A New Arabic Text of Mechanics: Sinan ibn Thabit on the Theory of Simple Machines

The Arabic manuscript Orient fol. 3306 preserved at the Staatsbibliothek in Berlin was in its original form a precious collection of Arabic scientific texts of mechanics and optics. It contains a fragment in one folio page consisting in a brief characterisation of the five simple machines: lever, windlass, pulley, wedge, and screw. This short text and is attributed to Sinān ibn Thābit, the son of Thābit ibn Qurra and a known mathematician and physician in Baghdad during the 10th century. It is a new source that has never been studied before. In the following article, we present the Arabic text of Sinan ibn Thabit and its English translation, accompanied with historical and analytical commentaries.

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by Mohammed Abattouy[1]


Note of the editor

This article was first published as Mohammed Abattouy, “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.


Table of contents

  1. Description of MS 3306 and its contents
  2. Bio-bibliography of Sinān ibn Thābit
  3. Survey of the Arabic tradition of the five simple machines
  4. The Arabic text and English translation
  5. Short analysis of the contents of the text
  6. Appendix: Description of the contents of MS 3306
  7. References


The Arabic manuscript Orient fol. 3306 preserved at the Staatsbibliothek in Berlin[2] was in its original form a precious collection of Arabic scientific texts of mechanics, containing also two tracts on optics. The original content of the manuscript is given on the first page of the codex. Among the texts listed on this page we find the following title: Multaqatāt Kitāb al-tām li-Sinān b. Thābit fī dhikr ’uṣūl al-khamsa (sic) (Extracts from the Complete Book by Sinān b. Thābit in the mention of the principles of the five [simple machines]). This title corresponds to a fragment in one folio page in the codex, namely the folio 132r-v (fig. 1a-b). The recto page of the folio consists in a brief characterisation of the five simple machines, the "five powers" of the Ancients (lever, windlass, pulley, wedge, and screw), while we find on the verso the description of various other machines. It appears that these two fragments were extracted from a longer text entitled originally Al-kitāb al-tām (the Complete Book) by Sinān ibn Thābit. Obviously, this scholar is the son of the well known scientist Thābit ibn Qurra, and he was himself a mathematician and physician in Baghdad during the 10th century.

The fragment attributed to Sinān ibn Thābit on simple machines conserved in the MS 3306 is a completely new source that has never been studied before. In the following, the Arabic text and its English translation are presented, with historical and analytical commentaries, including a bio-bibliography of Sinān ibn Thābit.

Fig. 1 (a-b): The title of Sinān's text on the first page of MS 3306 and the first line of the text on the top of folio 132r.

1. Description of MS 3306 and its contents

As it is attested by a note written on its first folio, the materials conserved in the MS Orient fol. 3306 of the Berliner Staatsbibliothek (State Library of Berlin) were copied or bound in one volume in 1090 H (1679). These materials form a collection of texts of physics (mainly mechanics and optics) of which the list is given on the first page of the codex. This collection contains 10 titles in the following order.

  • Risālat al-Jazarī fī a‛māl al-hiyal (Treatise of Al-Jazarī on the construction of machines).
  • Multaqaṭāt Kitāb al-tām li-Sinān b. Thābit fī dhikr uṣūl al-khamsa (sic) (Extracts from the Complete Book by Sinān ibn Thābit on the five powers).
  • Maqālat al-Khāzinī fī a‛māl al-kura tadūr bi-dhātiha (sic) (Treatise of Al-Khāzinī on the construction of a sphere that rotates by itself).
  • Sharḥ kitāb Biyanius (?) al-ḥakīm fī ṣan‛at marāyā al-muḥriqa (sic) (Commentary on the book of Biyanius (?) the sage on the art of burning mirrors).
  • Risāla fī … li-ma‛rifat al-ṣā‛a wa-anwā‛ al-rukhāma wa-ghayruhu (Treatise on … for the determination of the hour and different types of plates).
  • Kitāb Uqlīdīs al-ḥakīm fī ‛ilm al-manāẓir wa-kayfiyyāt al-shu‛ā‛ (The book of Euclid in the science of optics and the theory of rays).
  • Risāla fī ‛amal anwā‛ al-dawālīb al-mudawwara min tilqā’ dhātihā (Treatise on the construction of [various] types of wheels that move by themselves).
  • Fawā’id fī ma‛rifat mīzān al-‛adl wa ghayruhu (Utilities concerning the balance of justice and other things).[3]

