Read Ebook: The Beautiful Necessity Seven Essays on Theosophy and Architecture by Bragdon Claude Fayette

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This law of sex-expressiveness is of such universality that it can be made the basis of an analysis of the architectural ornament of any style or period. It is more than mere opposition and contrast. The egg and tongue motif, which has persisted throughout so many centuries and survived so many styles, exhibits an alternation of forms resembling phallic emblems. Yo and In are well suggested in the channeled triglyphs and the sculptured metopes of a Doric frieze, in the straight and vertical mullions and the flowing tracery of Gothic windows, in the banded torus, the bead and reel, and other familiar ornamented mouldings .

There are indications that at some time during the development of Gothic architecture in France, this sex-distinction became a recognized principle, moulding and modifying the design of a cathedral in much the same way that sex modifies bodily structure. The masonic guilds of the Middle Ages were custodians of the esoteric--which is the theosophic--side of the Christian faith, and every student of esotericism knows how fundamental and how far-reaching is this idea of sex.

The entire cathedral symbolized the crucified body of Christ; its two towers, man and woman--that Adam and that Eve for whose redemption according to current teaching Christ suffered and was crucified. The north or right-hand tower was called the sacred male pillar, Jachin; and the south, or left-hand tower , the sacred female pillar, Boaz, from the two columns flanking the gate to Solomon's Temple--itself an allegory to the bodily temple. In only a few of the French cathedrals is this distinction clearly and consistently maintained, and of these Tours forms perhaps the most remarkable example, for in its flamboyant fa?ade, over and above the difference in actual breadth and apparent sturdiness of the two towers , there is a clearly marked distinction in the character of the ornamentation, that of the north tower being more salient, angular, radial--more masculine in point of fact . In Notre Dame, the cathedral of Paris, as in the cathedral of Tours, the north tower is perceptibly broader than the south. The only other important difference appears to be in the angular label-mould above the north entrance: whatever may have been its original function or significance, it serves to define the tower sexually, so to speak, as effectively as does the beard on a man's face. In Amiens the north tower is taller than the south, and more massive in its upper stages. The only traceable indication of sex in the ornamentation occurs in the spandrels at the sides of the entrance arches: those of the north tower containing single circles, and those of the south tower containing two in one. This difference, small as it may seem, is significant, for in Europe during the Middle Ages, just as anciently in Egypt and again in Greece--in fact wherever and whenever the Secret Doctrine was known--sex was attributed to numbers, odd numbers being conceived of as masculine, and even, as feminine. Two, the first feminine number, thus became a symbol of femininity, accepted as such so universally at the time the cathedrals were built, that two strokes of a bell announced the death of a woman, three, the death of a man.

The vital, organic quality so conspicuous in the best Gothic architecture has been attributed to the fact that necessity determined its characteristic forms. Professor Goodyear has demonstrated that it may be due also in part to certain subtle vertical leans and horizontal bends; and to nicely calculated variations from strict uniformity, which find their analogue in nature, where structure is seldom rigidly geometrical. The author hazards the theory that still another reason why a Gothic cathedral seems so living a thing is because it abounds in contrasts between what, for lack of more descriptive adjectives, he is forced to call masculine and feminine forms.

CHANGELESS CHANGE

TRINITY, CONSONANCE, DIVERSITY IN MONOTONY, BALANCE, RHYTHMIC CHANGE, RADIATION

TRINITY

In architecture, this trinity of vertical, horizontal and curved lines finds admirable illustration in the application of columns and entablature to an arch and impost construction, so common in Roman and Renaissance work. This is a redundancy, and finds no justification in reason, because the weight is sustained by the arch, and the "order" is an appendage merely; yet the combination, illogical as it is, satisfies the sense of beauty because the arch effects a transition between the columns and the entablature, and completes the trinity of vertical, horizontal and curved lines . In the entrances to many of the Gothic cathedrals and churches the same elements are better because more logically disposed. Here the horizontal lintel and its vertical supports are not decorative merely, but really perform their proper functions, while the arch, too, has a raison d'?tre in that it serves to relieve the lintel of the superincumbent weight of masonry. The same arrangement sometimes occurs in classic architecture also, as when an opening spanned by a single arch is subdivided by means of an order .

