A. In the mathematical-historical concept, the Marathon result, one of the fifteen decisive world battles, was due to the historical phase that the Greeks were developing, the era of great demographic fractionation in which nations are not conquered, the Persians met the mathematical-historical process in the phase known as military disaster, after having gone through its first period.
B. That of Arbella (331) which, along with the Battles of Granicus (334), Issus (333) and other strategic victories, constituted the second period of great victories of the Macedonian Empire of Alexander the Great. This battle of Arbella is part of the victory of Macedonia against Persia, an Empire going through a phase of decadence and disintegration. That is, an Empire undergoing expansion, Macedonia, fulfilling or developing the second aggressive process, against an Empire going through its last phase of disintegration: Persia.
It is a fact of the conquest and struggle of two Empires in the field of supremacy. It is the development of the historical process in which an empire substitutes another one and the battles that in succession form a set in order to fulfill the process, and not Arbella alone, that is: Granicus (334 B.C.), Issus (333 B.C.) and Arbella (331 B.C.).
The Battle of Metaurus, year 207 B.C., between the Romans and the Carthaginians is a precursor to the defeat of Hannibal in Zama. In the historical process: displacement of the creating force (strategic and not metaphysical concept), from the East to the West and from the South to the North, in the area adjacent to Europe, and in this continent, the chronological order of the development of the empires was as follows: Persia, Carthage, Macedonia, Rome, the Visigoth and the Teutonic Empires, this latter one in the Germanic area.
In this manner, the Roman Empire replaced the Carthaginian and Macedonian Empires. The Romans in the first period of great strategic victories, conquered Macedonia in the phase of decadence and disintegration, in the 1st, 2nd and 3rd Roman-Macedonian War, and reduced it to a Roman province (164 .B.C.). Likewise, Rome in the first period conquers Carthage, first in Metaurus and then in Zama.
The first battle mentioned, along with Zama, is responsible for the military disaster of the Carthaginian Empire. This Empire had a very short conservation phase since it had a long first period of great victories between 650-340 B.C., as a consequence, the result of the Battle of Metaurus was due to the phases of the two first Empires confronting each other, this articulated to the general process of displacement of the creative force of Rome vs. Carthage.
C. The Battle of Arminius (year 9 of our era), was that in which Hermann, digitized by the Germanics with the name of Irminsul and later Latinized into Arminius, defeated the Roman legions commanded by Quintilius Varus, at the Teutoberg Forest or Teutoburgiensis Saltus. The Roman Empire had fulfilled the process of the first period of great victories and, as the mathematics of history indicates, having accomplished these three phases, the Empire tries to extend its rule and is stopped by the so called military disaster phase.
On the enemy’s side, the Teutonics or Germanics were undergoing a period of great demographic fractionation, where, according to mathematical principles, people are not conquered but are rather absorbed by people unified into empires or nations. The mentioned mathematical-historical principle says that “Victory in the defense is a characteristic of Great Demographic Fractionation. Strategic victories are reserved to the successful defense, they are only obtained to execute the region’s defense. It is the defense and counter offense phase”.
Among those we have analyzed up to now in the mathematical-historical concept, Arminius is as much a battle for liberty as Marathon. Both battles are also decisive.
D. The battle of Châlons-Sur-Marne (451 B.C.) or the battle of the Catalunian Plains, was a victory over Attila, the King of the Huns. I should first explain that in the mathematics of history, the Roman Empire began in the year 270 B.C. and lasted up to 129 B.C. (a duration of 141 years), it had a Great Depression era from 129 to 59 B.C. (a duration of 188 years), a second period of great strategic victories from 59 B.C. to 161 A.D. (a duration of 102 years). The Empire’s total duration was 575 years.