 Book 9 of 10 books on architecture. Introduction. This LibriVox recording is in the public domain, recording by Fredrik Carlson. 10 books on architecture by Vitruvius, translated by Morris Hickey Morgan. Book 9. Introduction. 1. The ancestors of the Greek have appointed such great honors for the famous athletes who are victorious at the Olympian, Pythian, Ismian and Niemian Games, that they are not only greeted with applause as they stand with palm and crown at the meeting itself, but even on returning to their several states in the triumph of victory, they ride into their cities and to their fathers' houses in four-horse chariots and enjoy fixed revenues for life at the public expense. When I think of this, I am amazed that the same honors and even greater are not bestowed upon those authors whose boundless services are performed for all time and for all nations. This would have been a practice all the more worth establishing, because in the case of athletes, it is merely their own bodily frame that is strengthened by their training, whereas in the case of authors, it is the mind, and not only their own, but also man's in general, by the doctrines laid down in their books for the acquiring of knowledge and the sharpening of the intellect. 2. What does it signify to mankind that Milo of Croton and other victors of his class were invincible? Nothing. Save that in their lifetime they were famous among their countrymen. But the doctrines of Pythagoras, Democritus, Plato and Aristotle and the daily life of other learned men spent in constant industry yield fresh and rich fruit not only to their own countrymen, but also to all nations, and they who from their tender years are filled with plentious learning which this fruit affords attained to the highest capacity of knowledge and can introduce into the state's civilized ways impartial justice and laws things without which no state can be sound. 3. Since therefore these great benefits to individuals and to communities are due to the wisdom of authors, I think that not only should palms and crowns be bestowed upon them, but that they should even be granted triumphs and judged worthy of being consecrated in the dwellings of the gods. Are there many discoveries which have been useful for the development of human life, I will cite a few examples. On reviewing these, people will admit that honors ought of necessity to be bestowed upon them. 4. First of all, among the many very useful theorems of Plato, I will cite one as demonstrated by him. Suppose there is a place or a field in the form of a square and we are required to double it. This has to be effected by means of lines correctly drawn for it will take a kind of calculations not to be made by means of a mere multiplication. The following is a demonstration. A square place 10 feet long and 10 feet wide gives an area of 100 feet. Now if it is required to double the square and to make one of 200 feet, we must ask how long will be the side of that square so as to get from this the 200 feet corresponding to the doubling of the area. Nobody can find this by means of arithmetic, for if we take 14, multiplication will give 196 feet if 15 to 125 feet. Therefore, since this is inexplicable by arithmetic, let a diagonal line be drawn from angle to angle of that square of 10 feet in length and width, dividing it into two triangles of equal size, each 50 feet in area. Taking this diagonal line as the length, describe another square. Thus we shall have in the larger square four triangles of the same size and the same number of feet as the two of 50 feet each, which were formed by the diagonal line in the smaller square. In this way, Plato demonstrated the doubling by means of lines as the figure appended at the bottom of the page will show. Then again, Pythagoras showed that a right angle can be formed without the contrivances of the artisan. Thus the result which carpenters reach very laboriously but scarcely to exactness, where their squares can be demonstrated to perfection from the reasoning and methods of his teaching. If we take three rules, one three feet, the second four feet and the third five feet in length join these rules together, where the tips touching each other so as to make a triangular figure, they will form a right angle. Now if a square be described on the length of each one of these rules, the square on the side of three feet in length will have an area of nine feet, of four feet, sixteen, of five, twenty-five, seven. Thus the area in number of feet made up of two squares on the sides three and four feet in length is equaled by that of the one square described on the side of five. When Pythagoras discovered this fact, he had no doubt that the muses had guided him in the discovery and it is said that he very gratefully offered sacrifice to them. This theorem affords a useful means of measuring many things and it is particularly serviceable in the building of staircases in buildings so that the steps may be at the proper levels. Eight. Suppose the height of the story from the flooring above to the ground below to be divided into three parts. Five of these will give the right length for the stringers of the stairway. Let four parts, each equal to one of the three composing the height between the upper story and the ground be set off from the perpendicular and there fix the lower ends of the stringers. In this manner, the steps and the stairway itself will be properly placed. A figure of this also will be found a pennant below. Nine. In the case of Archimedes, although he made many wonderful discoveries of diverse kinds, yet of them all, the following which I shall relate seems to have been the result of a boundless ingenuity. Hero, after gaining the royal power and Syracuse, resolved, as a consequence of his successful exploits, to place in a certain temple a golden crown which he had vowed to the immortal gods. He contracted for its making at a fixed price and weighed out a precise amount of gold to the contractor. At the appointed time, the latter delivered to the king's satisfaction an exquisitely finished piece of handiwork and it appeared that in weight the crown corresponded precisely to what the gold had weighed. Ten. But afterwards a charge was made that gold had been abstracted and an equivalent weight of silver had been added in the manufacture of the crown. Hero, thinking it an outrage that he had been tricked and yet not knowing how to detect the theft, requested Archimedes to consider the matter. The latter, while the case was still on his mind, happened to go to the bath and on getting into a tub observed that the more his body sank into it the more water ran out over the tub. As this pointed out the way to explain the case in question without a moment's delay and transported with joy he jumped out of the tub and rushed home naked crying with a loud voice that he had found what he was seeking. For as he ran he shouted repeatedly in Greek Eureka, Eureka. Eleven. Taking this as the beginning of his discovery it is said that he made two masses of the same weight as the crown one of gold and the other of silver. After making them he filled a large vessel with water to the very brim and dropped the mass of silver into it. As much water ran out as was equal in bulk to that of the silver sunk in the vessel. Then taking up the mass he poured back the lost quantity of water using a pint measure until it was level with the brim as it had been before. Thus he found the weight of silver corresponding to a definite quantity of water. Twelve. After this experiment he likewise dropped the mass of gold into the full vessel and on taking it out and measuring as before found that not so much water was lost but a smaller quantity namely as much less as a mass of gold lacks in bulk compared to a mass of silver of the same weight. Finally filling the vessel again and dropping the crown itself into the same quantity of water he found that more water ran over for the crown than for the mass of gold of the same weight. Hence reasoning from the fact that more water was lost in the case of the crown than in that of the mass he detected the mixing of silver with the gold and made the theft of the contractor perfectly clear. Thirteen. Now let us turn our thoughts to the researchers of Arcutus of Tarentum and Eratosthenes of Cyrene. They made many discoveries from mathematics which are welcome to men and so though they deserve our thanks for other discoveries they are particularly worthy of admiration for their ideas in that field. For example each in a different way solved the problem and joined upon Delos by Apollo in an oracle the doubling of the number of cubic feet in his altars. This done, he said, the inhabitants of the island would be delivered from an offence against the religion. Fourteen. Arcutus sold it by his figure of the semi-cylinders Eratosthenes by means of the instrument called mesolabe. 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. I find also much for admiration in the books of Democritus on Nature and in his commentary entitled Keira Kmeta in which he made use of his ring to seal with soft wax the principles which he had himself put to the test. Fifteen. These then were men whose researchers are an everlasting possession not only for the improvement of character but also for general utility. The fame of athletes however soon declines with their bodily powers. Neither when they are in the flower of their strength nor afterwards with posterity can they do for a human life which is done by the researchers of the learned. Sixteen. But although honors are not bestowed upon authors for excellence of character and teaching yet as their minds naturally looking up to the higher regions of the air or race to the sky on the steps of history it must needs be that not merely their doctrines but even their appearance should be known to posterity through time eternal. Hence men whose souls are aroused by the delights of literature cannot but carry enshrined in their hearts the likeness of the poet Aeneas as they do those of the gods. Those who are devotedly attached to the poems of Achius seem to have before them not merely his vigorous language but even his very figure. Seventeen. So two. Numbers born after our time will feel as if they were discussing nature face to face with the creatures or the art of rhetoric with Kikro. Many of our posterity will confer with Barrow on the Latin language. Likewise there will be numerous scholars who as they weigh many points with the wise among the Greeks will feel as if they were carrying on private conversations with them. In a word the opinions of learned authors though their bodily forms are absent gain strength as the time goes on and when taking part in councils and discussions have greater weight than those of any living men. Eighteen. Such Caesar are the authorities on whom I have depended and applying their views and opinions I have written the present books in the first seven treating of buildings and in the eighth of water. In this I shall set forth the rules for dialing showing how they are found through the shadows cast by the Gnomon from the Sun's rays in the firmament and on what principles these shadows lengthen and shorten. End of book nine introduction. Book nine chapters one to two of Ten Books on Architecture. This LibriVox recording is in the public domain recording by Fredrik Carlson. Ten Books on Architecture by Vitruvius translated by Morris Hickey Morgan. Chapter one. The Zodiac and the Planets. One. It is due to the divine intelligence and is a very great wonder to all who reflect upon it that the shadow of a Gnomon at the Ekenox is of one length in Athens and of another in Alexandria of another in Rome and not the same at Piazzensa or at other places in the world. Hence drawings for dials are very different from one another corresponding to the differences of situation. This is because the length of the shadow at the Ekenox is used in constructing the figure of the Analema in accordance with which the hours are marked to conform to the situation and the shadow of the Gnomon. The Analema is a basis for calculation deduced from the course of the sun and found by observation of the shadow as it increases until the winter solstice. By means of this through architectural principles and the employment of the compasses we find out the operation of the sun in the universe. Two. The word universe means the general assemblage of all nature and it also means the heaven that is made up of the constellation and the courses of the stars. The heaven revolves steadily around earth and sea on the pivots at the ends of its axis. The architect at these points was the power of nature and she put the pivots there to be as it were centers one of them above the earth and sea at the very top of the firmament and even beyond the stars composing the great bear. The other on the opposite side under the earth in the regions of the south. Round these pivots, termed in Greek poloi as centers, like those of turning lathe she formed the circles into which the heaven pauses on its everlasting way in the midst thereof the earth and sea naturally occupy the central point. Three. It follows from this natural arrangement that the central point in the north is high above the earth while on the south the region below it is beneath the earth and consequently hidden by it. Furthermore, across the middle and obliquely inclined to the south there is a broad circular belt composed of the twelve signs whose stars arranged in twelve equivalent divisions represent each a shape which nature has depicted. And so with the firmament and the other