Three is pre-eminently the number of architecture, because it is the number of space, which for us is three-dimensional, and of all the arts architecture is most concerned with the expression of spatial relations. The division of a composition into three related parts is so universal that it would seem to be the result of an instinctive action of the human mind. The twin pylons of an Egyptian temple with its entrance between, for a third division, has its correspondence in the two towers of a Gothic cathedral and the intervening screen wall of the nave. In the palaces of the Renaissance a threefold division--vertically by means of quoins or pilasters, and horizontally by means of cornices or string courses--was common, as was also the division into a principal and two subordinate masses .

The architectural "orders" are divided threefold into pedestal or stylobate, column and entablature; and each of these is again divided threefold: the first into plinth, die and cornice; the second into base, shaft and capital; the third into architrave, frieze and cornice. In many cases these again lend themselves to a threefold subdivision. A more detailed analysis of the capitals already shown to be twofold reveals a third member: in the Greek Doric this consists of the annulets immediately below the abacus; in the other orders, the necking which divides the shaft from the cap.

CONSONANCE

In the same way, in nature, a thing is echoed and repeated throughout its parts. Each leaf on a tree is itself a tree in miniature, each blossom a modified leaf; every vertebrate animal is a complicated system of spines; the ripple is the wave of a larger wave, and that larger wave is a part of the ebbing and flowing tide. In music this law is illustrated in the return of the tonic to itself in the octave, and its partial return in the dominant; also in a more extended sense in the repetition of a major theme in the minor, or in the treble and again in the bass, with modifications perhaps of time and key. In the art of painting the law is exemplified in the repetition with variation of certain colors and combinations of lines in different parts of the same picture, so disposed as to lead the eye to some focal point. Every painter knows that any important color in his picture must be echoed, as it were, in different places, for harmony of the whole.

These recurrences, these inner consonances, these repetitions with variations are common in architecture also. The channeled triglyphs of a Greek Doric frieze echo the fluted columns below . The balustrade which crowns a colonnade is a repetition, in some sort, of the colonnade itself. The modillions of a Corinthian cornice are but elaborated and embellished dentils. Each pinnacle of a Gothic cathedral is a little tower with its spire. As Ruskin has pointed out, the great vault of the cathedral nave, together with the pointed roof above it, is repeated in the entrance arch with its gable, and the same two elements appear in every statue-enshrining niche of the doorway. In classic architecture, as has been shown, instead of the arch and gable, the column and entablature everywhere recur under different forms. The minor domes which flank the great dome of the cathedral of Florence enhance and reinforce the latter, and prepare the eye for a climax which would otherwise be too abrupt. The central pavilion of the Ch?teau Maintenon, with its two turrets, echoes the entire fa?ade with its two towers. Like the overture to an opera, it introduces themes which find a more extended development elsewhere .

This law of Consonance is operative in architecture more obscurely in the form of recurring numerical ratios, identical geometrical determining figures, parallel diagonals and the like, which will be discussed in a subsequent essay. It has also to do with style and scale, the adherence to substantially one method of construction and manner of ornament, just as in music the key, or chosen series of notes, may not be departed from except through proper modulations, or in a specific manner.

