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different construction, and the several changes it has since undergone in form have served to establish a variety of styles, as we shall afterwards find.

Sewers, aqueducts, bridges, theatres, amphitheatres, baths and triumphal arches, all exhibit the arch in its most useful application, and as did the halls of the baths vaulting of stupendous span; the dome of the Pantheon being 142 feet 6 inches in diameter internally, covered by a hemispherical dome.

Symmetry, as understood by Vitruvius, seems to relate more to the proportions of the façade than to those of the detail; but he doubtless intended it to be understood that

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perfect harmony should subsist between them as well as between each particular member, however subordinate; as in the well-formed human figure, all the limbs being in due pro portion, the whole when combined produces true symmetry: and the same author insists very strenuously on a careful study of the rules upon which this is founded, proving that the effect desired cannot be produced by a mere effort of fancy, or what is coinmonly called

taste.

A building, though entirely devoid of ornament, may be rendered beautiful by the justness of its proportion, and the richest edifice wanting in this never can excite admiration: façades having but height and breadth, these two dimensions must be equal to each other, if we adopt the symmetrical proportions prescribed by Vitruvius, for he observes "the square includes the human figure either lying down or standing in an erect posture, the arms being stretched out." Temples, triumphal arches, and other buildings left us by the Greeks and Romans were decidedly designed upon this principle, as were most of the façades of the religious structures erected since the fall of the Roman empire.

In the "Songe de Poliphile,” originally published in Italian by Aldus in the year 1499, are some observations on setting out a façade, which convey some idea of the principles adopted for the formation of a perfect and harmonious design on the revival of Roman architecture.

"Draw a square figure, divided by three perpendicular and three horizontal lines, at equal distances from each other, forming sixteen squares; on the top of the square add a half square, which, similarly divided, makes altogether twenty-four squares: in the lower square draw two diagonals, crossing eight squares in the same manner; then form a lozenge above the great square, tracing within it four lines on the four principal points that separate the four sides of the void."

After understanding this figure, I thought within myself what can modern architects do, who esteem themselves so learned without letters or principles? They neither know rules nor dimensions, and therefore corrupt and deform all sorts of buildings, both public and private, despising nature, who teaches them to do well if they would imitate her: good workmen, besides their science, may enrich their work either by adding to or diminishing therefrom, the better to please the eye, but the mass should remain entire, with which all should be made to harmonise. By the mass is understood the body of the edifice, which, without any ornament, shows the knowledge and spirit of the master, for it is easy to embellish after any invention; the distribution and arrangement of the parts is also a matter of consideration; hence we may conclude that any workmen or their apprentices know how to ornament a work, but to invent lies only in the heads of the wise.

Taking from the square and a half, the lozenge and the diagonal lines leaves the three perpendicular and the three horizontal, except that in the middle, which terminates in the centre of the perpendicular, cutting it into four parts or portions; by this rule will be found two perfect squares, one above and one below, each containing four small squares, which form the opening or doorway; now if you take the diagonal of the lower square, it will show you what thickness must be given to the centre of the portico; if you carry it straight, the line will serve to denote the architrave and the point of the centre of the upper square will show you the centre of the arch or curve to be given to the door; turning a semicircle it will rest on the transverse line, which cuts the square and a half into two equal parts; but if done by any other means I do not esteem it perfect. This method was invented by ancient and expert masons, and observed in their arches and vaults, to give them both grace and solidity; the pedestal on which the columns rest commences at the level of the pavement by a plinth, and the whole is a foot high, furnished with mouldings; one portion is divided into architrave, frieze, and cornice, the latter being something more than the others; that is to say, if the architrave and frieze contained five parts, the cornice should be six. The whole twenty-four squares form a square and a half; then divide the upper half into six parts by five horizontal and five perpendicular lines, and draw a line from the centre of the fifth transverse to the corner of the great perfect square, where the architrave commences; then draw it perpendicular on the key of the archivolt, and it will show you the height to be given to the frontispiece above, the extremities of which should unite and relate to the projection of the cymatium and its mouldings.

