(Mohammed V-Agdal University, Rabat, Morocco
Foundation for Science, Technology and Civilisation (FSTC), Manchester, UK)1
THE FOLLOWING ARTICLE will be devoted to two main concerns:
- The description of the textual tradition of the Arabic corpus of the science of weights (‘ilm al-athqāl), a tradition of scientific and technical treatises reconstituted from manuscripts, most of which were never published. The components of this corpus, amounting to more than thirty texts, cover the whole range or scientific activity in Islamic lands from the 9th through to the 19th century. This group of texts is unified by a common theme: the spectrum of theoretical and practical problems related to the description, the functioning and the use of various types of balances, and especially of the steelyard, the balance with calibrated beam, unequal arms and moving weights.
- The interpretation of the Arabic corpus of the science of weights as a transformation in the history of mechanics. Such a transformation was represented by the creation of an independent theoretical branch that evolved from ancient contributions and nourished physical debates until the advent of modern science on the problems of equilibrium and the properties of weighing operations. As a result, ‘ilm al-athqāl should no more be confused with ‘ilm al-ḥiyal, understood as a general descriptive discourse on different types of machines.
Such an understanding of the historical significance of the Arabic science of weights brings about an important result, in the sense that this tradition was connected with the next important phase of the history of mechanics. Indeed, beyond cultural and linguistic boundaries, the Arabic science of weights afforded a foundation for the Latin scientia de ponderibus that emerged in medieval Europe from the 13th century.
1. THE BALANCE INSTRUMENT OF THE SCIENCE OF WEIGHTS
The balance is an instrument of our current life, charged with history and science. In Islamic classical times, this familiar instrument was the object of an extensive scientific and technical debate of which dozens of treatises on different aspects of its theory, construction, and use are the precious remains. Different sorts of balances were the object of such an extensive enquiry, including the normal equal-armed balance (called in Arabic mīzān, ṭayyār, and shāhīn), the steelyard (called qarasṭūn, qaffān, and qabbān) and sophisticated balances for weighing absolute and specific weights of substances.
Several drawings of balances are preserved in Arabic manuscripts, such as those of al-Khāzinī, al-Ḥarīrī, and al-Qazwīnī. Further, some specimens of the ancient balances survived and are presently kept in museums. For instance, the National Museum in Kuwait (item LNS 65 M) held an Islamic steelyard built in Iran between the 10th and the 12th centuries (fig. 1: Islamic steelyard from Iran kept in the National Museum, Kuwait City).* It is an instrument made of inlaid engraved steel, with marks on its beam. Its dimensions (height: 11.5 cm, length: 15.6 cm) show that it was used for weighing small quantities2. Two significant steelyards are owned by the Petrie Museum (University College, London). One of them (accession number Inv. 1935-457) is a huge balance (fig. 2: Islamic steelyard in Petrie Museum, London). A scale of silver is inlaid along its 2.37mlong, wrought-iron beam. It bears two suspending elements and corresponding calibrations: one ranging from 0 to 900 raṭl-s (I raṭl is approximately 1 pound); the other ranging from 900 to 1820 raṭl-s (almost a pound or about 450 grams)3.
The interest in the balance in Islamic scientific learning was culturally nurtured by its role as a symbol of good morals and justice. The Qur’an and the Ḥadīth appealed extensively to a strict observance of fair and accurate weighing practices with the balance. Considered the tongue of justice and a direct gift of God, the balance was made a pillar of the right society and a tool of good governance. These principles were recorded explicitly in several treatises on the balance, such as the introduction to Kitäb mīzān al-ḥikma by al-Khāzinī, where the balance is qualified as ‘‘the tongue of justice and the article of mediation.’’ Furthermore, it was counted as a fundamental factor of justice, on the same level with the “glorious Book of God,’’ and ‘‘the guided leaders and established savants.’’4
The balance most widely used in the Islamic lands of medieval times was the equal-armed platform scale, made mostly in copper. There were tiny balances for gold and jewels, average ones for retail traders, and huge balances for the merchants of grains, wood, wool, etc. In general, the balances had beams and weights made of steel or iron. Steelyards, called qarasṭūn or qabbān, were also widely employed. As reported in a historical source5, a site called Qarasṭūn existed in the ancient medina in Fez until the carly 20th century, probably because of a huge public balance set up there. Public balances are still located today in the fanādiq (bazaars) of the old medina. One can infer from these testimonies that a similar public weighing site must have been present in all the markets of Islamic cities.
The qarasṭūn or steelyard with a sliding weight was largely used since Antiquity. It is mentioned in Greek sources by its ancient name, the charistion, and was employed extensively in Roman times6. Composed of a lever or a beam (͑amūd) suspended by a handle that divides it into two unequal arms, the centre of gravity of the instrument is located under the fulcrum. In general the shorter arm bears a basin or a scale pan in which the object to be weighed is set, or suspended from a hook. The cursor-weight, rummāna in Arabic, moves along the longer arm in order to achieve equilibrium. This arm, which has generally a quadrangular cross section, bears two different scales which are engraved along the two opposite sides. Due to the fact that the steelyard can be suspended by two hooks, there are two independent graduations. According to the choice made, there will be different relations between the lengths of the longer and smaller arms of the lever, corresponding to the different scales. On the beam or near the fulcrum, the number of units or fractions corresponding to the capacity of the balance was engraved as was the official stamp of the authorities. The advantage of the steelyard is that it provides an acceptable precision in weighing and allows heavy loads to be supported by small counterweights. In addition, it can be carried around easily.
Another kind of balance is a combination of the ordinary balance and of the steelyard in the form of an equal-armed balance with mobile weight. A variety of it is the Maghribi balance presented in fig. 4.7 Further, a typical example of such an instrument is the balance of Archimedes described by al-Khāzinī according to an account by Menelaus fig. 6)8. In addition to its two equal arms to which two fixed scale pans are suspended, this balance had on one of the arms a cursor weight which could be hung up on different points of a small scale graduated in two series of divisions. Presented as an hydrostatical balance for the determination of specific gravities, it could also serve for ordinary weighing. A variety of the Archimedes’ balance consists in moving the scale pan on a part of the arm. This is the main property of the mīzān ṭabī’ī (natural or physical balance) designed by Muḥammad ibn Zakariyyā al-Rāzī. In this model with equal arms and without counterpoise, one of the scale pans is movable and might behave as a counterweight9.
Nowadays, the steelyard balance is called in some Arab countries al-mīzān al-qabbānī; in Morocco it is designated as mīzān al-kura. Despite the introduction of modern balances more or less sophisticated, since a long time ago (in the first half of the 19th century), the steelyards continue to be utilised in Arab and Islamic countries. They serve in popular markets and are widely used in some activities, such as in the slaughterhouses and in the shops of butchers. In Egypt, the industry of traditional steelyards is still active. Egyptian colleagues informed me that in the old city of Cairo, in an area called Ḥay taḥt al-rub’, near the Dār al-kutub, not far from the Azhar Mosque, artisans build steelyards according to traditional methods. These balances are used massively throughout the country, for example in the weighing of cotton in the country side. In other Arab countries, the fabrication of these balances disappeared completely. For instance, in Morocco, it vanished several decades ago, as a result of the introduction of modern balances and of the concurrence of the European industry of these same instruments. Therefore, the steelyards used in the country are imported from Southern Italy and Spain. But local artisans are able to repair the imported balances and to supply certain of their equipment, as I could see by direct observation during my visits to their shops in Fez recently.
