Upon his arrival at Milan a threefold problem confronted Bonaparte. His object was to prevent the escape of the Austrians, to preserve his communications with Switzerland, and, in case of an Austrian attack, to make a quick concentration for battle. The skill with which he solved this complex problem will become apparent, if we turn to the map and study the positions of the French forces immediately after the arrival of Moncey's corps. These forces numbered fifty-five thousand men. Thirty-two thousand were stationed along the Po from Placentia to the Stradella Pass on the great highway leading from Alessandria to Mantua; ten thousand were stationed on the Ticino; ten thousand on the Adda; and three thousand at Milan. Thus it will be seen that these forces were occupying the sides of the triangular space enclosed by the Ticino, the Po, and the Adda; and that they held possession of all the roads leading from the Alps to the Austrian base of operations on the Mincio. The ten thousand men on the Ticino not only protected the Italian entrance to the St. Gothard on the west side, but they were in a position to dispute the passage of the Ticino, should Melas cross to the north side of the Po and attempt to reach Mantua by way of Pavia and Milan. In the event that Melas should adopt this plan, the resistance that these ten thousand men could offer him would give Bonaparte time to unite all his forces for battle on the north side of the Po. The thirty-two thousand men on the south side of the Po closed with a barrier of steel the great highway leading from Alessandria to Mantua. On this road they had fortified a camp at the Stradella; and across the Po they had constructed five bridges, which would enable Bonaparte, in an emergency, to recross the river rapidly with these troops. The ten thousand men along the Adda not only covered the Italian entrance to the St. Gothard on the east side, but they were in a favorable position for holding in check Vukassovich's corps, should it attempt to march westward to the relief of Melas. It will be observed, too, that, should Melas attempt to escape by marching to Genoa, and thence to Mantua by way of Bobbio and Placentia, the French forces about Placentia and along the Adda could delay the progress of the Austrians long enough for Bonaparte to concentrate all his forces against them. Occupying a triangle in the heart of northern Italy, the French corps and divisions supported one another. In a few hours Bonaparte could concentrate nearly the whole of his army on the Po, on the Ticino, or on the Adda. In this position he held complete possession of the Austrian communications, and had his own with Switzerland strongly guarded. In this position he could concentrate quickly, and fight with nearly every advantage in his favor.