ENGINEERING
DONALD R. HILL
and
AHMAD Y. al-HASSAN
INTRODUCTION
In many cases the places and dates of origin of machines or techniques have not been established with any certainty. It is not proposed to devote much space to an examination of the evidence for the origin of any particular invention, particularly if it is known that it occurred before the advent of Islam in the first/seventh century. The estimated time and location of origin will be given, with an indication of the conjectural element in this estimate and the possible alternatives, if any. It should be noted that most pre-Islamic inventions were made in the Near East that witnessed the passage of several ruling empires from ancient times till the advent of Islam.
Medieval Islam was a prosperous and dynamic civilization, and much of its prosperity was due to an engineering technology that assisted in increasing the production of raw materials and finished products. In addition, the demand for scientific instruments, and the need to cater for the amusements and aesthetic pleasures of the leisured classes, was reflected in a tradition of fine technology based upon delicate mechanisms and sensitive control mechanisms. In this paper, the contribution of engineering to Islamic civilization will usually be demonstrated by specific examples, since space does not allow for a detailed survey of the interactions between technology and society. Similarly, the Islamic contribution to the development of modern engineering will be indicated by means of citing individual cases of technology transfer.
CIVIL ENGINEERING
Irrigation and water supply
For the sake of convenience it is necessary to divide the subject of civil engineering in the Muslim world into several sections, but in fact much of the subject is broadly contained within the field of irrigation and water supply. Dams are used to impound and divert irrigation water, bridges to cross canals and surveying techniques to align and level canals and qanats. Water-raising machines, which are discussed under mechanical engineering, are of course an integral part of hydraulic engineering schemes. In this section, therefore, we shall confine our attention to the principal irrigation systems, and to the means for transporting water to the fields and to urban communities.
There are four different types of irrigation. Basin irrigation, which was the method used in Egypt from ancient times until quite recently, consists of levelling large plots of land adjacent to a river or a canal, each plot being surrounded by dykes. When the water in the river reaches a certain level the dykes are breached, allowing the water to inundate the plots. It remains there until the fertile sediment settles, whereupon the surplus is drained back into the watercourse. Perennial irrigation is a method of watering crops regularly throughout the growing season by leading the water into small channels which form a matrix over the field. Water from the main artery – a river, major canal or qanat – is diverted into supply canals, then into smaller irrigation canals, and so on to the fields. Terrace irrigation is a method used in hilly country and consists of the formation of a series of terraces stepped down a hillside. Irrigation is by means of stored rainfall, wells, springs and occasionally qanats. Wadi irrigation depends upon sporadic rainstorms in otherwise arid lands. It consists of impounding the storm water behind dams and using this water to irrigate the fields adjacent to the watercourses. The famous dam at Ma’rib in the Yemen was the focal point of such a system. Following its original construction in the eighth century B.C.E. it was successively raised, not to impound water for long periods but to raise the wadi floods to increasingly higher levels in order to irrigate more and more land by means of a canal system which used the wadi itself as a drain. The final breakdown of the dam is thought to have occurred about a quarter-century before Muhammad’s birth. From the second century B.C.E. until the beginning of the first century C.E. the Nabateans in southern Palestine and Jordan developed a thriving agriculture based upon wadi irrigation. Whereas irrigation in the Yemen depended upon a single large dam, the Nabateans built thousands of little barriers sited across one wadi after another in order to divert or capture the one or two weeks of runoff occurring each year.
All these methods of irrigation originated in antiquity and it cannot be said that any radically new techniques have been added to the repertoire of Egyptian and Mesopotamian engineers. It could scarcely be otherwise: the basic problem of impounding the water, conducting it to the fields and finally draining the surplus remains as it has always been. Irrigation, and particularly perennial irrigation, however, is a branch of civil engineering which has always demanded a high degree of technical and administrative skills. The construction of dams, canals and qanats, matters to do with water flow and control, and elaborate surveying problems; all present themselves uncompromisingly and demand the attention of experts. From one area to another, there will always be differences in hydraulic conditions, climate, soil and terrain, so that the engineers must apply their knowledge and experience to produce the best system for a given set of conditions.