In his geographical book Aḥsan al-taqāsīm fī ma’rifat al-aqālīm, Muḥammad al-Muqaddasī, the Palestinian geographer of the 10th century, reports that the most accurate balances were those fabricated at Ḥarrān in northern Mesopotamia. Kūfa, in southern Iraq, was also famous for the accuracy of its balances. Other regions were celebrated for the honesty of the weighing practices of their merchants, such as Khurāsān. But others were better known for their fraudulent procedures. Various passages in the Qur’an show that as early as the advent of Islam, false balances were in use in the markets. Later narratives report that some jewelers and goldsmiths, in order to fraudulently weigh their wares, blew gently on the scale pan of their balance, stuck a small piece of wax under it, or merely used false weights. Al-Jawbarī (fl. 1216-22) described two such arrangements. In the one the beam of the balance consisted of a hollow reed containing quicksilver, which was closed at both ends. By a slight inclination of the beam, the quicksilver could be made to flow as desired to the side with weights or with goods and thus make one or the other appear heavier. In another case, the tongue of the balance was of iron and the merchant had a ring with a magnetic stone; by bringing the ring close to the balance, it moved down to the right or left10.
In order to reprimand these fraudulent tricks and deceitful behavior, and to implement the instructions of Islam about the strict observance of the just weighing, the Islamic society invented a specific institutional setting, represented by the office of ḥisbathis office was occupied by the muḥtasib, an officer regularly appointed to take charge of the harmonisation between the commands of Islam and the social practice, especially concerning the control of markets. As such, one of his main duties was to observe that correct scales and weights were used in commercial transactions11.
2. THE CORPUS OF THE SCIENCE OF WEIGHTS
The emergence of Arabic mechanics is an early achievement in the scientific tradition of Islam. Actually, already in the mid-9th century, and in close connection with the translation of Greek texts into Arabic, treatises on different aspects of the mechanical arts were composed in Arabic, but with a marked focus on balances and weights. These writings, composed by scientists as well as by mechanicians and skilful artisans, gave birth to a scientific tradition with theoretical and practical aspects, debating mathematical and physical problems, and involving questions relevant to both the construction of instruments and the social context of their use. Some of these Arabic treatises were translated into Latin in the 12th century and influenced the European science of weights.
The corpus of the Arabic science of weights covers the entire temporal extent of scientific activity in medieval Islam and beyond, until the I9th century. The reasons for such an abundance of literature on the problems of weighing can be explained, only by contextual factors, at least in part. In fact, the development of the science of weights as an autonomous branch of science was triggered by the eminent importance of balances for commercial purposes. In a vast empire with lively commerce between culturally and economically fairly autonomous regions, more and more sophisticated balances were, in the absence of standardisation, key instruments governing the exchange of currencies and goods, such as precious metals and stones. It is therefore no surprise that Muslim scholars produced numerous treatises specifically dealing with balances and weights, explaining their theory, construction and use. This literature culminated in the compilation by ͑Abd ar-Raḥmān al- Khāzinī, around 1120, of Kitāb mīzān al-ḥikma, an encyclopedia of mechanics dedicated to the description of an ideal balance conceived as a universal tool of a science at the service of commerce, the so-called ‘balance of wisdom.’ This was capable of measuring absolute and specific weights of solids and liquids, calculating exchange rates of currencies, and determining time (fig. 5a-b).
A complete reconstruction of the Arabic tradition of weights is currently being undertaken by the author. This project began in the context of a long-term co-operation with the Max Planck Institute for the His tory of Science in Berlin12. The work on the establishment of the Arabic corpus of the science of weights started by the systematic reconstruction of the entire codicological tradition of the corpus of texts dealing - on theoretical and practical levels - with balances and weights. By now most of the corpus has been edited and translated into English and is being prepared for publication with the appropriate commentaries.
The preliminary analysis of the texts investigated so far established the importance of the Arabic tradition for the development of the body of mechanical knowledge. The Arabic treatises turned out to be much richer in content than those known from the ancient tradition. In partic ular, they contain foundations of deductive systems of mechanics different from those inferred from extant Greek texts, as well as new propositions and theorems. On the other hand, the Arabic treatises also represent knowledge about practical aspects of the construction and use of balances and other machines missing in ancient treatises.
The first phase of the research on the Arabic science of weights was focused on establishing the scope of its extant corpus. Surprisingly, this corpus turned out to be much larger than usually assumed in the history of science. Up to now more than thirty treatises dating from the 9th through to the 19th centuries have been identified which deal with balances and weights in the narrow sense. The majority of these treatises has never before been edited or studied, and only exists in one or more manuscript copies. Some important manuscripts have been discovered or rediscovered even in the course of the research activities conducted by the author.
The textual constituents of the Arabic works on the problems of weights can be classified chronologically into three successive units. First, a set of Greek texts of mechanics extant in Arabic versions. Despite their Greek origin, these works can be regarded as an integral part of the Arabic mechanical tradition, at least because of the influence they exerted on the early works of Arabic mechanics. In the case of some of these texts, although they are attributed to Greek authors, their Greek originals are no more extant nor are they ascribed to their supposed Greek authors in antique sources. The second unit comprises founding texts composed originally in Arabic in the period from the 9th through to the 12th century. This segment of writing laid the theoretical basis of the new science of weights, in close connection with the translations and editions of texts stemming from Greek origins. The third phase covers the 14th through to the 19th century, and comprises mainly practical texts elaborating on the theoretical foundations laid in the earlier tradition. In the following sections of this article, the texts belonging to these three phases will be described in brief, with a short characterisation of some theoretical contents.
3. ARABIC VERSIONS OF GREEK TEXTS OF MECHANICS
The corpus of Greek texts that were known to scholars of the classical Islamic world through direct textual evidence and dealing with the problems of weighing and the theory of the balance are six in number:
1. Nutaf min al-ḥiyal
This is an Arabic partial epitome of Pseudo-Aristotle’s Mechanical Problems. The Problemata Mechanics, apparently the oldest preserved text on mechanics, is a Greek treatise ascribed to Aristotle, but composed very probably by one of his later disciples. It has long been claimed that this text was not transmitted to Arabic culture. It is possible now to affirm that the scholars of Islamic lands had access to it at least through a partial epitome entitled Nutaf min al-ḥiyal (elements/extracts of mechanics) included by al-Khāzinī in the fifth book of his Kitāb mizān al-ḥikma13.
The text of the Nutaf represents indeed a significant partial Arabic version of the Problemata Mechanica. Presented under a special title that indicates its character as an excerpt from a longer text, it is attributed directly to Aristotle (it begins with the sentence: “Qāla Arisṭūṭālis” (Aristotle said)). Its content consists of a reliable abridged version of the preliminary two sections or the pseudo-Aristotelian text where the theoretical foundation of the treatise is disclosed. Thus it includes a methodically arranged compendium of the introduction giving a definition of mechanics and of Problem I on the reason of the accurateness in the larger balances to the detriment of smaller ones. As edited in Kitāb mīzān al-ḥikma, the Nutaf is preceded by a relatively long technical discussion on the balance equilibrium dealing with the different cases of incidence of the axis on the balance beam. In his analysis of this question, Al-Khāzinī probably had in mind the Peripatetic second problem of the Problemata which investigates the accidents that arise from the suspension of the balance beam from above or from below14.
2-3. Maqāla fī ͑1-mīzān and Kitāb fi ͑1-thiql wa ͑1-khiffa
Maqāla fī ͑1-mīzān (Treatise on the Balance) and Kitāb fī ͑1-thiql wa ͑l- khiffa (Book on Heaviness and Lightness) are two texts ascribed to Euclid. Extant only in Arabic, the first one provides a geometrical treatment of the balance and presents a sophisticated demonstration of the law of the lever. It is not recorded if it was edited in Arabic, but there is enough evidence to conclude that this was probably the case. The second text survived in a version edited by Thābit ibn Qurra. It is an organised exposition - in 9 postulates and 6theorems - of dynamical principles or the motion of bodies in filled media, developing a rough analysis of Aristotelian type of the concepts of place, size, kind and force and applying them to movements of bodies15.