constellations round the earth and sea in glittering array completing their orbits according to the spherical shape of the heaven. Four. They are all visible or invisible according to fixed times. While six of the signs are passing along with the heaven above the earth the other six are moving under the earth and hidden by it's shadow. But there are always six of them making their way above the earth for corresponding to that part of the last sign which in the course of it's revolution falls under the earth and become concealed an equivalent part of the sign opposite to it is obliged by the law of their common revolution to pass up and having completed its circuit to emerge out of the darkness into the light of the open space on the other side. This is because the rising and setting of both are subject to one and the same power and law. Five. While these signs twelve in number and occupying each one twelve part of the firmament readily revolved from east to west the moon Mercury Venus the Sun as well as Mars Jupiter and Saturn differing from one another in the magnitude of their orbits as though their courses were at different points in a flight of steps passed through those signs in just the opposite direction from west to east in the firmament. The moon makes her circuit of the heaven in twenty eight days plus about an hour and with her return to the sign which is set forth completes a lunar month. Six. The Sun takes a full month to move across the space of one sign that is one-twelfth of the firmament. Consequently in twelve months she traverses the spaces of the twelve signs and on returning to the sign from which he began completes the period of a full year. Hence the circuit made by the moon thirteen times in twelve months is measured by the Sun only once in the same number of months. But Mercury and Venus their paths wreathing around the Sun's rays as their center retrograde and delay their movements and so from the nature of that circuit sometimes wait at stopping places within the spaces of the signs. Seven. This fact may best be recognized from Venus when she is following the Sun she makes her appearance in the sky after his setting and is then called the evening star shining most brilliantly. At other times she precedes him rising before daybreak in his name the morning star. Thus Mercury and Venus sometimes delay in one sign for a good many days and at others advance pretty rapidly into another sign. They do not spend the same number of days in every sign but the longer they have previously delayed the more rapidly they accomplish their journeys after passing into the next sign and thus they complete their appointed course. Consequently in spite of their delay in some of the signs they nevertheless soon reach the proper place in their orbits after freeing themselves from their enforced delay. Eight. Mercury on his journey through the heavens passes through the spaces of the signs in 360 days and so arrives at the sign from which he set out on his course at the beginning of his revolution. His average rate of movement is such that he has about 30 days in each sign. Nine. Venus on becoming free from the hindrance of the sun's rays crosses the space of the sign in 30 days though she thus stays less than 40 days in particular signs she makes good the required amount by delaying in one sign when she comes to a pause. Therefore she completes her total revolution in heaven in 185 days and once more enters the sign from which she previously began to move. Ten. Mars after traversing the spaces of the consolation for about 683 days arrives at the point from which he had before set out at the beginning of his course and while he passes through some of the signs more rapidly than others he makes up the required number of days whenever he comes to a pause. Later climbing with gentler pace against the revolution of the firmament travels through each sign in about 360 days and finishes in 11 years and 313 days returning to the sign in which he had been 12 years before. Saturn traversing the space of one sign in 29 months plus a few days is restored after 29 years and about 160 days to that in which he had been 30 years before. He is as it appears slower because the nearer he is to the outermost part of the firmament the greater is the orbit through which he has to pass. Eleven. The three that complete their circuits above the sun's course do not make progress while they are in the triangle which he has entered but retrograde and pause until the sun has crossed from that triangle into another sign. Some hold that this takes place because as they say when the sun is a great distance off the paths on which these stars wander are without light on account of that distance and so the darkness retards and hinders them. But I do not think that this is so. The splendor of the sun is clearly to be seen and manifest without any kind of obscurity throughout the whole firmament so that those very retrograde movements and pauses of the stars even to us. Twelve. 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. Rather will the following way of accounting for it prove to be correct. Heat summons and attracts everything towards itself. For instance we see the fruits of the earth growing up high under the influence of heat characterized and drawn up on the clouds at sunrise. On the same principle the mighty influence of the sun with its rays diverging the form of a triangle attracts the stars which follow him and as it were curbs and restraints those that proceed not allowing them to make progress but obliging them to retrograde towards themselves until it passes out into the sign that belongs to a different triangle. Thirteen. Perhaps the question will be raised why the sun by his great heat causes these tensions in the fifth sign from himself rather than in the second or third which are nearer. I will therefore set forth what seems to be the reason. His rays diverging through the firmament in straight lines as though forming an equilateral triangle that is to the fifth sign from the sun no more no less. If his rays were diffused in circuits spreading all over the firmament instead of in straight lines diverging to form a triangle they would burn up all the nearer objects. This is a fact which the Greek poet Euripides seems to have remarked for he says that places at a greater distance from the sun are in violent heat and that those which are nearer he keeps temperate. Thus in the play of Phaethon the poet writes Fourteen. The reason and the evidence of an ancient poet point to this explanation I do not see why we should decide otherwise than as I have written above on this subject. Jupiter whose orbit is between those of Mars and Saturn traverses a longer course than Mars and a shorter than Saturn. Likewise with the rest of these stars the farther they are from the outermost limits of the heaven and the orbits to the earth the sooner they are seen to finish their courses for those of them that have a smaller orbit often pass those that are higher going under them. Fifteen. For example place seven ants on a wheel such as Potter's use having made seven channels on the wheel above the center increasing successively in circumference and suppose those ants obliged to make a circuit in these channels in spite of having to move in a direction contrary to that of the wheel the ants must necessarily complete their journeys in the opposite direction and that ant which is nearest the center must finish its circuit sooner while the ant that is going round at the outer edge of the disc of the wheel must on account of the size of its circuit be much slower in completing its course even though it is moving just as quickly as the other. In the same way these stars that wiggle on against the course of the firmament are accomplishing an orbit on paths of their own but owing to the revolution of the heaven they are swept back as it goes round every day. Sixteen. The reason why some of these stars are temperate others hot and others cold appears to be this that the flame of every kind of fire rises to higher places consequently the burning rays of the sun make the ether in the regions of the course of Mars and so the heat of the sun makes him hot. Saturn on the contrary being nearest to the outermost limit of the firmament and bordering on the quarters of the heaven which are frozen is excessively cold. Hence Jupiter whose course is between the orbits of these two appears to have a moderate and very temperate influence intermediate between the cold and heat. I have now described as I have received them from the teacher the belt of the twelve signs of the seven stars that work and move in the opposite direction with the laws and numerical relations under which they pass from sign to sign and how they complete their orbits. I shall next speak of the waxing and waning of the moon according to the counts of my predecessors. Chapter 2. The Faces of the Moon. According to the teaching of Beroses who came from the state or rather civilization of the Caldees and was the pioneer of the Caldean learning in Asia, the moon is a ball one half luminous and the rest of a blue color. When in the course of her orbit she has passed below the disk of the sun she is attracted by his rays in great heat and turns thither her luminous side on account of the sympathy between light and light. Being thus summoned by the sun's disk and facing upward her lower half as it is luminous is invisible on account of the likeness to the air. When she is perpendicular to the sun's rays all her light is confined to her upper surface and she is then called the new moon. Chapter 2. As she moves on passing by to the east the effect of the sun upon her relaxes and the outer edge of the luminous side sheds its light upon the earth in an exceeding within line. This is called the second day of the moon. Day by day she is further relieved and turns and thus are numbered the third, fourth and following days. On the seventh day the sun being in the west and the moon in the middle of the firmament between the east and west she is half the extent of the firmament distant from the sun and therefore half of the luminous side is turned toward the earth. But when the sun and moon are separate by the entire extent of the firmament and the moon is in the east with the sun over against her in the west she is completely relieved by her still greater distance from his race and so on the fourteenth day she is at the full and her entire disk emits its light. On the succeeding days up to the end of the month she wanes daily as she turns in her course being recalled by the sun until she comes under his disk and race thus completing the count of the days of the month. Chapter 3. of Summers. A mathematician of great powers has left a different explanation in his teaching on this subject as I shall now set forth. 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. Of all the seven stars the moon traverses the shortest orbit and her course is nearest to the earth. Hence in every month on the day before she gets past the sun she is under the disk and race and is consequently hidden and invisible. When she is thus in conjunction with the sun she is called the new moon. On the next day reckoned as her second she gets past the sun and shows the thin edge of her sphere. Three days away from the sun she waxes and grows brighter removing further every day till she reaches the seventh when her distance from the sun is about one half extent of the firmament where her is luminous that is the half which faces toward the sun is lighted up by him. Four. On the fourteenth day being diametrically across the whole extent of the firmament from the sun she is at her full and rises when the sun is setting. Four as she takes her place over against him and distance to the whole extent of the firmament she thus receives the light from the sun throughout her entire orb. On the seventeenth day at sunrise she is inclining to the west. On the twentieth second day after sunrise the moon is about to meet heaven hence the side exposed to the sun is bright and the rest dark. Continuing thus her daily course she passes under the rays of the sun on about the twentieth day and so completes the account of the month. I will next explain how the sun passing through a different sign each month causes the days and hours to increase and diminish in length. End of book nine, chapter two Book nine, chapters three to six of ten books on architecture this Libervox recording is in the public domain recording by Fredrik Carlson ten books on architecture by Vitruvius translated by Morris Higgy Morgan. Chapter three the course of the sun through the twelve signs. One. The sun after entering the sign areas and passing through one eighth of it determines the vernal equinox. On reaching the tail of Taurus and the constellation of the Pleiades from which the front half of the Taurus projects he advances into a space greater than half the firmament moving towards the north. From Taurus he enters Gemini at the time of the rising of the Pleiades and getting higher above the earth he increases the length of the days. Next coming from Gemini into Cancer which occupies the shorter space in heaven and after traversing one eighth of it he determines the summer solstice. Continuing on he reaches the head and breast of Leo portions which are reckoned as belonging to Cancer. Two. After leaving the breast of Leo and the boundaries of Cancer the sun traversing the rest of Leo makes the days shorter diminishing the size of his circuit and returning to the same course that he had in Gemini. Next crossing from Leo into Virgo moving as far as the bosom of her garment he still further shortens his circuit making his course equal to what it was in Taurus. Advancing from Virgo by way of the bosom of her garment which forms the first part of Libra he determines the autumn equinox at the end of one eighth of Libra. Here his course is equal to what his circuit was in the sign areas. Three. When the sun has entered Scorpio at the time of the setting of the Pleiades the day is shorter as he advances toward the south. From Scorpio he enters Sagittarius and on reaching the thighs his daily course is still further diminished. From the thighs of Sagittarius which are reckoned as part of Capricornus he reaches the end of the first eighth of the letter where his course in heaven is shortest. Consequently this season from the shortness of the day is called Bruma or Dia's Brumales. Crossing from Capricornus into Aquarius he causes the days to increase to the length which they had when he was in Sagittarius. From Aquarius he enters Piscis at the time when Favonius begins to blow and here his course is the same as in Scorpio. In this way the sun pauses round through the signs lengthening or shortening the days and hours at definite seasons. I shall next speak of the other constellations formed by arrangements of stars and lying to the right and left of the belt of the signs in the southern and northern portion of the firmament. Chapter 4 The Northern Constellations 1. The Great Bear called in Greek Arctos or Helike has her warden behind her. Near him is the Virgin on whose right shoulder rests a very bright star which we called Harbinger of the Vintage and the Greeks Proturgates. But Spica in that constellation 2. Opposite there is another star coloured between the knees of the bear warden dedicated there under the name of Arcturus. 