DIVERSITY IN MONOTONY

No two trees put forth their branches in just the same manner, and no two leaves from the same tree exactly correspond; no two persons look alike, though they have similiar members and features; even the markings on the skin of the thumb are different in every human hand. Browning says,

"As like as a hand to another hand! Whoever said that foolish thing, Could not have studied to understand--"

Now every principle of natural beauty is but the presentment of some occult law, some theosophical truth; and this law of Diversity in Monotony is the presentment of the truth that identity does not exclude difference. The law is binding, yet the will is free: all men are brothers united by the ties of brotherhood, yet each is unique, a free agent, and never so free as when most bound by the Good Law. This truth nature beautifully proclaims, and art also. In architecture it is admirably exemplified in the metopes of the Parthenon frieze: seen at a distance these must have presented a scarcely distinguishable texture of sunlit marble and cool shadow, yet in reality each is a separate work of art. So with the capitals of the columns of the wonderful sea-arcade of the Venetian Ducal palace: alike in general contour they differ widely in detail, and unfold a Bible story. In Gothic cathedrals, in Romanesque monastery cloisters, a teeming variety of invention is hidden beneath apparent uniformity. The gargoyles of Notre Dame make similiar silhouettes against the sky, but seen near at hand what a menagerie of monsters! The same spirit of controlled individuality, of liberty subservient to the law of all, is exemplified in the bases of the columns of the temple of Apollo near Miletus--each one a separate masterpiece of various ornamentation adorning an established architectural form .

The builders of the early Italian churches, instinctively obeying this law of Diversity in Monotony, varied the size of the arches in the same arcade , and that this was an effect of art and not of accident or carelessness Ruskin long ago discovered, and the Brooklyn Institute surveys have amply confirmed his view. Although by these means the builders of that day produced effects of deceptive perspective, of subtle concord and contrast, their sheer hatred of monotony and meaningless repetition may have led them to diversify their arcades in the manner described, for a rigidly equal and regular division lacks interest and vitality.

BALANCE

If one were to establish an axial plane vertically through the center of a tree, in most cases it would be found that the masses of foliage, however irregularly shaped on either side of such an axis, just about balanced each other. Similarly, in all our bodily movements, for every change of equilibrium there occurs an opposition and adjustment of members of such a nature that an axial plane through the center of gravity would divide the body into two substantially equal masses, as in the case of the tree. This physical plane law of Balance shows itself for the most part on the human plane as the law of Compensation, whereby, to the vision of the occultist, all accounts are "squared," so to speak. It is in effect the law of Justice, aptly symbolized by the scales.

The law of Balance finds abundant illustration in art: in music by the opposition, the answering, of one phrase by another of the same elements and the same length, but involving a different sequence of intervals; in painting by the disposition of masses in such a way that they about equalize one another, so that there is no sense of "strain" in the composition.

In architecture the common and obvious recognition of the law of Balance is in the symmetrical disposition of the elements, whether of plan or of elevation, on either side of axial lines. A far more subtle and vital illustration of the law occurs when the opposed elements do not exactly match, but differ from each other, as in the case of the two towers of Amiens, for example. This sort of balance may be said to be characteristic of Gothic, as symmetry is characteristic of Classic, architecture.

RHYTHMIC CHANGE

There is in nature a universal tendency toward refinement and compactness of form in space, or contrariwise, toward increment and diffusion; and this manifests itself in time as acceleration or retardation. It is governed, in either case, by an exact mathematical law, like the law of falling bodies. It shows itself in the widening circles which appear when one drops a stone into still water, in the convolutions of shells, in the branching of trees and the veining of leaves; the diminution in the size of the pipes of an organ illustrates it, and the spacing of the frets of a guitar. More and more science is coming to recognize, what theosophy affirms, that the spiral vortex, which so beautifully illustrates this law, both in its time and its space aspects is the universal archetype, the pattern of all that is, has been, or will be, since it is the form assumed by the ultimate physical atom, and the ultimate physical atom is the physical cosmos in miniature.

This Rhythmic Diminution is everywhere: it is in the eye itself, for any series of mathematically equal units, such for example as the columns and intercolumnations of a colonnade, become when seen in perspective rhythmically unequal, diminishing according to the universal law. The entasis of a Classic column is determined by this law, the spirals of the Ionic volute, the annulets of the Parthenon cap, obey it .

