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A New Arabic Text of Mechanics: Sinan ibn Thabit on the Theory of Simple Machines (cont'd)

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5. Short analysis of the contents of the text

Sinān ibn Thābit's text presents a summarized theory of the five simple machines in the form of short descriptions of their functions. The machines are identified on the basis of two procedures: terminological meaning of their names and practical considerations on their use.

The five simple machines dealt with are: the windlass, the lever, the pulley, the screw and the wedge. These machines are called by the same Arabic terms employed in the translation of the Greek names of these instruments. The only difference is the name given to the wedge. Instead of the usual Arabic term used for this instrument, which is al-isfīn, it is called in MS 3306 as al-ajanan, probably an Arabization of its name in Greek, Syriac or Persian (fig. 6).

Figure 6: Table of the Arabic names of the simple machines in translated Greek sources and in Arabic texts.

The order in which the simple machines are quoted in the major sources that discussed the theory of simple machines in Greek and Arabic mechanics seem to be Book II of Heron's Mechanics. The only exception is the Mi'yār al-'uqūl ascribed to Ibn Sīnā, where the wedge is dealt with before the screw. For comparison, the simple machines are quoted in Pseudo-Aristotle's Mechanical Problems in the following relative order: the lever, the windlass, the wedge and the pulley, the lever being considered the basic machine to which all other simple machines are to be reduced, especially the windlass and the pulley.

The fact that the lever is not quoted in the first place in Sinān's text may testify an inclination to discard the Peripatetic view which consists in the reduction of all the simple machines to the lever, and thus to the circular motion it represents. On the other hand, Sinān ibn Thābit's text establishes a clear connection between the lever and the steelyard, referred to as qarastūn, the name of Greek origin that prevailed for this instrument in Arabic scientific literature in the 9th and 10th century. Thābit ibn Qurra, the father of Sinān, wrote a very influential treatise on it under the title Kitāb fī 'l-qarastūn.

The early date of Sinān's text is attested by his vocabulary, which is reminiscent of the Arabic technical terminology derived from the translation of the Greek sources of mechanics. Hence, the steelyard is called qarastūn and not qabbān or qaffān (the last two terms are found in texts dating from the second half of the 11th century). Further, the lever is designated by muhl and bārim. This synonymy denotes a transition between muhl, directly derived from the Greek mochlos, and al-bayram, the standard Arabic word (of Persian origin) used by al-Khāzinī in Kitāb mīzān al-hikma (12th century). On the other hand, Al-Khwārizmī's 10th-century text Mafātīh al-'ulūm establishes an explicit synonymy between the two when it identifies mukhl (muhl) and bayram-bārim. In the same section, Sinān affords two other Arabic names for the lever: qārus and jālis. As far as we know, these two terms are associated to the lever only in his text. In addition, the mention of two early and exotic terms for the lever (qārūs and jālis) denotes an early origin of the text, since these terms are not mentioned in any other later Arabic mechanical text.

Sinān's description of the machines is similar to Heron's nomenclature of these basic instruments, but with some refinements. This is the case of his description of the windlass. The characterization of the wedge as the only simple machine that cannot be replaced by any other one of the four other simple machines is identical in Heron and in Sinān. But the latter's description of the lever is an admirable concentrated piece of theory. It establishes a direct analogy between this simple instrument and the steelyard. This analogy is reminiscent of a similar approach in Pseudo-Aristotle's Mechanical Problems, even though Sinān's remark that most of the problems of heaviness and lightness are to be referred to the properties of the lever goes beyond the limits of the analogy established in Pseudo-Aristotle between the lever and the balance. The son of Thābit ibn Qurra was more likely referring here to a well-established Arabic tradition of study of the steelyard in his time that made this instrument the model of the balance and of the other simple machines.

