1640s, "an unprincipled popular orator or leader; one who seeks to obtain political power by pandering to the prejudices, wishes, ignorance, and passions of the people or a part of them," ultimately from Greek dēmagōgos "popular leader," also "leader of the mob," from dēmos "people, common people" (originally "district," from PIE *da-mo- "division," from root *da- "to divide") + agōgos "leader," from agein "to lead" (from PIE root *ag- "to drive, draw out or forth, move").
In a historical sense from 1650s, "a leader of the masses in an ancient city or state, one who sways the people by oratory or persuasion." Often a term of disparagement since the time of its first use (in Athens, 5c. B.C.E.). Form perhaps influenced by French démagogue (mid-14c.).
Indeed, since the term demagogos explicitly denotes someone who leads or shepherds the demos, the eventual use of this word as the primary epithet for a political panderer represents a virtual reversal of its original meaning. The word demagogos in fact implies that the people need someone to lead them and that political power, at least in part, is exercised appropriately through this leadership. [Loren J. Samons II, "What's Wrong With Democracy," University of California Press, 2004]
A Latin word in a similar sense was plebicola "one who courts (literally 'cultivates') the common people," from plebs "the populace, the common people" + colere "to cultivate."
Middle English -ik, -ick, word-forming element making adjectives, "having to do with, having the nature of, being, made of, caused by, similar to," from French -ique and directly from Latin -icus or from cognate Greek -ikos "in the manner of; pertaining to." From PIE adjective suffix *-(i)ko, which also yielded Slavic -isku, adjectival suffix indicating origin, the source of the -sky (Russian -skii) in many surnames. In chemistry, indicating a higher valence than names in -ous (first in benzoic, 1791).
In Middle English and after often spelled -ick, -ike, -ique. Variant forms in -ick (critick, ethick) were common in early Modern English and survived in English dictionaries into early 19c. This spelling was supported by Johnson but opposed by Webster, who prevailed.