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500 Years Later, Scientists Prove That Leonardo da Vinci’s Bridge Design Works
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To construct it they would have had to build a support structure nearly a thousand feet long, across a river, that could take the weight of a masonry arch bridge nearly a thousand feet long until the keystones could be put in. Not hard to imagine why it got rejected.
That was basically just the process of creating bridges back then, it's not far off from how it works today...
I don't think that was an avoidable issue, you need to build temporary support structures while bridge building is in progress. In other words, if an extensive support structure is a deal breaker for you, it turns out you're not building a bridge today.
Sure, but think of the scale of what they would need and the technology they had. 1000 feet long and as tall as a ship, carrying a stone structure that would weigh probably hundreds or thousands of tons, across what I'd imagine was a pretty busy waterway.