It is worthwhile to note that Sinān talks of the five simple machines in terms of 'asl (pl. 'usūl), meaning root, origin, and basic principle. In this perspective, Al-'usūl al-khams refer to the basic fundamental machines, on the basis of which other instruments may be conceived (they would be furū', consequences derived from them). This terminology is rooted in a usual dichotomy in Arabic thought, opposing 'usūl to furū', basic and primary things to consequences derived from them. In this context, the five powers are the basic machines from the combination of which other machines may be derived. Now the classification of machines and their combination is an important theme of Arabic mechanics, as for example in Mi'yār al-'uqūl attributed to Ibn Sīnā. It is thus possible that later sections in the complete version of Sinān ibn Thābit's work were precisely devoted to the classification of machines and their combination.

Finally, two interesting terminological instances are to be specially noted in Sinān's text. First, he used in the section about the pulley the word hila in the sense of means, intermediary. This is exactly one of the original senses of mechane in Greek. Secondly, the idea of the composition of motion in the section on the screw is worth to be highlighted also. The working of this machine is said to be generated by two motions, a circular one and a straight one (haraka mu'allafa min harakatayn, harakat al-istidāra wa-harakat al-istiqāma). There is no such clear and explicit idea of the composition of motions in the screw in Heron's discussion of this machine in the second book of his Mechanics.

6. Appendix: Description of the contents of MS 3306

The list of the texts mentioned on the first page of MS 3306 contains ten items. It is presented in the following in three forms: facsimile reproduction, transcription (both in fig. 7a-b), and in English translation, with commentaries on the titles of the texts.

Figure 7a-b: The first page of MS Berlin Staatsbibliothek 3306 and its transcription in Arabic.

English translation

"The books collected in this volume are:

• Risalat al-Jazarī fī a'mal al-hiyal (Treatise of Al-Jazarī on the construction of machines).
• Multaqatat Kitab al-tam li-Sinan b. Thabit fī dhikr usūl al-khamsa (sic) (Extracts from the Complete Book by Sinan ibn Thabit on the five powers).
• Maqalat al-Khazinī fī a'mal al-kura tadūr bi-dhatiha (sic) (Treatise of Al-Khazinī on the construction of a sphere that rotates by itself).
• Sharh kitab Biyanius (?) al-hakīm fī san'at maraya al-muhriqa (sic) (Commentary on the book of Biyanius (?) the sage on the art of burning mirrors).
• Risala fī … li-ma'rifat al-sa'a wa anwa' al-rukhama wa-ghayruhu (Treatise on… for the determination of the hour and different types of plates).
• Kitab Uqlīdīs al-hakīm fī ‘ilm al-manazir wa-kayfiyyat al-shu'a' (The book of Euclid in the science of optics and the theory of rays).
• Risala fī ‘amal anwa' al-dawalīb al-mudawwara min tilqa' dhatiha (Treatise on the construction of [various] types of wheels that move by themselves).
• Fawa'id fī ma'rifat mīzan al-'adl wa-ghayruhu (Utilities concerning the balance of justice and other things).

Commentaries on the titles

(1). Risalat al-Jazarī fī a'mal al-hiyal (Treatise of al-Jazarī on the construction/making of machines): this is a complete copy of Al-Jami' bayna al-'ilm wa al-'amal al-nafi' fī sina'at al-hiyal, the well-known work of Al-Jazarī (completed in 1206). This manuscript copy was not used in the recent edition and translation of al-Jazarī's treatise [31]. It occupies ff. 1b-131b and f. 133a-b. The short text of one folio of Sinan ibn Thabit is intercalated at its end on f. 132r-b.

(2). Multaqatat Kitab al-tam (sic) li-Sinan b. Thabit fī dhikr usūl al-khamsa (sic) (Extracts from The Complete Book of Sinan ibn Thabit on the Five Powers): This short fragment is the subject matter of the present article.