2. Opposite the head of the bear at an angle where the feet of the twins is the charioteer standing on the tip of the horn of the bull. Hence one of the same star is found on the tip of the left horn of the bull and in the right foot of the charioteer. Supported on the hand of the charioteer of the kids with the she-goat left shoulder. Above the bull and the ram is Percius having at his right with the play-heads moving beneath and at his left the head of the ram. His right hand rests on the likeness of Cassiopeia and with his left he holds the Gorgon's head by its top over the ram laying it at the feet of Adromeda. 3. Above Adromeda are the fishes one above her belly and the other above the backbone of the horse. The very bright star terminates both the belly of the horse and the head of Adromeda. Andromeda's right hand rests above the likeness of Cassiopeia and her left above the northern fish. The waterman's head is above that of the horse. The horse's hooves lie close to the waterman's knees. Cassiopeia is set apart in the midst high above the he-goat or the eagle and the dolphin and near them is the arrow. Father on is the bird whose right wing graces the head of the scepter of Cepheus with its left resting over Cassiopeia. Under the tail of the bird lie the feet of the horse. 4. Above the archer's scorpion and balance is the serpent reaching to the crown with the end of its snout. Next the serpent holder grasps the serpent above the middle in his hands and with his left foot treads squarely on the four parts of the scorpion. A little way from the head of the serpent holder is called kneeler. Their heads are the more readily to be distinguished as the stars which compose them are by no means dim. 5. The foot of the kneeler rests on the temple of the serpent which is entwined between the shebears called Septentrionus. The little dolphin moves in front of the horse. Opposite the bill of the bird is the lyre. The crown is arranged between the shoulders of the warden and the kneeler. In the northern circle are the two with their shoulder blades confronting and their breasts turned away from one another. The Greeks called the lesser bear, Kunosauro and the greater Elike. Their heads face different ways and their tails are shaped so that each is in front of the head of the other bear for the tails of both stick up over them. 6. The serpent is said to lie stretched out between their tails and in it there is a star called Polus shining near the head of the greater bear. At the nearest point the serpent wins its head round but is also flung in a fold round the head of the lesser bear and stretches out close to her feet. Here it twists back making another fold and lifting itself up bends its nose and right temple from the head of the lesser bear round towards the greater. Above the tail of the lesser bear of the feet of Cepheus and at this point at the very top of stars forming an equilateral triangle. There are a good many stars common to the lesser bear and Cepheus. I have now mentioned the constellation which are arranged in the heaven to the right of the east between the belt of the signs and the north. I shall next describe those that nature has distributed to the left of the east and the southern regions. 5. The southern constellations 1. Under the hegoat lies the southern fish facing towards the tail of the whale. The sensor is under the scorpion's sting. The four parts of the cantar are next to the balance and the scorpion and he holds in his hands the figure which astronomers call the beast. Beneath the virgin lion and crab is the twisted girdle formed by the snake extending over a whole line of stars is snout raised near the crab supporting the bow with the middle of his body near the lion and bringing his tail on which is the raven under and near the hand of the virgin. The region above his shoulders is equally bright. 2. Beneath the snake's belly at the tail lies the cantar near the bow and the lion is a ship named Argo. Her bow is invisible but her mast and the parts above the helm are in plain sight. The stern of the vessel joining the dog at the tip of his tail. The little dog follows the twins and his opposite the snake's head. The greater dog follows the lesser. Orion lies slant under the bull's hoof. In his left hand grasping his club and raising the other towards twins. 3. At his feet is the dog following a little behind the hair. The whale lies under the ram and the fishes and from his mane there is a slight sprinkling of stars called in Greek herpedoni regularly disposed towards each of the fishes. This ligature by which they hang is carried a great way inwards but reaches out to the top of the mane of the whale. The river formed of stars flows from a source at the left foot of Orion. But the water said to pour from the waterman flows between the head of the southern fish and the tail of the whale. 4. These constellations whose outlines and shapes in the heavens were designed intelligence I have described according to the view of the natural philosopher-democrates. But only those whose rising in settings we can observe and see with our own eyes. Just as the bears turned round the pivot of the axes without ever setting or sinking under the earth, there are likewise stars that keep turning round the southern pivot which on account of the inclination of the firmament lies always under the earth and being hidden there they never rise and emerge above the earth. Consequently the figures which they form are unknown to us on account of the interposition of the earth. The star Canopus proves this. It is unknown to our vicinity but we have reports of it from merchants who have been to the most distant parts of Egypt and to regions bordering on the uttermost boundaries of the earth. 6. Astrology and Weather Prognostics 1. I have shown how the firmament and the 12 signs with the constellation arranged to the north and south of them fly around the earth so that the matter may be clearly understood. For it is from this revolution of the firmament from the course of the sun through the signs in the opposite direction and from the shadows cast by equinoctial gnomes that we find the figure of the Analema. 2. As for the branch of astronomy which concerns the influences of 12 signs the 5 stars the sun and the moon upon human life we must leave all this to the calculations of the Caldians to whom belongs the art of casting nativities which enables them to declare the past and the future by means of calculations based on the stars. These discoveries have been transmitted by the men of genius and great acuteness who sprang directly from the nations of the Caldians. First of all by Borosus who settled in the island state of Kos where he opened a school. Afterwards anti-Pete pursued the subject then there was Arkinapolis who also left rules for casting nativities based not on the moment of birth but on that of conception. 3. When we come to the natural philosophy however Talus of Miletus Anaxagoras of Clasimini Pythagoras of Samus Cenophanes of Colophon and Democritus of Abdera have in various ways investigated the laws and the working of the laws by which nature governs it. In the track of their discoveries Evdoxus, Evctemon Calipus, Mito, Philippus Hipparchus, Aratus and others discovered the risings and settings of the constellations as well as weather prognostications from astronomy through the study of the calendars. This study they set forth and left to posterity. Their learning deserves the admiration of mankind for they were so solicitous as even to be able to predict long beforehand with divining mind the signs of the weather which was to fall in the future. On this subject therefore reference must be made to their labors and investigations. End of Book 9, Chapter 6 Book 9, Chapter 7 and 8 of 10 Books on Architecture This LibriVox recording is in the public domain recording by Fredrik Carlson Books on Architecture by Vitruvius translated by Morris Hickey Morgan Chapter 7 The Analemma and its Applications One In distinction from the subjects first mentioned we must ourselves explain the principles which govern the shortening and lengthening of the day. When the sun is at the equinoxes that is passing through areas or Libra, he makes the Gnomon cast a shadow equal to eight ninths of its own length in the latitude of Rome. In Athens the shadows is equal to three fourths of the length of the Gnomon at Rhodes to five sevenths at Tarentum to nine elevenths at Alexandria to three fifths and so at other places it is found that the shadows of equinoxial Gnomons are naturally different from one another. Hence wherever sundial is to be constructed we must take the equinoxial shadow of the place. If it is found to be as in Rome equal to eight ninths of the Gnomon let a line be drawn on a plane surface and in the middle thereof erect a perpendicular plumbed the line which perpendicular is called the Gnomon. Then from the line in the plane let the line of the Gnomon be divided off by compasses into nine parts and take the point designating the ninth part as a center to be marked by the letter A. Then opening the compasses from the center to the line in the plane we describe a circle. This circle is called the Meridian. Three. Then on the nine parts between the plane and the center of the Gnomon take eight and mark them off on the line in the plane to the point C. This will be the equinoxial shadow of the Gnomon. From that point marked by C let a line be drawn through the center at the point A and this will represent a ray of the sun at the equinox. Then extending the compasses from the center of the line in the plane mark off the equidistant points E on the left and I on the right on the two sides of the circumference and let a line be drawn through the center dividing the circle into two equal semicircles. This line is called by mathematicians the horizon. Four. Then take a fifteenth part of the entire circumference and placing the center of the compasses on the circumference at the point where the equinoxial ray cuts it at the letter F, mark off the points G and H on the right and left. Then lines must be drawn from this and the center to the line of the plane at the points T and R and thus one will represent the ray of the sun in winter and the other the ray in summer. Opposite E will be the point I where the line drawn through the center at the point A cuts the circumference, opposite G and H will be the points L and K and opposite C, F and A will be the point N. Five. Then diameters are to be drawn from G to L and from H to K. The upper will denote the summer and the lower the winter portion. These diameters are to be divided equally in the middle at the points M and O and those centers marked. Then through these marks in the center A draw a line extending to the two sides of the circumference at the points P and Q. This will be a line perpendicular to the equinoctial ray and it is called in mathematical figures the axis. From these same centers open the compasses to the ends of the diameters and describe semi-circles, one of which will be for summer and the other for winter. Six. Then at the points at which the parallel lines cut the line called horizon, the letter S is to be on the right and the letter V on the left and from the extremity of the summer circle at the point G draw a line parallel to the axis extending to the left hand semi-circle at the point H. This parallel line is called a logitimus. Then center the compasses at the point where the equinoctial ray cuts that line at the letter D and open them to the point where the summer ray cuts the circumference at the letter H. From the equinoctial center with rages extending to the summer ray describe the circumference of the circle of the months which is called meneus. Thus we shall have the figure of the analemma. Seven. This having been