Vitruvius

Marcus Vitruvius Pollio (born ca. 80/70 BC?; died ca. 25 BC) was a Roman writer, architect and engineer, active in the 1st century BC.

De architectura (The Ten Books On Architecture) (~ 15BC)

 * Morris Hicky Morgan translation (1914) unless otherwise stated

Book I

 * Owing to this favor I need to have no fear of want to the end of my life, and being thus laid under obligation I began to write this work for you, because I saw that you have built and are now building extensively, and that in future also you will take care that our public and private buildings shall be worthy to go down to posterity by the side of your other splendid achievements.
 * Preface, Sec. 3 (dedication to Imperator Caesar)


 * The architect should be equipped with knowledge of many branches of study and varied kinds of learning, for it is by his judgement that all work done by the other arts is put to test. This knowledge is the child of practice and theory.
 * Chapter I "The Education of the Architect" Sec. 1


 * Architects who have aimed at acquiring manual skill without scholarship have never been able to reach a position of authority to correspond to their pains, while those who relied only upon theories and scholarship were obviously hunting the shadow, not the substance. But those who have a thorough knowledge of both, like men armed at all points, have the sooner attained their object and carried authority with them.
 * Chapter I, Sec. 2


 * In all matters but particularly in architecture ...that which is signified is the subject of which we may be speaking and that which gives significance is a demonstration on scientific principles. ...One who professes himself an architect should be well versed in both directions.
 * Chapter I, Sec. 3


 * Neque enim ingenium sine disciplina aut disciplina sine ingenio perfectum artificem potest efficere.
 * For neither talent without instruction nor instruction without talent can produce the perfect craftsman.
 * Chapter I, Sec. 3; translation by Frank Granger
 * Neither natural ability without instruction nor instruction without natural ability can make the perfect artist.
 * Morris Hicky Morgan translation


 * Let him [who would be an architect] be educated, skillful with the pencil, instructed in geometry, know much history, have followed the philosophers with attention, understand music, have some knowledge of medicine, know the opinions of the jurists, and be acquainted with astronomy and the theory of the heavens.
 * Chapter I, Sec. 3


 * An architect ought to be an educated man so as to leave a more lasting remembrance in his treatises.
 * Chapter I, Sec. 4


 * Geometry... is of much assistance in architecture, and in particular it teaches us the use of the rule and compasses, by which especially we acquire readiness in making plans for buildings in their grounds, and rightly apply the square, the level, and the plummet. By means of optics... the light in buildings can be drawn from fixed quarters of the sky. ...Difficult questions involving symmetry are solved by means of geometrical theories and methods.
 * Chapter I, Sec. 4


 * As for philosophy, it makes an architect high-minded and not self-assuming, but rather renders him courteous, just, and honest without avariciousness. This is very important, for no work can be rightly done without honesty and incorruptibility.
 * Chapter I, Sec. 7


 * Philosophy treats of physics where a more careful knowledge is required because the problems which come under this head are numerous... So the reader of Ctesibius or Archimedes and the other writers of treatises of the same class will not be able to appreciate them unless he has been trained in these subjects by the philosophers.
 * Chapter I, Sec. 7


 * Music, also, the architect ought to understand so that he may have knowledge of the canonical and mathematical theory, and besides be able to tune ballistae, catapultae, and scorpiones to the proper key. For to the right and left in the beams are the holes in the frames through which the strings of twisted sinew are stretched by means of windlasses and bars, and these strings must not be clamped and made fast until they give the same correct note to the ear of the skilled workman.
 * Chapter I, Sec. 8


 * In theatres... there are the bronze vessels in which are placed in niches under the seats in accordance with the musical intervals on mathematical principles. These vessels are arranged with a view to musical concords or harmony, and apportioned in the compass of the fourth, the fifth, and the octave, and so on up to the double octave, in such a way that when the voice of an actor falls in unison with any of them its power is increased, and it reaches the ears of the audience with greater clearness and sweetness. Water organs too, and the other instruments which resemble them cannot be made by one who is without the principles of music.
 * Chapter I, Sec. 9


 * The architect should also have a knowledge of the study of medicine on account of the questions of climates, air, the healthiness and unhealthiness of sites, and the use of different waters. For without these considerations the healthiness of a dwelling cannot be assured.
 * Chapter I, Sec. 10


 * As for principles of law, he should know those which are necessary in the case of buildings having party walls, with regard to water dripping from the eaves, and also the laws about drains, windows, and water supply. And other things of this sort should be known to architects, so that... they may be careful not to leave disputed points for the householders to settle after the works are finished, and so that in drawing up contracts the interests of both employer and contractor may be wisely safe-guarded.
 * Chapter I, Sec. 10


 * From astronomy we find the east, west, south, and north, as well as the theory of the heavens, the equinox, solstice, and courses of the stars. If one has no knowledge of these matters, he will not be able to have any comprehension of the theory of sundials.
 * Chapter I, Sec. 10


 * Men have no right to profess themselves architects hastily, without having climbed from boyhood the steps of these studies and thus, nursed by the knowledge of many arts and sciences, having reached the heights of the holy ground of architecture.
 * Chapter I, Sec. 11


 * A liberal education forms... a single body. Those, therefore, who from tender years receive instruction in the various forms of learning, recognize the same stamp on all the arts, and an intercourse between all studies, and so they more readily comprehend them all.
 * Chapter I, Sec. 12


 * In the midst of all this great variety of subjects, an individual cannot attain to perfection in each, because it is scarcely in his power to take in and comprehend the general theories of them.
 * Chapter I, Sec. 13


 * Pytheos made a mistake by not observing that the arts are each composed of two things, the actual work and the theory of it. One of these, the doing of the work, is proper to men trained in the individual subject, while the other the theory is common to all scholars.
 * Chapter I, Sec. 15


 * Astronomers... have a common ground for discussion with musicians in the harmony of the stars and musical concords in tetrads and triads of the fourth and the fifth, and with geometricians in the subject of vision; and in all other sciences many points, perhaps all, are common so far as the discussion of them is concerned. But the actual undertaking of works which are brought to perfection by the hand and its manipulation is the function of those who have been specially trained to deal with a single art.
 * Chapter I, Sec. 16


 * As for men upon whom nature has bestowed so much ingenuity, acuteness, and memory that they are able to have a thorough knowledge of geometry, astronomy, music, and the other arts, they go beyond the functions of architects and become pure mathematicians. Hence they can readily take up positions against those arts because many are the artistic weapons with which they are armed. Such men, however, are rarely found, but there have been such at times; for example, Aristarchus of Samos, Philolaus, and Archytas of Tarentum, Apollonius of Perga, Eratosthenes of Cyrene, and among Syracusans Archimedes and Scopinas, who through mathematics and natural philosophy discovered, expounded, and left to posterity many things in connection with mechanics and with sundials.
 * Chapter I, Sec. 16


 * It is not as a very great philosopher, nor as an eloquent rhetorician, nor as a grammarian trained in the highest principles of his heart, that I have striven to write this work, but as an architect who has had only a dip into those studies.
 * Chapter I, Sec. 17


 * As regards the efficacy of the art and the theories of it, I promise and expect that in these volumes I shall undoubtedly show myself of very considerable importance not only to builders but also to all scholars.
 * Chapter I, Sec. 17


