Beeing invisible was a side effect of the ring. Remember that it was "invented" in "The Hobbit" which it was a rather childish (I mean for children, not naive) book. So that property of the ring existed before the emerging of the others and could not be changed by Tolkien. It was a lesser, but inevitable to mention power of the ring. Could anybody think that Sauron had any need to be invisible? Remember he was a spirit "dressed" with shape. So the One HAD to make you invisible just because it was written so in "Hobbit". As for the other rings it doesn' matter. It' unworthy to mention
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