h₂erk-es-
“bow, curved weapon”arc, arch, archer, arcade
Abstract from *h₂erk- giving Latin arcus, English arc, arch, archer, arcade.
Discussion
The PIE form *h₂erk-es- (bow, curved weapon) is a nominal derivative related to *h₂erḱ- (to hold, to ward off, to curve), formed with the neuter s-stem suffix *-es-. The literal sense is "the curved thing" — the bow as a weapon defined by its shape.
Latin arcus (bow, arch, curve) is the direct continuation and the source of a rich English vocabulary that spans weaponry, architecture, and mathematics: arc (a curve), arch (a curved structural span), arcade (a series of arches), archer (one who uses a bow), and the combining form arc-/arch- in technical terms (arc welding, arc lamp — both describing the curve of electrical discharge).
The architectural sense — the arch as a structural element — derives from the weapon sense: the stone arch mimics the shape of a drawn bow, transferring the bow's curved strength to masonry. Roman architects exploited this shape systematically, and the arch became the defining structural element of Roman engineering (aqueducts, bridges, triumphal arches). Every subsequent use of the arch in Western architecture descends from the Romans' insight that the bow's curve distributes force.
The mathematical term arc (a portion of a curve, particularly of a circle) preserves the geometric abstraction: the bow's shape reduced to pure form. Trigonometric functions measured by arc — arcsine, arccosine, arctangent — embed the PIE bow-word in the foundations of modern mathematics.
Greek does not clearly preserve this specific root for "bow" (Greek uses tóxon, from a different source — possibly Scythian). The absence of a Greek reflex for the bow-word is notable and may reflect a vocabulary replacement in the Hellenic branch.
The connection to *h₂erḱ- (to ward off, to defend — the root behind Latin arcēre and English arcade/arcane) is both phonological and conceptual: the bow both curves and defends. The weapon and the protective enclosure share the same root because they share the same shape — the curve that wards off.