Abu Amir Yusuf ibn Ahmad ibn Hud (; died ), more commonly known as al-Mu'taman, was a mathematician, and also one of the kings of the
Taifa of Zaragoza
The taifa of Zaragoza () was an independent Arab Muslim state in the east of Al-Andalus (present-day Spain) with its capital in Saraqusta (Zaragoza) city. It was established in the early 11th century as one of the many Taifa kingdoms that foll ...
. The name al-Mu'taman is itself a shortening of his full
regnal name
A regnal name, regnant name, or reign name is the name used by monarchs and popes during their reigns and subsequently, historically. Since ancient times, some monarchs have chosen to use a different name from their original name when they accede ...
al-Mu'taman Billah ().
Al-Mu'taman was the third king of the
Banu Hud
The Banu Hud ( ', the Hudid dynasty) were an Arab dynasty that ruled the ' of Zaragoza from 1039 until 1110.
The Hudid dynasty descends from Hud ibn Abd Allah ibn Musa ibn Salem al-Judhami (d. ca. 960).
In 1039, under the leadership of Al-Mus ...
dynasty, reigning from 1081 to 1085, at the height of power of Muslim Zaragoza, following the thriving period of his father
Ahmad al-Muqtadir. He continued his father's efforts and created around him a court of intellectuals, living in the beautiful palace of
Aljafería
The Aljafería Palace (; , Romanization of Arabic, tr. ''Qaṣr al-Jaʿfariyah'') is a fortified medieval palace built during the second half of the 11th century in the Taifa of Zaragoza in Al-Andalus, present day Zaragoza, Aragon, Spain. It was ...
, nicknamed as "the palace of joy".
As king, Al-Mu'taman was a patron of science, philosophy and arts, and was himself a scholar of considerable accomplishment. He knew
astrology
Astrology is a range of Divination, divinatory practices, recognized as pseudoscientific since the 18th century, that propose that information about human affairs and terrestrial events may be discerned by studying the apparent positions ...
,
philosophy
Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational an ...
, and especially
mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
, a discipline in which he wrote the most important treatise to come out of the
al-Andalus
Al-Andalus () was the Muslim-ruled area of the Iberian Peninsula. The name refers to the different Muslim states that controlled these territories at various times between 711 and 1492. At its greatest geographical extent, it occupied most o ...
region in the 11th century, the ''Kitab al-Istikmal'' ("Book of Perfection").
Biography and Kingship
Yusuf was born on an unknown date, certainly in Zaragoza, in the palace of
Aljaferia. When he ascended to the throne on the death of his father in 1081, the
taifa of Zaragoza
The taifa of Zaragoza () was an independent Arab Muslim state in the east of Al-Andalus (present-day Spain) with its capital in Saraqusta (Zaragoza) city. It was established in the early 11th century as one of the many Taifa kingdoms that foll ...
was at its peak. Al-Muqtadir divided his lands between his two sons: al-Mu'taman received the western part of the taifa with
Zaragoza
Zaragoza (), traditionally known in English as Saragossa ( ), is the capital city of the province of Zaragoza and of the autonomous communities of Spain, autonomous community of Aragon, Spain. It lies by the Ebro river and its tributaries, the ...
,
Tudela,
Huesca
Huesca (; ) is a city in north-eastern Spain, within the Autonomous communities of Spain, autonomous community of Aragon. It was the capital of the Kingdom of Aragon between 1096 and 1118. It is also the capital of the Spanish Huesca (province), ...
and
Calatayud
Calatayud (; 2014 pop. 20,658) is a Municipalities of Spain, municipality in the Province of Zaragoza, within Aragón, Spain, lying on the river Jalón (river), Jalón, in the midst of the Sistema Ibérico mountain range. It is the second-largest ...
, while
Mundhir received the coastal zone of the kingdom, including
Lérida
Lleida (, ; ; ''#Name, see below'') is a city in the west of Catalonia, Spain. It is the capital and largest town in Segrià, Segrià county, the Ponent, Ponent region and the province of Lleida. Geographically, it is located in the Catalan Cent ...
,
Monzón,
Tortosa
Tortosa (, ) is the capital of the '' comarca'' of Baix Ebre, in Catalonia, Spain.
