Both Uses

banish
in
Candide
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It was necessary for me to have been banished from the presence of Miss Cunegonde, to have afterwards run the gauntlet, and now it is necessary I should beg my bread until I learn to earn it; all this cannot be otherwise.†
Chpt 3 *

banished = expelled or gotten rid of
They often saw passing under the windows of their farm boats full of Effendis, Pashas, and Cadis, who were going into banishment to Lemnos, Mitylene, or Erzeroum.†
Chpt 30

banishment = to expel or get rid of

Definitions:

(1) (banish)
to expel or get rid of
in various senses, including:
- to force someone to leave a country as punishment
- to push an idea from the mind
(2) (meaning too rare to warrant focus)