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Bramante applied the Vitruvian circle inscribed with a square to his church designs to emphasize harmony and proportion, reflecting the Renaissance revival of classical ideals. This geometric relationship symbolizes the unity of the spiritual and earthly realms, aligning with the principles of Vitruvius, who advocated for the importance of symmetry in architecture. By integrating these shapes, Bramante aimed to create a visually balanced and aesthetically pleasing structure, most notably seen in his design for St. Peter's Basilica. This approach underscored the Renaissance belief in the mathematical foundations of beauty and order in art and architecture.

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