drawn and completed, the scheme of hours is next to be drawn on the base plates from the analemma according to the winter lines or those of summer or the equinoxes or the months and thus many different kinds of dials may be laid down and drawn by this ingenious method. But the result of all these shapes and designs is in one respect the same. Namely the days of the equinoxes and of the winter and summer solstices are always divided into 12 equal parts. Omitting details therefore not for fear of the trouble but lest I should prove tiresome by writing too much, I will state by whom the different classes and designs of dials have been invented. For I cannot invent new kinds myself at this late day nor do I think that I ought to display the inventions of others as my own. Hence I will mention those that have come down to us and by whom they were invented. Chapter 8 Sundials and water clocks. One. The semi-circular form hollowed out of a square block and cut under to correspond to the polar altitude is said to have been invented by Borosis de Caldean. The scaffold or hemisphere by Harry Starkers of Samas as well as the disk on a plain surface. The arachne by the astronomer of Doxus or as some say by Apollonius. The plinthium or lacunar like the one placed in the Circus Flaminius by Scopinas of Syracuse. The Prosta Historeumena by Parminio. The Prospan Clima by Theodosius and Andreas. The Pelicinum by Patroclus. The Cone by Dionysus Dorus. The Quiver by Apollonius. The men whose names are written above as well as many others have invented and left us other kinds as for instance the con arachne, the conical plinthium and the anti-Borion. Many have also left us written directions for making dials of these kinds for travelers which can be hung up. Whoever wishes to find their base plates can easily do so from the books of these writers provided only he understands the figure of the man. Methods of making water clocks have been investigated by the same writers and first of all by Sticebius the Alexandrian who also discovered the natural pressure of the air and pneumatic principles. It is worthwhile for students to know how these discoveries came about. Sticebius born at Alexandria was the son of a barber. Preeminent for natural ability in great industry he is said to have amused himself with wishing to hang a mirror in his father's shop in such a way that on being lowered and raced again its weight should be raced by means of a concealed cord he employed the following mechanical contrivance. Three. Under the roof beam he fixed a wooden channel in which he arranged a block of pulleys. He carried the cord along the channel to the corner where he set up some small piping. Into this a little ball attached to the cord was made to descend. As the weight fell into the narrow limits of the pipe it naturally compressed the enclosed air and as its fall was rapid it forced the mass of compressed air through the outlet into the open air thus producing a distinct sound by the concussion. Four. Hence Sticebius observing that sounds and tones were produced by the contact between the free air and that which was forced from the pipe made use of this principle in the construction of the first water organs. He also devised the methods of raising water, automatic contrivances and amusing things of many kinds including among them the construction of water clocks. He began by making an orifice in a piece of gold or by perforating again because these substances are not worn by the action of water and do not collect dirt so as to get stopped up. Five. A regular flow of water through this raises an inverted bowl called by the machinations the cork or drum. To this are attached a rack and a revolving drum both fitted with teeth at regular intervals. These teeth acting upon one another induce a measured revolution and movement. Other racks and other drums similarly toothed and subject to the same motion give rise by the revolution to various kinds of motions by which figures are moved, cones, devolve, pebbles or eggs fall trumpet sound and other incidental effects take place. Six. The hours are marked in these clocks on a column or a pellister and a figure emerging from the bottom points to them with a rod throughout the whole day. Their decrease or increase in length with the different days and months must be adjusted by inserting or withdrawing wedges. The shutoffs for regulating the water are constructed as follows Two cones are made one solid and the other hollow turned on a lathe so that one will go into the other and fit it perfectly. A rod is used to loosen or to bring them together thus causing the water to flow rapidly or slowly into the vessels according to these rules and by this mechanism water clocks may be constructed for use in winter. Seven. But it proves that the shortening or lengthening of the day is not in agreement with the insertion and removal of the wedges because the wedges may very often cause errors. The following arrangement will have to be made. Let the hours be marked off transversely on the column from the analema and let the lines of the months also be marked upon the column. Then let the column be made to revolve in such a way that as it turns continuously towards the figure and the rod with which the emerging figure points to the hours, it may make the hours short or long according to the respective months. Eight. There is also another kind of winter dial called the anaphoric and constructed in the following way. The hours indicated by bronze rods in accordance with the figure of the analema radiate from a center on the face. Circles are described upon it marking the limits of the months. Behind these rods there is a drum on which is drawn and painted the firmament with the circle of the signs. In drawing the figures of the 12 celestial signs one is represented by the larger and the next smaller proceeding from the center. Into the back of the drum in the middle are revolving axes inserted and around that axis is wound a flexible bronze chain at one end at which hangs the cork which is raised by the water and at the other a counter poise of sand equaled in weight to the cork. Nine. Hence the sand sings that the cork is raised by the water and in sinking turns the axes and the axes the drum. The revolution of this drum causes sometimes a larger and sometimes a smaller portion of the circle of the signs to indicate during the revolution the proper length of the hours corresponding to their seasons. For in every one of the signs there are as many holes as the corresponding month has days. And a boss which seems to be holding the representation of the sun on the dial designates the spaces for the hours. This as it is carried from hole to hole completes the circuit of a full month. Ten. Hence just as the sun during his passage through the constellations makes the days and hours longer or shorter so the boss on a dial moving from point to point in a direction contrary to that of the revolution of the drum in the middle is carried day by day sometimes over wider and sometimes over narrower spaces giving a representation of hours and days within the limits of each month. To manage the water so that it may flow regularly we must proceed as follows. Eleven. Inside behind the face of the dial plays a reservoir and let the water run down into it through a pipe and let it have a hole at the bottom. Fastened to it is a bronze drum with an opening through which the water flows into it from the reservoir. And closed in this drum there is a smaller one the two being perfectly jointed together by tenon and socket in such a way that the smaller drum revolves closely but easily in the larger like a stopcock. Twelve. On the lip of the larger drum there are 365 points marked off at equal intervals. The rim of the smaller one has a tongue fixed on its circumference with a tip directed towards those points and also in this rim is a small opening through which water runs into the drum and keeps the works going. The figures of the celestial signs being on the lip of the larger drum and this drum being motionless let the sign cancer be drawn at the top. With Capricornus perpendicular to it at the bottom, Libra at his spectator is right, Arius at his left and let the other signs be giving places between them as they are seen in the heavens. Twelve. Hence when the sun is in Capricornus the tongue on the rim touches every day one of the points in Capricornus on the lip of the larger drum and is perpendicular to the strong pressure of this running water. So the water is quickly driven through the opening in the rim to the inside of the vessel which receiving it and soon becoming full shortens and diminishes the length of the days and hours. But then owing to the daily revolution of the smaller drum, its tongue reaches the points in Aquarius, the opening will no longer be perpendicular and the water must give up its flow and run in a slower stream. Thus the less velocity with which the vessel receives the water the more the length of the days is increased. Fourteen. Then the opening in the rim passes from point to point in Aquarius and Piscus as though going upstairs and when it reaches the end of the first eighth of Arius the fall of the water is of medium strength indicating the equinoctial hours. From Arius the opening passes with the revolution of the drum through Taurus and Gemini to the highest points at the end of the first eighth of Cancer and when it reaches that point the power diminishes and hence with a slower flow its delay lengthens the days in the sign Cancer producing the hours of the summer solstice. From Cancer it begins to decline and during its return it passes through Leo and Virgo to the points at the end of the first eighth of Libra. Gradually shortening and diminishing the length of the hours until it becomes to the points in Libra where it makes the hours equinoctial once more. Fifteen. Finally the opening comes down more rapidly through Scorpio and Sagittarius and on its return from its revolution to the end of the first eighth of Capricornus the velocity of the stream renews once more the short hours of the winter solstice. The rules and forms of construction employed in designing dials have now been described as well as I could. It remains to give an account of machines and their principles. In order to make my treatise on architecture complete I will begin to write on this subject in the following book. End of book nine Maurice Hickey Morgan Book ten. Introduction One. In the famous and important Greek city of Ephesus there is said to be an ancient ancestral law the terms of which are severe but it's justice is not inequitable. When an architect accepts the charge of a public work he has to promise what the cost of it will be. His estimate is handed to the magistrate and his property is pledged as security until the work is done. When it is finished if the outlay agrees with his statement he is complimented by decrees and marks of honour. If no more than a fourth has to be added to his estimate it is furnished by the treasury and no penalty is afflicted. But when more than one fourth has to be spent in addition on the work the money required to finish it is taking from his property. Two. Would to God that this were also law of the Roman people not merely for public but also for private buildings. For the ignorant would no longer run riot with impunity but men who are well qualified by an exact scientific training would unquestionably adopt the profession of architecture. Gentlemen would not be misled into limitless and prodigal expenditure even to ejectments from their states and the architects themselves could be forced by fear of the penalty to be more careful in calculating and stating the limit of expense so that gentlemen would procure their buildings for that which they had expected or by adding only a little more. It is true that men who can afford to devote 400,000 to a work may hold on if they have to add another 100,000 from the pleasure which the hope of finishing it gives them. But if they are lauded with a 50% increase or with an even greater expense they lose hope sacrifice what they have already spent and are compelled to leave off broken in fortune and in spirit. 3. This fault appears not only in the matter of buildings but also in the shows given by magistrates whether of gladiators in the forum or of plays on the stage. Here neither delay nor postponement is permissible but the necessity of the case required that everything should be ready at a fixed time. The seats for the audience, the awning drawn over them and whatever in accordance with the customs of the stage is provided by machinery to please the eye of the people. These matters require careful thought and planning by a well trained intellect for none of them can be accomplished without machinery and without hard study skillfully applied in various ways. 4. Therefore since such are our traditions and established practices it is obviously fitting that the plans should be worked out carefully and with the greatest attention before the structures are begun. Consequently as we have no law or customary practice to compel this and as every year both preeters and ad-hours have to provide machinery for the festivals I have thought it not out of place Emperor since I have treated of buildings in the earlier books to set forth and teach in this which forms the final conclusion of my treatise the principles which govern machines. 