On πολιτικός, LSJ's "generally, having relation to public life, political, public, opp. κατʼ ἰδίας, Th. 8.89" is extremely misleading and may stem from a misunderstanding of Thucydides' text at 8.89.3. He says not κατʼ ἰδίας, but κατ᾽ ἰδίας δὲ φιλοτιμίας, "but with regard to private ambition," where the adjective ἴδιος has its usual meaning, "private." The idiom for "privately" is κατ' ἰδίαν, not κατʼ ἰδίας.