Final answer:
James Madison and Alexander Hamilton espoused a republican government in which powers are derived from the people, represented through elected officials, and balanced across separate branches. The concept of checks and balances alongside descriptive representation and enumerated powers were foundational to the structure of the American government.
Step-by-step explanation:
The quote from Alexander Hamilton in Federalist No. 17 speaks to the structure of government and the principle of republicanism as envisaged by the framers of the Constitution. In a republic, the power of self-defense is critical for each branch to maintain a balance and to prevent any one branch from dominating the others. This idea of checks and balances is further elaborated by James Madison, who emphasizes that a republican government must derive powers from the people and be accountable through elections and standards of behavior. The legislative authority, while predominant, must be divided, and the American federal system provides a double security for the rights of the people by dividing power between two levels of government and within each through separate departments.
Furthermore, descriptive representation and enumerated powers are concepts inherent to American republicanism. Descriptive representation involves legislatures reflecting the demographics of their constituencies, while enumerated powers are explicitly granted to the federal government by the Constitution. James Madison and other founders believed in constructing a government that integrates these core principles, with the aim of securing justice and countering the possibility of majority factions oppressing minorities. This is achieved by structuring a federal system that represents diverse interests and the societal division, ensuring the protection of rights for all groups within the republic.