points out two mechanical ways of juxtaposing form to create a painting: (1) either by reproducing the initial form (employing various symmetries such as reflectional, rotational or translational), or by modifying (or not) its dimensions. (2) By displacement of the initial form; pivoting around an imaginary axis in one direction or another. The choice of position (through translation and/or rotation), though based on the inspiration of the artist, is no longer attributed to the anecdotal. An objective and rigorous method, independent of the painter, replaces emotion or sensibility in the determination the placement of form, that is through translation and rotation. Schematic illustrations: Space and rhythm, according to Gleizes, are perceptible by the extent of movement (displacement) of planar surfaces. These elemental transformations modify the position and importance of the initial plane, whether they converge or diverge ('recede' or 'advance') from the eye, creating a series of new and separate spatial planes appreciable physiologically by the observer. Another movement is added to the first movement of translation of the plane to one side: Rotation of the plane. Fig. I shows the resulting formation that follows from simultaneous movements of rotation and translation of the initial plane produced on the axis. Fig II and Fig. III represent the simultaneous movements of rotation and translation of the rectangle, inclined to the right and to the left. The axis point at which movement is realized is established by the observer. Fig. IV represents the simultaneous movements of rotation and translation of the rectangle plane, with the position of the eye of the observed displaced left of the axis. Displacement toward the right (though not represented) is straightforward enough to imagine. With these figures Gleizes attempts to present, under the most simple conditions possible (simultaneous movements of rotation and translation of the plane), the creation of a spatial and rhythmic organism (Fig. VIII), with practically no initiative taken on the part of the artist who controls the evolutionary process. The planar surfaces of Fig. VIII are filled with hatching espousing the 'direction' of the planes. What emerges in the inert plane, according to Gleizes, through the movement followed by the eye of the observer, is "a visible imprint of successive stages of which the initial rhythmic cadence coordinated a succession of differing states". These successive stages permit the perception of space. The initial state, by consequence of the transformation, has become a spatial and