No Euclidean writing on mechanics is extant in Greek and no ancient source ascribes to the Greek geometer a work in this field. Nevertheless, the Arabic manuscript material imputes to him the authorship of these two short texts on the theory of the balance and on some problems of hydrostatic physics. The former was transmitted only in Arabic, where- as the latter is extant in Arabic and in Latin. In form, the two treatises follow the model of Greek mathematical works, as they rest on a set of axioms or postulates on the basis of which a number of mechanical theorems are then proved. The two short tracts complement each other in such a way that it was suggested that they are remnants of a single treatise on mechanics, possibly written by Euclid16. However, they might have been granted the Euclidean label for their strict deductive structure, probably during the process of the first editions of the Euclidean corpus in the Antiquity. At any rate, it seems that the two texts were transmitted to Arabic culture after they were already catalogued as Euclidean works.
The Pseudo-Euclidean treatise Maqāla fī ͑1-mīzānreflects the pattern of a work on the balance done in the context of the Archimedean geometrical statics, making use of its main procedures but without direct mention of the concept of centre of gravity. The short treatise is devoted exclusively to the study or the theory or the lever in deductive form, and presents a sophisticated demonstration of the law of the lever. It is composed of one definition, two axioms and four propositions. Three manuscript copies of the Maqāla are known today: Paris copy (Bibliothèque Nationale de France, MS 2457. folii 21b-22b) Tehran copy (Danishgāh Library, MS 1751, folii 62b-64a) and Mašhad copy (Central Library of Mašhad, MS Astane Quds D 5643, PP. 9-11)17.
The Arabic version of Kitāb Uqlīdis fī ͑l-thiql wa ͑l-khiffa wa qiyyās al-ajrām ba’ḍihā ilā ba’ḍ (Book of Euclid on heaviness and lightness and the comparison of bodies one to the other) is extant in Thābit ibn Qurra’s revised and corrected edition (iṣlāḥ). In general the editorial procedure of iṣlāḥ was applied to texts which were transmitted or/and translated under certain defective conditions, so that their first version in Arabic was requiring emendation by an expert. In the case of the present text, the procedure of iṣlāḥ meant a more or less heavy editorial revision, which resulted plausibly in that some of the material in the extant version might be accredited to Thābit’s revision enterprise18.
The text is extant in three manuscript copies: Berliner Staatsbibliothek MS 258 (Ahlward 6014), folii 439r-440v; London India Office, MS 923 (Loth 744), folii 98v-I0Ir; and Hayderabad, Andra Pradesh Government Oriental Manuscripts Library and Research Institute, Asafiyya Collection, MS Riyāḍī 327. folii 257b-258a19. It was also transmitted in two Latin versions, of which at least one was translated from Arabic. The two versions are not radically different from the Arabic text. The proofs of the theorems are, however, more elaborated in the Arabic version20.
4. A partial Arabic version of Archimedes’ On Flouting Bodies
Contrary to the highly creative impact Archimedes had on Arabic mathematics, it seems that his main mechanical treatises such as Equilibrium of planes and Quadrature of the parabola were not translated into Arabic. However, some elements of his theory of centres of gravity were disclosed in the mechanical texts of Heron and Pappus, whereas the main ideas of his hydrostatics were transmitted in a Maqāla fī ͑thiql wa ͑l-khiffa, extant in Arabic in several manuscript copies. This short tract consists in a summarised digest of the treatise on the floating Bodies, presenting mere statements or the postulates and propositions or Book I and the first proposition of Book II without proofs.
The Book of Archimedes on heaviness and lightness is a brief account of some Archimedean hydrostatical propositions (Book I and Book II-prop. I), without proofs. Similar to the texts on heaviness and lightness attributed to Euclid and to Menelaus which are extant in short digests in the Arabic tradition, it exists also in two manuscript copies: respectively in Paris and in Gotha: Maqala li-Arshimidis fi ͑1-thiql wa ͑l-khiffa (Paris, Bibliotheque Nationale, MS Codex 2457-n° 4: ff. 22v-23v), and Muqaddimat Arshimidis wa-qadhayahu fi ͑1-thiql wa ͑l-khiffa (Gotha, Forshung- und Landesbibliothek, Codex 1158-n° 2, folios 40v-41v)21. We can note easily notable differences between Paris’s copy and Gotha’s one.
The Arabic text of this Archimedean work was never fully edited before on the basis of the two extant manuscripts. Zotenberg transcribed and published in 1879 the contents of Paris MS, adding no more than some diacritical points, while Gotha MS was mentioned by E. Wiedemann in I906and M. Clagett (1959)22 in their respectively German and English translations.
The special importance of the short Arabic version of Archimedes’ On floating bodies is multiple. First, it stems from an old tradition, one of the MS sources (Paris MS) dating from the 10th century. Secondly, the Arabic text does not quite conform to the standard Greek one nor to the Latin translation. Now since the Greek and Latin versions are issued from uncertain traditions, the existence of an Arabic version having some original discrepancies in respect to the other existing texts is an important element for any editorial enterprise and for historical understanding of the processes of transmission and reception of this important Archimedian text.
5.6. Heron’s and Pappus’ Mechanics
Two important Greek texts of mechanics are tightly connected with the Arabic tradition of the science of weights; these are two huge treatises referred to as Mechanics of the Alexandrian scholars Heron (1st century) and Pappus (4th century). These texts are together major sources for the reconstruction of the history of ancient mechanical ideas. Given their composite character, only some of their chapters concern the foundations of theoretical mechanics as developed in the later Arabic tradition around the questions of weighing. Heron’s Mechanics was translated into Arabic by Qusṭā ibn Lūqā under the title Fī raf’ al-ashyā’ al-thaqīla (On lifting heavy loads)23. After the loss of the Greek original text, it survived only in this Arabic version. On the contrary of Heron’s Mechanics, Pappus mechanical treatise was preserved in Greek and in Arabic. Its Arabic version is titled Madkhal ilā ͑ilm al-ḥiyal/ (Introduction to the science of mechanics), by a translator who has not yet been identified, but there is enough evidence to affirm that this version saw the light in I0th century Baghdad24.
7. Menelaus’ hydrostatics
Menelaus is one of the scholars of the School of Alexandria in late Antiquity. Known for his Book on the spherical figures or Spherics, extant in Arabic in the edition of Manșūr b. ͑Ali b. ͑Irāq, he is also the author of a work on specific gravity: Kitāb Mānālaus ilā Tarṭas al-Malik fī ͑1-ḥīla allatī tu’rafu bihā miqdār kull wāḥidin min ͑iddat adjsām mukhtaliṭa [The book of Menelaus to the King Tartas on the artifice by which is known the quantity each one of many composite bodies], extant in Arabic in a unique manuscript source: El Escurial (Spain) Codex 960Arabe25.
Further, in Book IV of The Book of balance of wisdom, al-Khāzinī described a “balance of Archimedes” according to Menelaus26, without however giving the title of the latter’s work from which he extracted his description. According to al-Khāzinī, in order to ascertain the relation between the weight of gold and that of silver, Archimedes took two pieces of the two metals which were of equal weight, then immersed the scales in water, and produced an equilibrium between them by means of the movable weight: the distance of this weight from the centre of the beam gave him the number required. To find the quantity of gold and of silver contained in an alloy of these two metals, he determined the specific gravity of the alloy by weighing it first in air and then in water, and compared these two weights with the specific gravities of gold and silver. See fig. 6 for the balance of Archimedes given by al- Khāzinī.