It is sometimes said that large cities are one of the main characteristics of Islamic civilization, and it is of course true that great cities such as Baghdad, Cairo and Cordoba, with their flourishing economic, commercial and intellectual life, were a major component of that civilization. It hardly needs emphasizing, however, that life in these large urban centres would have been impossible without the support of a thriving agriculture. Many Muslim cities were founded after the advent of Islam – e.g. Baghdad , Basra and Shiraz –- and we therefore find that the efforts of the engineers were taxed to the utmost either in extending existing systems or in creating completely new ones.
From the start of the Islamic Caliphate Irrigation works and water distribution were prominent among the State’s achievements. When al-Basra was established during Umar’s period, he started simultaneously building some canals for conveying water and for irrigation. Two important canals were built linking al-Basra with the ‘Umar also devised the policy of cultivating barren lands by assigning such lands to those who undertook to cultivate them. This policy, which continued during the Umayyad period also, resulted in the cultivation of large areas of barren lands through the construction of irrigation canals by the State and by individuals.
The various governors who were appointed by the Umayyads constructed several works to prevent the formation of new swamps and to dry old ones, through the building of dams that regulated the flow of water. We find in the original Arabic sources details about the irrigation works which were constructed in When the Abbasids assumed power in the second/eighth century they followed the same policy. They expanded greatly the existing irrigation system, mainly to cater for the needs of the new city of
Although there was some irrigation in
There were many other irrigation systems in the Muslim world, ranging from the great canal networks of
. The mainstay of its fertility was the Sughd River , now called the Zarafshan, which flowed through the great cities of Samarkand and Bukhara . At the height of its prosperity in the third/ninth and fourth/tenth centuries this land was rich and fertile beyond compare, its agriculture supported by a vast network of canals extending for many miles around the two cities.
Given the large numbers of men required to construct, maintain and control the large irrigation systems, it is hardly surprising that most of the enterprises were under State control, although it was not unusual for work to be let out to subcontractors. There are several Arabic treatises which tell us a good deal about the methods used for surveying and some of them discuss the excavation of new canals and methods for maintaining existing ones. We shall discuss land surveying in a separate section, but a section on quantity surveying in a treatise written in It is not usually easy to separate irrigation from water supply because both systems were derived from the same hydraulic works. Thus a dam would provide for both the town supply and the needs of the farmers, with one main feeder channel going to the irrigation system and another into the town. Or a canal would be led out from the main feeder canal into the urban centre. It was collected in a reservoir inside, or just outside, the city walls, and was conducted from there through pipes or open channels to the baths, fountains, houses for ritual ablutions, private and public buildings, and gardens. A particularly impressive example of artificial storage reservoirs can still be seen just outside the city of
One of the most effective methods for providing water in regions without perennial streams is the qanat, an almost horizontal underground conduit that conducts water from an aquifer to the place where it is needed. The technique probably originated in northern
The qanat system was used by the Umayyad and the Abbasid caliphs. The Caliph Al-Mutawakkil (847-866) constructed a qanat system for the supply of water to his new palace at
Al-Karaji’s Inbat al-miyah al-khafiyya (The Bringing Out of Hidden Waters) is a technical treatise written about 1000 C.E. which gives good details on the finding of the water level, instruments for surveying, construction of the conduits, their lining, protection against decay, and their cleaning and maintenance