In recognition of the same principle of Rhythmic Diminution a building is often made to grow, or appear to grow lighter, more intricate, finer, from the ground upward, an end attained by various devices, one of the most common being the employment of the more attenuated and highly ornamented orders above the simpler and sturdier, as in the Roman Colosseum, or in the Palazzo Uguccioni, in Florence--to mention only two examples out of a great number. In the Riccardi Palace an effect of increasing refinement is obtained by diminishing the boldness of the rustication of the ashlar in successive stories; in the Farnese, by the gradual reduction of the size of the angle quoins . In an Egyptian pylon it is achieved most simply by battering the wall; in a Gothic cathedral most elaborately by a kind of segregation, or breaking up, analogous to that which a tree undergoes--the strong, relatively unbroken base corresponding to the trunk, the diminishing buttresses to the tapering limbs, and the multitude of delicate pinnacles and crockets, to the outermost branches and twigs, seen against the sky.

RADIATION

This law of Radiation enters largely into architecture. The Colosseum, based upon the ellipse, a figure generated from two points or foci, and the Pantheon, based upon the circle, a figure generated from a central point, are familiar examples. The distinctive characteristic of Gothic construction, the concentration or focalization of the weight of the vaults and arches at certain points, is another illustration of the same principle applied to architecture, beautifully exemplified in the semicircular apse of a cathedral, where the lines of the plan converge to a common center, and the ribs of the vaulting meet upon the capitals of the piers and columns, seeming to radiate thence to still other centers in the loftier vaults which finally meet in a center common to all.

Such are a few of the more obvious laws of natural beauty and their application to the art of architecture. The list is by no means exhausted, but it is not the multiplicity and diversity of these laws which is important to keep in mind, so much as their relatedness and co?rdination, for they are but different aspects of the One Law, that whereby the Logos manifests in time and space. A brief recapitulation will serve to make this correlation plain, and at the same time fix what has been written more firmly in the reader's mind.

Consider for a moment the manner in which Leonardo da Vinci's Last Supper, an acknowledged masterpiece, conforms to everyone of the laws of beauty enumerated above . It illustrates the law of Unity in that it movingly portrays a single significant episode in the life of Christ. The eye is led to dwell upon the central personage of this drama by many artful expedients: the visible part of the figure of Christ conforms to the lines of an equilateral triangle placed exactly in the center of the picture; the figure is separated by a considerable space from the groups of the disciples on either hand, and stands relieved against the largest parallelogram of light, and the vanishing point of the perspective is in the head of Christ, at the apex, therefore, of the triangle. The law of Polarity finds fulfilment in the complex and flowing lines of the draped figures contrasted with the simple parallelogram of the cloth-covered table, and the severe architecture of the room. The law of Trinity is exemplified in the three windows, and in the subdivision of the twelve figures of the disciples into four groups of three figures each. The law of Consonance appears in the repetition of the horizontal lines of the table in the ceiling above; and in the central triangle before referred to, continued and echoed, as it were, in the triangular supports of the table visible underneath the cloth. The law of Diversity in Monotony is illustrated in the varying disposition of the heads of the figures in the four groups of three; the law of Balance in the essential symmetry of the entire composition; the law of Rhythmic Change in the diminishing of the wall and ceiling spaces; and the law of Radiation in the convergence of all the perspective lines to a single significant point.

To illustrate further the universality of these laws, consider now their application to a single work of architecture: the Taj Mahal, one of the most beautiful buildings of the world . It is a unit, but twofold, for it consists of a curved part and an angular part, roughly figured as an inverted cup upon a cube; each of these is threefold, for there are two sides and a central parallelogram, and two lesser domes flank the great dome. The composition is rich in consonances, for the side arches echo the central one, the subordinate domes the great dome, and the lanterns of the outstanding minarets repeat the principal motif. Diversity in Monotony appears abundantly in the ornament, which is intricate and infinitely various; the law of Balance is everywhere operative in the symmetry of the entire design. Rhythmic Change appears in the tapering of the minarets, the outlines of the domes and their mass relations to one another; and finally, the whole effect is of radiation from a central point, of elements disposed on radial lines.