(3) Maqalat al-Khazinī [32] fī ‘amal kura tadūr bi-dhatiha (Treatise of Al-Khazinī on the construction of a sphere that rotates by itself): Abū 'l-Fath ‘Abd al-Rahman al-Khazinī flourished in Khurasan around 1115-31. The main domains of his scientific activity are astronomy, mechanics and scientific instruments. He is the author of the famous Kitab mīzan al-hikma, the book of the balance of wisdom. His other known works include a treatise on astronom¬ical instruments (Risala fī 'l-alat) and Maqala fī itikhadh kura tadūr bi-dhatiha, the text on the sphere that rotates by itself mentioned in this entry in MS Berlin 3306 (fig. 8).

Figure 8: The drawing of Al-Khazinī's sphere. Source: Maqala fī itikhadh kura tadūr bi-dhatiha, The Syrian National Library in Damascus, Al-Zahiriya Collection, MS 4871, folio 73r.

This text is known at present in two manuscript copies preserved respectively at the Syrian National Library in Damascus (al-Zahiriya Collection, MS 4871, ff. 73r-74r), and in the oriental collection at Oxford Library (MS Thurston 3, ff. 118-119r). It describes a celestial globe worked with weights. The instrument has the form of a solid sphere marked with the stars and the standard celestial circles and half sunk in a box. Its rotation is propelled by a weight falling in a leaking reservoir of sand. The sphere is mounted so as to rotate once a day. It functions like an automatic celestial instrument, and may be used to find directly several arcs of importance in spherical astronomy [33].

(4) Sharh kitab Biyanius [34] (?) al-hakīm fī san'at maraya (sic) al-muhriqa (Commentary on the book of Biyanius (?) the wise on the construction of the burning mirrors): The name of the author – obviously a Greek scholar – is without diacritic marks. The text belongs to an established tradition of works translated from the Greek or composed in Arabic on burning mirrors [35].

(5). Risala fī … li-ma'rifat al-sa'a wa anwa' al-rukhama wa-ghayruhu (Treatise on … for the determination of the hour and the kinds of the rukhama and other things): The text is on an astronomical instrument, a sort of gnomon for measuring time. Thabit ibn Qurra has written a text with a similar title: Kitab fī alat al-sa'at allatī tusamma rukhamat (Book on the instruments which give the hours, called the solar quadrants (rukhamat) [36].

(6) Kitab Uqlīdīs al-hakim fī ‘ilm al-manazir wa kayfiyyat al-shu'a' (The Book of Euclid on the science of optics and the qualities of the ray). This text stems obviously from the tradition of the Arabic edition of Euclid's Optics, but it bears a title completely different from all those occurring in the Arabic tradition. The title quoted in MS 3306 might be a very early instance of this Arabic tradition of Pseudo-Euclid's Manazir. The reference it contains to the shu'a' (ray) constitutes a valuable reference to an important feature of this tradition, the Euclidean ray theory [37].

(7). Unreadable title.

(8). Risala fī ‘amal anwa' al-dawalīb al-mudawwara min tilqa' dhatiha (Treatise on the making of different wheels that turn by themselves): seems to deal with self-rotating wheels, a topic of Arabic mechanics to which several treatises are devoted. An important text of this category occurs in several manuscripts with the title: Bakarat tadūr min dhatiha (or min tilqa' dhatiha) (Wheels that move by themselves). It has usually been assumed that it is a discussion of perpetual motion and as such dismissed as of no practical significance. The descriptions are difficult to understand and the accompanying illustrations are obscure. Nevertheless, the machines appear to embody important mechanisms and they would certainly repay further detailed study [38].

The affiliation between item 3 in MS 3306 and this text on perpetual motion can be established on the terminological basis: mahala and bakara are synonyms and they refer to the wheel. Furthermore, if this is established, this may give a clue to determine the author and the date of both works. The author of the former is indeed given as al-Kharijī, probably a deformation of the name of Muhammad ibn al-Husayn al-Karajī, a known mathematician of the 10th-11th century (d. ca. 1016). He is also author of a work on hidden waters (Kitab inbat al-miyyah al-khafiyya)[39]. This topic, connected with engineering and levelling, was considered traditionally as a branch of mechanics.

(9). Unreadable title.

