Short Answer 
A republic transitions from direct democracy by establishing a system where citizens elect representatives to make decisions on their behalf, promoting more efficient governance. It emphasizes proportionality and accountability, ensuring that elected officials reflect the interests of their constituents while maintaining the public’s trust in the democratic process.
Step 1: Transition from Direct Democracy
A republic begins by addressing the limitations of *direct democracy*, where every citizen votes on each issue. This system can lead to challenges in decision-making and can overwhelm citizens. In a republic, the focus shifts towards a more manageable governance structure, where citizens avoid the burden of agreeing on every decision.
Step 2: Establishing Representativeness
In a republican system, the government is formed through *representatives* who are elected by the citizens. This means that instead of every citizen participating in every decision, they vote for individuals who will represent their views and interests. This structure allows for more efficient governance and a voice for all constituents through their chosen representatives.
Step 3: Ensuring Proportionality and Accountability
A republic emphasizes *proportionality* by ensuring that elected representatives reflect the demographics and interests of the populace. This creates a government that is more responsive to the needs of its citizens. Furthermore, representatives are held accountable to their voters, ensuring that they act in the best interest of the public, fostering trust and maintaining democratic principles.