Archimedes’ balance consists of a balance of two equal arms from which two steady plates are hung. Furthermore, it has a minqala or rummāna (counterweight) on one of the arms which can be hung to some point of a little graduated scale marked with two series of divisions. Presented as a hydrostatical balance specialised in the determination of specific gravities of gold and silver, this instrument could also be employed in the ordinary operations o1 weighing.
Furthermore, the Arabic works on balances and weights linked with Menelaus contains another final text. In 1979, Anton Heinen discovered in Lahore (Pakistan) an Arabic manuscript containing a summary of Menelaus’ work by Ibn al-Haytham. He announced afterwards a project or edition including this text, besides Menelaus’ manuscript held in El-Escurial and al-Bīrūnī’s On the proportions between metals and jewels in volume, to reconstruct the corpus of the Arabic tradition of works on specific gravities27. Unfortunately, the sudden death of Heinen in April 1979 put an end to this project.
4. A PARTIAL ARABIC VERSION OF ARCHIMEDES’ ON FLOATING BODIES
In close connection with the translation and study of the above mentioned Greek sources, the scholars of the Islamic world composed in the period from the 9th up to the 12th century a set of original texts that laid the foundation for the new science of weights. To mention just the main treatises, these texts are seven in number:
8. Kitāb fī ͑l-qarasṭūn
Without contest, Kitāb fī ͑l-qarasṭūn by Thābit ibn Qurra (d. 901) is the most important text of the Arabic mechanical tradition; it was apparently one of the first Arabic texts to deal with the theory of the unequal-armed balance in Islam and to systematise its treatment. As such, and structured in the shape of a deductive theory of the steelyard based on dynamic assumptions, it established the theoretical foundation for the whole Arabic tradition. Thābit ibn Qurra’s fundamental treatise was translated into Latin in the 12th century by Gerard of Cremona under the title Liber karastonis28.
Kitāb fī ͑l-qarasṭūn is extant in four known copies, of which three contain complete texts with variant readings. Two of these, preserved in London (India Office MS 767-7) and Beirut (St.-Joseph Library, MS 223-11), were studied and published recently29. The third copy, formerly conserved in Berlin (Staatsbibliothek MS 559/9. ff. 2I8b-224a), was reported lost at the end of World War II. In October 1996, I rediscovered it in the Biblioteka Jagiellonska in Krakow (Poland). Recently, my attention was attracted over a partial fourth manuscript source that exists in the archives of the Laurentiana Library in Florence (MS Or. 118, ff. 71r-72r). Never mentioned before, this valuable three-page text includes the introductory two sections of Thābit’s treatise. This part of the text exposes the dynamic foundation of the treatise and an important passage that was thought of up to now to occur only in the Beirut copy (and thus known as Beirut scholium)30.
9. Kitāda fī ͑ṣifat al-wazn
Kitāb fī ṣifat al-wazn (Book on the conditions of equilibrium) by the same Thābit ibn Qurra is a five-section text on the balance and is about the conditions necessary to achieve equilibrium in weighing with balances, primarily the equal-armed sort31. Only in the third section is the uneven-armed balance or the steelyard (called here also qarasṭūn), touched upon. This slight treatment of the steelyard was probably prior to Thabit’s systematic investigation we find in Kitāb fī ͑ l- qarasṭūn. An important connection between the latter and ṣifat al-wazn is provided by the occurrence, in the last section of ṣifat al-wazn, of the statement of a proposition identical with the postulate that opens Kitāb fī ͑ l- qarasṭūn.
Thābit ibn Qurra’s On the conditions of equilibrium was intended as a manual adressed to practitioners of the art or weighing, essentially those specialised in the equal-armed balance. The theory exposed in it, is very elementary and deals with such questions as: what’s the cause of equilibrium which occurs between equal and unequal weights in the balance; what are the conditions to respect in order to obtain accurate weighings in various cases (equal or unequal weights, with equal or unequal levers, weighing in the same medium or in different media). Nevertheless, although the aim of this short treatise is more technical, it contains two passages relevant to theoretical analysis as expounded by the author in his major treatise on the steelyard.
10. Ziyyāda fī ͑ l-qarasṭūn
Ziyyāda fī ͑ l-qarasṭūn or An Addition on the theory of the qarasṭūn is a short anonymous text extant in a unicum copy preserved in MS Beirut 223 (folios I00-I06) mentioned above. In this codex, the Ziyyāda serves as an appendix to Kitāb fī ͑ l- qarasṭūn. The two texts are written in the same hand and display strong terminological affinities which include the basic vocabulary as well as the technical terms. Thābit ibn Qurra is mentioned twice in the Ziyyāda. This and several other elements induce us to consider it as an appendix intended to amplify the analysis developed in Thābit’s original work. The text of the Ziyyāda is composed of five propositions; the first four propositions are accompanied by geometrical proofs, whereas the fifth has only a statement. The first two are mere applications of the theorem of substitution or the Proposition VI of Kitāb fī ͑ l- qarasṭūn, whilst the last three establish a procedure for calculating the counterweight required to maintain equilibrium in a lever divided an evenly number of times32.
11. A text on the balance by Al-Ahwāzī
Muḥammad ibn ͑Abd-Allāh b. Manṣūr al-Ahwāzī is a mathematician of the I0th century. He is the author of a short text on the balance, extant in a unique copy preserved in Khuda Baksh Library in Patna (Codex 2928 folio 31) without title, save for the one provided by the curators of the library: Risāla fī ’l-mizān33.
Al-Ahwāzī’s treatise may be divided in several main sections devoted, respectively, to the distinction between the “normal balance” and the steelyard, the formulation or the law of the lever (illustrated by numerical examples), the problem of repairing and calibrating a beam by putting marks, the determination of the counterpoise (al-rummāna) when the original is lost, and, finally, the making of different balances: an equal-armed one behaving like a qarasṭūn (one of its plates is mobile along an arm of the balance), another one with three plates, and a third one with four plates suspended from the ends of two perpendicular and equal beams.
12. The treatises on centres of gravity of al-Qūhī and Ibn al-Haytham
These important contributions by two most important Islamic mathematicians of the 10th-11th centuries survived only through their reproduction by al-Khāzinī in a joint abridged version that opens the first book of his Kitāb mīzān al-ḥikma (main theorems relative to centres of gravity according to Abū Sahl al-Qūhī and Ibn al-Haytham al-Bașrī)34. We know from independent sources that al-Qūhī and Ibn al-Haytham wrote on centres of gravity, but their works have not yet been found. Al-Khāzinī’s text is, for the moment, the only source for their achievements in this field. The potential discovery of the complete versions of these texts will mean the recovery of fundamental sources35.
Al-Khāzinī’s edition consists in a very schematised exposition made of statements without proofs, but it shows clearly the familiarity of Arab scholars with the fundamental ideas of Greek works on centres of gravity, which they developed and deepened to a large extent.