Tortosa is located at above sea level, by the Ebro river, protected on its northern side by the mountains of the Cardó Massif, of which Buinaca, one of the hi ...
and
Dénia
Dénia (; ) is a historical coastal city in the province of Alicante, Spain, on the Costa Blanca halfway between Alicante and Valencia (city in Spain), Valencia, and the capital and judicial seat of the Comarques of the Valencian Community, ''c ...
.
The first external concern of the king was the threat posed by the
King of Aragon
This is a list of the kings and queens of Aragon. The Kingdom of Aragon was created sometime between 950 and 1035 when the County of Aragon, which had been acquired by the Kingdom of Navarre in the tenth century, was separated from Navarre in ...
,
Sancho Ramírez who aimed to extend his territories to the south, at the expense of Zaragoza. Al-Mu'taman counted on the services of the mercenary troops of the
Castilian lord
El Cid
Rodrigo Díaz de Vivar ( – 10 July 1099) was a Castilian knight and ruler in medieval Spain. Fighting both with Christian and Muslim armies during his lifetime, he earned the Arabic honorific ("the Lord" or "the Master"), which would evolve i ...
, who had been exiled by King
Alfonso VI for conducting raids against his interests in the
Taifa of Toledo
The Taifa of Toledo () was an Islamic polity (''taifa'') located in the centre of the Iberian Peninsula in the High Middle Ages. It was ruled by the Dhulnunids, a Hawwara Berber clan. It emerged after 1018 upon the fracturing of the Caliphate of ...
, then a tributary of the king. In 1081, El Cid therefore offered his service to the king of Zaragoza, al-Muqtadir, and remained with al-Mu'taman during his reign.
Al-Mu'taman also assigned to El Cid the task of reincorporating into Zaragoza the eastern territories of his relative Mundhir, an ally of Aragon. Clashes in the border area were constant, but neither managed to reunite the paternal territory.
El Cid contained the attacks of the Aragonese until 1083, when Sancho managed to take the line of fortifications that protected Zaragoza like
Graus
Graus () is a village in the Spanish province of Huesca, located in the Pyrenees at the confluence of rivers Esera and Isabena. It is the administrative capital of the region. It is one of the areas of Aragon in which is still preserved the Ara ...
in the east, as well as
Ayerbe, Bolea, Arascués and Arguedas. El Cid served Yusuf al-Mu'tamin until 1086, when he broke his ties with Zaragoza. The circumstances in which he refused to continue serving al-Mu'tamin and his heir Ahmad II al-Mustaʿin are not fully clear and still debated.
Al-Mu'taman also tried to strengthen relations with his vassal
king of Valencia, Abu Bakr, through marriage alliances. But Valencia was entangled in a complex game of alliances. Alfonso VI, skilfully using diplomacy, got al-Kadir, the
king of Toledo, to hand over the city in 1085 in exchange for his help to drive Abu Bakr from Valencia, which meant, in fact, the capture of Toledo for the king of Castile. Thus, the kingdom of Zaragoza was cut off from the rest of al-Andalus, which seriously weakened its economy and made it even more vulnerable to Christian attacks. The year of the loss of Valencia was also the year of the death of Yusuf al-Mu'tamin.
Intellectual life
Although it was common practice for royals to be well educated, both al-Mu'taman and his father were exceptional mathematicians. In medieval Islam, there was a
movement dedicated to the translation of ancient Greek texts, ranging from
philosophy
Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational an ...
, to
medicine
Medicine is the science and Praxis (process), practice of caring for patients, managing the Medical diagnosis, diagnosis, prognosis, Preventive medicine, prevention, therapy, treatment, Palliative care, palliation of their injury or disease, ...
, to
astronomy
Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...
, and the more influential mathematical texts. Both father and son, as well as medieval Islamic translators such as the
Banu Musa
Banu or BANU may refer to:
* Banu (name)
* Banu (Arabic), Arabic word for "the sons of" or "children of"
* Banu (makeup artist), an Indian makeup artist
* Banu Chichek, a character in the ''Book of Dede Korkut''
* Bulgarian Agrarian National Union ...
were known for their expansions on ancient Greek and Roman ideals. There was a stigma in the periods following medieval Islam that Islamic scholars only copied the ancient texts, offering no intellectual addition. Later it was proven that scholars such as
Ibn Qurra and al-Mu'taman offered their own input and original contributions beyond their transmission of ancient ideas.
Mathematics
250px, , discovered at the end of the 11th century by al-Mutaman.">Ceva's theorem, discovered at the end of the 11th century by al-Mutaman.
