K. The Battle of Orleans (May 7, 1942). At this time, the English and French were undergoing an era of Great Demographic Fractionation, and, according the mathematical-strategic concept, England did not have a strategic offensive capacity and, as we have already seen: “Victory in the defense if a characteristic of the era of great demographic fractionation. Strategic victories are reserved to the defensive. A successful offensive is only obtained to enforce the defense of the region”. It was thus impossible to detain the French mathematical-historical process.
The destruction of the undefeatable Armada of Phillip II in the year 1558. The Spanish Empire was at that time in the first period of great strategic victories (1479-1643). However, England was in an era of Great Fractionation and soon to begin the year 1783, year in which that phase was to end. We already know by the mathematical-historical principles of the characteristics of nations during that era and, in this case, furthermore, the advance of the creative force, developing, in chronological order the Turkish, Spanish, British Empires and the Federal Republic of Germany, and this second cycle of Europe and its adjacent area.
This is then the mathematical-historical reason for the result of this Battle, the truth and its pure cause.
L. The Battle of the Boyne (July 1, 1690). The British Empire was in the phase of the first period of Great Victories (1609-1783) and so was the French Empire, but the phase was coming to an end, so that in 1697 the Great Depression ended. The reason for the result of this Battle is that the phase which the English were undergoing, has as a characteristic, the unification of the geographical area with ethnic groups, that is, Great Britain. In this manner, then, the mathematical-historical process of the era of Unification in its second cycle of 1,700 years, had begun in the year 1609 to end various centuries later, estimated to be five or five and one-half centuries later.
M. The Battle of Syracuse (year 413 B.C.). In this Battle the Syracusans defeated the Athenians. The reason for this was that Athens was in the year of Great Demographic Fractionation, in its first mathematical-historical cycle, and by concept and principle, nations in this phase do not have a strategic offensive capacity to conquer, occupy and overcome. The Italian nations were also developing the era of great fractionation of the first mathematical-historical cycle of Europe.
The term “decisive battles” is a very broad concept. It must be determined if they are decisive in a war between empires, nations in conquest, or liberty of a continent or geographical areas, that make up large or medium spaces.
The battles in the 1st or 2nd period of Great Victories are, in their majority, decisive in the conquest of an empire or nation. Also in the phase of great depression, whether to occupy or to expel the enemy. Likewise in the military disaster, if it is one sole battle or the last one, if they are various from one or another part of the adversaries. In the phase of decadence or disintegration, the first battle that is fought indicates the beginning of the phase, and the last one, marks the end of the empire.
Lastly, in the phase of relative independence, the last one is the decisive battle to begin the phase and that provides liberty to the country. Man is the expression of the historical phase, battles are historical events that express said phase and they form the whole of the nation’s process. Everything is continuity in time and in space. Everything is decisive in the thread of the historical process.
In the field of Operational Strategy battles would be defined by the three Clausewitz rules: “The concentration of effort, the strong man’s actions and the decision for the battle in the principal theater of operations”.
In the area of National Strategy, High or Grand Strategy, its definition is given with precision, the mathematical-historical concept, the mathematical-historical principle and the mathematics of history, as has been exposed and analyzed in this modest work.