Milan
During Da Vinci's career as a military engineer in Milan, Da Vinci designed a easy to build footbridge to be used by the Milanese army. This was just one of many designs that Leonardo created during his time as a military engineer under Duke Sforza.
“Leonardo Da Vinci: Self-Supporting-Bridge.” Leonardo3, Leonardo Museum, www.leonardo3.net/en/l3-works/machines/1355-self-supporting-bridge.html.
Venice
Venice is where Leonardo created his designs for the Golden Horn bridge after Leonardo returned from the French incasion of Milan in 1499. He heard of the bid for the bridge from Turkish merchants in Venice at the time. Leonardo used his previous knowledge of geometry to design the bridge, including the parabolic curve, pressed bow, and keystone arch to stabilize the bridge despite it not having support beams.
Golden Horn
This is the location of Da VInci's Golden Horn bridge design. The design was requested by Sultan Bayezid II to connect Instanbul to Galata. The city was taken from Byzantium in 1453, and the Ottomons were adding more infrastructure to the city. The location of the bridge would probably be where the modern bridge called Halic on the map below is located. This would not connect Europe and Asia, but simply Instanbul with its neighboring town. Leonardo’s design was not selected as he provided only the designs and no instructions on how to build it.
MIT
In October 2019, engineers at MIT decided to test DaVinci’s design with a scaled model. The team built a model with a 1:500 scale, resulting in a 32-inch model. The model used materials that the engineers assumed would be used, such as stone and lacked the use of mortar. The engineers concluded that the design would have worked and would have been capable of surviving even earthquakes, but do not know how much of it was intentional and how much was pure coincidence of his choice. Either way, this demonstrates Leonardo’s understanding of geometry.