1. Machines and Implements 1. A machine is a combination of timbers cast and together chiefly efficacious and moving great weights. Such a machine is set in motion on scientific principles in circular rounds which the Greek call kyklike keneos. There is however a class intended for climbing termed in Greek acrobaticon another works by air which with them is called pneumaticon and a third for hoisting this the Greeks named Barolcos. In the climbing class our machine so disposed that one can safely climb up high by means of timbers set up on end and connected by crossbeams in order to view operations in the pneumatic class air is forced by pressure to produce sounds and tones as in an organon. 2. In the hoisting class heavy weights are removed by machines which raise them up and set them in position the climbing machines display no scientific principle but merely a spirit of daring. It is held together by dowels and crossbeams and twisted lashings and supporting props. A machine that gets its motive power by pneumatic pressure will produce pretty effects by scientific refinements but the hoisting machine has opportunities for usefulness which are greater and full of grandeur and it is of the highest efficacy when used with intelligence. 3. Some of these act on the principles of the meccane others on that of the organon. 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 as the Scorpio or Anasus Cyclae when they are turned. Therefore engines as well as machines are in principle practical necessities without which nothing can be unattended with difficulties. 4. All machinery is derived from nature and is founded on the teaching and instruction of the revolution of the firmament. Let us but consider the connected revolutions of the sun, the moon and the five planets without the revolution of which due to mechanism we should not have had the alternation of day and night nor the ripening of fruits. Thus when our ancestors had seen that this was so they took their models from nature and by imitating them were led on by divine facts until they perfected their contrivances which are so serviceable in our life. Some things with a view to a greater convenience they worked out by means of machines and their revolutions. Others by means of engines and so whatever they found to be useful for investigations for the arts and for the established practices they took care to improve step by step on scientific principles. 5. Let us first take unnecessary inventions such as clothing and see how the combination of warp and booth on the loom which does its work on the principle of an engine not only protects the body by covering it but also gives it honorable apparel. We should not have food in abundance unless yokes and plows for oxen and for all draught animals had been invented. If there had been no provision of windlesses, press beams and levers for presses we could not have had the shining oil nor the fruit of the vine to give us pleasure and these things could not be transported on land without the invention of the mechanism of carts or wagons nor on the sea without that of ships. 6. The discovery of the method of testing weights by steel yards and balances saves us from fraud by introducing honest practices into life. There are also innumerable ways of employing machinery about which it seems unnecessary to speak since they are at hand every day. Such as mills blacksmiths, bellows, carriages gigs, turning lathe and other things which are habitually used as general conveniences hence we shall begin by explaining those that rarely come to hand so that they may be understood. End of Book 10, Chapter 1 Book 10, Chapter 2 of Ten Books on Architecture This LibriVox recording is in public domain recording by Fredrik Carlson Ten Books on Architecture by Vitruvius translated by Morris Hickey Morgan Chapter 2 Hoisting Machines 1. First we shall treat of those machines which are of necessity made ready when temples and public buildings are to be constructed. Two timbers are provided strong enough for the weight of the loud. They are fastened together at the upper end by a bolt then spread apart at the bottom and so set up being kept upright by ropes attached at the upper ends and fixed at intervals all round. At the top is fastened a block which some call a wreckimus. In the block two sheaves are enclosed turning on axles. The traction rope is carried over the sheave at the top then let fall and pass round a sheave in a block below. Then it is brought back to a sheave at the bottom of the upper block and so it goes down to the lower block where it is fastened through a hole in that block. The other end of the rope is brought back and down between the legs of the machine. Two. Socket pieces are nailed to the hinder faces of the squared timbers at the point where they are spread apart and the ends of the windlass are inserted into them so that the axles may turn freely. Close to each end of the windlass are two holes so adjusted that hand spikes can be fitted into them. To the bottom of the lower blocks are fastened chairs made of iron whose prongs are brought to bear upon the stones which have holes bored in them. When one end of the rope is fastened to the windlass turned round by working the hand spikes the rope wins round the windlass gets taught and thus it raises the load to the proper height and to its place in the work. Three. This kind of machinery revolving with three sheaves is called a trispast. When there are two sheaves turning in the block beneath and three in the upper the machine is termed a pentaspast. But if we have to furnish machines for heavier loads we must use timbers of greater length and thickness providing them with correspondingly large bolts of the top and windlass is turning at the bottom. When these are ready let four stays be attached and left lying slack in front. Let the backstays be carried over the shoulders of the machine to some distance and if there is nothing to which they can be fastened sloping piles should be driven. The ground rammed down all round to fix them firmly and the ropes made fast to them. Four. A block should then be attached by a stout cord to the top of the machine and from that machine a rope should be carried to a pile and to a block tied to the pile. Let the rope be put in round the sheave of this block and brought back to the block that is fastened at the top of the machine. Round its sheave the rope should be passed and then should go down from the top and back to the windlass which is at the bottom of the machine and there be fastened. The windlass is now to be turned to fix the machine of itself without danger. Thus the machine of the larger kind will be set in position with its ropes in their places about it and it stays attached to the piles. Its blocks and traction ropes are arranged as described above. Five. But if the loads of the material for the work are still more colossal in size and weight we shall not entrust them to a windlass but set in an axle tree held by sockets as the windlass was and carrying on its large drum which some term a wheel but the Greeks call it Amphisis or Peritechion. Six. And the blocks of such machines are not arranged in the same but in a different manner for the rows of sheaves in them are doubled both at the bottom and at the top. The traction rope is passed through a hole in the lower block in such a way that the two ends of the rope are of equal length when it is stretched out and both portion are held there at the lower block by a cord and lashed so that they cannot come out either to the right or the left. Then the ends of the rope are brought up into the block at the top from the outside and passed down over its lower sheaves and so returned to the bottom and are passed from the inside to the sheaves in the lowest block and then are brought up on the right and left and returned to the top and round the highest set of sheaves. Seven. Passing over these from the outside they are then carried to the right and left of the drum there as to stay fast. Then another rope is wound round the drum and are carried to a capstan and when that is turned it turns the drum and the axle tree that ropes get taught as they wind round regularly and thus they raise the louse smoothly and with no danger but if a large drum is placed either in the middle or at one side without any capstan men can tread in it and accomplish the work more expeditiously. Eight. There is also another kind of machine ingenious enough and easy to use with speed but only experts can work with it. It consists of a single timber which is set up and held in place by stays on four sides. Two cheeks are nailed on below the stays. A block is fastened by ropes above the cheeks and a straight piece of wood above two feet long, six digits wide and four digits thick is put under the block. The blocks used have each three rows of sheaves side by side and since three traction ropes are fastened at the top of the machine then they are brought to the block at the bottom and passed from inside round the sheaves that are nearest the top of it then they are brought back to the upper block and passed inwards from outside round the sheaves nearest the bottom. Nine. On coming down to the block at the bottom they are carried round its second row of sheaves from the inside to the outside and brought back to the second row at the top passing around it and returning to the bottom then from the bottom they are carried to the summit where they pass round the highest row of sheaves and then return to the bottom of the machine. At the foot of the machine a third block is attached the Greeks call it epagon but our people artemon. This block fastened at the foot of the machine has three sheaves in it round which the ropes are passed and then delivered to men to pull thus three rows of men pulling without a capstan can quickly raise the load to the top. Ten. This kind of machine is called a polyspast because of the many revolving sheaves to which its dexterity and dispatched are due. There is also this advantage in the erection of only a single timber that by previously inclining it to the right or left as much as one wishes the load can be set down at one side. All these kinds of machinery described above are in their principle suited not only to the purposes mentioned but also to the loading and unloading of ships some kinds being set upright and others placed horizontally on revolving platforms. On the same principle ships can be hauled ashore by means of arrangements of ropes and blocks used on the ground without setting up timbers. Eleven. It may also not be out of place to explain the ingenious procedure of cursifron. Desiring to convey the shafts of the temple of Diana at Ephesus from the stone quarries and not trusting to carts lest their wheels should be engulfed by the great weights of the loud and softness of the roads in the plain, he tried the following plan. Using four inch timbers he joined two of them each as long as the shaft with two cross pieces set between them dovetailing all together and then leaded iron gudgions shaped like dovetails into the ends of the shafts as dowels are leaded and in the woodwork he fixed rings to contain the pivots and fastened wooden cheeks to the ends. The pivots being closed in the rings turned freely so when yokes of oxen began to draw the four inch frame they made the shaft revolve constantly turning it by means of the pivots and rings. Twelve. When they had thus transported all the shafts and it became necessary to transport the architraves cursifron's son Metagonus extended the same principle from the transportation of the shafts to the bringing down of the architraves. He made wheels each about 12 feet in diameter and closed the ends of the architraves in the wheels. In the ends he fixed pivots and rings in the same way. So when the four inch frames were drawn by oxen the wheels turned on the pivots and closed in the rings and the architraves which were enclosed like axles in the wheels soon reached the building in the same way as the shafts. The rollers used for smoothing the walks in polystri were served as an example of this method but it could not have been employed unless the distance had been short for it is not more than eight miles from the stone quarries to the temple and there is no hill but an uninterrupted plane. Thirteen. In our own times however when the pedestal of the colossal apollo in his temple had cracked with age they were afraid that the statue would fall and be broken and so they contracted for the cutting of a pedestal from the same quarries. The contract was taken by one Paconius. This pedestal was 12 feet long and 8 feet wide and 6 feet high. Paconius with confident pride did not transported by the method of metagonists but determined to make a machine of a different sort though on the same principle. Fourteen. He made wheels of about 15 feet in diameter and in these wheels he enclosed the ends of the stone then he fastened two inch crossbars from wheel to wheel round the stone encompassing it so that there was an interval of not more than one foot between bar and bar then he coiled a rope round the bars yoked up his oxen and began to draw on the rope. Consequently as it uncoiled it did indeed cause the wheels to turn but it could not draw them in a line straight along the road but kept swerving out to one side. Hence it was necessary to draw the machine back again. Thus by this drawing to and fro Paconius got into such financial embarrassment that he became insolvent. Fifteen. I will digress a bit and explain how these stone quarries were discovered. Pixodorus was a shepherd who lived in that vicinity. When the people of Ephesus were planning to build a temple of Diana in marble and debating whether to get the marble from Paris, Proconosus, Heraclia, or Thasus, Pixodorus drove out his sheep and was feeding his flock in that very spot. Then two rams ran at each other and each passing the other one of them after his charge struck his horns against a rock from which a fragment of extremely white color was dislodged. So it is said that Pixodorus left his sheep and the mountains and ran down to Ephesus carrying the fragment since that very thing was the question of the moment. Therefore they immediately decreed honors to him and changed his name so that instead of Pixodorus he should be called Evangelus. And to this day the chief magistrate goes out to that very spot every month and offers sacrifice to him and if he does not he is finished. End of Book 10, Chapter 2 Book 10, Chapter 3-6 of 10 books on architecture this LibriVox recording is in the public domain recording by Fredrik Carlson 10 books on architecture by Vitruvius translated by Morris Hickey Morgan Chapter 3 The elements of motion 1. I have briefly set forth what I thought necessary about the principles of hoisting machines in them two different things unlike each other work together as elements of their motion and power to produce these effects one of them is the right line which the Greeks term Ethhea the other is the circle which the Greeks call Keklate. But in point of fact neither rectilinear without circular motion nor revolutions without rectilinear motion can accomplish the racing of lords I will explain this that it may be understood. 