Gandalf: the Unilateral Coalition Builder

[Boromir88]

So why didn't Saruman try to take it from him when he had Gandalf locked up in Orthanc?

Could it be as simple as the ring being invisible while on it's bearers hands? We see in the Mirror of Galadriel that Sam does not see Galadriel's ring on her finger, but Frodo does for he is the bearer of the one. Could it be that Gandalf's ring was also invisible on his finger, and that Saruman just forgot Gandalf even had a ring?

I wonder if another factor could be that Saruman made his own ring of power. While there is not proof that the ring ever did anything for him and it seemed like a failed attempt. He obviously kept it on his finger for some purpose.