Banū Mūsā brothers

Moḥammad, Aḥmad, and Ḥasan were the three sons of Mūsā ibn Shākir,[4] who earlier in life had been a highwayman, but who became known as an astronomer in Khorasan.[5][note 1] The brothers are always listed in sources in what is assumed by scholars to be their order of seniority: Muhammed, Ahmad and Hasan.[6]

Musa befriended al-Ma'mun, a younger son of the Abbasid caliph Harun al-Rashid, and a governor of Khorasan who was staying in Merv. Al-Maʾmūn, who became caliph in 813, employed Musa as an astrologer and astronomer.[4] According to one story, al Ma’mun saw the Greek polymath Aristotle in a dream telling him about the importance of natural philosophy, which resulted in al-Ma’mun supporting the work done by scientists.[7]

After their father's death, the three brothers were cared for at the court of al-Maʾmūn.[1] who made Ishaq bin Ibrahim al-Mus’abi, a former governor of Baghdad, their guardian.[8] Al-Ma’mun recognized the abilities of the three boys, and enrolled them in the House of Wisdom, a library and a translation centre in Baghdad.[9] In Baghdad, where they apparently lived for the rest of their lives, they studied geometry, mechanics, music, mathematics and astronomy, trained by Yaḥyā bin Abī Manṣūr.[1][4]

Studying in the House of Wisdom, initially under Yahya ibn Abi Mansur,[4] the Banū Mūsā assisted in efforts to translate ancient Greek works into Arabic, by sending for Greek texts from the Byzantines, or going themselves to Byzantium to acquire old manuscripts.[3] During their working lives they used their wealth and energy towards the translation of these works.[6] They paid large sums for the works to be translated, and went so far as to learn Greek themselves.[10] On his way home to Baghdad from Byzantium, Muhammad met and recruited Thābit ibn Qurra,[3] a money changer from Harran. Thābit went on to make important discoveries in algebra, geometry, and astronomy.[4]

Under the direction of Al-Ma'mun, the Banū Mūsā worked with the most talented men available, including al-Khwarizmi, al-Kindi, Al-Ḥajjāj ibn Yūsuf ibn Maṭar, and the mathematician and translator Hunayn ibn Ishaq, who became a close friend of Muhammad.[1] Those scientists and translators who were sponsored by the brothers were paid about 500 dinars a month.[5] Had it not been for the brothers' efforts in translating Greek texts, many would have been lost and forgotten.[5] The Banū Mūsā wrote almost 20 books, the majority of which are now not extant.[3] Moḥammad was the most productive of the brothers; of his many works, one still exists.[4]

The Banū Mūsā worked together, but did have their own areas of expertise; Jafar Muhammad on mathematics and astronomy, Ahmad on technology, and al-Hasan on mathematics.[1] They are likely to have used portable instruments such as armillary spheres or dials when making their observations, which were recorded from around 847 to 869. From their Baghdad home, they observed stars in the constellation Ursa Major In 847-848, and measured the maximum and minimum altitudes of the Sun in 868-869. They also observed the September equinox in the Persian city of Samarra. To calculate the difference in latitude between Samarra and Nishapur, they organized simultaneous observations of a lunar eclipse.[11]

Whilst working for Al-Ma’mun, they travelled to a desert near Sanjar, in northern Mesopotamia, to measure the length of a degree of latitude along a meridian.[3] This measurement enabled them to obtain a value for the Earth's circumference.[4]

Under the patronage of the caliphs that followed al Ma’mun—al-Mu'tasim, al-Wathiq, and al-Mutawakkil—the brothers acquired great wealth and become influential in court. They used much of their wealth to collect the works of ancient writers, a practise that was later copied by other scholars at the House of Wisdom.[8][1] However, during the reign of al-Wathiq and al-Mutawakkil, internal rivalries arose between the scholars there. The Banū Mūsā became enemies of al-Kindi, and assisted in his persecution by al-Mutawakkil. They were later employed by al-Mutawakkil to construct a canal for the new city of al-Jaʻfariyya.[1]

The Banū Mūsā's employment by the caliphs for different civil engineering projects, including their involvement as part of a team that built the city of al-D̲j̲aʿfariyya for al-Mutawakki, led to them becoming involved involved in the politics of Baghdad. The peak of Muhammad's political activity came towards the end of his life, when Turkish commanders were starting to take control of the state. After the death of al-Mutawakkil, Muhammad helped al-Mustaʿīn to become nominated as caliph. Denied the throne, Al-Mustaʿīn's brother besieged Baghdad, and Muhammad was sent to estimate the size of the attacking army. After the siege, he was sent to find out the terms for al-Mustaʿīn to abdicate.