13. Al-Qūhī on the law of the lever
In the correspondence on scientific issues that occurred around 990-991 between al-Qūhīwith Abū Ishaq al-Șābī, we find precious information on some statements on the centres of gravity and the law of the lever by al-Qūhī36. The correspondence between al-Qūhīand al- Șābī represents an important document on a scientific discussion between an accomplished mathematician and an enthusiastic amateur in the 10th century. The debate on the barycentric theory intervenes in the correspondence as follows. The exchange began by a letter from al- Qūhī in which is stated, results of his research on centres of gravity. Further, he promised to send a copy of his book on this topic. In a subsequent letter, al-Șābī requested details on the subjects mentioned by al- Qūhī. Some time passes and al-Qūhī did not reply; this prompts al-Șābī to write again, repeating once more his precious requests. In his reply, al-Qūhī refers, among other topics, to the book he had written on centres of gravity, of which he has completed six chapters and plans to write four or five more. Al-Șābī’s answer comprises what he believes to be a counterexample to the unrestricted validity of the law of the lever. Later, al-Qūhī answers his correspondent objections and exposes the error in al-Șābī’s counterexample to the law of the lever, and he distinguished between “generally accepted” and “necessary” premises. It seems that the correspondence stopped at this point, as there is no record of a new objection from al-Șābī to al-Qūhī decisive arguments.
The sixth and last letter of this precious correspondence is the most important part from the point of view of statics. First, it provides decisive evidence that al-Qūhī had produced at the time of this epistolary exchange an alternative proof of the law of the lever in his treatise on centres of gravity. Al-Qūhī was an accomplished mathematician as shown by his extant work, and he never failed to provide mathematical proofs to his propositions. On the other hand, this part of the correspondence, besides providing important data on the mechanical debates in the 10th century, contains al- Qūhī’s detailed epistemological discussion of the status of the law of the lever. This discussion is a valuable historical document of which the argument did not occur elsewhere, as far as we know, in all the corpus of ancient and medieval mechanics.
14. Maqāla fī ͑ l-makāyyīl wa al-awẓān
Īlyā al-Maṭrān was the Archbishop of Nisibin (north Mesopotamia) in the first half of the 11th century. His Maqāla fī ͑ l-makāyyīl wa al-awẓān (Treatise of measures and weights) is essentially of practical interest, but it is based on the theory of the steelyard as elaborated in earlier Arabic works, and mixes theoretical and practical considerations37.
The Book of Measures and Weights is extant in five known copies: four are reserved in Cairo (Dar al-kutub, MS DR 92, MS DR I046, MS TR 199. MS TR 341), and one is in Paris (Bibliothèque Nationale, MS 206). There existed a complete copy in Gotha (MS 133 I), but it seems that it was lost38. The Paris copy is very incomplete, but the text can be reconstructed from the four Cairo MS copies, which were preserved in excellent condition. The relatively high number of extant copies is an indication on the diffusion and probable influence the work had.
15. Irshād dhawī al-’irfān ilā ṣinā’at al-qaffān
A fundamental and long-neglected treatise, the Irshād dhawī al-’irfān ilā ṣinā’at al-qaffān (Guiding the Learned Men in the Art of the Steelyard) was written by Abū Ḥātim al-Muẓaffar b. Ismā’īl al-Isfizārī. al-Isfizārī was a mathematician and mechanician who flourished in Khurasān (north-east Iran) around 1050-1110. His important treatise is extant in a unique manuscript copy preserved in Damascus (the Syrian National Library, al-Ẓāhiriyya collection, MS 4460, folii I6a-24a). In addition, an abridged version reproduced by al-Khāzinī includes a section on the construction and use of the steelyard, which is omitted from the Damascus manuscript39.
In this original text on the theory and practice o1 the unequal-armed balance, different textual traditions from Greek and Arabic sources are compiled together for the elaboration of a unified mechanical theory. Although this text is the most significative writing of al-Isfizārī, it has never been published nor translated into any language in full, before the author or this article began his investigations on it40.
In content, proofs and terminology, the treatise Irshād of al-Isfizārī reveals itself as a major source for the reconstruction of the tradition of Arabic theoretical mechanics. In it, al-Isfizārī attempted to build a theory of the science of weights based on the barycentric considerations borrowed from Pseudo-Euclid’s text on the balance Maqāla fī ͑ l-mīzān and the dynamic orientation that guided Thābit ibn Qurra in kitāb fī ͑ l-qarasṭūn.
The structure or the Irshād is elaborated in the form of four layers as follows. First, the problem of the center of gravity is discussed in relation to the law of the lever, then a proof of the law of the lever is presented, based on the demonstration of this theorem in Thābit ibn Qurra’s Kitāb fī ’1-qarasṭūn. The third layer is a systematic review of Pseudo-Euclid’s Maqāla fī ͑ l-mīzān; and finally Propositions 4-5 of Kitāb fī ’l-qarasṭūn are reworked in the last and fourth section.
16. Kitāb mīzān al-ḥikma
In the second part oi his book, al-Khāzinī described a sophisticated balance capable of measuring absolute and specific weights of solids and liquids and of calculating exchange rates of currencies. This balance was used for ordinary weighing, as well as for all purposes connected with the measuring of specific gravities, distinguishing of genuine and false metals, examining the composition of alloys, etc. In all these processes the plates are moved until equilibrium is obtained and the desired magnitudes in many cases can at once be read on the divisions of the beam. This balance, called by its author mīzān al-ḥikma (balance of wisdom, see fig. 8) and al-mīzān al-jāmi’ (the universal balance), represented the culminant point of centuries of developments in the science of weighing and of the determination of specific gravities in the Islamic world.
The famous Book of the Balance of Wisdom by al-Khāzinī deserves a special mention in the Arabic tradition of the science of weights. Conceived of by the author as an encyclopedia of mechanics, Kitāb mīzān al-ḥikma was completed by al-Khāzinī in 1121-22. The extensive treatise has the form of a real mine of information on all aspects of the theoretical and practical knowledge in the Islamic medieval area about balances. The book covers a wide range of topics related to statics, hydrostatics, and practical mechanics, besides reproducing abridged editions of several mechanical texts by or ascribed to Greek and Arabic authors. This huge summa of mechanical thinking provides a comprehensive picture of the knowledge about weights and balances available in the Arabic scientific milieu up to the early 12th century. Therefore, it represents a major source for any investigation on ancient and medieval Mechanic41.
17-21. Additional texts
The textual tradition of the Arabic science of weights between the 9th and the 12th centuries also contains additional sources that should be taken into account in any complete reconstruction of its corpus. Theses include the work of Muḥammad Ibn Zakariyyā al-Rāzī (865-923) on the natural balance42, extracts from texts on weights by Qusțā ibn Lūqā and Isḥāq ibn Ḥunayn43, Ibn al-Haytham’s largely expanded recension of Menelaus’ text on specific gravities (mentioned above)44, and two writings on specific gravity and the hydrostatical balance by ͑ Umar al-khayyām45.
5. TEXTS OF THE LATER PERIOD
The third and last phase of the Arabic writings on weights and balances is represented by a group of texts dating from the 14th to the 19th century and originating principally from Egypt and Syria. These two countries were unified during this long period by the Ayyubid, Mameluk, and Ottoman dynasties, respectively, and they constituted for centuries a unified economic and cultural space. Whence the raison d’être of this large amount of writings on the theoretical and practical problems of the balance and weights, since it was a direct outcome of the integration of economic and cultural activities in this vast area. The authors of these texts are mathematicians, mechanicians, and artisans. In the following some names and works are mentioned for illustration.
22. Masā’il fī ͑ l-mawāzīn (Problems on balances) by Ya’īsh b. Ibrāhīm al-Umawī: This short tract is by a mathematician of Andalusian origin who lived in Damascus (fl. 1373), and is known as the author of several arithmetical works46. His Masā’il consists of a small collection of problems about weighing with hydrostatic and normal balances. The text is part of the codex DR 86preserved in the Egyptian National Library in Cairo.
