Based on: beseitigen Plural: Beseitigungen
The core idea of this root was
sowing, throwing down, letting down
It’s the origin of words like semen, to sow, seminal and season and at least according to the German DWDS.de and Wiktionary, it’s also the origin of side and since.
Etymonline.com mentions a separate root for side and since, with a core notion of long, but German DWDS.de mentions that as a subbranch of the root mentioned here, so I decided to stick with that.