2. At centers inserted into the sheaves and these are fastened in the blocks and rope carried over the sheaves drawn straight down and fastened to a windlass causes the load to move upward from its place as the hand spikes are turned the pivots of this windlass lying as centers in right lines in its socket pieces and the hand spikes inserted in its holes make the loud rise when the ends of the windlass revolve in a circle like a lathe just so when an iron lever is applied to a weight which a great hands cannot move with the fulcrum which the Greeks called hopomocleon lying as a center in a right line under the lever and with the tongue of the lever placed under the weight one man's strength bearing down upon the head of it heaves up the weight. 3. 4. As the shorter four part of the lever goes under the weight from the fulcrum that forms the center the head of it which is farther away from that center on being depressed is made to describe a circular movement thus by pressure brings to an equilibrium the weight of a great very load by means of a few hands again if the tongue of an iron lever is placed under a weight and its head is not pushed down but on the contrary is heaved up the tongue supported on the surface of the ground will treat that as the weight and the edge of the weight itself as the fulcrum thus not so easily as by pushing down but by motion in the opposite direction the weight of the loud will nevertheless be raised if therefore the tongue of a lever lying on a fulcrum goes too far under the weight and its head exerts its pressure too near the center it will not be able to elevate the weight nor can it do so unless as described above the length of the lever is brought to equilibrium by the depression of its head. 4. This may be seen from the balances that we call steel yards when the handle is set as a center close to the end from which the scale hangs and the counter poise is moved along towards the other arm of the beam shifting from point to point as it goes farther or even reaches the extremity a small and inferior weight becomes equal to a very heavy object that is being weighed on account of the equilibrium that is due to the leveling of the beam thus as it withdraws from the center a small and comparatively light counter poise slowly turning the scale makes a greater amount of weight rise gently upwards and below. 5. So too the pilot of the biggest merchant man grasping the steering over by its handle which the Greeks call oiks and with one hand bringing it to the turning point according to the rules of his art by pressure about a center can turn the ship although she may be laden with a very large or even enormous burden of American dice and provisions and when her sails are set only half way up the mast a ship cannot run quickly and when the yard is hoisted to the top she makes much quicker progress because then the sails get the wind not when they are too close to the heel of the mast which represent the center but when they have moved farther away from it to the top. 6. as a lever thrust under a weight is harder to manage and does not put forth its strength if the pressure is exerted at the center but easily raises the weight when the extreme end of it is pushed down so sails that are only half way less affect but when they get farther away from the center and are hoisted to the very top of the mast the pressure at the top forces the ship to make greater progress though the wind is no stronger but just the same again take the case of oars which are fastened to the tholes by loops when they are pushed forward and drawn back by the hand if the ends of the blades are at some distance from the center the oars foam with the waves of the sea and drive the ship forward in a straight line with a mighty impulse while her prow cuts through the rare water. 7. and when the heaviest burdens are carried on poles by four or six porters at a time they find the centers of balance at the very middle of the poles so that by distributing the dead weight of the burden according to a definitely proportion division each laborer may have an equal share to carry on his neck for the poles from which the straps for the burden of the four porters hang are marked off at their centers by nails to prevent the straps from slipping to one side if they shift beyond the mark at the center they weigh heavily upon the place to which they have come nearer like the weight of a steel yard when it moves from the point of equilibrium towards the ends of the weighing apparatus. 8. in the same way oxen have an equal draw when their yoke is adjusted at its middle by the yoke strap to the pole but when their strength is not the same the stronger out does the other the strap is shifted so as to make one side of the yoke longer which helps the weaker ox thus in the case of both poles and yokes when the straps are not fastened at the middle but at one side the farther the strap moves from the middle the shorter it makes one side and the longer the other so if both ends are carried round in circles using as a center the point to which the strap has been brought the longer end a larger and the shorter end a smaller circle. 9. just as smaller wheels move harder and with greater difficulty than larger ones so in the case of poles and yokes the parts where the intervals from the center to end is less bear down hard upon the neck but where the distance from the same center is greater they ease the burden both for draw and carriage as in all these cases motion is obtained by means of right lines at the center of the circles so also farm wagons traveling carriages, drums mill screws, scorpions, ballastai press beams and all other machines produce the results intended on the same principles by turning about a rectilinear axis and by the revolution of a circle. 4. Engines for racing water. 1. I shall now explain the making of the different kinds of engines which have been invented for racing water will first speak of the tympanum although it does not lift the water high it raises a great quantity very quickly an axle is fashioned on a lathe or with the compasses it ends are shot with iron hoops and it carries round its middle a tympanum made of boards joined together it rests on posts which have pieces of iron on them under the ends of the axle. In the interior of this tympanum there are 8 cross pieces set at intervals extending from the axle to the circumference of the tympanum and dividing the space in the tympanum into equal compartments 2. Planks are nailed round the face of it leaving 6 inch apertures to admit the water. At one side of it there are also holes like those of a dove cut next to the axle one for each compartment. After being smeared with pitch like a ship the thing is turned by the thread of men and racing the water by means of the apertures in the face of the tympanum delivers it through holes next to the axle into a wooden trough set underneath with a conduit joined to it thus a large quantity of water is furnished for irrigation in gardens or for supplying the needs of saltworks. 3. But when it has to be raised higher the same principle will be modified as follows A wheel on an axle is to be made large enough to reach the necessary height. All round the circumference of the wheel there will be cubical boxes made tight with pitch and wax so when the wheel is turned by treading the boxes carried up full and again returning to the bottom will of themselves discharge into the reservoir what they have carried up. 4. But if it has to be supplied to a place still more high a double iron chain which will reach the surface when let down is passed round the axle of the same wheel with bronze buckets attached to it each holding about 6 pints. The turning of the wheel winding the chain round the axle will carry the buckets to the top and as they pass above the axle they must tip over and deliver it into the reservoir what they have carried up. 5. Water wheels and water mills 1. Wheels on the principles that have been described above are also constructed in rivers round their faces float boards are fixed which on being struck by the current of the river make the wheel turn as they move and thus by raising the water in the boxes and bringing it to the top they accomplish the necessary work through which being turned by the mere impulse of the river without any treading on the part of workmen. 2. Water mills are turned on the same principle everything is the same in them except that a drum with teeth is fixed into one end of the axle it is set vertically on its edge and turns in the same plane with the wheel. Next to this larger drum it is fixed but set horizontally and this is attached to the millstone Thus the teeth of the drum which is fixed to the axle make the teeth of the horizontal drum move and cause the mill to turn a hopper hanging over this contrivance supplies the mill with corn and mill is produced by the same revolution. 6. The water screw 1. There is also the method of the screw which raises a great quantity of water by as does the wheel. The method of constructing it is as follows A beam is selected the thickness of which in digits is equivalent to its length and feet this is made perfectly round The ends are to be divided off on their circumference with a compass into 8 parts by quadrants and octans and let the lines be so placed that if the beam is laid in a horizontal position the lines on the two ends may perfectly correspond with each other and intervals of the size part of the circumference of the beam may be laid off on the length of it then placing the beam in a horizontal position let perfectly straight lines be drawn from one end to the other so the intervals will be equal in the directions both of the periphery and of the length where the lines are drawn along the length the cutting circles will make intersections and definite points at the intersections 2. When these lines have been correctly drawn a slender width of the willow a straight piece cut from the agnus castus tree is taken, smeared with a liquid pitch and fastened at the first point of intersection then it is carried across obliquely to the succeeding intersections of longitudinal lines and circles and acid advances passing each of the points in due order and winding round it is fastened at each intersection and so, withdrawing from the first to the eighth point it reaches and is fastened to the line to which its first part is fastened, thus it makes as much progress in its longitudinal advance to the eighth point as in its oblique advance over eight points in the same manner widths for the eight divisions of the diameter fastened obliquely at the intersections on the entire longitudinal and peripheral surface make spiral channels which naturally look just like those of a snail shell 3. Other widths are fastened on the line of the first and on these still others it is smeared with liquid pitch and built up until the total diameter is equal to one eighth of the length these are covered and surrounded with boards fastened on to protect the spiral then these boards are soaked with pitch and bound together with strips of iron so that they may not be separated by the pressure of the water the ends of the shaft are covered with iron to the right and left of the screw are beams with cross pieces fastening them together at both ends in these cross pieces are holes sheathed with iron and into them pivots are introduced and thus the screw is turned by the treading of men 4. It is to be set up at an inclination corresponding to that which is produced in drawing the Pythagorean right angle triangle that is let its length be divided into five parts let three of them denote the height of the head of the screw thus the distance from the base of the perpendicular to the nozzle of the screw at the bottom will be equal to four of those parts a figure showing how this ought to be has been drawn at the end of the book right on the back I have now described as clearly as I could to make them better known the principles on which wooden engines for racing water are constructed and how they get their motion so that they may be of unlimited usefulness through their revolutions. End of book 10, chapter 