Did you ever pause to consider that parable and parabola come from the same root? I don’t think I’ve ever really thought about it, until my husband brought it up the other day. He was talking about parables and used the adjective parabolic to describe it…and then paused and said, “Huh, that’s usually just used in the mathematical sense, but I bet parable and parabola are actually related, don’t you think?” I did! And they are.
Both words are from the Greek parabolē, which means “a comparison,” literally “a throwing beside” or “a juxtaposition.” The word moved from Greek to Latin and hence down the line into the Latinate languages. Interestingly, common (vulgar) Latin even adopted it to mean “word,” which is where we ultimately get parler in French for “to speak.” In English, the word parable has been used to describe stories with a lesson since the 1200s.
Now parabola, the mathematical term used to describe the open bell-like curve formed when a plane cuts through a cone on an angle parallel to one side. It was named by Apollonius in 210 BC, but at the time it was the same Greek word used for the stories, since it was a juxtaposition, a throwing beside of a plane and a cone. Keeping in mind that mathematical terms were still presented in their original Greek and Latin for quite a lot of modern history, it’s not then surprising that our English word parabola–spelled with a different ending to differentiate it from the “story” meaning–dates only to the 1570s. The concept is of course far older, but the date is for the word itself as an English word.
As for parabolic, it was actually used to mean “figurative, pertaining to a parable” from the mid-1500s and didn’t get applied to the mathematical shape until the 1700s. So totally fine to use that one either way. 😉