Why exactly is the Latin language used for magical spells/incantations and insgesamt in arcane magic especially?

Magic is a fantasized version of medival scholars who would have studied math, science, and engineering in Latin oder Greek. It's simply a reference to that

I've always been under the impression that it's because magic is an ancient art. Old world stuff that has been forgotten and so most of it is written in ancient tongues, because that's when it was prevalent.