The Early Italian Renaissance (Quattrocento)

Filippo Brunelleschi, a Florentine goldsmith and sculptor turned architect, is credited by his early biographer Antonio Manetti with formulating, around 1415-1420, the mathematical rules of linear perspective, a system for representing three-dimensional space on a flat surface using a single vanishing point toward which all orthogonal lines converge. Brunelleschi is said to have demonstrated the principle through two small painted panels, now lost, showing the Florence Baptistery and the Piazza della Signoria, viewed through a peephole and a mirror in a way that proved the mathematical consistency of his construction. Although the panels themselves do not survive, the theory they embodied was soon formalized and published by Leon Battista Alberti in his treatise "On Painting" in 1435, giving artists a replicable geometric method rather than an intuitive approximation of depth. Brunelleschi's other towering achievement, the dome of Florence Cathedral, completed in 1436 after he won a public competition with an ingenious design using a double shell and a herringbone brick pattern to rise without traditional wooden centering, demonstrated the same combination of mathematical rigor and technical inventiveness that characterized his perspective studies, and the dome remains, to this day, the largest brick dome ever constructed.