The construction of qanats is in the hands of experts (muqanni) and the secrets of the profession are largely handed down by word of mouth from father to son. The termination of the qanat, either farmland to be irrigated or a community to be provided with potable water, or both, will be known in advance, as will the general location of likely aquifers. One of the main skills of the muqanni lies in determining, by examining the alluvial fans for traces of seepage and hardly noticeable changes in vegetation, precisely where the trial well is to be dug. When the excavators reach the impermeable layer the well is left for a few days while the muqanni estimates the potential yield of the well by hoisting up measured quantities of water and at the same time observing any fall in the water level. If necessary, further wells are sunk to ensure that genuine groundwater has been reached; the shaft with the highest yield is chosen as the ‘mother well’. The next step is for the surveyor – or senior muqanni – to determine the route, gradient and precise outlet of the qanat. The route will be selected according to considerations of terrain and, in some cases, questions of ownership. To start the survey, a long rope is let down into the mother well until it touches the surface of the water, and a mark is made on it at ground level. The surveyor then selects a spot on the route 30 to 50 yards from the mother well for the first ventilation shaft. A staff is held on this spot by a labourer, and the surveyor measures the fall with a level. Nowadays a modern surveying level may be used but in earlier times one of the instruments described in the section below on surveying was used. A second mark is made on the rope coinciding with the measurement on the staff; the distance from this mark to the lower end of the rope will be the depth of the first ventilation shaft. He continues to level in this way along the route, marking the rope at the location of each shaft, until he reaches the end of the rope. He has then reached a point on the ground at the same level as the surface of the water in the mother well. For the mouth of the qanat he now chooses a place below this level, but higher than the fields, and divides the drop from the level point to the mouth by the number of proposed ventilation shafts and adds this amount to the previously surveyed depth of each shaft. In this way be determines the gradient of the conduit, which is usually from 1 : 1000 to 1 : 500.
After completion of the survey, a number of guide shafts, about 300 yards apart, are driven under the supervision of the surveyor. Then the rope with the marked length of each vertical shaft is handed to the muqanni, who now begins to work with his assistants by driving the conduit into the alluvial fan, starting at the mouth. At first the conduit is an open channel, but it soon becomes a tunnel. Another team sinks ventilation shafts ahead of the tunnellers, and labourers haul the soil up to the surface through these shafts. Two oil lamps are kept burning on the floor of the conduit; sighting along these, the muqanni keeps the tunnel in alignment, and they also serve as a warning of poor air, since they go out before there is a danger of a man suffocating. As the work nears the mother well great care has to be taken in case the muqanni misjudges the distance and strikes the full well, in which event he might be swept away by the sudden flow. It can be seen, therefore, that the construction of qanats is a special example of the difficult and dangerous profession of mining (see Figure 1). It may be considered as one of the most successful of man’s inventions, since it has been in continuous use for over 2500 years.Fig. 1 – The qanat
Dams
Dams are required in most hydraulic systems, whatever their purpose, but the functions of dams vary. In wadi irrigation, as we have seen, they are used to trap the floodwaters that result from heavy but infrequent downpours, so that the water-level is raised above that of the surrounding fields, to which it can then be conducted under gravity. For perennial irrigation dams are used to divert water from streams or rivers into the canal network. The impounding of rivers behind dams gives more control over the supply throughout the year. As with wadi irrigation, it also allows the water in the reservoir to be gravity-fed into irrigation and town supply systems. A further advantage, if the water is to be used for hydro-power, is that there is a high, fairly constant head of water, which would not be the case if the river were unregulated.
There are two basic types of dam – gravity and arch. The first, as its name implies, relies upon the weight of the dam to withstand the pressure of the water. For additional strength, buttresses are sometimes added to the downstream wall. As with all hydraulic structures, good foundations are of the utmost importance, since failure can occur if the scouring action of the water undermines the foundations. Arch dams are designed to resist the force of the water and silt by horizontal arch action and are adaptable only to those sites where the length is small in comparison to the height and the sides of the valley are composed of good rock to resist the arch thrust at the haunches. With very rare exceptions true arch dams were not built before modern times.