 * Architecture depends on Order, Arrangement, Eurythmy, Symmetry, Propriety, and Economy.
 * Chapter II "The Fundamental Principles of Architecture" Sec. 1


 * Order gives due measure to the members of a work considered separately, and symmetrical agreement to the proportions of the whole. It is an adjustment according to quantity. By this I mean the selection of modules from the members of the work itself and, starting from these individual parts of members, constructing the whole work to correspond.
 * Chapter II, Sec. 2


 * Arrangement includes the putting of things in their proper places and the elegance of effect which is due to adjustments appropriate to the character of the work. Its forms of expression are these: ground plan, elevation, and perspective. ...All three come of reflexion and invention.
 * Chapter II, Sec. 2


 * Reflexion is careful and laborious thought, and watchful attention directed to the agreeable effect of one's plan. Invention, on the other hand, is the solving of intricate problems and the discovery of new principles by means of brilliancy and versatility.
 * Chapter II, Sec. 2


 * 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.
 * Chapter II, Sec. 3


 * Propriety is that perfection of style which comes when a work is authoritatively constructed on approved principles. It arises from prescription, from usage, or from nature.
 * Chapter II, Sec. 5


 * From prescription, in the case of hypaethral edifices, open to the sky, in honor 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.
 * Chapter II, Sec. 5


 * 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.
 * Chapter II, Sec. 5


 * There will be no propriety in the spectacle of an elegant interior approached by a low mean entrance.
 * Chapter II, Sec. 6


 * There will... 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.
 * Chapter II, Sec. 7


 * Economy denotes the the proper management of materials and of site, as well as a thrifty balancing of cost and common sense in the construction of works. ...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... Where there is no pitsand, we must use the kinds washed up by rivers or by the sea... and other problems we must solve in similar ways.
 * Chapter II, Sec. 8


 * The proper form of economy must be observed in building houses for each and every class.
 * Chapter II, Sec. 9


 * There are three departments of architecture: the art of building, the making of time-pieces, and the construction of machinery.
 * Chapter III "The Departments of Architecture" Sec. 1


 * All... must be built with due reference to durability, convenience, and beauty. Durability will be assured when foundations are carried down to the solid ground and materials wisely and liberally selected; convenience, when the arrangement of the apartments is faultless and presents no hindrance to use, and when each class of building is assigned to its suitable and appropriate exposure; and beauty, when the appearance of the work is pleasing and in good taste, and when its members are in due proportion according to correct principles of symmetry.
 * Chapter III, Sec. 2


 * When the morning breezes blow toward the town at sunrise, if they bring with them mists from marshes and, mingled with the mist, the poisonous breath of the creatures of the marshes to be wafted into the bodies of the inhabitants, they will make the site unhealthy.
 * Chapter IV "The Site of a City" Sec. 1


 * Nobody draws the light for covered wine rooms from the south or west, but rather from the north, since that quarter is never subject to change but is always constant and unshifting. So it is with granaries: grain exposed to the sun's course soon loses its good quality, and provisions and fruit, unless stored in a place unexposed to the sun's course, do not keep long.
 * Chapter IV, Sec. 2


 * Heat is a universal solvent, melting out of things their power of resistance, and sucking away and removing their natural strength with its fiery exhalations so that they grow soft, and hence weak, under its glow.
 * Chapter IV, Sec. 3


 * While all bodies are composed of the four elements, that is, of heat, moisture, the earthy, and air, yet there are mixtures according to natural temperament which make up the natures of all the different animals of the world, each after its kind.
 * Chapter IV, Sec. 5


 * If one of these elements, heat, becomes predominant in any body whatsoever, it destroys and dissolves all the others with its violence. ...Again if too much moisture enters the channels of a body, and thus introduces disproportion, the other elements, adulterated by the liquid, are impaired, and the virtues of the mixture dissolved. This defect, in turn, may arise from the cooling properties of moist winds and breezes blowing upon the body. In the same way, increase or diminution of the proportion of air or of the earthy which is natural to the body may enfeeble the other elements.
 * Chapter IV, Sec. 6


 * Our ancestors, when about to build a town or an army post, sacrificed some of the cattle that were wont to feed on the site proposed and examined their livers. If the livers of the first victims were dark-coloured or abnormal, they sacrificed others, to see whether the fault was due to disease or their food. They never began to build defensive works in a place until after they had made many such trials and satisfied themselves that good water and food had made the liver sound and firm. ...healthfulness being their chief object.
 * Chapter IV, Sec. 9


 * From food and water, then, we may learn whether sites are naturally unhealthy or healthy.
 * Chapter IV, Sec. 10


 * Marshes that are stagnant and have no outlets either by rivers or ditches, like the Pomptine marshes, merely putrefy as they stand, emitting heavy, unhealthy vapors. A case of a town built in such a spot was Old Salpia in Apulia... Year after year there was sickness, until finally the suffering inhabitants came with a public petition to Marcus Hostilius and got him to agree to seek and find them a proper place to which to remove their city.
 * Chapter IV, Sec. 12


 * After insuring on these principles the healthfulness of the future city... the next thing to do is to lay the foundations for the towers and walls. Dig down to solid bottom, if it can be found, and lay them therein, going as deep as the magnitude of the proposed work seems to require. They should be much thicker than the part of the walls that will appear above ground and their structure should be as solid as it can possibly be laid.
 * Chapter V "The City Walls" Sec. 1


 * Towns should be laid out not as an exact square nor with salient angles, but in circular form, to give a view of the enemy from many points. Defense is difficult where there are salient angles because the angle protects the enemy rather than the inhabitants.
 * Chapter V, Sec. 2


 * The thickness of the wall should, in my opinion, be such that armed men meeting on top of it may pass one another without interference. In the thickness there should be set a very close succession of ties made of charred olive wood, binding the two faces of the wall together like pins, to give it lasting endurance. For that is a material which neither decay, nor the weather, nor time can harm, but even though buried in the earth or set in the water it keeps sound and useful forever. And so not only city walls but substructures in general and all walls that require a thickness like that of a city wall, will be long in falling to decay if tied in this manner.
 * Chapter V, Sec. 3


 * The towers themselves must be either round or polygonal. Square towers are sooner shattered by military engines, for the battering rams pound their angles to pieces but in the case of round towers they can do no harm being engaged as it were in driving wedges to their center.
 * Chapter V, Sec. 5


 * The system of fortification by wall and towers may be made safest by the addition of earthen ramparts.
 * Chapter V, Sec. 5


 * Lay a second foundation enough inside the first... Having laid these two foundations... build cross walls between them uniting the outer and inner foundation in a comb like arrangement set like teeth of a saw. With this form of construction the burden of earth will be distributed into small bodies and will not lie with all its weight in one crushing mass so as to thrust out substructures.
 * Chapter V, Sec. 7


 * Dimension stone, flint, rubble, burnt or unburnt brick,—use them as you find them. For it is not every neighborhood or particular locality that can have a wall built of burnt brick like that at Babylon, where there was plenty of asphalt to take the place of lime and sand, and yet possibly each may be provided with materials of equal usefulness so that out of them a faultless wall may be built to last forever.
 * Chapter V, Sec. 8




 * Cold winds are disagreeable, hot winds enervating, moist winds unhealthy.
 * Chapter VI "The Directions of the Streets with Remarks on the Winds" Sec. 1


