Online Etymology Dictionary

invariability (n.): 1640s, from invariable + -ity. Invariableness is from 1650s.
invariable (adj.): early 15c., from Old French invariable (14c.) and directly from Medieval Latin invariabilis, from in- "not, opposite of" (see in- (1)) + variabilis "changeable" (see variable). Related: Invariably.
invariant (adj.): 1795, from in- (1) "not" + variant (adj.). As a noun, in mathematics, from 1851. Related: Invariance.
invasion (n.): mid-15c., from Old French invasion "invasion, attack, assaut" (12c.), from Late Latin invasionem (nominative invasio) "an attack, invasion," noun of action from past participle stem of Latin invadere "to go, come, or get into; enter violently, penetrate into as an enemy, assail, assault, make an attack on," from in- "in" (see in- (2)) + vadere "go, walk" (see vamoose).
invasive (adj.): mid-15c., from Middle French invasif (15c.) or directly from Medieval Latin invasivus "invasive," from invas-, past participle stem of invadere "go into; attack, invade," from in- "in" (see in- (2)) + vadere "go, walk" (see vamoose).
invective (n.): "an attacking in words," 1520s, from Medieval Latin invectiva "abusive speech," from Late Latin invectivus "abusive, scolding" from invect-, past participle stem of invehere "to carry in, bring in, introduce; assault, assail; attack with words" (see inveigh). For nuances of usage, see humor (n.). The earlier noun form in English was inveccion (mid-15c.), and invective (adj.) was in Middle English.
inveigh (v.): formerly also enveigh, late 15c., "to introduce," from Latin invehere "to bring in, carry in, introduce," also "assault, assail," from in- "against" (see in- (1)) + vehere "to carry" (see vehicle). Meaning "to give vent to violent denunciation" is from 1520s, from a secondary sense in Latin (see invective). Related: Inveighed; inveighing.
inveigle (v.): formerly also enveigle, etc., late 15c., "to blind (someone's) judgment," apparently an alteration of Middle French aveugler "delude, make blind," from Vulgar Latin *aboculus "without sight, blind," from Latin ab- "without" (see ab-) + oculus "eye" (see eye (n.)). The Latin word is a loan-translation of Greek ap ommaton "without eyes." Meaning "to win over by deceit, seduce" is 1530s. Related: Inveigler; inveiglment.
invent (v.): 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." 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.
invention (n.): early 15c., "finding or discovering of something," from Old French invencion (13c.) and directly from Latin inventionem (nominative inventio) "faculty of invention," noun of action from past participle stem of invenire "to come upon, find; find out; invent, discover, devise; ascertain; acquire, get earn," from in- "in, on" (see in- (2)) + venire "to come" (see venue). Sense of "thing invented" is first recorded 1510s; that of "act or process of finding out how to make or do" is from 1530s.
Invention is applied to the contrivance and production of something, often mechanical, that did not before exist, for the utilization of powers of nature long known or lately discovered by investigation. Discovery brings to light what existed before, but was not known. [Century Dictionary]
Earliest sense of the word in Middle English was "devised method of organization" (c. 1400), now obsolete. Meaning "finding or discovery of something" is preserved in Invention of the Cross, Church festival (May 3) celebrating the reputed finding of the Cross of the Crucifixion by Helena, mother of Constantine, in 326 C.E. The related classical Latin word for "a device, contrivance" was inventum.
inventive (adj.): early 15c., "skilled in invention," from Old French inventif (15c.), from Latin invent-, past participle stem of invenire "devise, discover, find" (see invention). Related: Inventively; inventiveness.
inventor (n.): c. 1500, "a discoverer, one who finds out" (now obsolete), from Latin inventor (fem. inventrix, source of French inventeur (15c.), Spanish inventor, Italian inventore) "contriver, author, discoverer, proposer, founder," agent noun from past participle stem of invenire "to come upon, find; find out; invent, discover, devise; ascertain; acquire, get earn," from in- "in, on" (see in- (2)) + venire "to come" (see venue). Meaning "one who contrives or produces a new thing or process" is from 1550s.
inventory (n.): early 15c., from Old French inventoire "detailed list of goods, a catalogue" (15c.), from Medieval Latin inventorium, alteration of Late Latin inventarium "list of what is found," from Latin inventus, past participle of invenire "to find, discover, ascertain" (see invention). Altered in Medieval Latin by influence of words in -orium; it properly belongs with words in -ary. Related: Inventorial; inventorially.
inventory (v.): "make a list or catalogue of," c. 1600, from inventory (n.). Related: Inventoried; inventorying.
inveracity (n.): 1789, from in- (1) "not, opposite of" + veracity.
Inverness: literally "mouth of the (River) Ness (for which see Nessie), from Inver-, element in place names in Scotland of Gaelic origin, usually of places at the confluence of a river with another or the sea, from Old Irish *in(d)ber- "estuary," literally "a carrying in," from Celtic *endo-ber-o-, from *endo- "in" (from PIE *en-do-, extended form of root *en; see in) + from *ber- "to carry," from PIE root *bher- (1) "to carry" (see infer).
inverse (adj.): in early use also enverse, mid-15c., from Latin inversus, past participle of invertere "turn about, turn upside-down, upset, reverse, invert" (see invert). Related: Inversely. As a noun, "inverted state or condition," 1680s, from the adjective.
inversion (n.): 1550s, "act of inverting;" 1590s, "state of being inverted," from Latin inversionem (nominative inversio) "an inversion," noun of action from past participle stem of invertere "turn about, turn upside-down" (see invert). Meteorological sense is from 1902. In old psychology, "homosexuality" (1895, short for sexual inversion) but in later psychology "identification with the opposite sex" (1958).
invert (v.): "to turn (something) in an opposite direction; reverse the position, order, or sequence of," 1530s, from Middle French invertir or directly from Latin invertere "turn upside down, turn about; upset, reverse, transpose," figuratively "pervert, corrupt, misrepresent," of words, "to use ironically," from in- "in, on" (see in- (2)) + vertere "to turn" (see versus). Related: Inverted; inverting; invertedly.
invertebrate (adj.): "having naturally no backbone," 1819, from Latin in- "not" (see in- (1)) + vertebratus (Pliny), from vertebra "joint or articulation of the body, joint of the spine" (see vertebra). As a noun, "an invertebrate animal," 1826.
invest (v.): late 14c., "to clothe in the official robes of an office," from Latin investire "to clothe in, cover, surround," from in "in, into" (see in- (2)) + vestire "to dress, clothe," from PIE *wes-ti-, suffixed form of root *wes- (4) "to clothe" (see wear (v.)).