Among these titles, only two are conserved in the volume as it is preserved at present in Berlin's Staatsbibliothek: a complete copy of the text of Al-Jazarī on machines in 132 folios, accompanied with beautiful drawings in colour, marked by a good artistic quality, and two fragments from the text attributed to Sinān ibn Thābit. These two fragments are written on the folio 132 recto-verso. This folio is inserted at the end of Al-Jazarī's treatise. Obviously, this folio 132 is part of a longer text on mechanics, but unfortunately this is the only surviving part. That the folio was originally part of a longer text is indicated by the fluent and normal course of discourse at the end of folio 132v and the way the last word (’imtalā’) is written, below the last line, so as to provide a reference to the first word on the next folio, which is no longer extant in the codex.[4]

The two faces of folio 132 include the following materials. The recto displays a theory of simple machines that will be dealt with in the rest of this article. The verso contains descriptions of several mechanical devices (fig. 2a-b). The latter are referred to by a sentence which looks like a header (it is written in bold): "hādhihi uṣūl mukhtalifa min uṣūl al-ḥiyal" (these are various basic machines). Then begins the description of a machine: unbūb ka’s al-‛adl (the pipe of the cup of justice). At the end of the description, the author states that this device was described in full in "Al-Kitāb al-tām alladhī minhu ikhtaṣartu hādhā" (the Complete Book from which I summarized this [extract]).[5]

Fig. 2(a-b): Folio 132 recto and folio 132 verso. The first containing the text of Multaqaṭāt Kitāb al-tām li-Sinān b. Thābit fī dhikr uṣūl al-khamsa, whilst the second includes the description of various machines (’uṣūl al-ḥiyal), being part of Sinān ibn Thābit's original treatise.

On the basis of the available data, it is possible to reconstruct the genesis of this text along three stages:

(1) First, Sinān ibn Thābit composed a book known as Al-Kitāb al-tām, of which at least a part is devoted to mechanical issues. Given the title of the book, we can suppose that the treatise has an encyclopaedic scope, and hence was conceived as a treatise on mathematical sciences in which a part deals with mechanics, including the theory of simple machines and the description of a series of simple devices.

(2) At least the section of Al-Kitāb al-tām devoted to the theory of simple machines was summarized (ikhtiṣār), probably by the author, namely Sinān ibn Thābit, but it is possible that this summary was achieved by another scholar.

(3) The fragment that survived on folio 132 in MS Berlin 3006 in its present form is an extract (multaqaṭāt) from this summary; as it was said above, such an extract may have been composed by another scholar than the author of the book. Several indications attest that the two pages of folio 132 are part of a longer text. The exceptional status of this folio 132 is that it represents the only surviving evidence known so far of Sinān's Al-Kitāb al-tām and the unique source we know of mentioning his interest for mechanics.

The last folio of MS Berlin 3306, namely folio 133, includes the last two pages of al-Jazarī's treatise. On the recto, we find a part of Al-Jazarī's text about a machine "zawraq fīhi malāḥ wa-fīhi zammāra" (a boat with a sailor and a flute). Then begins the colophon of Al-Jazarī's treatise preceded by the list of letters in abjad system used in the treatise (21 letters of the Arabic alphabet) and the symbols to which they correspond in the book. This means that originally the copy of Al-Jazarī's work preserved in MS 3306 was complete.[6]

In the list of the contents of MS Berlin 3306 as well as in the title of the text on simple machines, the fragment in folio 132 is attributed to Sinān ibn Thābit. That the author of this text is Sinān ibn Thābit, the son of Thābit ibn Qurra, is supported by different arguments. First of all, the text is ascribed in the manuscript to Sinān ibn Thābit, identified as the son of Thābit ibn Qurra by the editors of the German catalogue where MS 3306 is mentioned.[7] Furthermore, several indications attest that the fragment is of an early date and may have been written by Sinān in the first half of the 10th century. This is confirmed by the archaic style of the vocabulary, as it is shown by the following two significant instances: the lever is called muḥl; later on, the standard word for it was bārim or bayram; the same for qarasṭūn (= steelyard), transformed later on as qaffān and qabbān.[8]

On the other hand, as far as we know, there exists no scholar in the Islamic scholarship bearing the name Sinān ibn Thābit, but Abū Sa‛īd, the son of Thābit ibn Qurra. In addition, the text is bound with several early Arabic writings that still reflect traces of the Graeco-Arabic transmission period, as it is clearly shown in the table of contents of the codex. Nevertheless, no historical source ever mentioned a writing of Sinān ibn Thābit in mechanics, although this should not be considered a priori as a counter-argument to deny the possible existence of such an interest. The ongoing investigation on the corpus of Arabic mechanics and engineering and its achievements is changing; new discoveries were made and others are still to come. This has been proved in the field of theoretical mechanics, with the dramatic change generated by the recent research on the science of weight (‛ilm al-athqāl).[9]

The MS Berlin 3306 was published online on the website of the Max Planck Institute for the History of Science in Berlin, as a result of the investigation performed by the author of this article on this document in the Staatsbibliothek in Berlin. This electronic edition may be accessed here: Anonymus, Ms. or. fol. 3306, Arabisches manuscript.

