hi will, i don’t think it’s a partitive gen. a partitive gen expresses the whole of which something else is a part (as in your second e.g.). that’s not what the original quote does.
in that quote, i’m pretty sure that each genitive is a prolepsis of the subject of its ὡς clause; i don’t have a grammar on me but i know they pass into the genitive when brought forward from the subordinate into the principal clause. i.e. it means that man is the measure of ὡς τὰ ὄντα ἔστιν (how things which are, are), and of ὡς τὰ ο?κ ὄντα ο?κ ἔστιν (how things which aren’t, aren’t), and then τὰ ὄντα in each case is brought forward before ὡς and so flicks into the gen.
just to go a bit further into the original question, of getting a grasp of how participles work in this way, i think the specific answer is that in grk when an article is attached, it can express the agent or doer with a “time element”. you might or might not be able to bring that out in english, but i think it’s important to think about the grk directly.
to take a step back, nouns and verb forms can be formed from the same root, eg. π?αγ- which can relate to “doing” generally. i don’t have a grammar here but will try to show how it works generally:
if you want to express “someone doing”, you can build the root π?αγ- into:
(a) a noun by adding an agent suffix. here it’s -τω?, which gives π?αγ-τω?, and with assimilation of γ to the dental becomes π?άκτω?, or
(b) a verb by: (i) treating the root π?αγ- as a verb root, (ii) adding the participle suffix, and (iii) adding the article (although sometimes (iii) isn’t required in some common types of poetry, e.g. Homer and tragedy, where a participle without an article can act as a substantive).
(b)(i): treating π?αγ- as a verb root: since it ends in a guttural mute, -γ- will change into -σσ- or -ττ- (in Attic, -ττ-) for the present and imperfect tense. [another example of this is ανακ- becoming ἀνάσσω in Homeric grk.]
(b)(ii) adding the participle suffix to the verb root, the present participle will be π?άττ-ων, and the aorist ppl will be π?αγ-σας (the rule above about guttural mutes only applies to the present and imperfect tenses, not the aorist), and π?αγ-σας by assimilation becomes π?άξας.
(b)(iii) adding the article, you get ? π?άττων and ? π?άξας.
so, there are at least these 3 ways to express “someone doing” from the general root π?αγ-, i.e. π?άκτω?, ? π?άττ-ων and ? π?άξας.
now the difference between nouns and verbs as aristotle says in “On Interpretation” is that nouns express meaning “without time” (16a) whereas verbs express in addition time (16b), i.e.:
(a) (π?αγ- built into a verb form): ? π?άττ-ων can express that the subject is “doing” at the same time as the action of the main verb in the clause, and ? π?άξας can express that the subject “did” before the action of the main verb in the clause. (Sometimes this distinction breaks down in e.g. Homer, but at any rate the participle still expresses time), whereas
(b) (π?αγ- built into a noun form): π?άκτω? simply expresses the subject as a “someone who does”, without referring to time.
this might all sound like information overload, but i think it’s important to understand directly how grk works. taking your original example, the participle τὰ ὄντα means “things existing”, with the present tense expressing that they exist now (rather than “existed” or “will exist” &c). a good example of this is Iliad A.70:
ὃς εἴδη τά τ’ ?όντα τά τ’ ?σσόμενα π?ό τ’ ?όντα,
where the participle + article in red is present and refers to things now existing, whereas the participle + article in blue is in the future tense, and means things which will be. this is how the participle expresses the time element: if there was a noun formed from the root of this verb to express “someone/thing existing” (i can’t think of one, i’m not sure it exists), it wouldn’t express this time element (i.e. whether the subject of that noun is existing, or was, or will &c): the verb with it would have to express that.
[similarly, you get a difference of meaning if you want to express the action itself of the verb: if you:
(a) build the root π?αγ- into a noun form, adding the suffix -σις for this purpose, giving π?αγ-σις which is π?ᾶξις after assimilation of -γ-, this simply expresses a “doing” without reference to time, whereas if you
(b) build the same root into a verb, i.e. by article + infinitive, you get time aspect expressed in addition, depending on the tense of the infinitive.]
, cheers, chad.