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How did Napoleon’s victory at Rivoli lead to the surrender of Mantua?

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Napoleon I — French Revolutionary wars *Bonaparte on the Bridge at Arcole, 17 November 1796*, oil on canvas by Antoine-Jean Gros, 1796; in the Versailles Museum.

Napoleon’s victory at the Battle of Rivoli on January 14, 1797, was the decisive factor that led to the surrender of Mantua.

During this final Austrian attempt to break the Siege of Mantua, the Austrian forces were split: Baron Alvinczy descended the Adige River, while Giovanni di Provera advanced directly toward the fortress. Napoleon countered this by leaving a defensive screen to delay Provera and concentrating his remaining troops to rout Alvinczy’s main army at Rivoli.

Following this victory, Napoleon promptly regrouped his forces to intercept Provera, who had reached the outskirts of Mantua. Overwhelmed by these converging French forces, Provera was forced to capitulate on January 16. With the failure of these relief efforts and the destruction of the Austrian armies in the field, the garrison at Mantua was left without hope of rescue and surrendered on February 2, 1797, effectively completing the French conquest of northern Italy.1