 * Wind is a flowing wave of air, moving hither and thither indefinitely. It is produced when heat meets moisture, the rush of heat generating a mighty current of air. That this is the fact we may learn from bronze eolipiles, and thus by means of a scientific invention discover a divine truth lurking in the laws of the heavens. Eolipiles are hollow bronze balls, with a very small opening through which water is poured into them. Set before a fire, not a breath issues from them before they get warm; but as soon as they begin to boil, out comes a strong blast due to the fire. Thus from this slight and very short experiment we may understand and judge of the mighty and wonderful laws of the heavens and the nature of winds.
 * Chapter VI, Sec. 2


 * The diseases which are hard to cure in neighborhoods... are catarrh, hoarseness, coughs, pleurisy, consumption, spitting of blood, and all others that are cured not by lowering the system but by building it up. They are hard to cure, first, because they are originally due to chills; secondly, because the patient's system being already exhausted by disease, the air there, which is in constant agitation owing to winds and therefore deteriorated, takes all the sap of life out of their diseased bodies and leaves them more meager every day. On the other hand, a mild, thick air, without drafts and not constantly blowing back and forth, builds up their frames by its unwavering steadiness, and so strengthens and restores people who are afflicted with these diseases.
 * Chapter VI, Sec. 3
 * Some have held that there are only four winds: Solanus from the east; Auster from the south; Favonius from due west; Septentrio from the north. But more careful investigators tell us that there are eight.
 * Chapter VI, Sec. 4


 * To find the directions and quarters of the winds your method of procedure should be as follows. In the middle of the city place a marble amussium, laying it true by the level, or else let the spot be made so true by means of rule and level that no amussium is necessary. In the very center of that spot set up a bronze gnomon or "shadow tracker." At about the fifth hour in the morning, take the end of the shadow cast by this gnomon, and mark it with a point. Then, opening your compasses to this point which marks the length of the gnomon's shadow, describe a circle from the center. In the afternoon watch the shadow of your gnomon as it lengthens, and when it once more touches the circumference of this circle and the shadow in the afternoon is equal in length to that of the morning, mark it with a point. From these two points describe with your compasses intersecting arcs and through their intersection and the centre let a line be drawn to the circumference of the circle to give us the quarters of south and north. ...and thus we have designed a figure equally apportioned among the eight winds.
 * Chapter VI, Sec. 5-7


 * Let the directions of your streets and alleys be laid down on the lines of division between the quarters of two winds. On this principle of arrangement the disagreeable force of the winds will be shut out from dwellings and lines of houses. For if the streets run full in the face of the winds, their constant blasts rushing in from the open country, and then confined by narrow alleys, will sweep through them with great violence. The lines of houses must therefore be directed away from the quarters from which the winds blow, so that as they come in they may strike against the angles of the blocks and their force thus be broken and dispersed.
 * Chapter VI, Sec. 7-8


 * Remembering... that Eratosthenes of Cyrene, employing mathematical theories and geometrical methods, discovered from the course of the sun, the shadows cast by an equinoctial gnomon, and the inclination of the heaven that the circumference of the earth is two hundred and fifty-two thousand stadia, that is, thirty-one million five hundred thousand paces.
 * Chapter VI, Sec. 9


 * There are... many... names for winds derived from localities or from the squalls which sweep from rivers or down mountains.
 * Chapter VI, Sec. 10


 * There are the breezes of early morning; for the sun on emerging from beneath the earth strikes humid air as he returns, and as he goes climbing up the sky he spreads it out before him, extracting breezes from the vapor that was there before the dawn.
 * Chapter VI, Sec. 11


 * Some people do indeed say that Eratosthenes could not have inferred the true measure of the earth. Whether true or untrue, it cannot affect the truth of what I have written on the fixing of the quarters from which the different winds blow.
 * Chapter VI, Sec. 11


 * If the city is on the sea, we should choose ground close to the harbor as the place where the forum is to be built; but if inland, in the middle of the town.
 * Chapter VII "The Sites for Public Buildings" Sec. 1


 * For the temples, the sites for those of the gods under whose particular protection the state is thought to rest and for Jupiter, Juno, and Minerva, should be on the very highest point commanding a view of the greater part of the city. Mercury should be in the forum, or, like Isis and Serapis, in the emporium; Apollo and Father Bacchus near the theater; Hercules at the circus in communities which have no gymnasia nor amphitheatres; Mars outside the city but at the training ground, and so Venus, but at the harbor. It is moreover shown by the Etruscan diviners in treatises on their science that the fanes of Venus, Vulcan, and Mars should be situated outside the walls, in order that the young men and married women may not become habituated in the city to the temptations incident to the worship of Venus, and that buildings may be free from the terror of fires through the religious rites and sacrifices which call the power of Vulcan beyond the walls. As for Mars, when that divinity is enshrined outside the walls, the citizens will never take up arms against each other, and he will defend the city from its enemies and save it from danger in war.
 * Chapter VII, Sec. 1


 * Ceres also should be outside the city in a place to which people need never go except for the purpose of sacrifice.
 * Chapter VII, Sec. 2

Book II

 * His strange appearance made the people turn round, and this led Alexander to look at him. In astonishment he gave orders to make way for him to draw near, and asked who he was. "Dinocrates," quoth he, "a Macedonian architect, who brings thee ideas and designs worthy of thy renown. I have made a design for the shaping of Mount Athos into the statue of a man, in whose left hand I have represented a very spacious fortified city, and in his right a bowl to receive the water of all the streams which are in that mountain, so that it may pour from the bowl into the sea."
 * Introduction, Sec. 2


 * Quoth he [ Alexander ] "...as a newborn babe cannot be nourished without the nurse's milk, nor conducted to the approaches that lead to growth in life, so a city cannot thrive without fields and the fruits thereof pouring into its walls."
 * Introduction, Sec. 3


 * Dinocrates did not leave the king, but followed him into Egypt. There Alexander, observing a harbor rendered safe by nature, an excellent center for trade, cornfields throughout all Egypt, and the great usefulness of the mighty river Nile, ordered him to build the city of Alexandria, named after the king. This was how Dinocrates, recommended only by his good looks and dignified carriage, came to be so famous.
 * Introduction, Sec. 4


 * But as for me, Emperor, nature has not given me stature, age has marred my face, and my strength is impaired by ill health. Therefore, since these advantages fail me, I shall win your approval, as I hope, by the help of my knowledge and my writings.
 * Introduction, Sec. 4


 * I will prefix the motives which originally gave rise to buildings and the development of inventions in this field, following in the steps of early nature and of those writers who have devoted treatises to the origins of civilization and the investigation of inventions. My exposition will, therefore, follow the instruction which I have received from them.
 * Introduction, Sec. 5


 * They drew near, and observing that they were very comfortable standing before the warm fire, they put on logs and, while thus keeping it alive, brought up other people to it, showing them by signs how much comfort they got from it. In that gathering of men, at a time when utterance of sound was purely individual, from daily habits they fixed upon articulate words just as these had happened to come; then, from indicating by name things in common use, the result was that in this chance way they began to talk, and thus originated conversation with one another.
 * Chapter I "The Origin of the Dwelling House" Sec. 1


 * Therefore it was the discovery of fire that originally gave rise to the coming together of men, to the deliberate assembly, and to social intercourse.
 * Chapter I, Sec. 2


