Etymology
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Words related to *gwa-

acrobat (n.)
1845, from French acrobate "tightrope-walker" (14c.) and directly from a Latinized form of Greek akrobates "rope dancer, gymnastic performer," which is related to akrobatos "going on tip-toe, climbing up high," from akros "topmost, at the point end" (from PIE root *ak- "be sharp, rise (out) to a point, pierce") + Greek agential element -bates "one that goes, one that treads (in some manner), one that is based," from -batos, verbal adjective from stem of bainein "to go, walk, step," from PIE root *gwa- "to go, come."
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adiabatic (adj.)
"without transference, impossible (to heat)," 1838, with -ic + Greek adiabatos "not to be passed" (of rivers, etc.), from a- "not" (see a- (3)) + diabatos "to be crossed or passed, fordable," from dia "through" (see dia-) + batos "passable," from bainein "to go, walk, step," from PIE root *gwa- "to go, come." In thermodynamics, of a change in volume without change in heat.
advent (n.)
"important arrival," 1742, an extended sense of Advent "season preceding Christmas" (in reference to the "coming" of Christ), late Old English, from Latin adventus "a coming, approach, arrival," in Church Latin "the coming of the Savior," from past participle stem of advenire "arrive at, come to," from ad "to" (see ad-) + venire "to come," from a suffixed form of PIE root *gwa- "to go, come." Related: Adventual.
adventitious (adj.)
"of the nature of an addition from without, not from the essence of the subject; accidentally or casually acquired," c. 1600, from Medieval Latin adventitius "coming from abroad, extraneous," a corruption of Latin adventicius "foreign, strange, accidental," from advent- past participle stem of advenire "to arrive at, reach, come to" (see advent). Related: Adventitiously; adventitiousness.
adventure (n.)
Origin and meaning of adventure
c. 1200, aventure, auenture "that which happens by chance, fortune, luck," from Old French aventure (11c.) "chance, accident, occurrence, event, happening," from Latin adventura (res) "(a thing) about to happen," from fem. of adventurus, future participle of advenire "to come to, reach, arrive at," from ad "to" (see ad-) + venire "to come," from a suffixed form of PIE root *gwa- "to go, come."

Meaning developed through "risk; danger" (a trial of one's chances), c. 1300, and "perilous undertaking" (late 14c.) to "novel or exciting incident, remarkable occurrence in one's life" (1560s). Earlier it also meant "a wonder, a miracle; accounts of marvelous things" (13c.). The -d- was restored in English 15c.-16c.; attempt was made about the same time to restore it in French, but there it was rejected. Venture is a 15c. variant. German Abenteuer is a borrowing of the French word, apparently deformed by influence of Abend "evening."
amphisbaena (n.)
fabled serpent of ancient times, with a head at either end, late 14c., amphibena, from Medieval Latin, from Greek amphisbaena, from amphis "both ways" (see amphi-) + stem of bainein "to go, walk, step," from PIE root *gwa- "to go, come."
anabasis (n.)
1706, from Greek anabasis "military expedition," literally "a going up (from the coast)," especially in reference to the advance of Cyrus the Younger and his Greek mercenaries from near the Aegean coast into Asia, and the subsequent story of the retreat of the 10,000 narrated by Xenophon (401 B.C.E.). From anabainein "to go up, mount;" from ana "up" (see ana-) + bainein "to go, walk, step," from PIE root *gwa- "to go, come." Related: Anabatic.
avenue (n.)

c. 1600, "a way of approach" (originally a military word), from French avenue "way of access" (16c.), from Old French avenue "act of approaching, arrival," noun use of fem. of avenu, past participle of avenir "to come to, arrive," from Latin advenire "to come to, reach, arrive at," from ad "to" (see ad-) + venire "to come" (from a suffixed form of PIE root *gwa- "to go, come").

The meaning was extended to "a way of approach to a country-house," usually a straight path bordered by trees, hence, "a broad, tree-lined roadway" (1650s), then to "wide, main street" (by 1846, especially in U.S.). By late 19c. in U.S. cities it was used to form the names of streets without reference to character.

base (n.)

"bottom of anything considered as its support, foundation, pedestal," early 14c., from Old French bas "depth" (12c.), from Latin basis "foundation," from Greek basis "a stepping, a step, that on which one steps or stands, pedestal," from bainein "to go, walk, step," from PIE root *gwa- "to go, come."

The military sense "secure ground from which operations proceed" is from 1860. The chemical sense "compound substance which unites with an acid to form a salt" (1810) was introduced in French 1754 by French chemist Guillaume-François Rouelle (1703-1770). Sporting sense of "starting point" is from 1690s, also "destination of a runner" (1812). As a "safe" spot in a tag-like or ball game, suggested from mid-15c. (as the name of the game later called prisoner's base). Hence base-runner (1867), base-hit (1874), etc. Meaning "resources on which something draws for operation" (as in power-base, database, etc.) is by 1959.

basis (n.)
1570s, "bottom or foundation" (of something material), from Latin basis "foundation," from Greek basis "a going, a step; a stand, base, that whereon one stands," from bainein "to go, walk, step," from PIE root *gwa- "to go, come." Transferred and figurative senses (of immaterial things) are from c. 1600.