Final answer:
The specific precious stones inset in the sword of Gryffindor are not detailed in the Harry Potter series. Historical parallels suggest rubies, emeralds, or garnets could be imagined as part of the sword's design.
Step-by-step explanation:
The precious stones that are inset in the sword of Gryffindor from the Harry Potter series are not specified in the books or films. However, when looking at historical artifacts that contain precious stones and the skill of metal workers, one could imagine that the sword might have contained stones such as rubies, emeralds, or garnets. These stones were commonly used in historical treasures to signify nobility, strength, and valor, which are attributes befitting the sword of Gryffindor.