University of Virginia Library

OF FORMS.

If I am not mistaken, the principles of these, as of colours, are reducible to five, the line, triangle, circle, ellipse, and parabola.

The line generates all forms, as the ray of light does all colours. It goes on like the other, in its generations, step by step, producing first, by three fractions, the triangle, which of all others contains the smallest surfaces under the greatest of circuits. The triangle afterward, composed itself of three triangles at the centre, produces the square, which consists of four triangles from the central point; the pentagon, which consists of five; the hexagon, which consists of six; and so of the rest of the polygons, up to the circle, composed of a multitude of triangles, whose summits are at its centre, and the bases at its circumference: and which, contrary to the triangle, contains the greatest of surfaces under the smallest of peripheries. The form which has, hitherto, always been going on progressively, commencing with the line, relatively to a centre, up to the circle, afterwards deviates from it, and produces the ellipse, then the parabola, and finally all the other widened curves, the equations of which may all be referred to this last. So that, under this aspect, the indefinite line has no common centre: the triangle has three points in its bounding lines, which have a common centre; the square has four; the pentagon five; the hexagon six; and the circle has all the points of its circumference regulated conformably to one common and only centre. The ellipse begins to deviate from this regulation, and has two centres; and the parabola, as well as the other curves, which are analogous to it, have centres innumerable contained in their several axes, from which they remove farther and farther, forming something like funnels.

On the supposition of this ascending generation of forms,

from the line, through the triangle, up to the circle; and their descending generation, from the circle, through the ellipse, to the parabola, I deduce, from these five elementary forms, all the forms of Nature; as, with five primordial colours, I compose all the possible shades of colour.

The line presents the slenderest form, the circle the fullest, and the parabola the most obliquely fluted. In this progression, the circle, which occupies the middle between these two extremes, is the most beautiful of all elementary forms, as red in the most beautiful primordial colour. I presume not to say, that this form must be the most beautiful, because it is the figure of the stars, which, however, would be no contemptible reason; but, to employ only the testimony of our senses, it is the most grateful of both eye and touch; and the most susceptible of motion; finally, it is considered as most conformable to the taste of all nations, who employ it in their ornaments and architecture; and it is particularly conformable to the taste of children, who prefer it to every other, in the instruments of their amusement.

It is remarkable, that these five elementary forms have the same analogies to each other which the five primordial colours have among themselves; so that if you proceed to their ascending generation, from the sphere toward the line, you will have forms angular, lively, and gay, which shall terminate in the straight line. If, on the contrary, you descend from the sphere to the excavations of the parabola, you will be presented with a gradation of cavernous forms, so frightful in abysses and precipices.

Farther, if you join the elementary forms to the primordial colours, term for term, you will observe their principal character mutually strengthen each other, at least in the two extremes, and in the harmonic expression of the centre: for the first two terms will give the white ray, that of light itself; the circular form, united to the red colour, will produce a figure analogous to the rose, composed of spherical portions, with carmine tints, and, from the effect of this double harmony, deemed the most beautiful of flowers. Finally, black, added to the vacuity of the parabola, increases the gloom of retreating and cavernous forms.

With these fine elementary forms may be composed figures as agreeable as the shades produced from the harmonies of the five primordial colours. So that the more there shall

enter, into those mixed figures, of the two ascending terms of the progression, the more light and gay such figures will be; and the more the two descending terms shall predominate, the more heavy and dull will be the forms. Thus, the form will be more elegant, as the first term, the straight line shall have the predominance. For example, the column gives us pleasure, because it is a long cylinder, with the circle for its basis, and two straight lines, or a long quadrilateral figure, for its elevation. But the palm-tree, of which it is an imitation, pleases still more, because the stellated and radiating forms of its palms, likewise taken from the straight line, constitute a very agreeable opposition with the roundness of its stem; and if to this you unite the harmonic form by way of excellence, namely, the circular, you will add inexpressibly to the grace of this beautiful tree. This, likewise, Nature, who knows much more of the matter than we, has taken care to do, by suspending, at the basis of its divergent boughs, sometimes the oval date, and sometimes the rounded cocoa-nut.

In general, as often as you employ the circular form, you will greatly enhance the agreeableness of it, by uniting it with the two contraries of which it is composed; for you will then have a complete elementary progression. The circular form alone presents but one expression, the most beautiful of all, in truth; but united to its two extremes, it forms, if I may so express myself, an entire thought.

It is, farther, from these harmonies, that long ridges of mountains, overtopped by lofty peaks of a pyramidical form, separated by deep valleys, delight us by their gracefulness and majesty. If to these you add rivers meandering below, radiating poplars waving on their banks, flocks of cattle and shepherds, you will have vales similar to that of Tempe. The circular forms of the mountains, in such a landscape, are placed between their extremes, namely, the prominency of the rocks, and the cavity of the valleys. But if you separate from it the harmonic expressions, that is, the circular wavings of those mountains, together with their peaceful inhabitants, and allow the extremes only to remain, you will then have the dreary prospect of Cape Horn; angular, perpendicular rocks, hanging over fathomless abysses.

If to these you add oppositions of colour, as that of snow on the summits of the dusky rocks, the foam of the billows

breaking on the lurid shore, a pale sun in a gloomy sky, torrents of rain in the midst of summer, tremendous squalls of wind succeeded by sullen calms, a European vessel, on her way to spread desolation over the islands of the South Sea, running upon a rock when it is beginning to grow dark, firing from time to time guns, the signal of distress, the noise of which the echoes of those horrid deserts reverberate, the terrified Patagonian running in amazement to his cave; and you will have a complete view of that land of desolation, covered over with the shades of death.