Sauron didn't "Know to get Gollum;" Gollum walked into Mordor, driven there by his wickedness and enslavement to the Ring. Eventually he was caught, and imagineably, as the strange creature he was, the matter was told about to the higher authority. Besides the chance of orcs or whatever hearing him say something of the Ring, Sauron would certainly be able to recognize that Gollum had worn it; it was something Sauron himself forged, pouring much of his power into it.
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"He was sent by a mere prudent plan of the angelic Valar or governors; but Authority had taken up this plan and enlarged it, at the moment of its failure."
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