Extracts of : The Painter's Secret Geometry: A Study of Composition in Art. (Charles Bouleau)

In the artistic chaos of these last years, when the absolute liberation of the individual instinct has brought it to the point of frenzy, an attempt to identify the harmonic disciplines that have secretly, in every period, served as foundations for painting might well seem folly.

But this folly is in fact wisdom. It is the way to a kind of knowledge essential for whoever wants to paint. Essential, too, for whoever wants to look at pictures. The framework of a work of art is also its most secret and its deepest poetry.

Jacques Villon (1963)

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 savoir- faire which the budding artist must make haste to acquire. I found that these questions, when I tried to answer them, led far afield.
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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.

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Another construction derives so naturally from the rectangle: the rabatment of the small sides on the big. By placing the rectangle horizontally, the painters had to then, for reasons of balance, arrange a square to the right and the other one to the left, which naturally overlap partially. This very simple plan thus registers inside the frame two squares which cut themselves more or less as the rectangle is more or less long. These squares impose in turn their diagonals, which cross themselves by creating in the center a small square on the point the size of which varies with the stepping of two big squares, what creates very different combinations some of the others.
Sometimes, the lines of construction fade in front of orthogonal stemming from the summits of the small central square, which establish to them only a whole composition; sometimes still, these orthogonal create new lines of construction by their crossing with the diagonals of the square.
Finally, this plan can overlap in the diagonals of the rectangle, the intersection of which with the diagonals of squares still introduces variants.

Charles Bouleau

Giotto, Saint François

He makes spring the water of the mountain to quench a farmer.

The rabatment of the small sides of the rectangle is used here under its simplest form. The small central square on the point determines the position of the Saint. A side of the square gives the bottom of the saddle, a horizontal, to the intersection of diagonals, the height of the saddle. Two placed vertical lines too in intersections position trees. Obliques leaving a summit of the rectangle give the slope of the mountain and the figure...etc...

François Murez, Mont Blanc

The composition of this picture obeys the classic rules of the rabatment of the small sides of the rectangle.

rabatment on one side to form the square with its diagonals.

rabatment of the second side to form the second square

Display of the diagonals of the rectangle

Implementation of vertical lines and horizontal in the intersections of diagonals

Use of the anchorpoints of the vertical and horizontal to draw the other diagonals which bound elements of the picture

Other paintings of : Mont Blanc

Van Goyen, Landscape with 2 oaks (1641)

The composition of this picture also obeys the classic rules of the rabatment of the small sides of the rectangle.

Rembrandt, The 3 trees (1643)

The same composition as Van Goyen's picture meets itself in this engraving of Rembrandt. The light, however, is treated in contrast

Claude Lorrain (1604 – 1682), Landscape

A last example of an identical construction in this drawing of Lorrain. Three works of the same time and the same composition.

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Bibliography :
Charles Bouleau, The Painter's Secret Geometry: A Study of Composition in Art