It would be fatuous to contend that the prime object of a work of architecture is to obey and illustrate these laws. The prime object of a work of architecture is to fulfill certain definite conditions in a practical, economical, and admirable way, and in fulfilling to express as far as possible these conditions, making the form express the function. The architect who is also an artist however will do this and something beyond: working for the most part unconsciously, harmoniously, joyously, his building will obey and illustrate natural laws--these laws of beauty--and to the extent it does so it will be a work of art; for art is the method of nature carried into those higher regions of thought and feeling which man alone inhabits: regions which it is one of the purposes of theosophy to explore.

THE BODILY TEMPLE

Carlyle says: "There is but one temple in the world, and that is the body of man." If the body is, as he declares, a temple, it is not less true that a temple or any work of architectural art is a larger body which man has created for his uses, just as the individual self is housed within its stronghold of flesh and bones. Architectural beauty like human beauty depends upon the proper subordination of parts to the whole, the harmonious interrelation between these parts, the expressiveness of each of its function or functions, and when these are many and diverse, their reconcilement one with another. This being so, a study of the human figure with a view to analyzing the sources of its beauty cannot fail to be profitable. Pursued intelligently, such a study will stimulate the mind to a perception of those simple yet subtle laws according to which nature everywhere works, and it will educate the eye in the finest known school of proportion, training it to distinguish minute differences, in the same way that the hearing of good music cultivates the ear.

Those principles of natural beauty which formed the subject of the two preceding essays are all exemplified in the ideally perfect human figure. Though essentially a unit, there is a well marked division into right and left--"Hands to hands, and feet to feet, in one body grooms and brides." There are two arms, two legs, two ears, two eyes, and two lids to each eye; the nose has two nostrils, the mouth has two lips. Moreover, the terms of such pairs are masculine and feminine with respect to each other, one being active and the other passive. Owing to the great size and one-sided position of the liver, the right half of the body is heavier than the left; the right arm is usually longer and more muscular than the left; the right eye is slightly higher than its fellow. In speaking and eating the lower jaw and under lip are active and mobile with relation to the upper; in winking it is the upper eyelid which is the more active. That "inevitable duality" which is exhibited in the form of the body characterizes its motions also. In the act of walking for example, a forward movement is attained by means of a forward and a backward movement of the thighs on the axis of the hips; this leg movement becomes twofold again below the knee, and the feet move up and down independently on the axis of the ankle. A similar progression is followed in raising the arm and hand: motion is communicated first to the larger parts, through them to the smaller and thence to the extremities, becoming more rapid and complex as it progresses, so that all free and natural movements of the limbs describe invisible lines of beauty in the air. Coexistent with this pervasive duality there is a threefold division of the figure into trunk, head and limbs: a superior trinity of head and arms, and an inferior trinity of trunk and legs. The limbs are divided threefold into upper-arm, forearm and hand; thigh, leg and foot. The hand flowers out into fingers and the foot into toes, each with a threefold articulation; and in this way is effected that transition from unity to multiplicity, from simplicity to complexity, which appears to be so universal throughout nature, and of which a tree is the perfect symbol.

At certain periods of the world's history, periods of mystical enlightenment, men have been wont to use the human figure, the soul's temple, as a sort of archetype for sacred edifices . The colossi, with calm inscrutable faces, which flank the entrance to Egyptian temples; the great bronze Buddha of Japan, with its dreaming eyes; the little known colossal figures of India and China--all these belong scarcely less to the domain of architecture than of sculpture. The relation above referred to however is a matter more subtle and occult than mere obvious imitation on a large scale, being based upon some correspondence of parts, or similarity of proportions, or both. The correspondence between the innermost sanctuary or shrine of a temple and the heart of a man, and between the gates of that temple and the organs of sense is sufficiently obvious, and a relation once established, the idea is susceptible of almost infinite development. That the ancients proportioned their temples from the human figure is no new idea, nor is it at all surprising. The sculpture of the Egyptians and the Greeks reveals the fact that they studied the body abstractly, in its exterior presentment. It is clear that the rules of its proportions must have been established for sculpture, and it is not unreasonable to suppose that they became canonical in architecture also. Vitruvius and Alberti both lay stress on the fact that all sacred buildings should be founded on the proportions of the human body.