(10). Fawa'id fī ma'rifat mīzan al-'adl wa-ghayruhu: may be rendered as "Advantages/Utilities about the balance of justice". It deals probably with a mechanical balance. The balance is considered basically in the Islamic tradition as an instrument of justice, as it is clearly stated by al-Khazinī in his Kitab mīzan al-hikma [40].

7. References

• Abattouy, Mohammed 2000. "Al-Muzaffar al-Isfizarī ‘alim mikanīkī min al-qarnayn 5-6 H/11-12 M mu'allif Irshad dhawī al-'irfan ila sina'at al-qaffan" [al-Isfizarī a mechanician scholar from the 5-6 H/11-12 CE centuries, author of Guiding the Learned Men in the Art of the Steelyard]. In Quelques aspects de l'évolution des idées scientifiques. Antiquité et moyen âge. Rabat: Publications of the Faculty of Letters, pp. 135-175.
• Abattouy, M. 2001. "Greek Mechanics in Arabic Context: Thabit ibn Qurra, al-Isfizarī and the Arabic Traditions of Aristotelian and Euclidean Mechanics." Science in Context (Cambridge University Press) vol. 14: pp. 179-247.
• Abattouy, M. 2006. "The Arabic Transformation of Mechanics: The Birth of the Science of Weights". Published on www.MuslimHeritage.com in November 13, 2006. See the complete version of the article in PDF.
• Abattouy, M. 2007a. "‘Abd al-Rahman al-Khazinī." The Biographical Encyclopaedia of Astronomers. Edited by par T. Hockey. Berlin/New York: Springer Verlag, pp. 629-630.
• Abattouy, M. 2007b. "The Arabic Science of Weights ('ilm al-Athqâl): Textual, Tradition and Significance in the History of Mechanics." In A Shared Legacy, Islamic Science East and West". Edited by E. Calvo, M. Comes, R. Puig and M. Rius. Barcelona : Universitat de Barcelona, 2008, 83-114.
• Abattouy, M. 2011. "A New Arabic text of Mechanics: Sinan ibn Thabit on the Theory of Simple Machines", in Studies on the History of Sciences, edited by Ja'far Aghayani Chavoshi, Tehran, 1390/2011, pp. 19-38.
• Dold-Samplonius, Yvonne 1997. "Sinan ibn Thabit". In Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures, edited by Helaine Selin. Dordrecht/ Boston/ London: Kluwer Academic Publishers, p.902.
• Euclid 1956. The Thirteen Books of Euclid's Elements. Translated from the Text of Heiberg with Introduction and Commentary by Thomas L. Heath. New York: Dover, 3 vols.
• Garbers, K. 1936. "Eine Werk Thabit ibn Qurra's über ebene Sonnenuhren". Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik, Abteilung A: Quellen, 4 (1936), pp. 1-80.
• Hill, Donald R. 1974. The Book of Knowledge of Ingenious Mechanical Devices. An annotated translation of al-Jazarī's Treatise. Dordrecht: Reidel.
• Hill, D. R. 1991. "Arabic Mechanical Engineering: Survey of the Historical Sources." Arabic Sciences and Philosophy 1: pp. 167-186.
• Ibn abī 'Usaybi'a, Muwaffaq al-Dīn 1965. ‘Uyūn al-anba' fī tabaqat al-atibba'. Edited by Nizar Ridha. Beirut: Dar maktabat al-hayat.
• Ibn al-Nadīm 1871-72. Kitab al-Fihrist. 2 vols. Edited by Gustav Flügel, J. Roediger and A. Müller. Leipzig: F. C. W. Vogel.
• Ibn al-Qiftī 1903. Tarīkh al-hukama'. Edited by Julius Lippert. Leipzig: Dieterich'sche Verlagsbuchhandlung.
• Ibn Sīna, Al-Shaykh al-Ra'īs abū ‘Alī [1952] 1331 (solar Persian calendar). Mi'yar al-'uqūl. Edited with introduction and notes by Jalal al-Dīn Huma'ī. Tehran: Anjuman-i Athar-i Milli, n° 24.
• Ibn Sinan, Ibrahim 1948. Rasa'il Ibn Sinan. Haydarabad: Matba'at Jami'at Da'irat al-Ma'arif al-'Uthmaniyah.
• Kheirandish, Elaheh 1999. The Arabic Version of Euclid's Optics: Kitab Uqlīdis fī ikhtilaf al-manazir (Sources in the History of Mathematics and Physical Sciences, 16). 2 vols. New York, etc.: Springer Verlag.
• Luckey, Paul 1937-38. "Thabit b. Qurra's Buch über die ebene Sonnenuhren". Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik, Abteilung B: Studien, 4 (1938), pp. 95-148. Reprinted in Thabit ibn Qurra (d. 901). Texts and Studies. Frankfurt: Institut für Arabisch-Islamichen Wissenschaftern 1997 (Islamic Mathematics and Astronomy, vol. 22).
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• Mazahéri, Ali 1973. La Civilisation des eaux cachées. Traité de l'exploitation des eaux souterraines composé en 408/1017. Nice: I.D.E.R.I.C.
• Morelon, Régis 1987. Thâbit Ibn Qurra, Œuvres d'Astronomie, édition du texte arabe, traduction française et commentaire, Paris, Les Belles Lettres, 1987.
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• Rashed, R. 1996. Les Mathématiques Infinitésimales du IXème au XIème siécles. Vol. I: Fondateurs et commentateurs. Banū Mūsa, Thabit ibn Qurra, ibn Sinan, al-Khazin, al-Qūhī, ibn al-Samh, ibn Hūd. London: Al-Furqan Islamic Heritage Foundation.
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• Sa'īdan, Ahmad Salīm 1983. A'mal Ibrahīm ibn Sinan. Edited by A. S. Sa'īdan. Al-Kuwayt: al-Majlis al-watanī li-‘l-thaqafa wa-'l-funūn wa-‘l-‘adab, Qism al-turath al-'arabī, "al-Silsila al-turathiya; 6".
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• Toomer, Gerald J. Editor 1976. Diocles on Burning Mirrors: The Arabic Translation of the Lost Greek Original. Edited, with English translation and commentary. New York/Berlin/Heidelberg: Springer Verlag.
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End Notes

