Centaurus (Centauros) is the eponymous first of the cloud-born centaurs in Greek mythology. In Apollodorus he is the son of Ixion and the cloud Zeus shaped in Hera's likeness; from him descend the wild Thessalian centaurs, as distinct from Chiron, who was born separately from Cronus and Philyra. Hyginus makes Centaurus brother of Peirithous.
Adapted from Wikipedia, "Centaurus (Greek mythology)" · CC BY-SA 4.0
I.Birth from the cloud
After Ixion attempts to violate Hera, Zeus fashions a cloud in the goddess's likeness. Ixion mates with the cloud; Apollodorus says she bears Centaurus, who later mates with Magnesian mares on Pelion and fathers the double-formed centaurs.
Hyginus instead treats Nubes ("Cloud") as mother, with Ixion, of named centaurs and sometimes lists Centaurus beside Peirithous as Ixion's son. The atlas node nubes-ixion holds that Hyginus naming; Centaurus is the Apollodoran eponym of the herd.
II.Ancestor of the wild centaurs
From Centaurus come the violent centaurs of the Lapith wedding and of Heracles' adventures — creatures of the mountain forests, often drunk and hostile to guests. They are genealogically and morally set apart from Chiron, the just son of Cronus and Philyra.
Literary catalogues (Homer, Apollodorus, Ovid, Hyginus) name individual centaurs as members of this brood without always repeating the Centaurus step; the eponym explains the race as a whole.
III.Name and sky
Later astronomy associates a southern constellation Centaurus with a centaur figure — sometimes Chiron, sometimes a generic or other hero — but that star-lore is reception, not the same as the Thessalian genealogical Centaurus of Apollodorus.
Keep Centaurus distinct from named centaurs such as Nessus, Pholus, and Eurytion, who are descendants or herd-members rather than the eponymous first father.