In the Prince, Machiavelli's first chapter is extremely short, addressing two simple ideas: (1) his ideation of the number of principalities in existence and (2) how these principalities are acquired. States and powers are what Machiavelli introduce as having rule over men. It's interesting that he separates states from powers as the modern theoretical paradigm conceives states in terms of power, in other words, power is a descriptor states, not a competitor of the same. Of these rulers of men, Machiavelli conceives republics and principalities.
This concept of states and powers having rule over men actually competes with modern conceptions of rule as, to the United States of America as an example, rule is held by the people. As a result, the state is itself, the people which it rules.
Machiavelli addresses republics in another work but, fittingly, he addresses principalities in this work. He argues that principalities can be hereditary in nature, with a heritage of rule or it can be new with little history of responsible rule. What is interesting is that he does not distinguish between what constitutes a hereditary principality or a new principality. So readers are left to determine for themselves what actually constitutes a hereditary principality which can range from two rules to ten. However, it can be agreed that a family that has never ruled before constitutes a new principality.
Machiavelli uses Francesco Sforza as the example of "an entirely new" principality in his acquisition of power in Milan. Indeed, Sforza was recognized as the ruler among the people that he ruled but he would never be recognized as the legitimate Duke of Milan, rather, it would not come until Sforza's son, Ludivico would ascend the throne. After his accession of power, the Holy Roman Emperor recognized him as the Duke of Milan and it wasn't until then that more of states recognized Milan.
Machiavelli uses the, then, Kingdom of Spain and the annexation of the Kingdom of Naples as the example of a hereditary empire. Naples was acquired by Spain as a result of the death of their king.
Machiavelli speaks of individuals that are accustomed to living under the rule of a prince or that live in freedom. This is a somewhat interesting dichotomy that he draws as there is no middle-ground for Machiavelli. For those that live in democracies today, one might assume that they live in freedom but in Machiavelli's eyes it would be viewed as living under the rule of the prince. In this case, the prince would actually be the state, characterized as the people but, the people are not entirely free.
It would also be interesting to explore exactly how freedom is defined by Machiavelli. It may be that things like the Bill of Rights that Americans treasure are actually not allowances for people to live in freedom but possibly limitations on freedoms. This is because, in the U.S., the Supreme Court or, part of the state, actually has the interpretive voice of what these freedoms mean so, in a sense, they are not freedoms at all but rather, limitations.
The acquisition of the states or principalities, Machiavelli mentions, are acquired by the arms of the prince or of others or by fortune or ability. Now we are introduced to two conceptions of a principality and four ways that principalities can be acquired.
The arms of the prince
The arms of others (and the prince's)