The meaning "use money to produce profit" first attested 1610s in connection with the East Indies trade, and is probably a borrowing of a special use of Italian investire (13c.) from the same Latin root, via the notion of giving one's capital a new form. Figurative sense of "to clothe (with attributes)" is from c. 1600. The military meaning "to besiege, surround with hostile intent" also is from c. 1600. Related: Invested; investing.
investigable (adj.): "that may be investigated," c. 1400, from Late Latin investigabilis "that may be searched into," from Latin investigare "trace out, search after," from in- "in, into" (see in- (2)) + vestigare "to track, trace," from vestigium "footprint, track" (see vestige).
investigate (v.): c. 1500, back-formation from investigation or else from Latin investigatus, past participle of investigare "to trace out, search after," figuratively "search into, investigate," from in- "in, into" (see in- (2)) + vestigare "to track, trace," from vestigium "footprint, track" (see vestige). Related: Investigated; investigating.
investigation (n.): early 15c., from Old French investigacion (14c.), from Latin investigationem (nominative investigatio) "a searching into, a searching for," noun of action from past participle stem of investigare "to trace out, search after," figuratively "search into, investigate," from in- "in, into" (see in- (2)) + vestigare "to track, trace," from vestigium "a footprint, a track" (see vestige).
investigative (adj.): 1803, from Latin investigat-, past participle stem of investigare (see investigation) + -ive. Journalism sense is from 1951.
investigator (n.): 1550s, a native agent-noun formation from investigate, or else from Latin investigator "he that searches into," agent noun from past participle stem of investigare "to trace out, search after" (see investigation). Related: Investigatorial.
investiture (n.): late 14c., "ceremony of clothing in the insignia of office," from Medieval Latin investitura "an investing," from past participle stem of Latin investire "to clothe" (see invest). Related: Investive.
investment (n.): 1590s, "act of putting on vestments" (a sense now found in investiture); later "act of being invested with an office, right, endowment, etc." (1640s); and "surrounding and besieging" of a military target (1811); from invest + -ment.

Commercial sense of "an investing of money or capital" is from 1610s, originally in reference to the East India Company; general use is from 1740 in the sense of "conversion of money to property in hopes of profit," and by 1837 in the sense "amount of money invested." For evolution of the commercial senses, see invest.
investor (n.): 1580s, "one who clothes;" 1862, "one who invests money," agent noun from invest.
inveteracy (n.): "long continuance," 1690s, from inveterate + -cy.
inveterate (adj.): late 14c., "old," from Latin inveteratus "of long standing, chronic, old," past participle of inveterare "become old in," from in- "in, into" (see in- (2)) + verb from vetus (genitive veteris) "old" (see veteran). From early 15c. as "firmly established by long continuance;" from c. 1500, of persons, "hardened, confirmed" (in habit, etc.). Related: Inveterateness.
inviable (adj.): 1909, in biology, from in- (1) "not" + viable. Related: Inviability.
invictus: Latin adjective, "unconquered, unsubdued, invincible," from in- "not, opposite of" (see in- (1)) + victus, past participle of vincere "to conquer, overcome" (see victor).
It matters not how strait the gate,
How charged with punishments the scroll,
I am the master of my fate,
I am the captain of my soul.