6 book 10, chapter 7 to 10 of 10 books on architecture this LibriVox recording is in the public domain recording by Fredrik Carlson 10 books on architecture by Vitruvius translated by Morris Hickey and Morgan chapter 7 the pump of Sticebius one next I must tell about the machine of Sticebius which raises water to a height it is made of bronze and has at the bottom a pair of cylinders set a little way apart and there is a pipe connected with each the two running up like the prongs of a fork side by side to a vessel which is between the cylinders in this vessel are valves accurately fitting over the upper vents of the pipes which stop up the vent holes and keep what has been forced by pressure into the vessel from going down again two over the vessel a cowl is adjusted like an inverted funnel and fastened to the vessel by means of a wedge thrust through a staple to prevent it from being lifted off by the pressure of the water that is forced in on top of this a pipe is jointed called the trumpet which stands up vertically valves are inserted in the cylinders beneath the lower vents of the pipes and over the openings which are in the bottoms of the cylinders three pistons smoothly turned rubbed with the oil and inserted from above into the cylinders work with the rods and levers upon the air and water in the cylinders and as the valves stop up the openings force and drive the water and expansion through the vents of the pipes into the vessel from which the cowl receives the inflated currents and sends them through the pipe at the top and so water can be supplied for a fountain from a reservoir at a lower level four this however is not the only apparatus which Sticebius is said to have thought out but many more of various kinds are shown by him to produce effects borrowed from nature by means of water pressure and compression of the air for example blackbirds singing by means of waterworks and angobati and figures that drink and move and other things that are found to be pleasing to the eye and the air five of these I have selected what I considered most useful and necessary and I've thought it best to speak in the preceding book about timepieces and in this about the methods of raising water the rest which are not subservient to our needs but to pleasure and amusement may be found in the commentary of Sticebius himself by any who are interested in such refinements chapter eight the water organ one with regard to water organs however I shall not fail with all possible brevity and precision to touch upon their principles and to give us efficient description of them a wooden base is constructed and on it is set an altar shaped box made of bronze uprights fastened together like ladders are set up on the base to the right and to the left of the altar they hold the bronze pump cylinders the movable bottoms at which carefully turned on a lathe have iron elbows fastened to the centers and joined to levers and are wrapped in fleeces of wool and the tops of the cylinders are openings each about three digits in diameter close to these openings are bronze dolphins mounted on joints and holding chains in their mouths on which hang symbol shaped valves let down under the openings in the cylinders two inside the altar which holds the water is a regulator shaped like an inverted funnel under which there are cubes each about three digits high keeping a free space below between the lips of the regulator and the bottom of the altar tightly fixed on the neck of the regulator is the wind chest which supports the principal part of the contrivance called in Greek the Canon moussikos running longitudinally there are four channels in it if it is a tetrachord six if it is a hexacord eight if it is an octacord three each of the channels has a cock in it furnished with an iron handle these handles when turned open vent holes from the wind chest into the channels from the channels to the canal there are vertical openings corresponding to vent holes in a board above which board is termed PNUX in Greek between this board and the Canon are inserted sliders pierced with holes to correspond and rubbed with oil so that they can easily be moved and slid back into place again they close the above mentioned openings and are called the plinths they're going and coming now closes and now opens the holes four these sliders have iron jacks fixed to them and connected with the keys and the keys when touched make the sliders move regularly to the upper surface of the openings in the board where the wind finds aggress from the channels rings are soldered and into them the reeds of all the organ pipes are inserted from the cylinders there are connecting pipes attached to the neck of the regulator and directed towards the vent holes in the wind chest in the pipes are valves turned on a lace and set where the pipes are connected with the cylinders when the wind chest has received the air these valves will stop up the openings and prevent the wind from coming back again five so when the levers are raced the elbows draw down the bottoms of the cylinders as far as they can go and the dolphins which are mounted on joints let the symbols fall into the cylinders thus filling the interiors with air then the elbows raising the bottoms within the cylinders by repeated and violent blows and stopping the openings above by means of the symbols compress the air which is enclosed in the cylinders and force it into the pipes through which it runs into the regulator and through its neck into the wind chest with a stronger motion of the levers still more compressed streams through the apertures of the cocks and fills the channels with wind six so when the keys touched by the hand drive the sliders forward and draw them back regularly alternately stopping and opening the holes they produce resonant sounds in a great variety of melodies conforming to the laws of music with my best efforts I was driven to set forth an obscure subject clearly in writing but the theory of it is not easy nor thoroughly understood by all save only those who have had some practice in things of this kind if anybody has failed to understand it he will certainly find when it comes to know the thing itself that it is carefully and exquisitely contrived in all respects chapter nine the hodo meter one the drift of our retreat is now turns to a useful invention of the greatest ingenuity transmitted by our predecessors which enables us while sitting in a carriage on the road or sailing by sea to know how many miles of a journey we have accomplished this will be possible as follows let the wheels of the carriage be each four feet in diameter so that if a wheel has a mark made upon it and begins to move forward from that mark in making its revolution on the surface of the road it will have covered the definite distance of twelve and a half feet on reaching the mark at which it began to revolve two having provided such wheels let a drum with a single tooth projecting beyond the face of its circumference be firmly fastened to the inner side of the hub of the wheel then above this let a case be firmly fastened to the body of the carriage containing a revolving drum set on edge and mounted on an axle on the face of the drum there are 400 teeth placed at equal intervals in engaging the tooth of the drum below the upper drum has moreover one tooth fixed to its side and standing out farther teeth then above let there be a horizontal drum similarly toothed contained in another case with its teeth engaging the tooth fixed to the side of the second drum and let as many holes be made in this third drum as will correspond to the number of miles more or less it does not matter that a carriage can go in a day's journey let a small round stone be placed in every one of these holes and in the receptacle or case containing that drum let one hole be made with a small pipe attached through which when they reach that point the stone placed in the drum may fall one by one into a bronze vessel set underneath in the body of the carriage four thus as the wheel in going forward carries with it the lowest drum and as the tooth of this at every revolution strikes against the teeth of the upper drum and makes it move along the result will be that the upper drum is carried around once for every 400 revolutions of the lowest and that the tooth fixed to this side pushes forward one tooth of the horizontal drum since therefore with 400 revolutions of the lowest drum the upper will revolve once the progress made will be a distance of 5000 feet or one mile hence every stone making a ringing sound as it falls will give warning that we have gone one mile the number of stones gathered from beneath encountered will show the number of miles in the day's journey five on board ship also the same principle may be employed with a few changes an axel is passed through the sides of the ship with it's ends projecting and wheels are mounted on them four feet in diameter with projecting float boards fastened around their faces and striking the water the middle of the axel in the middle of the ship carries a drum with one tooth projecting beyond it's circumference here a case is placed containing a with 400 feet at regular intervals engaging the tooth of the drum that is mounted on the axel and having also one other tooth fixed to it's side and projecting beyond it's circumference six above in another case fastened to the former is a horizontal drum toothed in the same way and with it's teeth engaging the tooth fixed to the side of the drum that is set on edge so that one of the teeth of the horizontal drum is struck at each revolution of that tooth and the horizontal drum is thus made revolve in a circle let holes be made in the horizontal drum in which holes small round stones are to be placed in the receptacle or case containing that drum let one hole be opened with a small pipe attached through which a stone as soon as the obstruction is removed falls with a ringing sound into a bronze vessel seven so when the ship is making headway whether under oars or under a gale or wind the float porch on the wheels will strike against the water and be driven violently back thus turning the wheels and they revolving will move the axel and the axel the drum the tooth of which as it goes round strikes one of the teeth of the second drum at each revolution and makes it turn a little so when the float porch have caused the wheels to revolve four hundred times this drum having turned round once will strike a tooth of the horizontal drum with a tooth that is fixed to its side hence every time the turning of the horizontal drum brings a stone to a hole it will let the stone out through the pipe thus by the sound and the number the length of the voyage will be shown in miles I have described how to make things that may be provided for use and amusement in times that are peaceful and without fear chapter ten catapults or scorpions one I shall next explain the symmetrical principles on which scorpions and ballistic may be constructed inventions devised for defense against danger and in the interest of self preservation the proportions of these engines are all computed from the given length of the arrow which the engine is intended to throw and the size of the holes in the capitals through which the twisted sinews that hold the arms are stretched is one ninth of that length two the height and breadth of the capitals itself must then conform to the size of the holes the boards at the top and bottom of the capitals which are called peritreti should be in thickness equal to one hole and in breadth to one and three quarters except that their extremities where they equal one hole and a half the side post on the right and left should be four holes high excluding the tenants at five twelfths of a hole thick the tenants half a hole the distance from a side post to the hole is one quarter of a hole and it is also one quarter of a hole from the hole to the post in the middle the breadth of the post in the middle is equal to one hole and one eighth the thickness to one hole three the opening in the middle post where the arrow is laid is equal to one fourth of the hole the four surrounding corners should have iron plates nailed to their sides and faces or should be studded with bronze pins and nails the pipe called syrix in greek has a length of 19 holes the strips which some term cheeks nailed at the right and left of the pipe have a length of 19 holes and a height and thickness of one hole two other strips enclosing the windlass are nailed onto these three holes long and half a hole in breadth the cheek nailed onto them named the bench or by some the box and made fast by means of the dovetail tenants is one hole thick and seven twelfth of a hole in height the length of the windlass is equal to holes the thickness of the windlass to three quarters of a hole four the latch is seven twelfths of a hole in length and one quarter in thickness so also its socket piece the trigger or handle is three holes in length and three quarters of a hole in breadth and thickness the trough in the pipe is sixteen holes in length one quarter of a hole in thickness and three quarters in height the height of the standard on the ground is equal to eight holes the breadth of the standard where it is fast and into the plane is three quarters of a hole its thickness two thirds of a hole the height of the standard up to the tenon is twelve holes its breadth three quarters of a hole and its thickness two thirds it has three struts each nine holes in length half a hole in breadth and five twelfths in thickness the tenon is one hole in length and a half in length five the