Which prior meaning of pars does pars orationis draw from?
I'm wondering if just as the notion of grammatical "person" makes (I think) an analogy with roles in drama (the roles of the speaker, the one spoken to, and the one spoken about), maybe pars orationis in Latin means some prior sense of pars more specific than just "any ol' part". Lewis & Short's entry for pars doesn't mention pars orationis.
If pars is merely a calque of Greek μέρος, as in Aristotle's Poetics 1456b20, then my same question applies. Aristotle there seems to use the word much more broadly, dividing λέξις ("diction as a whole") into "letter, syllable, conjunction, joint, noun, verb, case, phrase"—a lot more than the usual "two parts of speech" usually attributed to him.
I'm especially wondering if pars would tend to make such matters of debate as "What is the true number of parts of speech?" seem meaningful or meaningless. If pars just means any ol' division of a whole, then "How many parts of speech are there?" would seem as nonsensical as "How many parts of a sphere are there?" "Uh, as many as you divide it into." But if pars suggests something more like a fundamental element, as in chemistry the "periodic table of the elements", this would suggest that the Ancient Latin grammarians were thinking that there was a single, true categorization of fundamental "parts" to be found.
So, does pars orationis evoke a meaning like what we would in English typically call an "element", or merely any "division" of a whole, or does it evoke something else?