[William Ernest Henley, "Invictus"]
invidious (adj.): c. 1600, from Latin invidiosus "full of envy, envious" (also "exciting hatred, hateful"), from invidia "envy, grudge, jealousy, ill will" (see envy (n.)). Envious is the same word, but passed through French. Related: Invidiously; invidiousness.
invigilate (v.): "to watch diligently" (archaic), 1550s, from Latin invigilatus, past participle of invigilare "watch over, be watchful, be devoted," from in- "in" (see in- (2)) + vigilare "to watch, keep awake, not sleep" (see vigil). In late 19c. especially in reference to student exams. Related: Invigilated; invigilating.
invigilation (n.): "the act of watching," 1871, noun of action from invigilate (v.). Perhaps from German, where it is used earlier than in English.
invigilator (n.): 1890, agent noun from invigilate.
invigorate (v.): 1640s, from in- (2) + vigor (n.) + -ate (2). Earlier verb was envigor (1610s), from Old French envigorer. Related: Invigorated; invigorating.
invigorating (adj.): 1690s, adjective from present participle of invigorate. Related: Invigoratingly.
invigoration (n.): 1660s, noun of action from invigorate. Perhaps modeled on French invigoration.
invincibility (n.): 1670s, from invincible + -ity. Invincibleness is recorded from 1610s.
invincible (adj.): early 15c., from Old French invincible (14c.) or directly from Latin invincibilis "unconquerable," from in- "not" (see in- (1)) + vincibilis "to be gained, easily maintained, conquerable," from vincere "to overcome" (see victor). Related: Invincibly.

The noun meaning "one who is invincible" is from 1630s. Invincible ignorance, an ignorance which the person having it lacks means to overcome, is from Church Latin ignorantia invincibilis (Aquinas). The Invincible Armada was the Spanish of 1588. Related: Invincibly.
inviolability (n.): 1660s, from inviolable + -ity.
inviolable (adj.): mid-15c., "that is to be kept without violation" (of an oath, etc.), from Latin inviolabilis "inviolable, invulnerable," from in- "not, opposite of" (see in- (1)) + violabilis "that may be injured, easily wounded," from violare "to do violence to" (see violation). Meaning "having a right or guaranty of immunity" (of a place of sanctuary, etc.) is from 1570s. Meaning "incapable of being injured" is from 1520s. Related: Inviolably.
inviolate (adj.): "unbroken, intact," early 15c., from Latin inviolatus "unhurt," from in- "not, opposite of" (see in- (1)) + violatus (see violation).
invisibility (n.): 1560s, from Late Latin invisibilitas, from Latin invisibilis "not visible, unseen" (see invisible).
invisible (adj.): mid-14c., "not perceptible to sight, incapable of being seen," from Old French invisible (13c.), from Latin invisibilis "unseen, not visible," from in- "not" (see in- (1)) + visibilis (see visible). Meaning "kept out of sight" is from 1640s. As a noun, "things invisible," from 1640s. Invisible Man is from H.G. Wells's novel (1897); invisible ink is from 1680s. Related: Invisibly.
invision (n.): "want of vision," 1640s, from in- (1) "not, opposite of" + vision (n.).
invita Minerva: Latin adverbial phrase, used with reference to literary or artistic creation, "without inspiration," literally "Minerva unwilling;" i.e. "without inspiration from the goddess of wisdom;" ablative fem. of invitus "against the will, unwilling, reluctant," according to de Vaan from PIE compound *n-uih-to- "not turned to, not pursuing," related to the source of invitation. With Minervā, ablative absolute of Minerva.
invitation (n.): mid-15c., "act of inviting, solicitation," from Latin invitationem (nominative invitatio) "an invitation, incitement, challenge," noun of action from past participle stem of invitare "invite, treat, entertain," originally "be pleasant toward," from in- "toward" (see in- (2)).

The second element is obscure. Watkins suggests a suffixed form of the PIE root *weie- "to go after something, pursue with vigor" (see gain (v.)); de Vaan also traces it to a PIE form meaning "pursued." Meaning "the spoken or written form in which a person is invited" is from 1610s.