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Perspective Geometry Philosophy

The three major arts, architecture, painting, and sculpture, entered among the liberal arts when their products were acknowledged as products of the intellect; arts that formerly were considered as mechanical or manuals. At that time, a breakthrough took place in painting; when perspective demonstrates how the physical world can be represented as naturally as it is perceived by the painter’s eye. Ever since the pictorial space was not any more symbolic; it transformed into a visual world of things seen or imagined. While in architecture, spaces that gives the impression of going beyond their real dimensions were literally built in perspective, like Bramante’s illusory apse in Santa Maria Presso di San Satiro. In sculpture, it suffices to mention the Gates of Paradise of Ghiberti, with its gilded bronze panels depicting biblical stories in perspective. Perspective was extensively practiced during the Renaissance, feeding the imagination of the artists toward new forms of expression, toward a new visual world. The historical line of perspective, as practice, can be traced through several cultures; among of which the early advanced manifestations are the frescoes of Pompeii. As theory, the Optics of Euclid is the first treatise dealing with the apparent size of objects, introducing the concepts of visual rays and cone of vision. During the Middle Age, when perspective was known as optics, new treatises on this subject were written, until the Renaissance brought into light a new generation of treatises devoted to the theory and practice of perspective as such. Since then, the long tradition of perspective keeps going nowadays.


Despite its long tradition, it is quite difficult to explain why perspective has not yet been recognized as an independent branch of geometry, as it should be. Instead, perspective is misconceived as part of other geometries that omit its long tradition as representation. In fact, perspective relates with other geometries, even with the Euclidean one, however, no other geometry but perspective alone can explain all the methods and techniques of representing space. In a broadest sense, all kind of perspective, such as linear, anamorphic, curvilinear, spherical, panorama, accelerated, illusory, quadratura, or any other; are based on theorems, postulates, and models, formulated since Alberti up to contemporary theorists. All this knowledge conforms a general theory of perspective, ever since studied up till now, a geometry that we may call: Perspective Geometry

Stained-Glass in perspective