What the nine rings and the seven rings look like?

[Joy]

Gandalf's ring was Narya, the Ring of Fire. It had a red stone. There is less description of his ring than of the others. It was given to him by Cirdan the Shipwright.

Galadriel's ring was Nenya, the Ring of Water. It was also called the Ring of Adament, which is represented by a Diamond.

Elrond's ring was Vilya, the Ring of Air. It was called the Ring of Sapphire also. It was given to him by Gil-galad.

I have read somewhere that the Elven rings Narya and Vilya were both given to Gil-galad and he then gave them away, to Cirdan and to Elrond respectivly. Then Cirdan recognizing who Gandalf was, a Maia of highest wisdom, then gave Narya to him. Could somebody correct me if I am wrong.