The selection of the materials of construction was influenced partly by the design of the dam and partly by availability. Earth dams were common and are still in widespread use today. They are perfectly satisfactory for certain kinds of service, provided they have a core of clay or other impermeable material and plenty of overflow capacity, but they are not really suitable for high dams. In certain areas, notably lower Iraq, earth dams were almost universal; they were (and are) quite adequate for diverting rivers into canal systems and, in any case, the cost of transporting large quantities of stone would have been prohibitive. In other areas, where higher dams were needed, some form of masonry construction was necessary. This could be of dressed stone, mortared or not, random rubble or concrete. Quite frequently, dams were constructed by building two masonry walls with a gap between them, and then filling the gap with cheaper material such as earth or rubble. If the dam was designed to discharge overflow water from its crest, this had to be of stone or concrete, since earth would quickly have been worn away by the action of the water.
Roman and Sasanid dams were carefully maintained, but the demands for irrigation water and power was so great that in the more populous provinces dams became more numerous than they had been in pre-Islamic times. Many new dams were necessary as part of the extensions to the hydraulic systems in Iraq .
Perhaps the most impressive of these dams, the remains of which can still be seen, was a diversion dam over the River ‘Uzaym at the point where it leaves the hills called the Jabal Harmin. The main body of the dam is a masonry wall 575 feet long which at the western end turns through a right angle and continues for 180 feet to form one bank of the canal called Nahr al-Batt. The dam has a maximum height of something over 50 feet, but this rapidly reduces towards the sides. In fact for the first 150 feet at the eastern end, the dam is only 13 feet high. The cross-section of its central portion has a neat trapezoidal profile, 10 feet thick at the crest and 50 feet thick at the base. The water face is vertical and the air face is built to a uniform slope with the masonry stepped. The dam was built of cut masonry blocks throughout, connected with lead dowels poured into grooves. This is quite a common Muslim technique and in the ‘Uzaym dam was apparently used as a complete alternative to mortared joints. The alignment of the structure is not straight, and this reflects an attempt, as usual, to utilize the natural shape of the site as advantageously as possible.In
The Buwayhids held the real power in Iraq and Iran from 320/932 until 454/1062, and the greatest builder of the dynasty was ‘Adud al-Dawla. Among his works was the impressive dam called the Band-i Amir, built about 349/960 over the River Kurr in the province of Fars between Shiraz and Istakhr. This dam was seen by the geographer al-Muqaddasi shortly after it was constructed. He speaks of it as follows:
‘Adud al-Dawla closed the river between This dam, which is some 30 feet high and 250 feet long still survives. It is made of solid masonry and does make use of a rubble masonry core. Iron bars set in lead were used to connect the blocks. Both Al-Muqaddasi and Ibn al-Balkhi agree that the stones were set in mortar, and this, in addition to binding the whole construction together, would also have served to make the dam watertight. The use of “tempered cement and sifted sand” indicates that the engineers were aware of the need for careful preparation of their mortar. Al-Balkhi writes ”even an iron tool could not scratch it” This indicates that the mortar was of excellent quality and that the dam was a very thorough and solid piece of work. It is not at all surprising that it has had such a long and useful life.
There are many Muslim dams in
Fig 2 – Mestella dam: desilting sluices
Bridges
Suspension bridges with cables made of woven bamboo strips were used in China no later than the first century B.C.E. but there is no record, of its use in western Islam or Europe before the Renaissance. This does not mean that they were not used and indeed it would be strange if this simple and effective method of crossing ravines was unknown in the Zagros, the Taurus and the mountainous regions of Spain and North Africa . Similarly, we have no firm evidence for the use of cantilever bridges in Islam, apart from Afghanistan , where they had been built from, at the latest, the fifth century C.E. onwards. These are also an excellent method of crossing ravines in hilly country, but being made of timber they do not have a long life nor do they leave traces, particularly since in many cases modern bridges may have been built at their sites. Usually a timber substructure is built into a masonry abutment on either bank, and the longitudinal and transverse beams to carry the roadway extend from the top of this supporting structure. At the centre the two cantilever spans support a short beam section (see Figure 3). Large modern steel bridges, such as the Forth railway bridge in Scotland , are built on exactly the same principle. In the fourth/tenth century a bridge over the River Tab in Iran was described briefly by Ibn Hawqal. He says that the river was crossed by a wooden bridge “suspended between the sky and the water, its height above the water about 10 cubits”. He may, of course, have seen a suspension bridge, but the cantilever type seems more likely, especially since he makes no mention of ropes.
