1650s as an architectural order, from Corinth, the ancient Greek city-state. In classical times Corinth was notorious for its luxury and licentiousness among the Greek states (and for not scorning trade and profit); hence Corinthian, noun and adjective, in various slang or colloquial sense in English, especially "a swell, a man about town" (early to mid-19c. but especially in the 1820s).
"a spiral thing," 1560s, from Latin helix "spiral," from Greek helix (genitive helikos), related to eilein "to turn, twist, roll," from PIE *wel-ik-, from root *wel- "to turn, revolve" (see volvox).
helix he·lix (hē'lĭks)
n. pl. he·lix·es or hel·i·ces (hěl'ĭ-sēz', hē'lĭ-)
A spiral form or structure.
The folded rim of skin and cartilage around most of the outer ear.
A three-dimensional curve that lies on a cylinder or cone, so that its angle to a plane perpendicular to the axis is constant.
In geometry, a three-dimensional spiral shape, resembling a spring.