There is a great question here about the etymology behind the term 'reflexive' for binary relations. How about 'connex' and 'transitive'? Where do these names come from?
I expect that transitivity is related to the idea of transitive verbs in grammar based on the etymology for reflexivity, but I can't see the relation exactly. Connex I have no idea about, it looks kind of like convex?
The mathematical meaning of connex is a new use of an obsolete English adjective meaning ‘connected’, for which the OED has citations from 1653, 1677, and 1685. It is derived from Latin connexus, classical Latin cōnexus, the past participle of connectō. The idea is that a connex order is ‘connected’ in the sense that no two elements are incomparable.
The mathematical sense of transitive goes back at least to De Morgan; the OED has a citation from 1856 for him. The word derives from Latin transeō ‘to pass over’; the idea is that the relationship makes a transition through the intermediate term.