The geometrical plane figures which play the most important part in architectural proportion are the square, the circle and the triangle; and the human figure is intimately related to these elementary forms. If a man stand with heels together, and arms outstretched horizontally in opposite directions, he will be inscribed, as it were, within a square; and his arms will mark, with fair accuracy, the base of an inverted equilateral triangle, the apex of which will touch the ground at his feet. If the arms be extended upward at an angle, and the legs correspondingly separated, the extremities will touch the circumferences of a circle having its center in the navel (Illustrations 45, 46).
[Illustration 50]
The figure has been variously analyzed with a view to establishing numerical ratios between its parts (Illustrations 47, 48, 49). Some of these are so simple and easily remembered that they have obtained a certain popular currency; such as that the length of the hand equals the length of the face; that the span of the horizontally extended arms equals the height; and the well known rule that twice around the wrist is once around the neck, and twice around the neck is once around the waist. The Roman architect Vitruvius, writing in the age of Augustus Cæsar, formulated the important proportions of the statues of classical antiquity, and except that he makes the head smaller than the normal (as it should be in heroic statuary), the ratios which he gives are those to which the ideally perfect male figure should conform. Among the ancients the foot was probably the standard of all large measurements, being a more determinate length than that of the head or face, and the height was six lengths of the foot. If the head be taken as a unit, the ratio becomes 1:8, and if the face—1:10.
Doctor Rimmer, in his Art Anatomy, divides the figure into four parts, three of which are equal, and correspond to the lengths of the leg, the thigh and the trunk; while the fourth part, which is two-thirds of one of these thirds, extends from the sternum to the crown of the head. One excellence of such a division aside from its simplicity, consists in the fact that it may be applied to the face as well. The lowest of the three major divisions extends from the tip of the chin to the base of the nose, the next coincides with the height of the nose (its top being level with the eyebrows), and the last with the height of the forehead, while the remaining two-thirds of one of these thirds represents the horizontal projection from the beginning of the hair on the forehead to the crown of the head. The middle of the three larger divisions locates the ears, which are the same height as the nose (Illustrations 45, 47).
Such analyses of the figure, however conducted, reveals an all-pervasive harmony of parts, between which definite numerical relations are traceable, and an apprehension of these should assist the architectural designer to arrive at beauty of proportion by methods of his own, not perhaps in the shape of rigid formulæ, but present in the consciousness as a restraining influence, acting and reacting upon the mind with a conscious intention toward rhythm and harmony. By means of such exercises, he will approach nearer to an understanding of that great mystery, the beauty and significance of numbers, of which mystery music, architecture, and the human figure are equally presentments—considered, that is, from the standpoint of the occultist.
V
LATENT GEOMETRY
[Illustration 51: THE HEXAGRAM AND EQUILATERAL TRIANGLE IN NATURE]
It is a well known fact that in the microscopically minute of nature, units everywhere tend to arrange themselves with relation to certain simple geometrical solids, among which are the tetrahedron, the cube, and the sphere. This process gives rise to harmony, which may be defined as the relation between parts and unity, the simplicity latent in the infinitely complex, the potential complexity of that which is simple. Proceeding to things visible and tangible, this indwelling harmony, rhythm, proportion, which has its basis in geometry and number, is seen to exist in crystals, flower forms, leaf groups, and the like, where it is obvious; and in the more highly organized world of the animal kingdom also; though here the geometry is latent rather than patent, eluding though not quite defying analysis, and thus augmenting beauty, which like a woman is alluring in proportion as she eludes (Illustrations 51, 52, 53).
[Illustration 52: PROPORTIONS OF THE HORSE]