General Principles. — It would appear that all the principal Roman triumphal arches with single openings were a square, either comprising or excluding their attics: that the centre from whence the archivolt was struck was the centre of the square, or if the façade was more than a square, as the arch of Trajan at Ancona, then where the two diagonals crossed the centre was fixed. The width of the opening is generally half the entire extent, sometimes three parts out of seven.

These triumphal arches were generally surmounted by a group of figures, or the car and horses of the conqueror, accompanied by his companions in arms and the trophies obtained from the enemy; these, as shown on several medals, appear to be equal in height to of the entire edifice upon which they are placed, the attic and entablature representing, and the columns and pedestals the other; and as the former are nearly equal in their height, it follows that the horse and his rider, or the car and its triumphant hero, were double the height of the pedestal on which they were placed, for so we may consider the attic which contained the inscription, the body of the arch being a perfect square, and in correct proportion, without the attic. The depths of these arches varied; that of Constantine at Rome is nearly the same as the width of the great centre opening; many of the others are less than that proportion; but it seems that the cube was the measure that

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bounded the propor tions, as shown in fig. 1053. The several Roman examples selected differ in arrangement, but not in principle, from the description given by Poliphile: take away the pedestals on which the columns placed, and then four squares in height include half the tympanum, and eighteen squares the entire figure, 6 of which may be considered as devoted to the arch, and the other 12 to supports: or, if we comprise the whole façade in 20 squares, and abstract the 8 which belong to the opening between the pedestals, we have 4 for each pier or support, and 4 for the entablature, the supported being only the quantity contained in the two supports: resistance to the arch, or its thrust, requires a different arrangement from that of a portico, but we nevertheless find definite proportions made use of, and a double quantity given to masses which have to bear weight as well as resist thrust.

Fig. 1049.

ARCH OF AUGUSTUS AT RIMINI.

The Arch of Augustus at Rimini has the height of its order determined by the length of the frieze.

The Arch of Augustus at Aosta resembles that of Titus in arrangement; it is a perfect square comprising the attic.

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The Arch of Sergius at Pola is a perfect square, without attic, like that of Titus.

The Arch of Titus at Rome, raised by the senate and Roman people to com memorate the conquest of Judæa, is one of the best examples of proportion that remain: built of white marble, it is a monument of constructive art, some of the blocks being 9 feet square, and 2 feet thick; the arch is composed of eleven voussoirs 16 feet deep. For a detailed account of its construction and ornament the reader is referred to the "Architectural Antiquities of Rome."

The proportions are a square, as is the opening of the archway, up to the springing; and not a double square, as described by Serlio. The pedestals are in height nearly half the opening of the archway, which Palladio observes was the ordinary proportion given by the ancients. The entire length of the upper member of the cornice in this example is 48 feet, which dimension corresponds with the entire height, almost to a fraction: the width of the opening is 17 feet 6 inches, a trifle more than one-third of the entire width: bounding the façade by a parallelogram, excluding the attic, and drawing two diagonals, we obtain the centre from which the arch is struck, which rule will apply to the other

Fig. 1051.

ARCH OF SERGIUS AT POLA.

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triumphal arches with a single opening, though varying materially from the principles laid down by Poliphile, and adopted by Serlio and other architects at the revival of Italian architecture. The Arch

of Titus is a square comprising its entire façade; that of Poliphile a square up to the under side of the entablature; consequently, the opening of the triumphal way is in width half the height to the top of the impost upon which the archivolt rests, while in the more ancient the entire aperture without the arch is a square.

In the Arch of Poliphile the entablature and pediments are nearly equal in quantity to each of the piers upon which they are carried; and the piers themselves are in width only one quarter of the whole breadth of the façade it will be found, however, that nearly the same proportions exist between supports and supported in both examples.

The Arch of Augustus at Susa has a single arch: proportion a square to the top of the entabla

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ture, opening a square to the springing: width divided into four, two given to the opening and one to each pier, which has a three-quarter column at the angle: attic as high as piers are wide.

In arches with three openings, as those of Septimus Severus and Constantine, these

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