Had the Austrian armies succeeded in invading France simultaneously, Bonaparte would have detached a containing force[3] against one army, and then have massed his remaining forces against the other. By repeating this manoeuvre, first against one army and then against the other, he would have attempted to defeat both. In this case, the Austrian armies would enter France from different directions; one from the east, the other from the southeast, separated by Switzerland and the French Alps; and since the French armies, even while falling back, would still be between the Austrian armies, Bonaparte would, from his central position, have the advantage of interior lines, and could rapidly combine his forces against his adversaries in succession. How well he would have succeeded in this manoeuvre can best be judged by what he accomplished by similar manoeuvres. In the Italian campaign of 1796-97, when the Austrians advanced against Bonaparte on both sides of Lake Garda, he united his forces at the foot of the lake; and, by throwing a strong force against one and then against the other of the advancing armies, defeated both in succession before they could unite. In these manoeuvres, with a total force of forty-five thousand soldiers, he defeated seventy-two thousand Austrians. In the campaigns of Arcole and Rivoli, the Austrians likewise advanced with divided forces. In the former, forty thousand Frenchmen opposed seventy thousand Austrians; in the latter, forty-four thousand Frenchmen opposed sixty-five thousand Austrians. By skilful combinations, similar to those just described, Bonaparte defeated the Austrian armies in both campaigns. In 1814, when the Prussians, under Blucher, and the Austrians, under Schwarzenberg, were advancing from different points of the French frontier upon Paris, the results obtained by Napoleon's leaving a retarding force before one army, and by massing his remaining forces against the other, were still more remarkable. With a force numerically inferior to either army opposed to him, he succeeded in winning battle after battle. Though in the campaign of 1814 we find strategical problems with which we are not now concerned, yet Napoleon's victories there in the face of such odds show what he might have accomplished had Kray and Melas crossed the French frontiers and advanced on Paris. But the combination that offered Bonaparte the greatest chance of success yet remains to be considered. Should Masséna be able single-handed to hold in check the Austrians in Italy, Bonaparte could unite the Army of Reserve, forty thousand strong, to Moreau's army of one hundred and thirty thousand. This junction would give Bonaparte one hundred and seventy thousand soldiers with whom to attack the one hundred and twenty thousand Austrians under Kray. With such a superiority in numbers, Bonaparte would probably have annihilated the Austrian forces in the valley of the Danube.