The Painter's Secret Geometry: A Study of Composition in Art
Book by Harcourt, Brace & World, 1963

INTRODUCTION
After gazing for a long time at the Death of Sardanapalus in the Louvre and making some notes on its composition, I was rash enough to pursue this line, turning to the Entry of the Crusaders into Constantinople, the Massacre of Scio, the Women of Algiers. This research and the pleasure it yields had taken hold of me. After Delacroix came Poussin and Cézanne; then David and Seurat... It was the beginning of five years spent in questioning hundreds of artists through thousands of canvases. This book is not a treatise on painting. It is a study of the internal construction of works of art, a search for the formulae that have guided, over the centuries, the distribution of the various plastic elements. The framework of a painting or carving, like that of the human body or that of a building, is discreet; sometimes, indeed, it makes one forget its existence; but it cannot be absent, for it is what gives a work of art those 'principal lines' of which Delacroix speaks in his Journal.

Throughout the book I shall always try to look at the paintings in question in my capacity as a painter. I shall be searching for the genesis of the work rather than for the secrets of its formal beauty. I shall try always to resist the temptation to find the criterion of aesthetic value by applying some favoured formula; not being either a mathematician or a philosopher, I shall never attempt to prove that a work of art is a paragon of beauty simply because it may fit some highly exacting and scientific schema. Nor is this book a history of composition. I shall take certain liberties with the time sequence. Due weight must be given to certain resemblances, resulting from affinities between artists of different periods: as in the case of Cézanne, Delacroix and Rubens. Conversely, in order to follow the use of geometrical figures (or of some other compositional device) through the centuries, I shall be obliged to treat certain painters in several chapters, under different headings. In spite of all this, the chronological order will often come to the fore, reflecting as it does the movement of ideas and the fact that every artist is at the start a pupil.

We shall find, as we go along, that there are many valid solutions to the problem of the distribution of forms within a work; we shall recognize, too, that artists like change, follow fashions and are subject to currents of taste. In the midst of all these fluctuations we shall come across fixed points: the books on painting. The venerable treatises by Cennino Cennini, Piero della Francesca, Leonardo da Vinci, Alberti, Dürer and Lomazzo, the relevant passages in the writings of Delacroix and others less well known, will guide us in our search and will steady us, forcing us constantly to put the artist back into the atmosphere of his own time. What is the art of composing a picture, and why, as a student, was one told so little about it? Is it a matter of instinct and flair? Some people assure us, nonetheless, that an extremely subtle and secret mathematical science lurks underneath the apparent spontaneity of the masters. Others, it is true, state that it is only a false science, a few tricks, a kind of savoirfaire which the budding artist must make haste to acquire. I found that these questions, when I tried to answer them, led far afield. To begin with, the complexity of the subject is great: the organization of plastic ideas is a response to needs that are not confined to the domain of painting. The requirements of monumental art have to be taken into account in any work of large dimensions, in painting and in decorative sculpture as in architecture. Then there is the effect of the picture-frame on its contents--an effect which, though it remains very general, has a determining influence on the way the painted surface is organized, engendering in it geometrical figures that are often highly complex.

The evolution of ideas and forms in the course of time plays a greater part than the quite abstract requirements just mentioned. There is a geometry of the Middle Ages. It has its own peculiar features, and it disappears with the civilization that was expressed in it. The more and more complicated figures traced with the compasses are in due course abandoned, and at the beginning of the Renaissance an aspiration towards simplicity and an intense dislike of overloading create the conditions favourable to a new enthusiasm--the enthusiasm for applying to the plastic arts relationships of musical origin, whose philosophical beauty had already been praised by Plato in the Timaeus. These relationships were first studied by theorists and then applied by architects; but the painters were not slow to lay hold on them; and they constitute an essential element in the style of the Italian Renaissance. There is more than one way, however, of using musical relationships: starting from them, one can create a disequilibrium, a swinging movement which, much admired during the Baroque period, gave them a new life at the very moment when they were about to fall into disuse. But the Middle Ages were not completely dead--not everywhere. The taste for geometry persisted, though simplified; circles and arcs of circles, even the golden section, were still used; and the simple but imperious action of the rectangular shape of the picture continued to exercise its effect through changing fashions and styles. This form, of itself, creates a division of the contents, which may be either a discreet indication or a rigid discipline. A painting is not simply a plane surface; it undertakes the conquest of space, and the different stages of its conquest are bound, in their turn, to be expressed in the composition: there is the conquest by means of geometry in three dimensions, and also the conquest by means of light and shade. The progress of this leads to a plastic art of illusion obeying the same laws of stability and weight as the real. It is characteristic of contemporary painting that in it each one of these methods of composition triumphs in its own right, as though all that till now was jumbled together were suddenly revealed in its pure state.

And to this analytical activity in painting today a book like the present one surely, in its way, bears witness.