2. The Angular Forms, including squares, oblongs, cubes, &c.

3. The Triangular, including zigzags, diamonds, &c.

4. The Circular, including all spots, discs, and radiations.

All these can be blended or mixed so as to form endless varieties. For instance, the square and the circle can intersect each other in different proportions, so as to give an entirely new effect to the pattern, each time the balance is altered or the phase of the repetition varied. The illustration will explain this. (Fig. [18].)

Right angles may intersect each other so as to produce the whole gamut of Chinese lattice-work decoration, and all the Celtic and Scandinavian entwined patterns, from which so many of the embroideries in the Italian pictures of the fourteenth and fifteenth centuries are probably descended.

The Moorish patterns are geometrical, and are created on the principle of avoiding in art the representation of any created thing. They show much ingenuity in keeping clear of any possible meaning. Most of these conventional patterns are founded on the ogee-arch and a kind of honeycomb pattern, involved and inverted. Their tiles, which nearest approach textile design, have, indeed, certain vegetable forms added to the others, but always geometrically arranged as no vegetables ever grew.

Geometrical patterns begin with primitive forms, and come down to the floor-cloth designs of to-day. They can be extracted in endless variety from the combinations of the kaleidoscope. This style is well suited for pavements in mosaic—either secular or ecclesiastical.

The Opus Alexandrinum furnishes us with most beautiful examples and adaptations for large or small spaces, so as to form the richest or the simplest floor decorations. How worthily a church may be thus adorned may be seen on the vast area of the floor of Santa Maria Maggiore in Rome, or that of the Church of St. Mark in Venice.

The nearest approach to the Opus Alexandrinum in textiles has been in Patchwork, of which a more artistic use may yet be made. We might exercise ingenuity in this direction, giving really fine and effective designs to our workers in patches, whose productions are, in general, simply alarming.

The fine quilting patterns of the sixteenth and seventeenth centuries are almost always geometrical, and make the best background to more resplendent embroideries overlying them, which is partly owing to their being only forms, and conveying no idea or inherited meaning. These expressionless designs are well fitted for spaces and borders in which the centres are elaborated, and require enclosing or framing; likewise, they are suited for large areas, which must not be perfectly plain, and yet not too disturbing to the eye, so as to distract it from the more important ornaments on the wall or ceiling. They suit carpets in passages or on staircases much better than any other kind of design, and form the best figured backgrounds for pictures. Both eye and mind often need repose, and therefore the simpler the geometrical pattern is, the better. Complicated and too ingenious combinations are painfully fatiguing. Simplicity and flatness are the greatest merits in such forms, as in shadowless patterns for textiles, and especially for embroideries.