 * And so, as they kept coming together in greater numbers into one place, finding themselves naturally gifted beyond the other animals in not being obliged to walk with faces to the ground, but upright and gazing upon the splendor of the starry firmament, and also in being able to do with ease whatever they chose with their hands and fingers, they began in that first assembly to construct shelters. Some made them of green boughs, others dug caves on mountain sides, and some, in imitation of the nests of swallows and the way they built, made places of refuge out of mud and twigs. Next, by observing the shelters of others and adding new details to their own inceptions they constructed better and better kinds of huts as time went on.
 * Chapter I, Sec. 2


 * At first they set up forked stakes connected by twigs and covered these walls with mud. Others made walls of lumps of dried mud, covering them with reeds and leaves to keep out the rain and the heat. Finding that such roofs could not stand the rain during the storms of winter, they built them with peaks daubed with mud, the roofs sloping and projecting so as to carry off the rain water.
 * Chapter I, Sec. 3


 * The Phrygians... select a natural hillock, run a trench through the middle of it, dig passages, and extend the interior space as widely as the site admits. Over it they build a pyramidal roof of logs fastened together, and this they cover with reeds and brushwood, heaping up very high mounds of earth above their dwellings. Thus their fashion in houses makes their winters very warm and their summers very cool.
 * Chapter I, Sec. 5


 * From these early beginnings, and from the fact that nature had... equipped their minds with the powers of thought and understanding, thus putting all other animals under their sway, they next gradually advanced from the construction of buildings to the other arts and sciences, and so passed from a rude and barbarous mode of life to civilization and refinement.
 * Chapter I, Sec. 6


 * Taking courage and looking forward from the standpoint of higher ideas born of the multiplication of the arts, they gave up huts and began to build houses with foundations, having brick or stone walls, and roofs of timber and tiles; next, observation and application led them from fluctuating and indefinite conceptions to definite rules of symmetry. Perceiving that nature had been lavish in the bestowal of timber and bountiful in stores of building material, they... embellished them with luxuries.
 * Chapter I, Sec. 7


 * This book does not show of what architecture is composed, but treats of the origin of the building art, how it was fostered, and how it made progress, step by step, until it reached its present perfection.
 * Chapter I, Sec. 8


 * There is no kind of material, no body, and no thing that can be produced or conceived of, which is not made up of elementary particles; and nature does not admit of a truthful exploration in accordance with the doctrines of the physicists without an accurate demonstration of the primary causes of things, showing how and why they are as they are.
 * Chapter I, Sec. 9


 * Thales thought that water was the primordial substance of all things. Heraclitus of Ephesus... thought that it was fire. Democritus and his follower Epicurus thought that it was the atoms, termed by our writers "bodies that cannot be cut up" or, by some "indivisibles." The school of the Pythagoreans added air and the earthy to the water and fire. Hence, although Democritus did not in a strict sense name them, but spoke only of indivisible bodies, yet he seems to have meant these same elements, because when taken by themselves they cannot be harmed, nor are they susceptible of dissolution, nor can they be cut up into parts, but throughout time eternal they forever retain an infinite solidity.
 * Chapter II "On the Primordial Substance according to the Physicists" Sec. 1


 * All things... appear to be made up and produced by the coming together of these elements, so that they have been distributed by nature among an infinite number of kinds of things. Hence I believed it right to treat of the diversity and practical peculiarities of these things as well as of the qualities which they exhibit in buildings, so that persons who are intending to build may understand them and so make no mistake, but may gather materials which are suitable to use in their buildings.
 * Chapter II, Sec. 2


 * Bricks... should not be made of sandy or pebbly clay, or of fine gravel, because when made of these kinds they are in the first place heavy; and secondly when washed by the rain as they stand in walls, they go to pieces and break up, and the straw in them does not hold together on account of the roughness of the material. They should rather be made of white and chalky or of red clay, or even of a coarse grained gravelly clay. These materials are smooth and therefore durable; they are not heavy to work with, and are readily laid.
 * Chapter III "Brick" Sec. 1


 * Bricks should be made in Spring or Autumn so that they may dry uniformly.
 * Chapter III, Sec. 2


 * Bricks will be most serviceable if made two years before using; for they cannot dry thoroughly in less time. When fresh undried bricks are used in a wall, the stucco covering stiffens and hardens into a permanent mass, but the bricks settle and... the motion caused by their shrinking prevents them from adhering to it, and they are separated from their union with it. ...at Utica in constructing walls they use brick only if it is dry and made five years previously, and approved as such by the authority of a magistrate.
 * Chapter III, Sec. 2


 * There are also half bricks. ...As the bricks are always laid so as to break joints, this lends strength and a not unattractive appearance to both sides of such walls.
 * Chapter III, Sec. 4


 * In the states of Maxilua and Callet, in Further Spain, as well as in Pitane in Asia Minor, there are bricks which, when finished and dried, will float on being thrown into water. The reason why they can float seems to be that the clay of which they are made is like pumice-stone. So it is light, and also it does not, after being hardened by exposure to the air, take up or absorb liquid. ...They have therefore great advantages; for they are not heavy to use in building and, once made, they are not spoiled by bad weather.
 * Chapter III, Sec. 4


 * In walls of masonry the first question must be with regard to the sand, in order that it may be fit to mix into mortar and have no dirt in it. The kinds of pitsand are these: black, gray, red, and carbuncular. Of these the best will be found to be that which crackles when rubbed in the hand, while that which has much dirt in it will not be sharp enough. Again: throw some sand upon a white garment and then shake it out; if the garment is not soiled and no dirt adheres to it, the sand is suitable.
 * Chapter IV "Sand" Sec. 1


 * If there are no sandpits from which it can be dug, then we must sift it out from river beds or from gravel or even from the sea beach. This kind however has these defects when used in masonry: it dries slowly... and such a wall cannot carry vaultings. Furthermore, when sea-sand is used in walls and these are coated with stucco, a salty efflorescence is given out which spoils the surface.
 * Chapter IV, Sec. 2


 * Pitsand used in masonry dries quickly, the stucco coating is permanent, and the walls can support vaultings. I am speaking of sand fresh from the sandpits. For if it lies unused too long after being taken out, it is disintegrated by exposure to sun, moon, or hoar frost, and becomes earthy. So when mixed in masonry, it has no binding power on the rubble, which consequently settles and down comes the load which the walls can no longer support.
 * Chapter IV, Sec. 3


 * Fresh pitsand, however, in spite of all its excellence in concrete structures, is not equally useful in stucco, the richness of which, when the lime and straw are mixed with such sand, will cause it to crack as it dries on account of the great strength of the mixture. But river sand, though useless in "signinum" on account of its thinness, becomes perfectly solid in stucco when thoroughly worked by means of polishing instruments.
 * Chapter IV, Sec. 3


 * With regard to lime we must be careful that it is burned from a stone which, whether soft or hard, is in any case white. Lime made of close-grained stone of the harder sort will be good in structural parts; lime of porous stone, in stucco. After slaking it, mix your mortar, if using pitsand, in the proportions of three parts of sand to one of lime; if using river or sea-sand, mix two parts of sand with one of lime. These will be the right proportions for the composition of the mixture. Further, in using river or sea-sand, the addition of a third part composed of burnt brick, pounded up and sifted, will make your mortar of a better composition to use.
 * Chapter V "Lime" Sec. 1