[31] See Hill 1974 and al-Hasan 1979.

[32] Without diacritic points.

[33] This short description of al-Khazini's device is extracted from Abattouy 2007a. A full description of the instrument is given in Emilie Savage-Smith, Islamicate Celestial Globes. Their History, Construction, and Use. Washington, D. C.: The Smithsonian Institution Press, 1985.

[34] Without diacritic points.

[35] See on this topic Toomer 1976, Rashed 1993, Rashed 1997a, and Rashed 1997b.

[36] This theoretical text on plane sundials sundials by Thabit ibn Qurra was edited and translated in Garbers 1936 and commented upon in Luckey 1937-38. It was also edited and translated in Morelon 1987, pp. 131-164.

[37] The textual tradition of the Arabic tradition of Euclid's Optics is described in Kheirandish 1999.

[38] The extant manuscript copies of this text as listed by Hill (1991, pp. 178-179) are the following: Sülemaniye U. Kütüphanesi, Istanbul, Hagia Sophia 2755, item 1, Bodleian Library, Oxford 954 - Marsh 669, item 2, Leiden, Bibliotheek der Rijksuniversiteit Leiden, Codex Orientalis 499, ff. 74-87r, Gotha Universitäts-Bibliothek, Codex Gotha 1348, ff. 109-124r, and Florence Bibliotheca Medici Laurentiana, Codex Or. 152, ff. 82-90. MS Berlin 3306 must be added to this list, even though the pages corresponding to this reference are missing.

[39] See the French translation of this text in Mazahéri 1973.

[40] Al-Khzazinī 1940, p. 4.

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by: Mohammed Abattouy, Tue 07 February, 2012