Eureka (word)
The exclamation 'Eureka!' is attributed to the ancient Greek scholar Archimedes. He reportedly proclaimed "Eureka! Eureka!" after he had stepped into a bath and noticed that the water level rose, whereupon he suddenly understood that the volume of water displaced must be equal to the volume of the part of his body he had submerged. (This relation is "not" what is known as Archimedes' principle—that deals with the "upthrust" experienced by a body immersed in a fluid.) He then realized that the volume of irregular objects could be measured with precision, a previously intractable problem. He is said to have been so eager to share his discovery that he leapt out of his bathtub and ran naked through the streets of Syracuse.
Carantania
Another possible etymology is that it may have been formed from a toponymic base "carant-" which ultimately derives from pre-Indo-European root *"karra" meaning 'rock', or that it is of Celtic origin and derived from *"karantos" meaning 'friend, ally'. Its Slovene name was adopted from the Latin *"carantanum". The toponym "Carinthia" (Slovene: < Proto-Slavic "*korǫt’ьsko") is also claimed to be etymologically related, deriving from pre-Slavic *"carantia". The name, like most toponyms beginning with *Kar(n)- in this area of Europe, are in turn most likely linked to the pre-Roman tribe of the Carni that once populated the eastern Alps.