Middle English mēten, from Old English metan "to find, find out; fall in with, encounter, come into the same place with; obtain," from Proto-Germanic *motjanan (source also of Old Norse mæta, Old Frisian meta, Old Saxon motian "to meet," Gothic gamotijan), from PIE root *mod- "to meet, assemble." Related to Old English gemot "meeting."
By c. 1300, of things, "to come into physical contact with, join by touching or uniting with;" also, of persons, "come together by approaching from the opposite direction; come into collision with, combat." Abstractly, "to come upon, encounter (as in meet with approval, meet one's destiny) by late 14c. Sense of "come into conformity with, be or act in agreement with" (as in meet expectations) is by 1690s.
Intransitive sense, of people, "to come together" is from mid-14c.; of members of an organized body or society, "to assemble," by 1520s. Related: Met; meeting. To meet (someone) halfway in the figurative sense "make mutual and equal concessions to" is from 1620s. Well met as a salutation of compliment is by mid-15c.
Old English findan "come upon, meet with; discover; obtain by search or study" (class III strong verb; past tense fand, past participle funden), from Proto-Germanic *findan "to come upon, discover" (source also of Old Saxon findan, Old Frisian finda, Old Norse finna, Middle Dutch vinden, Old High German findan, German finden, Gothic finþan), originally "to come upon."
The Germanic word is from PIE root *pent- "to tread, go" (source also of Old High German fendeo "pedestrian;" Sanskrit panthah "path, way;" Avestan panta "way;" Greek pontos "open sea," patein "to tread, walk;" Latin pons (genitive pontis) "bridge;" Old Church Slavonic pǫti "path," pęta "heel;" Russian put' "path, way;" Armenian hun "ford," Old Prussian pintis "road"). The prehistoric sense development in Germanic would be from "to go" to "to find (out)," but Boutkan has serious doubts about this.
Germanic *-th- in English tends to become -d- after -n-. The change in the Germanic initial consonant is from Grimm's Law. To find out "to discover by scrutiny" is from 1550s (Middle English had a verb, outfinden, "to find out," c. 1300).
c. 1500, "to find, discover" (obsolete), a back-formation from invention or else from Latin inventus, past participle of invenire "to come upon; devise, discover."
The general sense of "make up, fabricate, concoct, devise" (a plot, excuse, etc.) is from 1530s, as is that of "produce by original thought, find out by original study or contrivance." Related: Invented; inventing.
representing the common pronunciation of the verbal phrase come on, by 1929. Come on! as an urge to advance or go with is from mid-15c. (see come).