By August 1805, Napoleon had realized that the strategic situation had changed fundamentally. Facing a potential invasion from his continental enemies, he decided to strike first and turned his army's sights from the English Channel to the Rhine. His basic objective was to destroy the isolated Austrian armies in Southern Germany before their Russian allies could arrive. On 25 September, after great secrecy and feverish marching, 200,000 French troops began to cross the Rhine on a front of 260 km (160 mi). Austrian commander Karl Mack had gathered the greater part of the Austrian army at the fortress of Ulm in Swabia. Napoleon swung his forces to the southeast and the Grande Armée performed an elaborate wheeling movement that outflanked the Austrian positions. The Ulm Maneuver completely surprised General Mack, who belatedly understood that his army had been cut off. After some minor engagements that culminated in the Battle of Ulm, Mack finally surrendered after realizing that there was no way to break out of the French encirclement. For just 2000 French casualties, Napoleon had managed to capture a total of 60,000 Austrian soldiers through his army's rapid marching. The Ulm Campaign is generally regarded as a strategic masterpiece and was influential in the development of the Schlieffen Plan in the late 19th century. For the French, this spectacular victory on land was soured by the decisive victory that the Royal Navy attained at the Battle of Trafalgar on 21 October. After Trafalgar, Britain had total domination of the seas for the duration of the Napoleonic Wars.
How many casualties did the French suffer at the Battle of Ulm?
2000