Although the technology is 21st century, I can't help conjuring up Ken Follett's Pillars of Earth with its vivid descriptions of how early Gothic cathedrals were built, the experimentation, and the tragedies that happened along the way. I'm pretty sure that today's engineers have a better understanding of structural physics as well as more sophisticated technology to keep everything in place while the stone masons do their thing. And yet, tinkering with a massive hunk of stone is not for the faint of heart. Nor for the faint of pocket. The repair bills are in the multi millions.
Want to know more? Check out this fascinating Washington Post feature on the damage and techniques for repair. Really interesting even if you're not an engineer.