made several excursions into the country, recommended by the waiter at his hotel, with whom, on this and similar points, he had established confidential relations.†
Chpt 25

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)