One Ring to find them!

[rudeboy]

The verse "One ring to find them", from the Ring verse, suggests that with the Ruling ring Sauron should be able to find the other rings easily! Except maybe the 3, but only because they weren't tainted with his evil! Why then did he have to put Celebrimbor to torture to find them? Is it because no-one was wearing them at the time?

[Alatariel]

This is from "Of the Rings of Power and the Third Age" in The Silmarillion:
And while he wore the One Ring he could perceive all the things that were done by means of the lesser rings, and he could see and govern the very thoughts of those that wore them.

But the Elves were not so lightly to be caught. As soon as Sauron set the One Ring upon his finger they were aware of him; and they knew him, and perceived that he would be master of them, and of all that they wrought. Then in anger and fear they took off their rings. But he, finding that he was betrayed and that the Elves were not deceived, was filled with wrath; and he came against them with open war...But the elves fled from him; and three of their rings they saved, and bore them away, and hid them.
Skipping a bit...
But Sauron could not discover them, for they were given into the hands of the Wise, who concealed them and never again used them openly while Sauron kept the Ruling Ring.
I think that pretty well explains it - since the rings were concealed and never used while Sauron had the Ring, he could never discover them.

[Elrond of Rivendell]

I think the initial question of this thread concerned the other rings of power (the Seven and the Nine).

While it is clear that in the time of the War of the Ring, Sauron had a total power over all the Nine still existing, it may be that this power only developed after the forging of the One Ring, and did not appear simultaneously with it.
So, at the beginning, each person wearing a ring of Power would benefit of some timeframe, in which he/she would be still free of will. It may be that Sauron perceived this timespace as particularly dangerous, so he tried to accelerate his triumphating over the other Ring-bearers, e.g. by finding out their exact positions.

Greetings,
EfR