How did Machiavelli distinguish monarchies from republics?

In the political thought of Niccolò Machiavelli, the traditional classical tripartism—which categorized governments as monarchy, aristocracy, or democracy—was replaced by a fundamental dichotomy between princely rule and republican rule.1

Machiavelli distinguished these two forms based on the location of sovereignty:

• Monarchies (or Principalities): Sovereignty is vested in the hands of a single ruler. In his analysis, Machiavelli focused on how such rulers acquire and maintain power, often emphasizing the necessity of relying on one's own arms and the strategic use of virtù to command fortune.12
• Republics: Sovereignty is vested in a plurality or collectivity of power holders. Machiavelli reduced the classical categories of aristocracy and democracy into this single republican classification. In his work, particularly the Discourses on the First Ten Books of Livy, he explored how republics preserve liberty and transform human ambition into a stable political community, often highlighting the importance of civic virtue.1345

While Machiavelli is often associated with the amoral exercise of power in principalities, he also demonstrated a deep, idealistic commitment to the republican tradition, viewing it as a means to combat corruption and foster the common good.36