Final answer:
The quote from the Texas Constitution that supports both republicanism and popular sovereignty is 'All political power is inherent in the people,' reflecting the ideals of a republican government as defined by James Madison.
Step-by-step explanation:
In the context of the Texas Constitution, the statement that supports both republicanism and popular sovereignty is: "All political power is inherent in the people." This complements the republican belief system mentioned by James Madison, who stated a government is republican if it derives its powers from the people and is run by elected representatives. The quote from the Texas Constitution embodies this definition as it emphasizes the source of political authority resting within the people themselves, allowing for the election of their representatives and not a monarchy or a ruling class.