seh₁-ḱ-lo-
“cycle, recurring age”cycle, secular, century, saeculum
Extended form giving Latin saeculum, English cycle, secular, century.
Discussion
The PIE form *seh₁-ḱ-lo- (cycle, a recurring period, an age) derives from the root *seh₁-ḱ- (to cut, to divide time), with the suffix *-lo- forming a diminutive or resultative noun. The meaning is "a cut portion of time that recurs" — a cycle, a generation, an era.
Latin saeculum (a generation, a century, an age of the world) is the central reflex and one of the most culturally loaded words in Roman civilisation. A saeculum was originally the longest human lifespan — roughly a hundred years — and the lūdī saeculārēs (Secular Games) were held once per saeculum to mark the passing of an age. From saeculum English derives: secular (of this age/world, as opposed to the eternal — the secular vs. the sacred), century (centum + a saeculum-related concept, though the direct derivation is from centuria), and the rarely used saecular.
The secular/sacred opposition is one of the most consequential semantic developments in Western civilisation. Secular originally meant "of this generation, of this temporal cycle" — it became "worldly, non-religious" only because Christian Latin contrasted the temporal saeculum (the passing age of this world) with aeternitas (the eternal kingdom of God). Every modern debate about secularism, secular education, and the separation of church and state deploys a PIE root about time-cycles in a theological framework developed by 4th-century Church Fathers.
Greek may preserve a related form in the word for time or harvest season, though the precise Greek cognate is debated. The Germanic branch does not clearly continue this specific formation, though the concept of "age/cycle" appears through other roots.
The suffix *-lo- in *seh₁-ḱ-lo- is the same diminutive-resultative suffix found in many PIE formations (cf. Latin -ulus/-ula, Germanic -el). The original sense may have been "a little cutting of time" — a generation-span viewed as a small segment of the larger temporal whole.