In Greek «Theogony» (the origin or genealogy of the gods - verse 142-146)
Cyclops (ΚΥΚΛΩΨ - ΚΥΚΛΟΣ = Circle)  

We read,  [οί δή τοι τά μέν άλλα θεοίς εναλίγκιοι ήσαν, μούνος δ` οφθαλμός μέσσω ενέκειτο μετόπω. Κύκλωπες δ` όνομ` ήσαν επώνυμον, ουνέκ` άρά σφεων κυκλοτερής οφθαλμός έεις ενέκειτο μετώπω ισχύς δ` ηδέ βίη καί μηχαναί ήσαν έπ` έργοις.]
Cyclops (=Κύκλωπες)  took their names of the technique to build big and strong walls (Cyclopean walls) the shape of a circle living a small opening as  a passage protecting their cave and stock. The myth that Cyclops were monsters with one eye is not a fact, but they considered as strong wealthy selfish and ruthless
(not having an eye for the poor)
they were the first herdsman
people to capture the animals and breed them (no cultivators), and to create the first communities.
(in Homer Odyssey lines 382 - 390: Cyclop Polyphemus is not mentioned to have one eye but with eyebrows and eyelashes when  Odysseus and his men blinded him)


Centaurs (Κένταυρος - κεντά=prick or jab + ταύρος=bull) prick the bull with a long rod or cane  

Centaurs took their names from chasing oxen and other livestock on a horseback they considered as the first (cowboys),  The myth that Centaurs where monsters half man and half horse is not true, and no female Centaurs ever been mentioned. Wild horses existed plentiful on many Greek regions, a wild horse figure engraved on stone shown below from Paleolithic age was found at Pelion (Volos museum).
Man's  names Ιππόστρατος, Ιπποδάτης, Ιππιοχάρμης, Philippus, etc. and female given names Ιππου-κρήνη (Ίππος-hippos=horse), Ιπποθόη, Ιππονόη, Ιππώ, etc we find in «Theogony» also names were given to horses.
Many of this Centaurs considered as wise and skillful in medicine and pottery (the name Pelion originates from mixing Πηλό-pilos=clay for pottery).     

A wild horse figure engraved on stone from Paleolithic age was found at Pillion (Volos museum).