They were certainly capable of measuring the height. The tools have been known since antiquity. They couldn't build something like this without them.
And they were definitely competing with each other to build the tallest and most spectacular cathedral. There wasn't an official record book, but the architects were always aware of who was claiming to be tallest. If they didn't want to take the claim for granted, it was easy enough to go measure it yourself.
Just for one example: Ulm Minster was specifically designed to be taller than the one at Cologne:
It's actually a little ungainly-looking for that. The tower is out of proportion to the rest of it.
It wasn't just cathedrals. They were doing the same things with bell towers. The Leaning Tower of Pisa doesn't need to be that tall -- and if they'd built a more reasonably-sized tower, it would have been more stable.
Comments
They were certainly capable of measuring the height. The tools have been known since antiquity. They couldn't build something like this without them.
And they were definitely competing with each other to build the tallest and most spectacular cathedral. There wasn't an official record book, but the architects were always aware of who was claiming to be tallest. If they didn't want to take the claim for granted, it was easy enough to go measure it yourself.
Just for one example: Ulm Minster was specifically designed to be taller than the one at Cologne:
https://en.wikipedia.org/wiki/Ulm_Minster
It's actually a little ungainly-looking for that. The tower is out of proportion to the rest of it.
It wasn't just cathedrals. They were doing the same things with bell towers. The Leaning Tower of Pisa doesn't need to be that tall -- and if they'd built a more reasonably-sized tower, it would have been more stable.