 * The reason why lime makes a solid structure on being combined with water and sand seems to be this: that rocks, like all other bodies, are composed of the four elements. Those which contain a larger proportion of air, are soft; of water, are tough from the moisture; of earth, hard; and of fire, more brittle. Therefore, if limestone, without being burned, is merely pounded up small and then mixed with sand and so put into the work, the mass does not solidify nor can it hold together. But if the stone is first thrown into the kiln, it loses its former property of solidity by exposure to the great heat of the fire, and so with its strength burnt out and exhausted it is left with its pores open and empty. Hence, the moisture and air in the body of the stone being burned out and set free, and only a residuum of heat being left lying in it, if the stone is then immersed in water, the moisture, before the water can feel the influence of the fire, makes its way into the open pores; then the stone begins to get hot, and finally, after it cools off, the heat is rejected from the body of the lime.
 * Chapter V, Sec. 2


 * Consequently, limestone when taken out of the kiln... though its bulk remains the same as before, it is found to have lost about a third of its weight owing to the boiling out of the water. Therefore, its pores being thus opened and its texture rendered loose, it readily mixes with sand, and hence the two materials cohere as they dry, unite with the rubble, and make a solid structure.
 * Chapter V, Sec. 3


 * Pozzolana.—There is... a kind of powder which from natural causes produces astonishing results. It is found in the neighborhood of Baiae and in the country belonging to the towns round about Mt. Vesuvius. This substance when mixed with lime and rubble not only lends strength to buildings of other kinds, but even when piers of it are constructed in the sea, they set hard under water.
 * Chapter VI "Pozzolana" Sec. 1


 * What is called "sponge stone" or "Pompeian pumice" appears to have been reduced by burning from another kind of stone to the condition of the kind which we see. The kind of sponge-stone taken from this region is not produced everywhere else, but only about Aetna and among the hills of Mysia which the Greeks call the "Burnt District," and in other places of the same peculiar nature. ...it seems to be certain that moisture has been extracted from the tufa and earth, by the force of fire, just as it is from limestone in kilns.
 * Chapter VI, Sec. 2-3


 * When different and unlike things have been subjected to the action of fire and thus reduced to the same condition, if after this, while in a warm, dry state, they are suddenly saturated with water, there is an effervescence of the heat latent in the bodies of them all, and this makes them firmly unite and quickly assume the property of one solid mass.
 * Chapter VI, Sec. 4


 * There will still be the question why Tuscany, although it abounds in hot springs, does not furnish a powder out of which, on the same principle, a wall can be made which will set fast under water. ...The properties of the soil are as different and unlike as are the various countries. ...Hence it is not in all the places where boiling springs of hot water abound that there is the same combination of favourable circumstances... For things are produced in accordance with the will of nature; not to suit man's pleasure, but as it were by a chance distribution.
 * Chapter VI, Sec. 5


 * While in Campania the burning of the earth makes ashes, in Tuscany the combustion of the stone makes carbuncular sand. Both are excellent in walls but one is better to use for buildings on land, the other for piers under salt water.
 * Chapter VI, Sec. 6


 * Next comes the consideration of stone quarries from which dimension stone and supplies of rubble to be used in building are taken and brought together.
 * Chapter VII "Stone" Sec. 1


 * The stone in quarries is found to be of different and unlike qualities. In some it is soft... in others it is medium... in still others it is hard as in lava quarries. There are also numerous other kinds: for instance, in Campania, red and black tufas; in Umbria, Picenum, and Venetia, white tufa which can be cut with a toothed saw like wood.
 * Chapter VII, Sec. 1


 * All these soft kinds [of stone] have the advantage that they can be easily worked as soon as they have been taken from the quarries. Under cover, they play their part well; but in open and exposed situations the frost and rime make them crumble, and they go to pieces. On the seacoast, too, the salt eats away and dissolves them, nor can they stand great heat either.
 * Chapter VII, Sec. 2


 * Travertine and all stone of that class can stand injury whether from a heavy load laid upon it or from the weather; exposure to fire, however, it cannot bear, but splits and cracks to pieces at once. This is because in its natural composition there is but little moisture and not much of the earthy, but a great deal of air and of fire. Therefore, it is not only without the earthy and watery elements, but when fire, expelling the air from it by the operation and force of heat, penetrates into its inmost parts and occupies the empty spaces of the fissures there comes a great glow and the stone is made to burn as fiercely as do the particles of fire itself.
 * Chapter VII, Sec. 2


 * There are also several quarries called Anician in the territory of Tarquinii, the stone being of the color of peperino. ...Neither the season of frost nor exposure to fire can harm it, but it remains solid and lasts to a great age, because there is only a little air and fire in its natural composition, a moderate amount of moisture, and a great deal of the earthy. Hence its structure is of close texture and solid, and so it cannot be injured by the weather or by the force of fire. Monuments in the neighborhood of the town of Ferento which are made of stone from these quarries... gracefully carved. Old as these are, they look as fresh as if they were only just finished. Bronze workers, also, make molds for the casting of bronze out of stone from these quarries and find it very useful in bronze-founding.
 * Chapter VII, Sec. 3-4


 * Since, on account of the proximity of the stone-quarries... nearest to the city, necessity drives us to make use of their products, we must proceed as follows if we wish our work to be finished without flaws. Let the stone be taken from the quarry two years before building is to begin, and not in winter, but in summer. Then let it lie exposed in an open place. Such stone as been damaged by the two years of exposure should be used in the foundations. The rest, which remains unhurt, has passed the test of nature and will endure in those parts of the building which are above ground. This precaution should be observed, not only with dimension stone, but also with the rubble which is to be used in walls.
 * Chapter VII, Sec. 5


 * There are two styles of walls "opus reticulatum," now used by everybody and the ancient style called "opus incertum." Of these, the reticulatum looks better, but its construction makes it likely to crack... On the other hand, in the opus incertum, the rubble lying in courses and imbricated, makes a wall which though not beautiful, is stronger.
 * Chapter VIII "Methods of Building Walls" Sec. 1


 * Both kinds should be constructed of the smallest stones, so that the walls, being thoroughly puddled with the mortar, which is made of lime and sand, may hold together longer. If the stones used are soft and porous, they are apt to suck the moisture out of the mortar and so to dry it up. But when there is abundance of lime and sand, the wall, containing more moisture, will not soon lose its strength, for they will hold it together. But if the moisture is sucked out of the mortar by the porous rubble, and the lime and sand separate and disunite, the rubble can no longer adhere to them and the wall will in time become a ruin.
 * Chapter VIII, Sec. 2


 * Leave a cavity behind the [wall] facings, and on the inside build walls two feet thick, made of red dimension stone or burnt brick or lava in courses, and then bind them to the fronts by means of iron clamps and lead. ...the beds and builds, all settling equally and bonded at the joints, will not let the work bulge out, nor allow the fall of the face walls which have been tightly fastened together.
 * Chapter VIII, Sec. 4


 * 6 A wall is called isodomum when all the courses are of equal height; pseudisodomum, when the rows of courses do not match but run unequally. Both kinds are strong: first, because the rubble itself is of close texture and solid, unable to suck the moisture out of the mortar, but keeping it in its moist condition for a very long period; secondly, because the beds of the stones, being laid smooth and level to begin with, keep the mortar from falling, and, as they are bonded throughout the entire thickness of the wall, they hold together for a very long period.
 * Chapter VIII, Sec. 6