2. Bio-bibliography of Sinān ibn Thābit 

Abū Sa‛īd Sinān ibn Thābit ibn Qurra al-Ḥarrānī is a well known scholar of the 10th century. He is mentioned in the classical and modern sources as a mathematician, astronomer, physician and historian. He was the son of Thābit ibn Qurra (d. 288 H/ 901), the famous Harranian scholar who flourished in Baghdad and excelled in different fields of science and medicine, including mathematics, astronomy and mechanics. Two sons of Abū Sa‛īd Sinān ibn Thābit distinguished themselves in science and medicine. The first one, Abū Isḥāq Ibrāhīm ibn Sinān, was a genius mathematician. He left valuable works, such as his famous treatise on analysis and synthesis. He died in Baghdad in 335 H/946-947 when he was only 38 years old.[10] The second one is Abū 'l-Ḥasan Thābit b. Sinān (b. Thābit b. Qurra) who excelled in medicine and died in 363 H/973-73.[11]

Sinān ibn Thābit was the personal physician of two Abbasid Caliphs, Al-Muqtadir (r. 908-932) and Al-Qāhir (r. 932-934). He served also Al-Rādhī (934-940), with whom he entertained good relationships. The latter asked him to convert to Islam, but Sinān was not ready to embrace Islam and change his religion. Being afraid to disobey the Caliph's request, he fled to Khurasan. He came back to Baghdad after the destitution of Al-Qāhir. But later on, he converted to Islam and died in Baghdad as a Muslim at the beginning of Dhū-'l-qi‛da 331 H (August 943).[12]

Sinān ibn Thābit was the representative of the second generation of Harranian scientists and physicians in the Abbasid court in Baghdad, in the aftermath of the arrival and settlement of his father Thābit ibn Qurra in the Abbasids' capital in the middle of the 9th century. By converting to Islam, he put an end to the Sabian tradition of the prestigious family his father had founded in the capital of the Muslim empire, and strengthened its integration in the Muslim society. For a long time before and after him, scholars originating from Harran occupied eminent positions among the intellectual, scientific and medical elite at the caliphal court and in the high spheres of society.

Ibn abī ’Uṣaybi‛a mentioned that Abū Sa‛īd Sinān ibn Thābit was well versed in the sciences like his father, and he was gifted in astronomy and in the art of medicine. He described in detail the efforts deployed by Sinān ibn Thābit in the organisation of hospitals and enumerated the moral qualities of Sinān, such as his commitment under Al-Muqtadir to provide medical care to prisoners in Baghdad and to poor people in the suburbs of the city.[13]

Besides his distinction in medicine and astronomy, Sinān was also a historian and a gifted mathematician. Ibn al-Nadīm ascribed to him two texts in mathematics: Kitāb fī 'l-istiwā‛ (Book of levelling), and Iṣlāḥuhu li-kitāb (…)[14] fī al-‛uṣul al-handasiyya, wa zāda fī hādhā al-kitāb shay‛an kathīran (his revision/edition of The Book… of Geometrical Principles, to which he added a great deal). Later on, Ibn al-Qiftī provides the full title of this book and states that this treatise of ’uṣūl handasiyya that Sinān ibn Thābit edited and augmented was the work of A/Iflāṭun (Plato?).[15] It is possible to conjecture that this book of 'uṣūl' worked out by Sinān ibn Thābit was a book of mathematical sciences in which our scholar enriched a Greek original text, and added one or more chapter, one of them dealing with mechanics. In this case, this book should bear in certain copies the name of Al-Kitāb al-tām, from which the fragment of '’uṣūl' on simple machines was extracted. However, no evidence is available to support such a conjecture, and one is bound to suppose that al-Kitāb al-tām stands as an independent writing of Sinān, even though none of his bio-bibliographers made any mention of it.

