Proportion is that agreeable harmony between the several parts of a building, which is the result of a just and regular agreement of them with each other; the height to the width, this to the length, and each of these to the whole.
Eurythmy is beauty and fitness in the adjustments of the members. This is found when the members of a work are of a height suited to their breadth, of a breadth suited to their length, and, in a word, when they all correspond symmetrically.
Uniformity is the parity of the parts to one another; each corresponding with its opposite, as in the human figure. The arms, feet, hands, fingers, are similar to, and symmetrical with, one another; so should the respective parts of a building correspond. In sacred buildings, for instance, the diameter of the columns and the width of the triglyphs must be similar. In the balista, by the size of the hole which the Greeks call περίτρητον; in ships, by the space between the thowls, which space in Greek is called διπηχαικὴ, we have a measure, by the knowledge of which the whole of the construction of a vessel may be developed.
Symmetry is a proper agreement between the members of the work itself, and relation between the different parts and the whole general scheme, in accordance with a certain part selected as standard. Thus in the human body there is a kind of symmetrical harmony between forearm, foot, palm, finger, and other small parts; and so it is with perfect buildings. In the case of temples, symmetry may be calculated from the thickness of a column, from a triglyph, or even from a module; in the ballista, from the hole or from what the Greeks call the περἱτρητος; in a ship, from the space between the tholepins διἁπηγμἁ; and in other things, from various members.
Consistency is found in that work whose whole and detail are suitable to the occasion. It arises from circumstance, custom, and nature. From circumstance, which the Greeks call θεματισμὸς, when temples are built, hypæthral and uninclosed, to Jupiter, Thunderer, Coelus, the Sun and Moon; because these divinities are continually known to us by their presence night and day, and throughout all space. For a similar reason, temples of the Doric order are erected to Minerva, Mars, and Hercules; on account of whose valour, their temples should be of masculine proportions, and without delicate ornament. The character of the Corinthian order seems more appropriate to Venus, Flora, Proserpine, and Nymphs of Fountains; because its slenderness, elegance and richness, and its ornamental leaves surmounted by volutes, seem to bear an analogy to their dispositions. A medium between these two is chosen for temples to Juno, Diana, Bacchus, and other similar deities, which should be of the Ionic order, tempered between the severity of the Doric and the slenderness and delicacy of the Corinthian order.
Propriety is that perfection of style which comes when a work is authoritatively constructed on approved principles. It arises from prescription (Greek: θεματισμὡ), from usage, or from nature. From prescription, in the case of hypaethral edifices, open to the sky, in honour of Jupiter Lightning, the Heaven, the Sun, or the Moon: for these are gods whose semblances and manifestations we behold before our very eyes in the sky when it is cloudless and bright. The temples of Minerva, Mars, and Hercules, will be Doric, since the virile strength of these gods makes daintiness entirely inappropriate to their houses. In temples to Venus, Flora, Proserpine, Spring-Water, and the Nymphs, the Corinthian order will be found to have peculiar significance, because these are delicate divinities and so its rather slender outlines, its flowers, leaves, and ornamental volutes will lend propriety where it is due. The construction of temples of the Ionic order to Juno, Diana, Father Bacchus, and the other gods of that kind, will be in keeping with the middle position which they hold; for the building of such will be an appropriate combination of the severity of the Doric and the delicacy of the Corinthian.
In respect of custom, consistency is preserved when the vestibules of magnificent edifices are conveniently contrived and richly finished: for those buildings cannot be said to be consistent, to whose splendid interiors you pass through poor and mean entrances. So also, if dentilled cornices are used in the Doric order, or triglyphs applied above the voluted Ionic, thus transferring parts to one order which properly belong to another, the eye will be offended, because custom otherwise applies these peculiarities.
Propriety arises from usage when buildings having magnificent interiors are provided with elegant entrance-courts to correspond; for there will be no propriety in the spectacle of an elegant interior approached by a low, mean entrance. Or, if dentils be carved in the cornice of the Doric entablature or triglyphs represented in the Ionic entablature over the cushion-shaped capitals of the columns, the effect will be spoilt by the transfer of the peculiarities of the one order of building to the other, the usage in each class having been fixed long ago.
Natural consistency arises from the choice of such situations for temples as possess the advantages of salubrious air and water; more especially in the case of temples erected to Æsculapius, to the Goddess of Health, and such other divinities as possess the power of curing diseases. For thus the sick, changing the unwholesome air and water to which they have been accustomed for those that are healthy, sooner convalesce; and a reliance upon the divinity will be therefore increased by proper choice of situation. Natural consistency also requires that chambers should be lighted from the east; baths and winter apartments from the south-west; picture and other galleries which require a steady light, from the north, because from that quarter the light is not sometimes brilliant and at other times obscured, but is nearly the same throughout the day.
Finally, propriety will be due to natural causes if, for example, in the case of all sacred precincts we select very healthy neighbourhoods with suitable springs of water in the places where the fanes are to be built, particularly in the case of those to Aesculapius and to Health, gods by whose healing powers great numbers of the sick are apparently cured. For when their diseased bodies are transferred from an unhealthy to a healthy spot, and treated with waters from health-giving springs, they will the more speedily grow well. The result will be that the divinity will stand in higher esteem and find his dignity increased, all owing to the nature of his site. There will also be natural propriety in using an eastern light for bedrooms and libraries, a western light in winter for baths and winter apartments, and a northern light for picture galleries and other places in which a steady light is needed; for that quarter of the sky grows neither light nor dark with the course of the sun, but remains steady and unshifting all day long.
Economy consists in a due and proper application of the means afforded according to the ability of the employer and the situation chosen; care being taken that the expenditure is prudently conducted. In this respect the architect is to avoid the use of materials which are not easily procured and prepared on the spot. For it cannot be expected that good pit-sand, stone, fir of either sort, or marble, can be procured every where in plenty, but they must, in some instances, be brought from a distance, with much trouble and at great expense. In such cases, river or sea-sand may be substituted for pit-sand; cypress, poplar, elm, and pine, for the different sorts of fir; and the like of the rest, according to circumstances.
Economy denotes the proper management of materials and of site, as well as a thrifty balancing of cost and common sense in the construction of works. This will be observed if, in the first place, the architect does not demand things which cannot be found or made ready without great expense. For example: it is not everywhere that there is plenty of pitsand, rubble, fir, clear fir, and marble, since they are produced in different places and to assemble them is difficult and costly. Where there is no pitsand, we must use the kinds washed up by rivers or by the sea; the lack of fir and clear fir may be evaded by using cypress, poplar, elm, or pine; and other problems we must solve in similar ways.