If you have read post-Classical śāstra, you will have certainly encountered the formulation above, describing the three foundational disciplines as focusing on
words (pada), i.e., grammatical analysis in Vyākaraṇa
sentences (vākya), i.e., textual linguistics in Mīmāṃsā
means of knowledge (pramāṇa), i.e., epistemology in Nyāya
The tripartition is handy and catchy, but clearly post-classical, also since the idea of distinguishing schools according to their “forte” and studying each of them in a technical way is probably itself post-classical. Thus, when did the tripartition originate, and by whom? When and where did it become standard?
As for the first question, until now, I have encountered it in Jayanta (10th c. Kashmīr), in a non-standard form, so that it may be thought that Jayanta lies just before its standardization.
As for the last question, in the following quote by Veṅkaṭanātha (13th c. Tamil Nadu) the standardisation seems complete:
The knowers of the śāstra divide the śāstra into three, according to the division into words, sentences and means of knowledge.
(padavākyapramāṇabhedena hi tredhā vibhajanti śāstraṃ śāstravidaḥ)
When and wher did you encounter this tripartition first?