:::As for Brunellescchi, What and extraordinary engineer!  
 :::He obviously fully grasped the principals of Gothic ribbed vaulting, and then looked at those coffers in the Pantheon and saw exactly what they achieved: lightness and strength, very similar to a ribbed vault. (The Gothic vault compartments at Florence Cathedral are almost impossibly huge, so the impact of Ancient Roman structures had not been lost on Arnolfo (or whoever it was who designed those vaults.)  I must say that climbing up through the shells of that dome was a highlight of my life.