�Decadence and disintegration is the phase in which strategic offensives are useless to back up the continental or intercontinental empire. Effective strategic potentiality is effective for the imperial body or nation, but it is always useless for the second empire of the mathematical-historical cycle, that is, when the nation is about to go through the era of great demographic fractionation�. The Turkish Empire had gone through the phases of the first period of great victories (1250-1392), the great depression (1392-1422), second period of great victories (1432-1572) and was about to develop the phase of decadence and disintegration with a brief duration of the conservation phase. Although Lepanto was at the end of 1571 is it considered as the beginning of the phase of decadence.� H. The Battle of Valmy (September 28, 1792). The ethnic group of the Germanic area was undergoing the Great Demographic Fractionation era. France was ending its phase of Great Depression (1697-1793), in which, generally, the Empire is invalid in order to afterwards be able to expel the invaders. At the end of this phase, begins the second period of great victories in 1793. �Victory in the defense is a characteristic of the era of great demographic fractionation. Strategic victories are reserved for the defensive.� Successful offensive is only achieved in order to enforce the defense of the region.� It is the defense and counter-offense phase�. According to this mathematical-historical principle, the Germanic ethnic group did not have an offensive strategic ability.� On the other hand, France was about to end its second period of Great Strategic Victories.�� I. The Battle of Bailen (July 15, 1808).� The result of this battle was due to the independent value that territories in the historical process of the corresponding ethnic group have. An empire is developed, it expands towards its neighbors, when they are undergoing the depressive phase, but when they recover they expel the invader. There is no permanent occupation but it is rather temporary. Thus, there exists a historical force that provides unity and sovereignty to each geographical area, with its corresponding ethnic group. To the expansion of the French Empire in its second period of Great Victories, there follows a setback that is known as the Military Disaster, which was the Battle of Waterloo in the year 1815. Likewise, as in the French retreat from Spain, essentially marked by the Battle of Bailen. �Conservation is a phase of Empire maintenance. Any strategic operation in this phase should be closely analyzed, including the human means factor. Victories and defeats alternate with each other. It is more a phase of the defensive in the maintenance of conquered geographical regions of the imperial body�. This mathematical-historical principle was influential in the victory of Bailen.