 * Our workmen, in their hurry to finish, devote themselves only to the facings of the walls, setting them upright but filling the space between with a lot of broken stones and mortar thrown in anyhow. This makes three different sections in the same structure; two consisting of facing and one of filling between them. The Greeks, however, do not build so; but laying their stones level and building every other stone lengthwise into the thickness, they do not fill the space between, but construct the thickness of their walls in one solid and unbroken mass from the facings to the interior. Further, at intervals they lay single stones which run through the entire thickness of the wall. These stones... by their bonding powers... add very greatly to the solidity of the walls.
 * Chapter VIII, Sec. 7


 * One who in accordance with these notes will take pains in selecting his method of construction, may count upon having something that will last.
 * Chapter VIII, Sec. 8


 * In Sparta, paintings have been taken out of certain walls by cutting through the bricks, then have been placed in wooden frames, and so brought to the Comitium to adorn the aedileship of [C. Visellius] Varro and [C. Licinius] Murena.
 * Chapter VIII, Sec. 9


 * At Halicarnassus, the house of that most potent king Mausolus, though decorated throughout with Proconnesian marble, has walls built of brick which are to this day of extraordinary strength, and are covered with stucco so highly polished that they seem to be as glistening as glass. That king did not use brick from poverty; for he was choke-full of revenues, being ruler of all Caria.
 * Chapter VIII, Sec. 10


 * Since such very powerful kings have not disdained walls built of brick, although... they might often have had them not only of masonry or dimension stone but even of marble, I think that one ought not to reject buildings made of brick-work, provided that they are properly "topped."
 * Chapter VIII, Sec. 16


 * The laws of the state forbid that walls abutting on public property should be more than a foot and a half thick. ...Now brick walls, unless two or three bricks thick, cannot support more than one story; certainly not if they are only a foot and a half in thickness.
 * Chapter VIII, Sec. 17


 * With the present importance of the city [of Rome] and the unlimited numbers of its population, it is necessary to increase the number of dwelling-places indefinitely. Consequently, as the ground floors could not admit of so great a number living in the city, the nature of the case has made it necessary to find relief by making the buildings high. In these tall piles reared with piers of stone, walls of burnt brick, and partitions of rubble work, and provided with floor after floor, the upper stories can be partitioned off into rooms to very great advantage. The accommodations within the city walls being thus multiplied as a result of the many floors high in the air, the Roman people easily find excellent places in which to live.
 * Chapter VIII, Sec. 17


 * On the top of the wall lay a structure of burnt brick, about a foot and a half in height, under the tiles and projecting like a coping. ...when the tiles on the roof are broken or thrown down by the wind so that rain-water can leak through, this burnt brick coating will prevent the crude brick from being damaged, and the cornice-like projection will throw off the drops beyond the vertical face, and thus the walls, though of crude brick structure, will be preserved intact.
 * Chapter VIII, Sec. 18


 * With regard to burnt brick... If not made of good clay or if not baked sufficiently, it shows itself defective... when exposed to frosts and rime. Brick that will not stand exposure on roofs can never be strong enough to carry its load in a wall. Hence the strongest burnt brick walls are those which are constructed out of old roofing tiles.
 * Chapter VIII, Sec. 19


 * As for "wattle and daub" I could wish that it had never been invented. The more it saves in time and gains in space, the greater and the more general is the disaster that it may cause; for it is made to catch fire, like torches. It seems better, therefore, to spend on walls of burnt brick, and be at expense, than to save with "wattle and daub," and be in danger. And, in the stucco covering, too, it makes cracks from the inside by the arrangement of its studs and girts. For these swell with moisture as they are daubed, and then contract as they dry, and by their shrinking cause the solid stucco to split. But since some are obliged to use it either to save time or money, or for partitions on an unsupported span, the proper method of construction is as follows. Give it a high foundation so that it may nowhere come in contact with the broken stone-work composing the floor...
 * Chapter VIII, Sec. 20


 * In Spring all trees become pregnant, and they are all employing their natural vigor in the production of leaves and of the fruits that return every year. The requirements of that season render them empty and swollen, and so they are weak and feeble because of their looseness of texture. This is also the case with women who have conceived. Their bodies are not considered perfectly healthy until the child is born.
 * Chapter IX "Timber" Sec. 1


 * With the ripening of the fruits in Autumn the leaves begin to wither and the trees, taking up their sap from the earth through the roots, recover themselves and are restored to their former solid texture. But the strong air of winter compresses and solidifies them.
 * Chapter IX, Sec. 2


 * In felling a tree we should cut into the trunk of it to the very heart, and then leave it standing so that the sap may drain out drop by drop throughout the whole of it. ...Then and not till then, the tree being drained dry and the sap no longer dripping, let it be felled and it will be in the highest state of usefulness.
 * Chapter IX, Sec. 3


 * When the juices of trees have no means of escape, they clot and rot in them, making the trees hollow and good for nothing.
 * Chapter IX, Sec. 4


 * The oak... has not the efficacy of the fir, nor the cypress that of the elm.
 * Chapter IX, Sec. 5


 * Fir: it contains a great deal of air and fire with very little moisture and the earthy, so that, as its natural properties are of the lighter class, it is not heavy. Hence, its consistence being naturally stiff, it does not easily bend under the load, and keeps its straightness when used in the framework. But it contains so much heat that it generates and encourages decay, which spoils it; and it also kindles fire quickly because of the air in its body, which is so open that it takes in fire and so gives out a great flame.
 * Chapter IX, Sec. 6


 * The part which is nearest to the earth... is without knots and is "clear." But the upper part, on account of the great heat in it throws up branches into the air through the knots and this... is called "knotwood" because of its hardness and knottiness. The lowest part, after the tree is cut down and the sapwood of the same thrown away, is split up into four pieces and prepared for joiner's work, and so is called clearstock.
 * Chapter IX, Sec. 7


 * Oak... lasts for an unlimited period when buried in underground structures. ...when exposed to moisture... it cannot take in liquid on account of its compactness, but, withdrawing from the moisture, it resists it and warps, thus making cracks.
 * Chapter IX, Sec. 8


 * The winter oak... is very useful in buildings but when in a moist place it takes in water to its centre... and so it rots. The Turkey oak and the beech both... take in moisture to their centre and soon decay. White and black poplar, as well as willow, linden, and the agnus castus... are of great service from their stiffness. ...they are a convenient material to use in carving.
 * Chapter IX, Sec. 9


 * In swampy places, alder piles driven close together beneath the foundations of buildings take in the water which their own consistence lacks and remain imperishable forever, supporting structures of enormous weight and keeping them from decay. Thus a material which cannot last even a little while above ground, endures for a long time when covered with moisture.
 * Chapter IX, Sec. 10


 * The elm and the ash... when put in shape for use in buildings... are tough and having no stiffness... soon bend. But when they become dry with age, or are allowed to lose their sap... they get harder, and from their toughness supply a strong material for dowels to be used in joints and other articulations.
 * Chapter IX, Sec. 11


 * The hornbeam... is not a wood that breaks easily and is very convenient to handle. Hence the Greeks call it "zygia," because they make of it yokes for their draught animals... Cypress and pine are also just as admirable; for although they... are apt to warp when used in buildings... they can be kept to a great age without rotting because the liquid contained within their substances has a bitter taste which by its pungency prevents the entrance of decay or of those little creatures which are destructive. Hence buildings made of these kinds of wood last for an unending period of time.
 * Chapter IX, Sec. 12


