Back to the -ment words. These ones all have a c in them. A hard c, not that pain in the ass soft c.
Comment showed up in the late fourteenth century from the Old French coment and Late Latin commentum, both of which meant comment. It’s from the classical Latin comminisci, to contrive, which means it was more like plan or devise than comment. It’s thought that the com- prefix is only intensive here, and the menisci is from meminisse, to remember, from the Proto Indo European men-, to think. Which. Yeah. Not related to the -ment we learned about last week.
Compliment showed up in the late sixteenth century as complement, and yes, that’s where complement comes from, too. Both are from the classical Latin complementum, completion—which makes sense for the latter, but the former? Apparently something that was complimentary (as in, free), was completing the obligation of politeness, and then in Italian that changed to “expression of respect or civility”, and that influenced nineteenth century English to make it saying something nice. Anyway, complementum comes from complere, to complete. The com- prefix is intensive again and the plere means to fill, from the Proto Indo European pele-, to fill. To complement (or compliment) is to really fill something. And the -ment is just a Latin suffix.
Compartment showed up in the mid sixteenth century from the Middle French compartiment, a partition. That word’s from the Italian compartimento, compartment, which was then taken from the Late Latin compartiri, to divide. Once again, the com- is intensive, and the partiri is from partis, which is from the Proto Indo European pere-, grant or allot. I’m not even sure where the -ment showed up from here.
Finally today, we’re looking at inclement. It showed up in the mid seventeenth century from the French inclément and classical Latin inclementem, which means merciless and now I’m disappointed that we don’t use this word more. The in- means opposite of and clementum has to do with things being nice or mild. It’s a mix of the Proto Indo European word klei-, to lean, and -menos, which I can’t really find much about but definitely isn’t related to the other -ment words.
TL;DR: If it isn’t a common word you know + -ment, it’s not related to anything else apparently.