ἀρχαί (archai)
ἀρχαί is an Ancient Greek form of ἀρχαῖος, meaning “ancient, old”. It is the accusative plural neuter adjective.
Found 247 times in the Ancient Greek texts on Socratos.
Where it is used
Thucydides, History of the Peloponnesian War 5.47.9: ὀμνύντων δὲ Ἀθήνησι μὲν ἡ βουλὴ καὶ αἱ ἔνδημοι ἀρχαί, ἐξορκούντων δὲ οἱ πρυτάνεις· ἐν Ἄργει δὲ ἡ βουλὴ καὶ οἱ ὀγδοήκοντα καὶ οἱ ἀρτῦναι, ἐξορκούντων δὲ οἱ ὀγδοήκο …
Diogenes Laertius, Vitae philosophorum 1.prol.20: … οῖμεν πρόσκλισιν δόγμασιν ἀκολουθίαν ἔχουσιν, οὐκέτʼ ἂν προσαγορεύοιτο αἵρεσις· οὐ γὰρ ἔχει δόγματα. αἵδε μὲν ἀρχαὶ καὶ διαδοχαὶ καὶ τοσαῦτα μέρη καὶ τόσαι φιλοσοφίας αἱρέσεις.
Aristophanes, Clouds 1197: ἁρχαὶ τὰ πρυτανεῖʼ, ἀλλʼ ἕνῃ τε καὶ νέᾳ;
All forms of ἀρχαῖος (declension table)
Source: Socratos (socratos.org), a free reader for Ancient Greek and Latin. Grammar from the Perseus Treebank and Morpheus; dictionary entries from Liddell-Scott-Jones, A Greek-English Lexicon (Perseus Digital Library, CC BY-SA). Counts are from the texts on Socratos.