 * The cedar and the juniper tree have the same uses and good qualities... from the cedar is produced an oil called cedar oil. Books as well as other things smeared with this are not hurt by worms or decay. ...the grain of the wood is straight. The statue of Diana in the temple at Ephesus is made of it, and so are the coffered ceilings both there and in all other famous fanes, because that wood is everlasting.
 * Chapter IX, Sec. 13


 * The larch... is not only preserved from decay and the worm by the great bitterness of its sap, but also it cannot be kindled with fire nor ignite of itself, unless like stone in a limekiln it is burned with other wood. ...This is because there is a very small proportion of the elements of fire and air in its composition, which is a dense and solid mass of moisture and the earthy, so that it has no open pores through which fire can find its way... Further, its weight will not let it float in water.
 * Chapter IX, Sec. 14


 * The leaves of these [larch] trees are like those of the pine; timber from them comes in long lengths, is as easily wrought in joiner's work as is the clearwood of fir, and contains a liquid resin, of the color of Attic honey, which is good for consumptives.
 * Chapter IX, Sec. 17


 * Trees which grow in places facing the course of the sun are not of porous fiber but are solid, being drained by the dryness... The trees in sunny neighborhoods, therefore, being solidified by the compact texture of their fiber, and not being porous from moisture, are very useful, so far as durability goes, when they are hewn into timber. The lowland firs, being conveyed from sunny places, are better than those highland firs, which are brought here from shady places.
 * Chapter X "Highland and Lowland Fir" Sec. 1

Book III

 * Delphicus Apollo Socratem omnium sapientissimum Pythiae responsis est professus. Is autem memoratur prudenter doctissimeque dixisse, oportuisse hominum pectora fenestrata et aperta esse, uti non occultos haberent sensus sed patentes ad considerandum. Utinam vero rerum natura sententiam eius secuta explicata et apparentia ea constituisset!
 * Apollo at Delphi, through the oracular utterance of his priestess, pronounced Socrates the wisest of men. Of him it is related that he said with sagacity and great learning that the human breast should have been furnished with open windows, so that men might not keep their feelings concealed, but have them open to the view. Oh that nature, following his idea, had constructed them thus unfolded and obvious to the view.
 * Preface, Sec. 1


 * Of course, we need not be surprised if artistic excellence goes unrecognized on account of being unknown; but there should be the greatest indignation when, as often, good judges are flattered by the charm of social entertainments into an approbation which is a mere a pretence.
 * Introduction, Sec. 3
 * The design of a temple depends on symmetry, the principles of which must be most carefully observed by the architect.
 * Chapter I, Sec. 1


 * Then again, in the human body the central point is naturally the navel. For if a man be placed flat on his back, with his hands and feet extended, and a pair of compasses centered at his navel, the fingers and toes of his two hands and feet will touch the circumference of a circle described therefrom.
 * Chapter I, Sec. 3


 * These rules for symmetry were established by Hermogenes, who was also the first to devise the principal of the pseudodipteral octastyle.
 * Chapter III, Sec. 8


 * Then, too, the columns at the corners should be made thicker than the others by a fiftieth of their own diameter, because they are sharply outlined by the unobstructed air around them, and seem to the beholder more slender than they are.
 * Chapter III, Sec. 11


 * For the eye is always in search of beauty, and if we do not gratify its desire for pleasure by a proportionate enlargement in these measures, and thus make compensation for ocular deception, a clumsy and awkward appearance will be presented to the beholder.
 * Chapter III, Sec. 13


 * The steps in front must be arranged so that there shall always be an odd number of them; for thus the right foot, with which one mounts the first step, will also be the first to reach the level of the temple itself.
 * Chapter IV, Sec. 4


 * Hence, as the line of sight to the upper part is the longer, it makes that part look as if it were leaning back. But when the members are inclined to the front, as described above, they will seem the beholder to be plumb and perpendicular.
 * Chapter V, Sec. 13

Book IV

 * I have therefore thought that it would be a worthy and very useful thing to reduce the whole of this great art to a complete and orderly form of presentation, and then in different books to lay down and explain the required characteristics of different departments.
 * Introduction, Sec. 1


 * The third order, called Corinthian, is an imitation of the slenderness of a maiden; for the outlines and limbs of maidens, being more slender on account of their tender years, admit of prettier effects in the way of adornment.
 * Chapter I, Sec. 8


 * For we must not build temples according to the same rules to all gods alike, since the performance of the sacred rites varies with the various gods.
 * Chapter VIII, Sec. 6


 * Altars should face the east, and should always be placed on a lower level than are the statues in the temples, so that those who are praying and sacrificing may look upwards towards the divinity.
 * Chapter IX, Sec. 1

Book V

 * Furthermore, since I have observed that our citizens are distracted with public affairs and private business, I have thought it best to write briefly, so that my readers, whose intervals of leisure are small, may be able to comprehend in a short time.
 * Introduction, Sec. 3


 * Basilicas should be constructed on a site adjoining the forum and in the warmest possible quarter, so that in winter business men may gather in them without being troubled by the weather.
 * Chapter I, Sec. 4
 * But basilicas of the greatest dignity and beauty may also be constructed in the style of that one which I erected, and the building of which I superintended at Fano.
 * Chapter I, Sec. 6


 * Voice is a flowing breath of air, perceptible to the hearing by contact. It moves in an endless number of circular rounds, like the innumerably increasing circular waves which appear when a stone is thrown into smooth water, and which keep on spreading indefinitely from the centre unless interrupted by narrow limits, or by some obstruction which prevents such waves from reaching their end in due formation. When they are interrupted by obstructions, the first waves, flowing back, break up the formation of those which follow.
 * Alternate translation: The voice is a flowing breath, made sensible to the organ of hearing by the movements it produces in the air. It is propagated in infinite numbers of circular zones, exactly as when a stone is thrown into a pool of standing water countless circular undulations are generated therein, which, increasing as they recede from the center, spread out over a great distance, unless the narrowness of the locality or some obstacle prevent their reaching their termination; for the first line or waves, when impeded by obstructions, throw by their backward swell the succeeding circular lines of waves into confusion. Quoted by Ernst Mach, The Science of Mechanics: A Critical and Historical Account of its Development (1893, 1960) Tr. Thomas J. McCormack
 * Chapter IV, Sec. 6


 * In the same manner the voice executes its movements in concentric circles; but while in the case of water the circles move horizontally on a plane surface, the voice not only proceeds horizontally, but also ascends vertically by regular stages. Therefore, as in the case of the waves formed in the water, so it is in the case of the voice: the first wave, when there is no obstruction to interrupt it, does not break up the second or the following waves, but they all reach the ears of the lowest and highest spectators without an echo.
 * Chapter IV, Sec. 7


 * Hence the ancient architects, following in the footsteps of nature, perfected the ascending rows of seats in theatres from their investigations of the ascending voice, and by means of the canonical theory of the mathematicians and that of the musicians, endeavoured to make every voice uttered on the stage come with greater clearness and sweetness to the ears of the audience. For just as musical instruments are brought to perfection of clearness in the sound of their strings by means of bronze plates or horn, so the ancients devised methods of increasing the power of the voice in theatres through the application of harmonics.
 * Chapter IV, Sec. 8


