How did Raphael use linear perspective in The School of Athens?

In The School of Athens, Raphael employs linear perspective to create a sense of majestic order and spatial depth within a two-dimensional fresco.1

He defines the architectural setting using pilasters and barrel vaults that recede toward a single vanishing point. By utilizing this mathematical system, Raphael establishes a stable, structured environment that guides the viewer's eye through an interweaving pattern of figures. This arrangement ultimately draws focus to the central figures of Plato and Aristotle, who are positioned precisely at the converging point of the perspectival space.1

This technique allows Raphael to achieve a balance between the complex, varied poses of the philosophers and the grand, architectural clarity of the scene, effectively synthesizing the intellectual themes of the work through its spatial composition.1