'Public,' 'republic,' 'publish,' and 'popular' all stem from Latin 'populus' (people).
Of or concerning the people as a whole; done, perceived, or existing in open view; the people of a country or community as a whole.
From Old French 'public,' from Latin 'publicus' (of the people, pertaining to the state, common, open to all), an alteration of the earlier form 'poplicus,' from 'populus' (the people, the citizenry). The shift from 'poplicus' to 'publicus' was influenced by 'pubes' (adult men, those of fighting age) — the public conceived as the body of adult male citizens who constituted the Roman political community. The ultimate origin of 'populus' is debated: most scholars classify it as Etruscan or from a pre-Indo-European Italic substrate, with no secure PIE
The word 'republic' literally means 'a public thing' — from Latin 'res publica' (thing of the people). The Roman Republic was not named for a form of government but for an ideal: that the state belonged to its people, not to a king. When the French Revolution abolished the monarchy and declared a 'République,' they were reaching