The branch of Indo-European that became Greek had some changes that were much different from the changes that took place in the Germanic branch. Consequently, we may have words that bear no resemblence to each other that derive from the same Indo-European root. A fascinating pair are siren and quartz, which are the only English descendants of IE *twer-. *Twer- apparently meant to grasp or hold, or hard. In Greek mythology, a siren was a creature who grasped or enthralled. An American warning siren was named after the sirens in the Odyssey, inappropriately capturing the sense of the sound of the Siren's song, rather than the idea of enthrallment. Quartz is a slavic word, a variant of zwerg, which meant dwarf.(1) For some reason, the English word dwarf is not thought to be related.
1. Other central-european words derived from supernatural entities are cobalt, from Kobold (an imp) and nickel, from a word for goblin.