O.E. ecg "corner, edge," also "sword," from P.Gmc. *agjo (cf. O.N. egg, see egg (v.); Ger. Eck "corner"), from PIE base *ak- "sharp, pointed" (cf. L. acies, Gk. akis "point;" see acrid). Spelling development of O.E. -cg to M.E. -gg to Mod.E. -dge represents a widespread shift in pronunciation. To get the edge on (someone) is U.S. colloquial, first recorded 1911. Edge city is from Joel Garreau's 1992 book of that name. Razor's edge as a perilous narrow path translates Gk. epi xyrou akmes.
"to move edgeways (with the edge toward the spectator), advance slowly," 1620s, originally nautical, from edge (n.). The verb meaning "urge on, incite" (16c.) usually is a mistake for egg (v.).