Hundreds of million of people around the world already knew what Vita means before the PSV even existed. The word is used in many languages, it's part of e.g. the term Curriculum Vitae (better known as CV).
It's not derived from modern Italian, but already centuries ago from Latin.
Vita has been used as part of brand names for ages, today you can find it in e.g. Vitasoy (Hongkong), Vitakraft, Vitamalz (both Germany), Opel Vita (that's the name of the Corsa in Japan), Vita Foods etc. I've also seen pharmacies named Vita (which makes sense).
In European literature, there's also the centuries-old use of the term Vita to describe a famous or ficticous person's life. Today, at least in Germany, the term is still occasionally used in e.g. Feuilleton articles (Feullieton is the literature and arts section of German newspaper - you see, we use French foreign words as well).
I always liked the word Vita, but I still think it's a lame name for a gaming device.










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