23. Risāla fī ͑ amal al-mīzān al-ṭabī’ī by Taqī al-Dīn ibn Ma’rūf: The author is a well known mathematician, astronomer, and mechanician (born in Damascus I525-died in Istanbul in 1585). His short treatise on making the natural balance describes what was transmitted to Taqī al-Dīn in a previous narrative on the balance that he ascribes to the mathematician Ghiyyāth al-Dīn al-Kīshī (died in Samarkand in 1429) It is part of the collections of the municipal library of Alexandria, Egypt.
24. ͑ Amal mīzān li-ṣarf al-dhahab min ghayr ṣanj (The construction of a balance to concert gold without standard weight) by Abū ͑l-’Abbās Aḥmad ibn al-Sarrāj. The author, who was alive around 417 AH (1319-20) and 748 AH (1347-8), was the most important specialist of astronomical instrumentation in the Mamluk period47. His short text is the sixth item of the codex MR 30 conserved in the Egyptian National Library in Cairo.
25-28. The Egyptian astronomer Muḥammad ibn Abī al-Fatḥ al-Ṣūfī (d. 1543) composed several treatises on the theory and the practice of the steelyard balance which enjoyed a wide diffusion. Al-Ṣūfī seems to be the last original representative of the classical Arabic tradition of works on balances and weights. With him, this tradition arrives at an end, in the same time as pre-classical physics in Europe was operating a deep transformation that integrated the science of weights in modern physics. Here are his main treatises, known in several extant copies preserved exclusively in Cairo and Damascus, attesting to their widespread use in Egypt and Syria over the centuries:
25. Risāla fī ṣinā’at al-qabbān (Treatise in the art of the steelyard): a systematic description of the steelyard and its use in different situations, showing a clear acquaintance with steelyards. The text is explicitly writ ten for the practitioners;
26. Irshād al-wazzān li-ma’rifat al-awzān bi ͑ l-qabbān (Guide to the weigher in the knowledge of the weights of the steelyard): similar to the previous text;
27. Risāla fī qismat al-qabbān (Treatise on the division of the steelyard): contains arithmetical and geometrical problems on the calculation of the parts of the steelyard;
28. Risāla fī iṣlāḥ fasād al-qabbān (Treatise on repairing the defectuosity of the steelyard): very detailed analysis of the different cases of deficiency of a steelyard and the solutions to repair these deficiencies.
Other later texts include:
29. Nukhbat al-zamān fī şinā’at al- qabbān: a short text on the steelyard by ͑Uthmān b. ͑Ala’ al-Dīn al-Dimashqī, known as Ibn al-Malik (fl. 1589);
30. Risālat al-jawāhir fī ͑ilm al-qabbān (Treatise of jewels in the science of the steelyard): a ten-chapter text written by Khièr al-Burlusī al-Qabhānī (d. in 1672);
31. Two writings on the “scienceˮ (͑ilm) and the “descriptionˮ (ta’rīf) of the steelyard by ͑Abd al-Majīd al-Sāmūlī (18th century);
32. Al-‘lqd al-thamīn fimā yata’allaq bi-‘l-mawāzīn (The high priced necklace in what concerns the balances): a systematic treatise on the balance and weights, by Ḥasan al-Jabartī (1698-1774);
33. Several short texts dealing with the principles and the construction of the steelyard by Muḥammad al-Ghamrī (died before 1712);
34. Risāla fī ͑1-qabbān by Muḥammad b. al-Ḥusayn al-’Ațțār (d. I8I9), a Syrian author, is among the very last works written in Arabic in the style of the earlier mechanical tradition48.
For some other texts, the authorship is not yet firmly established, as they do not bear any name and they are catalogued as “anonymous texts”. In this last category, we mention the following three tracts, which are very probably connected with the texts of the later period above:
35. First, a huge summa titled Al-qawānīn fī ṣifat al-qabbān wa ͑1- mawāzīn (The laws in the description oi the steelyard and the balances): Codex TR 279ff. I-62in the Cairote Dār al-kutub;
36. Then a short text, Bāb fī ma’rifat ͑amal al- qabbān (Chapter in the knowledge of making the steelyard): Cairo, Dār al-kutub, MS K3831/1, and MS RT 108/1;
37. An untitled tract of which the beginning is “hādhihi risāla fī ͑ilm al-qabbānˮ: Cairo, Dār al-kutub, in the same MS k3831;
38. And finally two short tracts (Risāla mukhtaṣara fī ͑ilm al- qabbān and Risāla fī ͑ilm șinā’at al-qabbān) preserved in Damascus (National Library, al-Ẓāhiriyya Collection, MS 4)49.
The texts mentioned so far afford a precious testimony to the fact that scientific and technical works - sometimes with a high level of originality - continued to be composed in Arabic in the field of mechanics until the 19th century. This corresponds with similar information derived from recent research in other fields of Arabic sciences, such as astronomy and mathematics. The ongoing research into this later phase will undoubtedly change our appreciation of the historical significance of Arabic science and of its place in the general history of science and culture.
6. THE STATUS OF THE SCIENCE OF WEIGHTS
The availability of the major part of the Arabic texts on the problems of weights and balances makes it possible, for the first time, to address the question of the historical significance of this large corpus of mechanical works.
The investigation or this question has already led to a far-reaching conclusion. This corpus represents no less than the transformation of the ancient mechanics into a systematic science of weights and balances. As disclosed in the treatises of Pseudo-Aristotle, Philon, Heron, and Pappus, the Greek classical doctrine of mechanics was shaped as a collection or descriptions and riddles about machines, instruments, and common observation. In contradistinction, the new Arabic science of weights is focused on a relatively small range of subjects - mainly the theory of the balance and equilibrium and the practical issues of weighing with different instruments. On the conceptual level, it is built on a dynamic foundation and seeks to account for mechanical phenomena in terms of motion and force. As such, it restores a strong link between mechanics and natural philosophy. This new science of weight lasted in Arabic culture until the 19th century and constituted since the 12th century a basis for the Latin scientia de ponderibus that developed in western Europe.
The emergence of the Arabic science of weights has been proclaimed by al-Fārābī (Ca. 870-950) in his Iḥṣā’ al-’ulūm, where he produced an authoritative reflexion on the epistemological status of mechanics that set the stage for the question once and for all. In particular, he set up a demarcation line between the science of weights and the science of machines, and considered both as mathematical disciplines.
Al-Fārābī differentiated in his system between six principal sciences: those of language, logic, mathematics, nature, metaphysics and politics. Mathematics is subdivided into seven disciplines: arithmetics, geometry, perspective, astronomy, music, the science of weights (͑ ilm al-ḥiyal) and the science of devices or machines ('ils ul-JiynJ). The last two are characterised as follows:
As for the science of weights, it deals with the matters of weights from two standpoints: either by examining weights as much as they are measured or are of use to measure, and this is the investigation of the matters of the doctrine of balances ( ͑umūr al-qawl fī ͑l-mawāzīn), or by examining weights as much as they move or are of use to move, and this is the investigation of the principles of instruments ( ͑uṣūl al-ālāt)by which heavy things are lifted and carried from one place to another.
As for the science of devices, it is the knowledge of the procedures by which one applies to natural bodies all that was proven to exist in the mathematical sciences... in statements and proofs unto the natural bodies, and [the act of] locating [all that], and establishing it in actuality. The sciences of devices is therefore that which supplies the knowledge of the methods and the procedures by which one can contrive to find this applicability and to demonstrate it in actuality in the natural bodies that are perceptible to the senses50.