In France, during the Middle Ages, a Gothic cathedral became, at the hands of the secret masonic guilds, a glorified symbol of the body of Christ. To practical-minded students of architectural history, familiar with the slow and halting evolution of a Gothic cathedral from a Roman basilica, such an idea may seem to be only the maunderings of a mystical imagination, a theory evolved from the inner consciousness, entitled to no more consideration than the familiar fallacy that vaulted nave of a Gothic church was an attempt to imitate the green aisles of a forest. It should be remembered however that the habit of the thought of that time was mystical, as that of our own age is utilitarian and scientific; and the chosen language of mysticism is always an elaborate and involved symbolism. What could be more natural than that a building devoted to the worship of a crucified Savior should be made a symbol, not of the cross only, but of the body crucified?

The cathedral builders excelled all others in the artfulness with which they established and maintained a relation between their architecture and the stature of a man. This is perhaps one reason why the French and English cathedrals, even those of moderate dimensions are more truly impressive than even the largest of the great Renaissance structures, such as St. Peter's in Rome. A gigantic order furnishes no true measure for the eye: its vastness is revealed only by the accident of some human presence which forms a basis of comparison. That architecture is not necessarily the most awe-inspiring which gives the impression of having been built by giants for the abode of pigmies; like the other arts, architecture is highest when it is most human. The mediaeval builders, true to this dictum, employed stones of a size proportionate to the strength of a man working without unusual mechanical aids; the great piers and columns, built up of many such stones, were commonly subdivided into clusters, and the circumference of each shaft of such a cluster approximated the girth of a man; by this device the moulding of the base and the foliation of the caps were easily kept in scale. Wherever a balustrade occurred it was proportioned not with relation to the height of the wall or the column below, as in classic architecture, but with relation to a man's stature.

It may be stated as a general rule that every work of architecture, of whatever style, should have somewhere about it something fixed and enduring to relate it to the human figure, if it be only a flight of steps in which each one is the measure of a stride. In the Farnese, the Riccardi, the Strozzi, and many another Italian palace, the stone seat about the base gives scale to the building because the beholder knows instinctively that the height of such a seat must have some relation to the length of a man's leg. In the Pitti palace the balustrade which crowns each story answers a similar purpose: it stands in no intimate relation to the gigantic arches below, but is of a height convenient for lounging elbows. The door to Giotto's campanile reveals the true size of the tower as nothing else could, because it is so evidently related to the human figure and not to the great windows higher up in the shaft.

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 .

The figure has been variously analyzed with a view to establishing numerical ratios between its parts . 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 Caesar, formulated the important proportions of the statues of classical antiquity, and except that he makes the head smaller than the normal , 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.

LATENT GEOMETRY

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 .

The first painter who deliberately rather than instinctively based his compositions on geometrical principles seems to have been Fra Bartolommeo, in his Last Judgment, in the church of St. Maria Nuova, in Florence. Symonds says of this picture, "Simple figures--the pyramid and triangle, upright, inverted, and interwoven like the rhymes of a sonnet--form the basis of the composition. This system was adhered to by the Fratre in all his subsequent works" . Raphael, with that power of assimilation which distinguishes him among men of genius, learned from Fra Bartolommeo this method of disposing figures and combining them in masses with almost mathematical precision. It would have been indeed surprising if Leonardo da Vinci, in whom the artist and the man of science were so wonderfully united, had not been greatly preoccupied with the mathematics of the art of painting. His Madonna of the Rocks, and Virgin on the Lap of Saint Anne, in the Louvre, exhibit the very perfection of pyramidal composition. It is however in his masterpiece, The Last Supper, that he combines geometrical symmetry and precision with perfect naturalness and freedom in the grouping of individually interesting and dramatic figures. Michael Angelo, Andrea del Sarto, and the great Venetians, in whose work the art of painting may be said to have culminated, recognized and obeyed those mathematical laws of composition known to their immediate predecessors, and the decadence of the art in the ensuing period may be traced not alone to the false sentiment and affectation of the times, but also in the abandonment by the artists of those obscurely geometrical arrangements and groupings which in the works of the greatest masters so satisfy the eye and haunt the memory of the beholder .