Fig. 3 –Types of bridges
There are frequent references to pontoon bridges in the works of Arabic writers. They were very common in Iraq for crossing the two rivers and the major irrigation canals. In the fourth/tenth century there were two pontoon bridges over the Tigris at Baghdad , but only one was in use; the other, having fallen into disrepair, was closed, because few people used it. Ibn Jubayr, writing towards the close of the sixth/twelfth century, described a bridge of large boats over the Euphrates at Hilla. It had chains on either side “like twisted rods” which were secured to wooden anchorages on the banks. He also mentions a similar, but larger, bridge over a canal near Baghdad . There were also pontoon bridges on the rivers of Khuzistan, the Iranian province adjoining Iraq , and on the Helmand river in Sijistan (now western Afghanistan ). There seems to have been a pontoon bridge at Fustat (now Old Cairo) in Egypt for many years. In the early part of the fourth/tenth century, al-Istakhri says that one bridge crossed from the city to the island and a second bridge from the island to the far bank of the river. About two centuries later, al-Idrisi describes the same arrangement, adding that there were thirty boats in the first bridge and sixty in the second.
Before the introduction of modern materials the masonry arch provided the best solution for the spanning of watercourses and other obstacles. Although they are relatively expensive to build, well-constructed arch bridges can last for centuries and they do not interfere with river traffic to the same extent as pontoon bridges or the many piers of multiple-span beam bridges. Their durability is proved by the survival of many medieval bridges, intended only for the passage of people and animals, but now sustaining the full load of modern traffic.
Many Roman, Hellenistic and Sasanid arch bridges remained in use in the Muslim world, and the more impressive of these are described in the writings of the Arabic geographers. The Muslims, following the traditions of their predecessors, also built many fine arch bridges. In areas where good building stone was not available, notably in parts of Building construction
Many fine buildings were constructed in the first Islamic century: the Dome of the Rock in Jerusalem , the Great Mosque in Damascus , the second Great Mosques in Kufa and Basra and the desert palaces of the Umayyads – to name only some of the more notable buildings. Once established, the tradition for fine architecture continued to flourish in Islam, as witnessed, for example, by al-Mansur’s Baghdad , the works of Ibn Tulun in Egypt , the Great Mosque of Cordoba and the Alhambra palace in Granada , the complex of splendid buildings in Isfahan and so on. Many well-illustrated books have been devoted to describing Islamic buildings and it is clearly beyond the scope of this chapter to attempt even a brief summary of the Muslim architectural achievement. Instead, we shall confine our attention to the most basic element in any building – the materials of construction.
The Muslim geographers usually tell us which type of material was used to construct a given town or city. This could be unfired bricks (labin or tub), fired bricks (ajurr), stone (hajar) or timber. In medieval times timber was more plentiful than it is today, but even so the practice of constructing the main structures of buildings in this material was not widespread. The city of Bukhara was mostly timber-built and the houses in the town of Siraf on the Gulf were made of teak, and timber was also widely used in parts of Spain . Perhaps the most important example of timber used as a structural material is the Dome of the Rock in Jerusalem , in which the dome itself consists of two independent wooden shells, the outer one covered with lead sheets. In general, however, timber was used in conjunction with other materials where some resistance to tensile stresses was necessary, as in lintels over doors and windows, and roof rafters.