 * In accordance with the foregoing investigations on mathematical principles, let bronze vessels be made, proportionate to the size of the theatre, and let them be so fashioned that, when touched, they may produce with one another the notes of the fourth, the fifth, and so on up the double octave.
 * Chapter V, Sec. 1


 * On this principle of arrangement, the voice, uttered from the stage as from a centre, and spreading and striking against the cavities of the different vessels, as it comes in contact with them, will be increased in clearness of sound, and will wake an harmonious note in unison with itself.
 * Chapter V, Sec. 3


 * It was left by Aristoxenus, who with great ability and labour classified and arranged in it the different modes. In accordance with it, and by giving heed to these theories, one can easily bring a theatre to perfection, from the point of view of the nature of the voice, so as to give pleasure to the audience.
 * Chapter V, Sec. 6


 * These are, of course, some things which, for utility's sake, must be made of the same size in a small theatre, and a large one: such as the steps, curved cross-aisles, their parapets, the passages, stairways, stages, tribunals, and any other things which occur that make it necessary to give up symmetry so as not to interfere with utility.
 * Chapter VI, Sec. 7

Book VI

 * When his companions wished to return to their country, and asked him what message he wished them to carry home, he bade them say this: that children ought to be provided with property and resources of a kind that could swim with them even out of a shipwreck.
 * Introduction, Sec. 1


 * All the gifts which fortune bestows she can easily take away; but education, when combined with intelligence, never fails, but abides steadily on to the very end of life.
 * Introduction, Sec. 3


 * If our designs for private houses are to be correct, we must at the outset take note of the countries and climates in which they are built.
 * Chapter I, Sec. 1


 * Hence, men that are born in the north are rendered over-timid and weak by fever, but their wealth of blood enables them to stand up against the sword without timidity.
 * Chapter I, Sec. 4


 * There is nothing to which an architect should devote more thought than to the exact proportions of his building with reference to a certain part selected as the standard.
 * Chapter II, Sec. 1


 * Bedrooms and libraries ought to have an eastern exposure, because their purposes require the morning light, and also because books in such libraries will not decay.
 * Chapter IV, Sec. 1


 * Even peasants wholly without knowledge of the quarters of the sky believe that oxen ought to face only in the direction of the sunrise.
 * Chapter VI, Sec. 1
 * When it appears that a work has been carried out sumptuously, the owner will be the person to be praised for the great outlay which ha has authorized; when delicately, the master workmen will be approved for his execution; but when proportions and symmetry lend it an imposing effect, then the glory of it will belong to the architect.
 * Chapter VIII, Sec. 9


 * In fact, all kinds of men, and not merely architects, can recognize a good piece of work...
 * Chapter VIII, Sec. 10

Book VII

 * It was a wise and useful provision of the ancients to transmit their thoughts to posterity by recording them in treatises, so that they should not be lost, but, being developed in succeeding generations through publications in books, should gradually attain in later times, to the highest refinement of learning.
 * Introduction, Sec. 1


 * " nothing suffers annihilation, but at dissolution there is a change, and things fall back to the essential element in which they were before. "
 * Introduction, Sec. 1
 * In order that the mortar in the joints may not suffer from frosts, drench it with oil-dregs every year before winter begins. Thus treated, it will not let the hoarfrost enter it.
 * Chapter I, Sec. 6


 * The fact is that pictures which are unlike reality ought not be approved, and even if they are technically fine, this is no reason why they should offhand be judged to be correct, if their subject is lacking in the principles of reality carried out with no violations.
 * Chapter V, Sec. 4


 * " the gravity of a substance depends not on the amount of its weight, but on its nature. "
 * Chapter VIII, Sec. 3


 * Burn shavings and splinters of pitch pine, and when they turn to charcoal, put them out, and pound them into mortar with size. This will make a pretty black for fresco painting.
 * Chapter X, Sec. 3


 * They make a fine purple colour by treating bilberry in the same way and mixing it with milk.
 * Chapter XIV, Sec. 2


 * Every hot spring has healing properties because it has been boiled with foreign substances, and thus acquires a new useful quality.
 * Chapter III, Sec. 4


 * Copious springs are found where there are mines of gold, silver, iron, copper, lead, and the like, but they are very harmful.
 * Chapter III, Sec. 5


 * At Jaffa in Syria and among the Nomads in Arabia, are lakes of enormous size that yield very large masses of asphalt, which are carried off by the inhabitants thereabouts.
 * Chapter III, Sec. 8


 * Some springs are acid, as at Lyncestus and in Italy in the Velian country, at Teano in Campania, and in many other places. These when used in drinks have the power of breaking up stones in the bladder, which form in the human body.
 * Chapter III, Sec. 17


 * There are also in some places springs which have the peculiarity of giving fine singing voices to the natives, as at Tarsus in Magnesia and in other countries of that kind.
 * Chapter III, Sec. 24

Book VIII

 * " water from clay pipes is much more wholesome than that which is conducted through lead pipes, because lead is found to be harmful for the reason that white lead is derived from it, and this is said to be hurtful to the human system. "
 * Chapter VI, Sec. 10


 * Hence, water ought by no means to be conducted in lead pipes, if we want to have it wholesome. That the taste is better when it comes from clay pipes may be proved by everyday life, for though our tables are loaded with silver vessels, yet everybody uses earthenware for the sake of purity of taste.
 * Chapter VI, Sec. 11


 * To guard against this, we must proceed as follows. Let down a lighted lamp, and if it keeps burning, a man may make the descent without danger. 
 * Chapter VI, Sec. 13

Book IX

 * Noting all these things with the great delight which learning gives, we cannot but be stirred by these discoveries when we reflect upon the influence of them one by one.
 * Introduction, Sec. 14
 * In a word, the opinions of learned authors, though their bodily forms are absent, gain strength as time time goes on, and, when taking part in councils and discussions, have greater weight than those of any living men.
 * Introduction, Sec. 17


 * The word "universe" means the general assemblage of all nature, and it also means the heaven that is made up of the constellations and the courses of the stars.
 * Chapter I, Sec. 2


 * The moon makes her circuit of the heaven in twenty-eight days plus about an hour, and with her return to the sign from which she set forth, completes a lunar month.
 * Chapter I, Sec. 5


 * If then, at this great distance, our human vision can discern that sight, why, pray, are we to think that the divine splendor of the stars can be cast into darkness?
 * Chapter I, Sec. 12


 * It is no secret that the moon has no light of her own, but is, as it were, a mirror, receiving brightness from the influence of the sun.
 * Chapter II, Sec. 3

Book X

 * The difference between "machines" and "engines" is obviously this, that machines need more workmen and greater power to make them take effect, as for instance ballistae and the beams of presses. Engines, on the other hand, accomplish their purpose at the intelligent touch of a single workman,...
 * Chapter I, Sec. 3


 * All machinery is derived from nature, and is founded on the teaching and instruction of the revolution of the firmament.
 * Chapter I, Sec. 4


 * Next I must tell about the machine of Ctesibius, which raises water to a height.
 * Chapter VII, Sec. 1


 * For siege works against bold and venturesome men should be constructed on one plan, on another against cautious men, and on still another against the cowardly.
 * Chapter XVI, Sec. 1


 * "For not all things are practicable on identical principles,"
 * Chapter XVI, Sec. 5


 * Thus by such victory, not by machines but in oppositions to the principle to the principles of machines, has the freedom of states been preserved by the cunning of architects.
 * Chapter XVI, Sec. 12