Sculpture, even more than painting, is based on geometry. The colossi of Egypt, the bas-reliefs of Assyria, the figured pediments and metopes of the temples of Greece, the carved tombs of Revenna, the Della Robbia lunettes, the sculptured tympani of Gothic church portals, all alike lend themselves in greater or less degree to a geometrical synopsis . Whenever sculpture suffered divorce from architecture the geometrical element became less prominent, doubtless because of all the arts architecture is the most clearly and closely related to geometry. Indeed, it may be said that architecture is geometry made visible, in the same sense that music is number made audible. A building is an aggregation of the commonest geometrical forms: parallelograms, prisms, pyramids and cones--the cylinder appearing in the column, and the hemisphere in the dome. The plans likewise of the world's famous buildings reduced to their simplest expression are discovered to resolve themselves into a few simple geometrical figures. . This is the "bed rock" of all excellent design.

But architecture is geometrical in another and a higher sense than this. Emerson says: "The pleasure a palace or a temple gives the eye is that an order and a method has been communicated to stones, so that they speak and geometrize, become tender or sublime with expression." All truly great and beautiful works of architecture from the Egyptian pyramids to the cathedrals of Ile-de-France--are harmoniously proportioned, their principal and subsidiary masses being related, sometimes obviously, more often obscurely, to certain symmetrical figures of geometry, which though invisible to the sight and not consciously present in the mind of the beholder, yet perform the important function of co?rdinating the entire fabric into one easily remembered whole. Upon some such principle is surely founded what Symonds calls "that severe and lofty art of composition which seeks the highest beauty of design in architectural harmony supreme, above the melodies of gracefulness of detail."

There is abundant evidence in support of the theory that the builders of antiquity, the masonic guilds of the Middle Ages, and the architects of the Italian Renaissance, knew and followed certain rules, but though this theory be denied or even disproved--if after all these men obtained their results unconsciously--their creations so lend themselves to a geometrical analysis that the claim for the existence of certain canons of proportion, based on geometry, remains unimpeached.

The plane figures principally employed in determining architectural proportion are the circle, the equilateral triangle, and the square--which also yields the right angled isosceles triangle. It will be noted that these are the two dimensional correlatives of the sphere, the tetrahedron and the cube, mentioned as being among the determining forms in molecular structure. The question naturally arises, why the circle, the equilateral triangle and the square? Because, aside from the fact that they are of all plane figures the most elementary, they are intimately related to the body of man, as has been shown , and the body of man is as it were the architectural archetype. But this simply removes the inquiry to a different field, it is not an answer. Why is the body of man so constructed and related? This leads us, as does every question, to the threshold of a mystery upon which theosophy alone is able to throw light. Any extended elucidation would be out of place here: it is sufficient to remind the reader that the circle is the symbol of the universe; the equilateral triangle, of the higher trinity ; and the square, of the lower quaternary of man's sevenfold nature.

The square is principally used in preliminary plotting: it is the determining figure in many of the palaces of the Italian Renaissance; the Arc de Triomphe, in Paris is a modern example of its use . The circle is often employed in conjunction with the square and the triangle. In Thomas Jefferson's Rotunda for the University of Virginia, a single great circle was the determining figure, as his original pen sketch of the building shows . Some of the best Roman triumphal arches submit themselves to a circular synopsis, and a system of double intersecting circles has been applied, with interesting results, to fa?ades as widely different as those of the Parthenon and the Farnese Palace in Rome, though it would be fatuous to claim that these figures determined the proportions of the fa?ades.

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