My grandmother's mother is my "great grandmother," so my great grandmother's mother is my "great great grandmother"? Is that right?

My great-great-great-grandfather was a pirate.

The vase which Mary accidentally dropped and smashed had belonged to Tom's great-grandmother. It had been a family heirloom.

My great-grandmother was born in the nineteenth century.

This tree was planted by Tom's great-grandmother.

This is my great-grandfather.