Mohammed died in January 873; the years his brothers died are not known.[6]

The Banū Mūsā's astronomical observations were recorded in nearly a dozen books. They are known to have made many observations on the Sun and the Moon.[3]

Kitāb bayyana fīhī bi-ṭarīq taʿlīmī wa-madhhab handasī annahū laysa fī khārij kurat al-kawākib al-thābitah kurah tāsiʿah[12] ("Book on the Mathematical Proof by Geometry that there Is not a Ninth Sphere Outside the Sphere of the Fixed Stars") is a lost book by Ahmed.[3][13] Also referred to as the Kitāb al-Hay’a ("Book of Astronomy"), or the Kitāb Ḥarakāt al-falak al-ūlā ("Book on the First Motion of the Celestial Sphere"), the work analysed the Ptolemy's geocentric model of the cosmos, in which a ninth sphere is responsible for the motion of the heavens, and instead considered that the Sun, the Moon, the planets, and the stars all moved of their own volition.[3]

Cover of the digitized version of the Kitāb al-Daraj (Princeton University Library)

The other astronomical or astrological works by the Banū Mūsā are:

• Kitāb al-Daraj (Arabic: كتاب الدرج; "The Book of Degrees"), a work by Ahmad.[4]
• Book on the First Motion of the Celestial Sphere (Kitāb Ḥarakāt al‐falak al‐ūlā), an extant work containing a critique of the Ptolemaic system. Muhammad in this book denied the existence of the Ptolemaic 9th sphere which Ptolemy thought was responsible for the motion;[3][13]
• Kitāb fī ʿamal al-asṭurlāb ("Book on the Construction of the Astrolabe"), a work quoted by the 11th century Persian scholar al-Biruni;[3]
• Kitāb fī sanat al-shams ("Book on the Solar Year"), which was once attributed to Thābit ibn Qurra;[3]
• Ruyʾat al-hilāl ʿalá raʾy Abī Jaʿfar[14] ("On the Visibility of the Crescent"), by Muhammad;[3]
• Book on the Beginning of the World, by Muhammad,[3] now lost;[13]
• A non-extant zij by Ahmad was mentioned by the Egyptian astronomer and mathematician Ibn Yunus in his Az-Z0j al-Kabir al-Hdkim, written in c. 990;[3][15]
• A separate non-extant zij by the Banū Mūsā was mentioned by Ibn Yunus.[3][16]
• A translation of a Chinese work called A Book of Degrees on the Nature of Zodiacal Signs;[3]

The calculation by Moḥammad and Aḥmad of the Sun’s mean motion in a year agreed with the result obtained by al-Bīrūnī—that a solar year was 365 days and less than 6 hours long. Aḥmad independently reached a similar conclusion in 851–852. They observed the longitude of Regulus from their house on a bridge in Baghdad in 840–841, 847–848, and 850–851, and made observations of Sirius, Al-Bīrūnī used data about the Moon obtained by the Banū Mūsā in his calculations of the nativities (mawleds) of the years.[4]

The Banū Mūsā were some of the earliest scholars to adopt Greek mathematics. They differed in their approaches to the concepts of area and circumference, giving them numerical values rather than considering them in terms of ratios.[1]

A page of the Kitāb maʻrifat masāḥat al-ashkāl al-basīṭah wa-al-kurīyah (Columbia University, New York)

The most important of the works produced by the Banū Mūsā was the Kitāb Maʿrifah masāḥat al-ashkāl al-basīṭah wa-al-kuriyyah ("Book on the Measurement of Plane and Spherical Figures"),[17], which was edited by Naṣīr al‐Dīn al‐Ṭūsī in the 13th century. A Latin translation by the 12th century Italian astrologer Gerard of Cremona appeared entitled Liber trium fratrum de geometria and Verba filiorum Moysi filii Sekir. This treatise on geometry, which is similar to Archimedes', On the measurement of the circle and On the sphere and the cylinder.[1] was used extensively in the Middle Ages, and was quoted by authors such as Thābit ibn Qurra, Ibn al‐Haytham, Leonardo Fibonacci (in his Practica geometriae), Jordanus de Nemore, and Roger Bacon.[3] It includes theorems not known to the Greeks.[18] The book was re-published in Latin with an English translation by the American historian Marshall Clagett, who has also summarized how the work influenced mathematicians during the Middle Ages.[4]

The other known mathematical works by the Banū Mūsā were:

• 3 works relating to Conic Sections, by the astronomer Apollonius of Perga, including lī-kitāb Abulūnyūs fī al-maḫrūṭāt ("Conic Sections of Apollonius"),[3] a recension of the work, which was first translated to Arabic by Hilāl al-ḥimṣī and Thābit ibn Qurra[9] (a lost book written by Muhammed).[13]
• Kitāb al-shakl al-mudawwar al-mustaṭīl ("The Book of the Elongated Circular Figure"),[19][20] a mathematical treatise by al-Hasan—and the only one that is attributed to him— now lost.[4][13] It contained a description of a procedure used to draw an ellipse using a length of string, a technique that is now known as the "gardener's construction";[3]
• Fī tathlīth al-zāwiyah ("Reasoning on the Trisection of an Angle"), by Aḥmad;[3][21] The treatise involved the use moving geometric objects as moving. using kinematic methods to attempt to solve the classical problem of trisecting an angle.[1]The manuscript and medieval Latin translations are extant.[13] The two known manuscripts containing the treatise, MS. Marsh 720 and MS. Thurston 3, are held in the Bodleian Library at Oxford University.[21]
• Kitāb al-shakl al-handasī alladhī bayyanahu Jālīnūs ("Book on a Geometric Proposition Proved by Galen").[3] A lost book by Muhammed.[13]

A blood-measuring device, from Kitab al-Hiyal al-Naficah ("The Book of Ingenious Devices"), Aga Khan Museum, Toronto

The Banū Mūsā are noted for their work in the field of automation, which they utilized in toys and other devices made for entertainment, and which were in advance of similar inventions by their Greek predecessors.[3] The brothers are credited with inventing the first music sequencer as an example of an early type of programmable machine.[22]

Kitab al-Hiyal al-Naficah (""The Book of Ingenious Devices""), the only surviving work by Aḥmad,[4] describes 100 inventions, 80 of which are examples of trick vessels designed to hold liquids.[23][10] The other inventions in the book include mechanical fountains, a "hurricane" lamp, self-trimming and self-feeding lamps, a form of gas mask for use underground, and a grabbing tool, constructed in the same way as a modern clamshell grab, for recovering underwater objects.[23]

The inventions employ innovative engineering ideas, such as automatic one-way and two-way valves, mechanical memories, devices capable of responding to feedback, and delay mechanisms. Most of them were operated by water pressure.[10] The trick vessels are unimportant in themselves; their significance is the means by which they were developed. The Banū Mūsā evolved their ideas to include small pressure variations and conical valves, their first known use as automatic controllers.[23]

The other technology-based works by the Banū Mūsā were:

• Kitāb fī al-qarasṭūn ("A Book on the Qarasṭūn"),[24] a treatise on the weight balance, or steelyard.[9] There is a similar work on the same subject written by Thabit bin Qurra, who was a student of the brothers.[13]
• On Mechanical Devices, a work on pneumatic devices, written by Ahmad.[9]
• A Book on the Description of the Instrument Which Sounds by Itself, an extant work about musical theory. The manuscript is held in Beirut.[9][13]
• Kitāb al-masʾalah allatī alqāhā ʿalá Sanad ibn ʿAlī,[25] a lost treatise containing a discussion between Ahmad and the Persian Jewish scholar Sanad ibn Ali, possibly about the difficulties encountered by the Banū Mūsā due to the failure by their agent Al-Farghani to properly build the Jaʻfariyya canal.[4][13]

• Manuscript facsimile of the Kitāb al-Daraj held in the Princeton University Library (Islamic Manuscripts, Garrett no. 501H)
• Manuscript facsimile of The Book of Ingenious Devices held in the Vatican Library (Manuscript Vaticani Arabi 317)
• Manuscript facsimile of Kitāb al-mutawassiṭāt kept at Columbia University, New York (via the Internet Archive). The treatise Kitāb maʻrifat masāḥat al-ashkāl al-basīṭah wa-al-kurīyah is located from pp. 253–265 (f. 116 to 122).
• Banū Mūsā (1979) [9th century]. Hill, Donald R. (ed.). The Book of Ingenious Devices. Dortrecht, Netherlands; Boston; London: D. Reidel. ISBN 978-90277-0-833-5. (PDF version)
• Muḥammad ibn MūsáIbn Shākir; Gerard of Cremona; Curtze, M. (1885) [before 873]. Der liber trium fratrum de geometria (in Latin and German). Halle: Druck von E. Blochmann & sohn – via Hathi Trust Digital Library.