antifix has the breadth of a hole and one eighth and the thickness of one hole the smaller support which is behind termed in greek anti-basis is eight holes long three quarters of a hole broad and two thirds thick its prop is twelve holes long and has the same breadth and thickness as the smaller support just mentioned above the smaller support is its socket piece or what is called the cushion half holes long one and a half high and three quarters of a hole broad the windlass cup is two and seven twelfths holes long two thirds of a hole thick and three quarters broad the cross pieces where the tenons have the length of holes the breadth of three quarters and the thickness of two thirds of a hole the length of an arm is seven holes its thickness at its base two thirds of a hole and at its end one half a hole its curvature is equal to two thirds of a hole six these engines are constructed according to these proportions or with additions or diminishes four if the height of the capitals is greater than the width when they are called high tensioned something should be taken from the arms so that the more the tension is weakened by height of the capitals the more the strength of the blow is increased by shortness of the arms but if the capitol is less high or if the arm load tensioned is used the arms on account of the strength should be made a little longer so that they may be drawn easily just as it takes four men to raise a load with a lever five feet long and only two men to lift the same load with a ten feet lever so the longer the arms the easier they are to draw and the shorter the harder I have now spoken of the principles applicable to the parts and proportions of the capitals Chapter 10 Book 10, chapters 11 to 13 of Ten Books on Architecture this LibriVox recording is in the public domain recording by Fredrik Carlson Ten Books on Architecture by Vitruvius translated by Morris Hickey Morgan Chapter 11 Ballistae One, Ballistae are constructed on varying principles to produce an identical result some are worked by hand spikes some by blocks and pulleys others by capstones others again by means of drums No Ballistae however is made without regard to the given amount of weight of the stone which the engine is intended to throw hence their principle is not easy for everybody but only for those who have knowledge of the geometrical principles employed in calculation and in multiplication Two, for the holes made in the capitals through the openings of which the strings made of twisted hair generally women's or of sinew are proportionate to the amount of weight in the stone which the Ballistae is intended to throw and to the principle of mass as in capitals the principle is that of the length of the arrow therefore in order that those who do not understand geometry may be prepared beforehand so as not to be delayed by having to think the matter out at a moment of peril in war I will set forth what I myself know by experience will be depended upon and what I have in part gathered from the rules of my teachers and wherever Greek weights bear a relation to the measures I shall reduce and explain them so that they will express the same corresponding relation in our weights Three, a Ballistae intended to throw a two pound stone will have a hole of five digits in its capital four pounds six digits and six pounds seven digits ten pounds eight digits twenty pounds ten digits forty pounds twelve and a half digits sixty pounds thirteen and a half digits eighty pounds fifteen and three quarters digits one hundred pounds one foot and one and a half digits one hundred and twenty pounds one foot and two digits one hundred and forty pounds one foot and three digits one hundred and sixty pounds one foot and a quarter one hundred and eighty pounds digits, 200 pounds, 1 foot and 6 digits, 240 pounds, 1 foot and 7 digits, 280 pounds, 1 foot and a half, 320 pounds, 1 foot and 9 digits, 360 pounds, 1 foot and 10 digits. 4. Having determined the size of the hole, design the scuttola, termed in Greek peritretos, angles in length and two and one-sixth in breadth. Bisect it by a line drawn diagonally from the angles, and after this, bisecting, bring together the outlines of the figure so that it may present a rhomboidal design, reducing it by one-sixth of its length and one-fourth of its breadth at the obtuse angles. In the part composed by the curvatures into which the points of the angles run out, let the holes be situated and let the breadth be reduced by one-sixth. Moreover, let the hole be longer than it is brought by the thickness of the bolt. After designing the scuttola, let its outline be worked down to give it a gentle curvature. 5. It should be given the thickness of seven-twelfths of a hole. The boxes are two holes in height, one and three-quarters in breadth, two-thirds of a hole in thickness except the part that is inserted in the hole, and at the top one-third of a hole in breadth. The side posts are five holes and two-thirds in length, the curvature half a hole, and their thickness thirty-seven-forty-eighthths of a hole. In the middle, their breadth is increased as much as it was near the hole in the design by the breadth and thickness of a hole, the height by one-fourth of a hole. 6. The inner strip on the table has a length of eight holes, a breadth and thickness of half a hole. These tenons are one hole and one-sixth long and one-quarter of a hole in thickness. The curvature of this strip is three-quarters of a hole. The outer strip has the same breadth and thickness as the inner, but the length is given by the obtuse angle of the design and the breadth of the side posts at its curvature. The upper strips are to be equal to the lower, the crosspieces of the table, one-half of a hole. 7. The shafts of the ladder are thirteen holes in length, one hole in thickness, the space between them is one hole and a quarter in breadth, and one and one-eighths in depth. Let the entire length of the ladder on its upper surface, which is the one adjoining the arms and fasten to the table, be divided into five parts. Of these, let two parts be given to the member which the Greeks call Keloinion, its breadth being one and one-sixth, its thickness one-quarter and its length eleven holes and one-half. The claw projects half a hole and the winging three-sixteenths of a hole. What is at the axis, which is termed the face, the crosspieces of three holes, eight? The breadth of the inner slips is one-quarter of a hole, their thickness one-sixth. The cover joint or lid of the Keloinion is dovetailed into the shafts of the ladder, and is three-sixteenths of a hole in breadth and one-twelfth in thickness. The thickness of the square piece on the ladder is three-sixteenths of a hole. The diameter of the round axle will be equal to that of the claw, but at the pivot seven-sixteenths of a hole. The stays are holes in length, one-quarter of a hole in breadth at the bottom, and one-sixth in thickness at the top. The base, termed eskada, has the length of holes and the anti-base of four holes. Each is one hole in thickness in breadth. A supporter is jointed on, half way up, one-and-a-half holes in breadth and thickness. Its height bears no relation to the hole, but will be such as to be serviceable. The length of an arm is six holes. It's thickness at the base two-thirds of a hole, and at the end one-half a hole. I have now given those symmetrical proportions of ballistae and catapults, which I thought most useful, but I shall not omit, so far as I can express it in writing, the method of stretching and turning the strings of twisted sinew or hair. Chapter 12 The Stringing and Tuning of Catapults 1. Beams of very generous length are selected, and upon them are nailed socket pieces in which windlesses are inserted. Good way along their length, the beams are incised and cut away to form framings, and in these cuttings the capitals of the catapults are inserted, and prevented by wedges from moving when the stretching is going on. Then the bronze boxes are inserted into the capitals, and the little iron bolts, which the Greeks call epizygitis, are put in their places in the boxes. 2. Next the loops of the strings are put through the holes in the capitals, and passed through to the other side. Next they are put upon the windlesses, and wound round them in order that the strings stretch out taut on them by means of the hand spikes, and being struck by the hand may respond with the same sound on both sides. Then they are wedged tightly into the holes, so that they cannot slacken. So in the same manner they are passed through to the other side, and stretch taut on the windlesses by means of the hand spikes until they give the same sound. Thus with the tight wedging, catapults are tuned to the proper pitch by musical sense of hearing. On these things I have said what I could. There is left for me in the matter of sieges, to explain how generals can win victories and cities be defended by means of machinery. Chapter 13 Siege Machines 1. It is related that the battering ram for sieges was originally invented as follows. The Carthaginians pitched their camp for the siege of Kadith. They captured an outwork in attempt to destroy it, but having no iron implements for its destruction they took a beam, and racing it with their hands, and driving the end of it repeatedly against the top of the wall they threw down the top courses of stones, and thus step by step in regular order they demolished the entire redoubt. 2. Afterwards a carpenter from Tyre, bright by name and by nature, was led by this invention into setting up a moss from which he hung another crosswise like a steel-yard, and so by swinging it vigorously to and fro he threw down the wall of Kadith. Geras of Kalsudon was the first to make a wooden platform with wheels under it, under which he constructed a framework of uprights and cross-pieces, and within it he hung the ram, and covered it with ox-hide for the better protection of the men who were stationed in the machine to batter the wall, as the machine made but slow progress he first gave it the name of the tortoise of the ram. 3. These were the first steps then taken towards that kind of machinery, but afterwards when Philip the son of Amintus was besieging Byzantium it was developed in many varieties and made handier by Polyaedus the Thessalian. His pupils were Diadas and Karius who served with Alexander. Diadas shows in his writings that he invented movable towers which he used also to take apart and carry around with the army, and likewise the borer and the scaling machine by means of which one can cross over the wall on a level with the top of it, as well as the destroyer called the raven, or by others the crane. 4. He also employed the ram mounted on wheels, an account of which he left in his writings. As for the tower he says that the smallest should be not less than sixty cubits in height and seventeen in breadth, but diminishing to one-fifth less at the top the uprights for the tower being nine inches at the bottom and half a foot at the top. Such a tower he says ought to be ten stories high with windows in it on all sides. 5. This larger tower he adds was one hundred and twenty cubits high and twenty-three and a half cubits broad, diminishing like the other to one-fifth less. The uprights one foot at the bottom and six digits at the top. He made these large towers twenty stories high, each story having a gallery rounded three cubits wide. He covered the towers with a raw hide to protect them from any kind of missile. 6. The tortoise of the battering ram was constructed in the same way. It had, however, a base of thirty cubits square and a hide excluding the pediment of thirteen cubits. The height of the pediment from its bed to its top was seven cubits. Issuing up and above the middle of the roof for not less than two cubits was a gable, and on this was reared a small tower four stories high, in which on the top floor scorpions and catapults were set up, and on the lower floors a great quantity of water was stored to put out any fire that might be thrown on the tortoise. Inside of this was set the machinery of the ram, termed in Greek κριάδικη, in which was placed a roller turned on a lathe, and the ram, being set on top of this produced its great effect when swung to and fro by means of ropes. It was protected like the tower with raw hide. 7. He explained the principles of the borer as follows, that the machine itself resembled the tortoise, but that in the middle it had a pipe lying between upright walls, like the pipe usually found in catapults and ballistae, fifty cubits in length and one cubit in height, in which a windlass was set transversely. On the right and left at the end of the pipe were two blocks, by means of which the iron pointed beam which lay in the pipe was moved. There were numerous rollers enclosed in the pipe itself under the beam, which made its movements quicker and stronger. Numerous arches were erected along the pipe above the beam, which was in it, to hold up the raw hide in which this machine was enveloped. 8. He thought it needless to write about the raven, because he saw that the machine was of no value. With regard to the scaling machine, termed in Greek Ἰπίπαθρα, and the naval contrivances which, as he wrote, could be used in boarding ships, I have observed that he merely promised with some earnestness to explain their principles, but that he has not done so. I have set forth what was written by dieters on machines and their construction. I shall now set forth the methods which I have learned from my teachers and which I myself believe to be useful. End of book 10, chapter 13.