The choice of material to be used in a particular building depends upon a number of factors: the availability of a material locally, cost, time and the purpose of the building. Thus it is noticeable that cut masonry was often preferred for religious buildings whereas other large buildings in the same region might be constructed from cheaper materials. Syria can be said to be the region, par excellence, for fine stonework in ashlar masonry, i.e. masonry in which each block is carefully cut to size, with straight edges and plane surfaces. This tradition has persisted in Syria to the present day; the local limestone weathers to a beautiful amber colour that is very pleasing to the eye. Ashlar work was also common in Spain (doubtless due to Syrian influence), Egypt and parts of North Africa . Sometimes money and time were saved by building the wall in random rubble and facing it with ashlar. The mortar was based upon either lime or gypsum mixed with soft sand.
The use of unfired bricks was common in early Antiquity and is still widespread today. The clay which is the main constituent of the bricks is readily available in many parts of the world and houses made from this material are warm in winter and cool in summer. Moreover, its use is not confined to the building of small dwelling houses. Some of the multi-storey houses in southern Arabia are made of unfired bricks, and they can also be used in vaults and domes. They cannot, however, be used in areas with high rainfall, for heavy rains cause severe deterioration to the walls to the point of making them disintegrate. The labina generally has a geometric, fairly regular shape, that of a parallel-sided rectangle, whose variable dimensions often have the ratio 4 x 2 x 1 (e.g. length 56 cm, width 28, thickness 14, or 36 x 18 x 9) but in South Arabia 45 x 35 x 5 is usual and in Iran 20 x 20 x 4. To prepare the mixture for the bricks, the loam or clay is thoroughly soaked, mixed with straw and chaff and trodden with the bare feet. It is then carried in baskets to the moulders. Each moulder has a wooden mould, just an open frame. He covers the ground with a thin layer of chaff, puts the moulding frame flat on the ground, throws a quantity of the mud-straw mix into the mould, beats it into the corners with his bare hands, and scrapes off any surplus with a small straight-edge. He lifts the frame with a swift movement, leaving the fresh brick on the ground, and places the frame next to the brick just made. Moulding row after row in this way, he makes about 250 bricks in an hour. Unfired bricks are jointed with a mortar made with a mixture of lime or ash and are usually lined with a coating of earth mixed with lime or plaster.
Burnt bricks were already made in the fourth millenium B.C.E in Babylonia and in Iran . kilns have been unearthed going back into the first millenium B.C.E. They are still in common use in many parts of the Muslim world. They are generally smaller than unfired bricks, and the preparation of the clay for them is more thorough – it has to be slaked and sieved to clean it of impurities, and additives are sometimes included, e.g. grey sand to give the bricks a whitish tinge. After moulding they are left in the open, lying fiat, for 24 hours, and then turned on edge and left to dry for another three days before being stacked in the kiln. The kiln is similar to that of the potters, and consists of a furnace with a firing room on top of it. Buildings made exclusively from burnt bricks are rare. More usually they are combined with other materials. The Qasr al-Hayr al-Gharbi in Syria , for example, built in the first Islamic century, consists of a wall of limestone, fired bricks and unfired bricks at the top. Burnt bricks were (and are) used for certain parts of buildings such as arches, vaults and staircases, and put to good use by architects to vary the decoration of their works. From the sixth/twelfth century, the glazed brick has offered the possibility of obtaining similar effects to those of mosaic.
The technique of cobwork (tabya) was described in detail by Ibn Khaldun in his Muqaddima, which implies that he thought it a characteristically Muslim practice. Earth with which chalk and crushed baked earth or broken stones are often mixed is rammed between two boards kept parallel by beams. The wall is plastered over, often in such a way as to simulate joints of heavy bond-work beneath. When this plaster falls, the regularly spaced holes left by the beams become visible. In the Muslim West cobwork became general in the fifth/eleventh and sixth/twelfth centuries, especially in military building. In the Maghrib it seems to have been an importation from In urban communities, quality control of building was exercised by an official called the muhtasib. His duties were very wide-ranging, since he was appointed by the ruler to supervise the affairs of the market, including the maintenance of moral standards and religious observance; quality and quantity control over retailers and manufacturers; sanitation and water supply; and checking the manufacture of building materials. In this last respect the hisba manuals (books written for the guidance of the muhtasib) contain a good deal of useful information. For example, the widths of walls and the dimensions of beams were checked with wooden templates, to ensure that the measurements were not less than the minimum specified.
