To succeed offensively in Italy, the Austrians had therefore to outnumber greatly the French. The French superiority in position counterbalanced the Austrian superiority in numbers. The Austrian plan allowed Bonaparte with inferior forces to hold in check for a time a large Austrian army in Italy, and left him free to direct his remaining forces upon the important points of the theatre of operations. By uniting the Army of Reserve with Moreau's army, he could outnumber his adversary in Germany; or by uniting the Army of Reserve with a corps of Moreau's army, he could descend upon the rear of Melas, and decide in a single battle the fate of Italy.
By remaining on the defensive in Germany, Kray gave Bonaparte the opportunity of taking the offensive there. This allowed him to make use of the angular base of operations formed by eastern France and northern Switzerland. Bonaparte, however, could derive no advantage from the angular base except by taking the offensive; for should he simply defend the line of the Rhine, he would be obliged to occupy both the Swiss and French sides of the river. In other words, he would be obliged to divide his forces, to lengthen and weaken his line, thus giving his adversary the opportunity either to defeat the French forces in detail, or to force a passage across the river at some weak point. Furthermore, it was important that Bonaparte should take the offensive for other reasons than those already given; for should he once force the position of the Rhine and Black Forest, he would find no other great natural obstacles in his front as he descended the Danube towards the Austrian capital.
Because the strong position of the Rhine and Black Forest is a long distance from Austria; because the more direct route between France and Austria is through the valley of the Danube; because no great natural obstacles, forming strong defensive positions, lie across this route near the Austrian capital; and because a French victory in the valley of the Danube would probably give the French commander an opportunity to make such dispositions as should paralyze the operations of an Austrian army in Italy,--it follows that the main effort for supremacy between France and Austria should take place in the valley of the Danube. There Austria should take the offensive; there she should show her full strength; there she should make one mighty effort to decide her own or her adversary's fate. "It is in the valley of the Danube," says the Archduke Charles, "that the blows are to be struck which are decisive of the fate of France or Austria."