A possible connection between the Qur'an 17:22-36 and Noahide law might be:
# Qur'an 17:22 Avodah zarah - Do not worship false gods. (1st Noahide law)— [[Prohibition of Idolatry]] #1# Qur'an 17:23 Birkat Hashem - blasphemy. (5th Noahide law)— [[Prohibition of Blasphemy]] #2# Qur'an 17:32 Gilui arayot - Do not be sexually immoral (4th Noahide law)— [[Prohibition of Sexual Immorality]] #4# Qur'an 17:33 Shefichat damim - Do not murder. (2nd Noahide law)— [[Prohibition of Homicide]] #3# Qur'an 17:34 Dinim - Set up a system — [[Imperative of honest, effective courts, police and laws. (7th Noahide law)Legal System]] #7# Qur'an 17:35 Gezel - Do not steal or kidnap (3rd Noahide law)— [[Prohibition of Theft]] #5# Qur'an 17:36 Ever min ha-chai - Do not eat — [[Prohibition of any living animal (6th Noahide law)Limb of a Living Creature]] #6??? (although the last is specifically mentioned by the Qur'an 2:173; 5:3)