Surveying
The basic requirements for public works surveying, as in the setting-out of large buildings, the excavation of canals, etc. are levelling and alignment. Whereas nowadays levelling is done with an optical instrument and a graduated staff, in earlier times two such staffs were needed in conjunction with a simple but effective instrument. Three such instruments are described in an Iraqi treatise of the fifth/eleventh century. The first of these is a wooden board about 70 cm long by 8 cm wide. In the centre of the board a line is drawn which meets both edges at a right angle. A plumb line is fixed to this line, near one of the edges. Two hooks are fixed to this edge (see Figure 4a). The second instrument consists of an equilateral triangle, with two hooks soldered to the ends of one of its sides. A narrow hole is drilled through the centre of this side, to take the cord of a plumb line (Figure 4b). To use either instrument, it was suspended to a wire or cord stretched tightly between the two graduated staffs. One end of the wire was moved up and down until the plumb line coincided with the line on the board or the corner of the triangle. The difference between the readings on the two staffs gave the level difference. The third instrument is called the ‘reed-level’. A narrow longitudinal hole is bored through a long straight reed, and a radial hole is made into this bore at the centre. The reed was held roughly horizontally by two assistants between the two staffs, which were held vertically by two other assistants. A fifth assistant then allowed water to drip into the central hole from a piece of rag. When the flow of water from each end of the reed was equal the reed was truly horizontal. As with the first two instruments, the surveyor then read and recorded the heights on the two staffs. Quite accurate levelling could be carried out over long distances by repeating the operation with any of these instruments. At the end of the survey the ‘rises’ and ‘falls’ were totalled and the difference between the totals gave the difference in level between the start and finish points.Fig. 4
For setting out straight lines and for measuring distances ropes were used, with knots at intervals to mark the dimensions. A rotatable alidade, provided with sighting holes and mounted on a plane surface, could also be used for alignment. The astrolabe, which we shall meet in a later section as an instrument for astronomical observation and computation, was also widely used for land surveying. Here we are concerned only with the back of the instrument, which consisted of an alidade turning about a central pivot, its ends moving over a graduated circle, each quadrant of which was divided into 90 degrees. In the lower half of the face was a rectangle, one side of which was divided radially into decimals, the other side into duo-decimals (see Figure 5).
Fig. 5
The instrument was used for alignment and measuring the angles between two points, but a number of Arabic writers also describe the solution of various triangulation problems using the astrolabe. The two matching squares into which the rectangle is divided are used for this purpose. Although the squares are divided into ten and twelve equal parts respectively, the choice of number is purely a matter of convenience. With the astrolabe freely suspended the alidade is adjusted so that a distant object is viewed through the sights simultaneously. When this happens the real right-angled triangle formed by the distance of the object and its height is reproduced on a small scale within the confines of one square on the astrolabe, by an exactly similar right-angled triangle. The real and similar triangles have a common line for hypotenuse. The ratio of the lengths of the sides of the triangle on the astrolabe is the same as the ratio of the height and distance of the object, so that if either of these is known the other may readily be calculated. If neither is known, the observer reads the angle from one station, moves back a measured distance, and again reads the angle. Since the Muslims had perfected the methods of both plane and spherical trigonometry, problems of this sort could easily be solved. For the surveyor in the field, however, it was clearly preferable to use the constructive methods provided by the astrolabe, and manuals for his use were prepared by scientists. Other problems solved by the use of the astrolabe included finding the width of a river, or the distance between two points separated by an impassable obstruction.
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