The Geometry of Art and Life - Matila Ghyka | Ratio | GeometryMany have been drawn especially for this book. Introduction And it was then that all these kinds of things thus established received their shapes from the Ordering One, through the action of Ideas and Numbers. In the same way that Plato conceived the "Great Ordering One" or "the One ordering with Art," o as arranging the Cosmos harmoniously according to the preexisting, eternal, paradigma, archetypes or ideas, so the Platonic-or rather, neo-Platonic-view of Art con- ceived the Artist as planning his work of Art according to a pre- existing system of proportions, as a "symphonic" composition, ruled by a "dynamic symmetry" corresponding in space to musical eurhythmy in time. This technique of correlated proportions was in fact transposed from the Pythagorean conception of musical harmony: the intervals between notes being measured by the lengths of the strings of the lyra, not by the frequencies of the tones but the result is the same, as length and numbers of vibra In the same way Plato's Aesthetics, his conception of Beauty, evolved out of Harmony and Rhythm, the role of Numbers therein, and the final correlation between Beauty and Love, were also bodily taken from the Pythagorean doctrine, and then developed by Plato and his School. Let us point out at once that "symmetry" as defined by Greek and Roman architects as well as the Gothic Master Build- ers, and by the architects and painters of the Renaissance, from Leonardo to Palladio, is quite different from our modern term symmetry identical disposition on either side of an axis or plane "of symmetry". We cannot do better than to give the definition of Vitruvius: "Symmetry resides in the correlation by measure- ment between the various elements of the plan, and between each of these elements and the whole.
Book - The Painter's Secret Geometry a study of composition in art
The Geometry of Art and Life