Considering the two main branches of mechanics as genuine mathematical sciences, al-Fārābī located their objects respectively in the study of weights and machines. Hence, ͑ilm al-athqāl is centered on the principles of the balances and of lifts, investigated with reference to measure and motion, whereas ͑ilm al-ḥiyal is conceived of as the application to natural bodies of mathematical properties (lines, surfaces, volumes, and numbers). As such, it includes various practical crafts: the overseeing of constructions, the measurement of bodies, the making of astronomical, musical, and optical instruments, as well as the fabrication of hydraulic mechanisms, mirrors, and tools like bows, arrows and different weapons51.
In this context, the main function of ilm al-ḥiyal consists of bringing the geometrical properties from potentiality (quwwa) to actnality (fi’l) and to apply them to real bodies by means of special engines (bi-’1-ṣan’a)52. Developing an Aristotelian thesis53, al-Fārābī endows the science of machines with an eminent task, to actualise the mathematical properties in natural bodies. Such a iunction or actualisation could not be extended to ͑ilm al-athqāl. In fact, weight and motion, the two notions that delimit its field of investigation, can hardly be taken as geometric properties of natural bodies, limited by al-Fārābī to spatial and numerical aspects, in accordance with the canonical Euclidean paradigm that banishes all the material properties or magnitudes from the realm of geometry.
The distinction of the science of weights from the different crafts of practical mechanics, is a crucial result or al-Fārābī’s theory. The emphasis laid by the Second Master on ͑ilm al-athqāl can not be stressed enough. It means no less than a solemn announcement of the emergence of an independent science of weights. With roots in the long tradition of the ancient mechanics, this new discipline came to light in the second half of the 9th century in the works of Thābit ibn Qurra and his colleagues in Arabic science54. It is this important scientific achievement that was recorded by al-Fārābī while building his system of knowledge.
Al-Fārābī’s thesis had a long-lasting resonance in Arabic learning and was never seriously challenged. The fundamental singularity of the science of weights as an independent branch within the mathematical arts, distinct from the science of machines, became a feature of subsequent theories of science. For confirmation a great number of cases, in different kinds of works and in various literary contexts, can be called upon. Hereinafter, some of these are presented in chronological order.
In his Risāla fī aqsām al-‘ulūm al-'aqliyya (Epistle on the parts of rational sciences), Ibn Sīnā (980-1037) enumerated the mechanical arts, considered as ‘secondary constituents’ of geometry, as ͑ilm al-ḥiyal al-mutaḥarrika (the science of movable machines, i.e., automata)55, the pulling of weights (jarr al-athqāl), the science of weights and balances (͑ilm al-awzān wa al-mawāzin), and the ‘science of particular machines’ (͑ilm al-ālāt al-juz’iyya)56. Ibn Sīnā establishes a clear distinction between the science of weights and balances, the craft of pulling heavy loads, and the art of devices. In addition, the latter is subdivided into the arts of automata and of particular machines. Likewise, the pulling of weights, included in the science of weights by al-Fārābi, is assigned as a specific branch of geometry. The main point, however, in Ibn Sīnā's schema is the emphasis laid on the science of awzān and mawāzīn in which weights and balances are combined. The reference to the wazn instead of the thigl could be interpreted as a privilege given to the statical standpoint. Indeed, the wazn is a constant quantity measurable in a balance, whereas the thiql is that quantity - called gravity or heaviness - which varies during the weighing process and depends on the position of the weighed object relatively to a particular point, the centre of the world or the fulcrum of the balance57.
In his discussion on the divisions of science in Maqāṣid al-falāsifa (The Intentions of philosophers), al-Ghazālī (1058-1111) subsumed the science of weights (͑ilm al-athqāl) as an independent branch under the mathematical arts and differentiates it from the study of ingenious devices (͑ilm al-ḥiyal)58. Ibn Rashīq, a Moroccan mathematician of the late I3th century, assumed a similar demarcation between weights and machines, and founded the latter on the former: the science of weights, of balances, and of catapults (͑ilm al-athqāl wa ͑ 1-mawāzīn wa ͑1-majānīq) deals with the downward motion of heavy bodies and constitutes the foundation of the science of machines (wa-yatarattab ͑alā ͑ilm al-athqāl ͑ilm al-ḥiyal)59. In his biography of al-Isfizārī, al-Bayhaqī did not confuse the two, when he reported that al-Isfizārī “was mostly inclined to astronomy and to the science of weights and machines (͑ilm al-athqāl waal-ḥiyal)60.” This corresponds to what we know of his extant works in mechanics, the Irshād being clearly a book of athqāl, whereas al-Isfizārī’s work on ḥiyal is represented by a collection of compiled summaries (sometimes with comments) extracted irom the mechanical works of Heron, Apollonius and Banū Mūsā61. Later on, Taqī al-Dīn ibn Ma’rūf, the I6th century mechanician, followed the same pattern. Accounting for the books he read in his scientific curriculum, he mentioned, in addition to texts of mathematics, “books of accurate machines (kutub al-ḥiyal al-daqīqa), treatises of the science of the steelyard and of the balance (rasā’il ͑ilm al-qarasṭūn wa al-mīzān), and of the pulling of weights (wa-jar al-athql)62.ˮ
Sometimes ͑ilm al-athqāl is referred to as ͑ilm marākiz al-athqāl, one of its branches which enjoyed great reputation. A good instance of this is the following quotation extracted from the correspondence between Al-Qūhī and Al-Ṣābī. In a letter to Al-Qūhī, al-Ṣābī says:
We did not obtain a complete book on this science, I mean centres of gravity (marākiz al-athqāl), nor was there done any satisfactory work by one of the ancients or one of the moderns. In my opinion it is in the rank of a singular science which merits to have a book of basic principles (al-ṣinā’a al-mufrada allatī yuḥtāj an yu’mal lahā kitāb ͑uṣūl)63.
A century later, al-Isfizārī qualified the centres of gravity as “the most elevated and honorable of the parts of the mathematical sciences” and defined it as:
The knowledge of the weights of loads of different quantities by the [determination of the] difference of their distances from their counterweights (Irshād, f. 16b).
Al-Khāzinī further specifies further the definition of his predecessor when he explains that the study of the steelyard is founded upon the science of the centres of gravity (wa ͑alayhi mabnā al-qaffān)64. Therefore, it is obvious that the expression marākiz al-athqāl is intended to account for the statical aspect of ͑ilm al-athqāl, by the study of forces as they are related to weights, such as in the case of levers and scales. This same thesis is assumed by other Islamic scholars65.
In contrast, the tradition of ḥiyal delimits the contours of a distinct discipline, centred on the investigation of the methods of applicability of mathematical knowledge to natural bodies. As represented in several Greek and Arabic mechanical texts, written by Heron, Pappus, Philon, Banū Mūsā and al-Jazarī, the tradition of ḥiyal is focused on the description of machines and the explanation of their functions. Book I of Heron’s treatise contains principles of theoretical mechanics, but the rest, more than three quarters of the whole, is predominantly about different kinds of devices. The same applies to the treatise of Pappus. As for Philon of Byzantium (fl. 230), his Pneumatics is just a catalogue of machines worked by air pression66.
