I actually started this one months ago but went and got distracted by other things. Well, there’s no time like the present I guess.
Succeed, proceed and exceed all have the same root word, as do success, process and excess. And yes, the word cede is also related. See, the “ceed” part comes from the classical Latin cedere, which means go or move, and that is also the origin word for cede. It seems odd since cede means yield or to give up a right, but there is a lapsed definition where it means to go or leave. If you cede something, it does mean, in a sense, that you’re leaving it or withdrawing from it.
Like most similar words, language took a root and added different prefixes to make it work. Exceed, for example, which is ex plus ceed. Exceed showed up in the late fourteenth century from the Old French exceeder and classical Latin excedere, both of which have the same meaning. The ex- prefix means out, and combined with the “go or move” definition of cedere, you get “go out”. If you take it in the sense of running out of something, you can see where exceed came from. Excess, which also came in the late fourteenth century, comes from the Latin excessus (going beyond something), and also from excedere.
It might surprise you, but succeed’s prefix is sub-. The word itself showed up in the late fourteenth century, first in the line-of-succession sense, then about a century later in the winning sense. It was taken from the Old French succeder, which came from the classical Latin succedere. I guess it sounded awkward to say “subceed”, so the b was dropped (which happens in alot of words, by the way). Success has a similar story. It showed up in the 1530s as simply a result or outcome, and it comes from the Latin successus, which means an advance or a positive outcome. And of course successus is the past participle of succedere.
Procede also showed up in the late fourteenth centuryas a word for “continue on” taken from the Old French proceder and classical Latin procedere. No big surprises there. It’s just another combination of cedere, this time with the prefix pro-, which means forward. So it’s “go forwards” in a metaphorical sense. And from that we also have process, from the Latin processus, another past participle.
TL;DR: Latin. I could probably use that for any one of these.