Other works of mathematics are attributed to Sinān ibn Thābit, such as his edition of a text of Archimedes on the triangles,  translated previously by Yūsuf al-Qiss from Syriac.[16] The bio-bibliographers mention also that he performed the revision of the works of the mathematician al-Kūhī (Iṣlāḥuhu li-‛ibārat Abī Sahl al-Kūhī fī jamī‛i kutubihi). The fact that al-Kūhī asked Sinān to revise his writings is a sign of competence and recognition of his abilities, and testifies to the privileged relationships between the two scholars. Given what we know of Sinān's work, we can suppose that the revision went far beyond the linguistic and stylistic presentation of the texts to reach certain aspects of the contents. [17]

3. Survey of the Arabic tradition of the five simple machines 

As far as we know, no historical source mentioned that Sinān ibn Thābit wrote a text of mechanics titled Al-Kitāb al-tām nor reported about his interest in mechanics. Thus, the material preserved in Codex Berlin 3306 and ascribed to this author is a new and unknown component of the Arabic corpus of mechanics, and one of the rare Arabic writings on the theory of simple machines or the five powers. This theory was directly inspired from Greek works translated into Arabic, such as the mechanical treatises of Pseudo-Aristotle, Heron and Pappus. Besides Sinān ibn Thābit’s fragment, the main treatises which we know of today as having developed the theory of the five simple machines in Arabic mechanics are: Mi‛yār al-‛uqūl, a Persian treatise attributed to Ibn Sīnā and Al-Isfizārī’s summary of the second book of Heron’s Mechanics.

Mi‛yār al-‛uqūl dur fan jar athqāl (The Measure of mind or the art of dragging weights) is a Persian treatise attributed to Abū ‛Alī al-Ḥusayn ibn Sīnā (980-1037). It deals with the description of the five simple machines and of their use in displacing heavy loads. As such, the text is a precious source for the reconstruction of the theory of the five powers in Islamic science in the 10th and 11th centuries. Mi‛yār al-‛uqūl is not just a mere summary of the Greek theory of simple machines as it was transmitted in Hellenistic sources. It represents the first systematic classification of those machines, individually and in combination.[18]

Mi‛yār al-‛uqūl describes the five simple machines in four chapters. In the first two chapters, the author follows closely Heron’s characterization of the five powers, and borrows the essential part of his descriptions and drawings of the simple machines from Heron's Mechanics. The machines are quoted in this order: miḥwar (windlass), muḥl (lever), bakara (pulley, wheel), lawlab (screw) and isfīn (wedge).[19] The description of each machine is accompanied by a diagram and illustrated by a geometrical figure. The second part of the treatise, composed of chapters 3 and 4, contains descriptions of combinations of the five simple machines. Like Heron, ibn Sīnā classifies these combinations by the principle of likeness or unlikeness of the constituent five powers. Thus, in chapter 3, he describes combinations of like simple machines: windlasses, pulleys and levers. Then, in chapter 4, he goes beyond the limits of Heron’s classification when he successively analyses all probable combinations and considers all practically probable pair wise combinations of unlike simple machines: windlass-pulley, windlass-lever, windlass-screw. Finally, in chapter 4-section 5, he describes a mechanism which is essentially a combination of four simple machines; only the wedge is left apart (fig. 3a-b).

Fig. 3 (a-b): The five simple machines of the ancients, plus the "inclined plane", a device to which modern mechanicians reduced the wedge and the screw. Adapted from Unit 3: Simple machines, p. 2.

Another work in the Islamic tradition on simple machines is contained in Al-Isfizārī's epitome of the second book of Heron's Mechanics. This summarized version exists in two known manuscript sources: MS 351 at the John Rylands Library in Manchester (UK) and MS Q‛620 H-G at the ‛Uthmāniyya University Library in Hyderabad (India). Composed of a series of epitomes and commentaries on selected parts of the mechanical works of Heron, Apollonius and Banū Mūsā, this text has never been studied nor edited and was mentioned so far only in some studies by the author of this article (fig. 4).[20]

Fig. 4 (a-b): The five simple machines in the Arabic version of Heron's Mechanics: (1) the windlass, (2) the lever, (3) the wedge, (4) the pulley and (5) the screw. Source: Andhra Pradesh Government Oriental Manuscripts Library and Research Institute in Hyderabad, MS Riyādhī 396, respectively on folios 14v, 15v, and 16r.


4. The Arabic text and English translation 

In the following, a transcription of the text of Sinān's fragment is provided, with English translation. It should be pointed out that because of difficulties in reading some words of the last paragraph in the manuscript; the t