An important constituent of the Greek traditional doctrine of mechanics - as it is disclosed in the texts by Pseudo-Aristotle, Heron and Pappus - is represented by the theory of the simple machines (the windlass, the lever, the pulley, the wedge, and the screw). Those simple machines were dealt with in Arabic science by several scholars such as Ibn Sīnā67, al-Isfizārī68, and Sinān ibn Thābit69 under the name of ḥiyal. Besides this trend on the basic simple machines and their combinations, the science of ḥiyal also included a description of other categories of machines necessary in daily life and useful for civil engineering. The most well known works describing these kind of engines, are the texts of machines by Banū Mūsā and al-Jazarī. Kitāb al-ḥiyal by the Banū Mūsā comprises a large variety of devices, the vast majority of which consist of trick vessels for dispending liquids. The book of al-Jazarī al-Jāmi’ fī ṣinā’at al-ḥiyal enlarges this same feature in an unprecedented way. The author incorporates in it the results of 25 years of research and practice on various mechanical devices (automata, musical machines, clocks, fountains, vessels, water-raising machines, etc.)70
The conception of ḥiyal as the practical component of mechanics is additionally corroborated by the contents of a chapter of the Mafātīḥ al-‘ulūm by Muḥammad b. Yūsuf al-Khwārizmī (10th century). Chapter 8 of Book II of this lexicographic encyclopedia is dedicated to “şinā’al-ḥiyal, tusammā bi al-yūnāniyya manjanīqūnˮ (the art of machines, called in Greek manjanīqūn). Besides a short mention of machines for the traction of weights, the ḥiyal described are essentially of two types: automata (ālāt al-ḥarakāt) and hydraulic devices (ḥiyal ḥarakāt al-mā’)71. The author devotes great attention to the first two kinds; this might be taken as evidence of the pre-eminence of these machines in the domain of ḥiyal in his time. Significantly, al-Khwārizmī - like Ibn Sīnā - classifies the weight-pulling machines in the field of ḥiyal in contrast with their arrangement among that of athqāl by al-Fārābī.
The analysis of the overall significance of the Arabic medieval science of weights showed that this tradition does not represent a mere continuation of the traditional doctrine of mechanics as inherited from the Greeks. Rather, it means the emergence of a new science of weights recognised very early on in Arabic learning as a specific branch of mechanics, and embodied in a large scientific and technical corpus. Comprehensive attempts at collecting and systematising (as well as updating with original contributions) the mainly fragmentary and unor ganised Greco-Roman mechanical literature that had been translated into Arabic, were highly successful in producing a coherent and orderly mechanical system. In this light, a redefinition of Arabic mechanics becomes necessary, initially by questioning its status as a unified field of knowledge. Such a redefinition may be worked out briefly by setting a sharp distinction between ͑ilm al-athqāl and ͑ilm al-ḥiyal. The latter corresponds to the traditional descriptive doctrine of machines, whereas the core structure of the ͑ilm al-athqāl is determined by the balance-lever model and its theoretical and practical elaborations. Uniting the theoretical treatment of the balance with concrete practical information about its construction and use, and adopting an integrative treatment of physics and mechanics, overcoming their original separation in Antiquity, the new science of weights distinguishes itself by turning mechanics from being originally a marginal part of geometry into an independent science providing the theoretical branch of mechanics.
On the methodological level, the new science of weights was marked by a close combination of experimentation with mathematisation. The Aristotelian qualitative procedures were enriched with quantitative ones, and mathematics was massively introduced in the study of mechanical problems. As a result, mechanics became more quantitative and the results of measures and experiments took more and more weight in mechanical knowledge. Certainly, the fundamental concepts of Aristotelian physics continued to lie in the background, but the scholars were able to cross their boundaries and to accomplish remarkable discoveries in physical ideas. For instance, the generalisation of the theory of centres of gravity to three-dimensional objects, the introduction of a dynamic approach in the study of problems of statics and hydrostatics, the improvement of the procedures and methods for the determination of specific weights and of weighing instruments, the development of the theory of heaviness and the establishment of a theory of the ponderable lever. Further, the treatment of the law of equilibrium by Thābit ibn Qurra and al-Isfizārī opened the horizon of a unified theory of motion in which the dichotomies of natural-violent, upward-downward motions vanish, exactly as they disappear in the concomitant motions of the two arms of a balance lever. In this physical system, indeed, the weight of the body might be considered the cause of the downward as well as of the upward motion, overcoming the Aristotelian balking at making weight a cause of motion. For their part, al-Qūhī and Ibn al-Haytham had the priority in formulating the hypothesis that the heaviness of bodies vary with their distance from a specific point, the centre of the earth. Moreover, they contributed to unify the two notions of heaviness, with respect to the centre of the universe and with respect to the axis of suspension of a lever. In his recension of the works of his predecessors, al-Khāzinī pushed forward this idea and drew from it a spectacular consequence regarding the variation of gravity with the distance from the centre of the world. All this work represented strong antecedents to the concept of positional weight (gravitas secundun situm) formulated by Jordanus in the 13th century72.
7. FOR AN INTERCULTURAL HISTORY OF MECHANICS
The historians of mechanics, from Pierre Duhem until Marshal Clagett, assumed that the foundation of the science of weights must be credited to the school of Jordanus in Europe in the I3th century. Now it appears that this science emerged much earlier in Islamic science, in the 9th century. Moreover, the first steps of the Latin scientia de ponderibus should be considered as a direct result of the Arabic-Latin transmission, and especially as a consequence of the translation of two major Arabic texts in which the new science and its name are disclosed, Kitāb fī ͑l-qarasṭūn by Thābit ibn Qurra and Iḥṣā’ al-‘ulūm by al-Fārābī.
Indeed, the very expression scientia de ponderibus was derived from the Latin translation of al-Fārābī’s Iḥṣā’ al-’ulūm. Versions of this text were produced both by Gerard of Cremona and Dominicus Gundissalinus. The latter made an adapted version of the Iḥṣā’ in his De scientiis and used it as a framework for his own De divisione philosophiae, which later became a guide to the relationships between the sciences for European universities in the 13th century. In the two texts, Gundissalinus reproduced - sometimes verbatim - al-Fārābī’s characterisation of the sciences of weights and devices, called respectively scientia de pon-deribus and sciencia de ingeniis73. The reason for this close agreement is easy to find: he could not rely on any scientific activity in this field in his times in Latin74. Among all the sciences to which Gundissalinus dedicated a section, the science of weights, of devices, and of optics were obviously less known in the Latin west in the I2th century. Even the antique Latin tradition represented by Boece and Isidore of Sevilla could not furnish any useful data for a sustained reflection on their epistemo logical status. It must also be added that Gundissalinus seems to ignore all their developments in the Arabic science, including Thābit ibn Qurra's book on the theory of the balance and Ibn al-Haytham's achievements in optics. Hence, the effort of theorisation deployed by Gundissalinus, by showing the state of the sciences in the late I2th century in Western Europe, throws light on a considerable underdevelopment in several sciences. This concerns, particularly, the different branches of mechanics75.
As said before, Liber karastonis is the Latin translation by Gerard of Cremona of Kitāb fi ͑l-qarasṭūn. The general structure of both Arabic and Latin versions is the same, and the enunciations of the theorems are identical. Yet the proofs might show greater or lesser discrepancies. None of the Arabic extant copies of Thābit's Kitāb seem to be the direct model for Gerard's translation. The Latin version was repeatedly copied and distributed in the Latin West until the I7th century, as it is documented by several dozens of extant manuscript copies. This high number of copies instructs on the wide diffusion of the text. Further, the treatise was embedded into the corpus of the science of weights which was understood to be part of the mathematical arts or quadrivium, together with other works on the same topic, in particular the writings of Jordanus Nemorarius in the science of weights76. In addition, at least one version of Thābit's work was known in Latin learning as a writing of scientia de ponderibus. This version is the Excerptum de libro Thebit de ponderibus, a Latin text which appears frequently in the codexes. It is precisely a digest of the logical strucure of Liber de karastonis, in the shape of statements of all the theorems77.
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