The mathematics of history is a human reality. We are facing an undeniable fact, the logical organization of the events of history, without a pure mathematics that is not derived from one that is integral or from a differential equation but, within the mathematical concept of applied sciences where pure results are not achieved with the �Standard Meter�, the model unit of measure that is in Paris that, although it is kept hermetically sealed, is always under the influence of that which is material.� Remembering one of Plato�s maxim: �Vital force has been given to us by God, so that, by observing the sky�s circular motion, we may apply it to the cyclical form of the kingdom of our own thoughts, for they both are their relatives, the difference being that ours are perturbed whilst theirs are free from all perturbation�. SOCIAL CYCLE At the beginning of the cycle we warned of a remarkable change.� The ancient nation reduced to a state of servitude has remarkably improved its position and already has a small participation in the harvest. From this moment on, its material and spiritual progress accentuates itself. Since the worker obtains a benefit from his work, his interest increases and, accordingly, improves his tools, worked more and production intensifies.� By this phenomenon repeating itself in all servants, the result is a general increase in wealth. Some more intelligent or more active, specialize. This is how trades are born. The use of money is extended.� Thus, wealth, which was then motionless in the hands of the dominating class, can pass on to the servile class and, a minority, made up of the most intelligent, active or fortunate, begins to become wealthy. With this, there appears a new wealthy aristocracy. We observe that the ancient division of society changes, giving room so that part of the ancient servants go on to constitute a middle class. One of these minorities, already wealthy, will make up the new aristocracy of wealth or high middle class. Very soon, the high middle class will not be happy with its wealth and will want to invest in city governments. From this moment on, the struggle between the new aristocracy and the old one begins.� This struggle will also follow a law, which is the one we know as �The Law of two steps forward and one step backwards� or Oscillating Law. In this struggle, the new aristocracy is supported by the nation from where it came. Four centuries after the beginning of the cycle, the new aristocracy is the winner and the government of the city is turned over to it. At this time, the middle class or petit bourgeoisie, has organized in unions or trades, and also wants its place in the government. One new struggle begins between these classes and the high middle class, and through successes and reversals, always obeying the oscillating law, the petit bourgeoisie finally joins the city governments.