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The initial military maneuvers began in September 1806. In a notable letter to Marshal Soult detailing the plan for the campaign, Napoleon described the essential features of Napoleonic warfare and introduced the phrase le bataillon-carré ('square battalion'). In the bataillon-carré system, the various corps of the Grande Armée would march uniformly together in close supporting distance. If any single corps was attacked, the others could quickly spring into action and arrive to help. Napoleon invaded Prussia with 180,000 troops, rapidly marching on the right bank of the River Saale. As in previous campaigns, his fundamental objective was to destroy one opponent before reinforcements from another could tip the balance of the war. Upon learning the whereabouts of the Prussian army, the French swung westwards and crossed the Saale with overwhelming force. At the twin battles of Jena and Auerstedt, fought on 14 October, the French convincingly defeated the Prussians and inflicted heavy casualties. With several major commanders dead or incapacitated, the Prussian king proved incapable of effectively commanding the army, which began to quickly disintegrate. In a vaunted pursuit that epitomized the "peak of Napoleonic warfare," according to historian Richard Brooks, the French managed to capture 140,000 soldiers, over 2,000 cannons and hundreds of ammunition wagons, all in a single month. Historian David Chandler wrote of the Prussian forces: "Never has the morale of any army been more completely shattered." Despite their overwhelming defeat, the Prussians refused to negotiate with the French until the Russians had an opportunity to enter the fight.

 What river did the French cross to engage the Prussian army?
the Saale