The main work of al-Mu'taman was his ''Kitab al-Istikmal'' (''Book of Perfection''). This book was a compendium of the Greek mathematics of
Euclid
Euclid (; ; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of geometry that largely domina ...
and
Archimedes
Archimedes of Syracuse ( ; ) was an Ancient Greece, Ancient Greek Greek mathematics, mathematician, physicist, engineer, astronomer, and Invention, inventor from the ancient city of Syracuse, Sicily, Syracuse in History of Greek and Hellenis ...
among others, but also contained the teachings of
Thabit ibn Qurra Thabit () is an Arabic name
Arabic names have historically been based on a long naming system. Many people from Arabic-speaking and also non-Arab Muslim countries have not had given name, given, middle name, middle, and family names but rather a ...
, the Banu Musa and
Ibn al-Haytham
Ḥasan Ibn al-Haytham (Latinization of names, Latinized as Alhazen; ; full name ; ) was a medieval Mathematics in medieval Islam, mathematician, Astronomy in the medieval Islamic world, astronomer, and Physics in the medieval Islamic world, p ...
, and included some theorems and proofs not found in earlier extant sources. The book only persists as fragments from several anonymous manuscripts, not including any preface or introduction, but it is clear from the remaining content that the intention was to organize and comprehensively describe the known results in Euclidean geometry in a single self-contained work.
[ It is possible al-Mu'taman listed his sources in a now-lost introductory section, but none of the remaining fragments credit past authors or works for any of the content.]
The ''Kitab al-Istikmal'' was not completed but it was still seen as an important work from the eleventh-century king. The encyclopedist Ibn al-Akfani said that had the ''Istikmal'' been completed, it would have made the existing geometrical literature superfluous.[ Ibn Aknin suggested that the ''Istikmal'' should be read by mathematicians alongside such works as the '' Elements'' of ]Euclid
Euclid (; ; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of geometry that largely domina ...
, ''On the Sphere and Cylinder'' of Archimedes
Archimedes of Syracuse ( ; ) was an Ancient Greece, Ancient Greek Greek mathematics, mathematician, physicist, engineer, astronomer, and Invention, inventor from the ancient city of Syracuse, Sicily, Syracuse in History of Greek and Hellenis ...
, and ''Conics'' of Apollonius
Apollonius () is a masculine given name which may refer to:
People Ancient world Artists
* Apollonius of Athens (sculptor) (fl. 1st century BC)
* Apollonius of Tralles (fl. 2nd century BC), sculptor
* Apollonius (satyr sculptor)
* Apo ...
. Because this was not a completed piece of work it was never as widely copied or taught as the works of Euclid or Archimedes. A copy was sent to Egypt by Maimonides
Moses ben Maimon (1138–1204), commonly known as Maimonides (, ) and also referred to by the Hebrew acronym Rambam (), was a Sephardic rabbi and Jewish philosophy, philosopher who became one of the most prolific and influential Torah schola ...
, and from there it spread to Baghdad in the 14th century, but did not directly influence later European mathematicians.
The ''Kitab al-Istikmal'' deals with irrational numbers
In mathematics, the irrational numbers are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers. When the ratio of lengths of two line segments is an irrational number, ...
, conic sections
A conic section, conic or a quadratic curve is a curve obtained from a Conical surface, cone's surface intersecting a plane (mathematics), plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is ...
, quadrature of the parabolic segment, volumes and areas of various geometric objects, and the drawing of the tangent
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is, intuitively, the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points o ...
to a circle, among other mathematical problems. In the work appears an attempt to classify mathematics into Aristotelian categories. The classification includes a chapter for arithmetic
Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms.
...
, two chapters for geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...
and two others for stereometry.
The ''Kitab al-Istikmal'' contains the first known formulation of Ceva's theorem, which only became known in Europe after 1678 from Italian geometer Giovanni Ceva's treatise ''De lineis rectis''. It is unknown whether Al-Mu'taman discovered this theorem himself or obtained it from another source, and it is also unknown whether Ceva rediscovered the theorem independently.
The theorem can be stated as follows: "Let ABC be a triangle and D, E, F points on the sides BC, CA, and AB. We draw the lines AD, BE and CF. These three lines intersect at one point if and only if .
See also
* List of Arab scientists and scholars
Arab scientists and scholars from the Muslim World, including Al-Andalus (Spain), who lived from antiquity up until the beginning of the modern age, include the following. The list consists primarily of scholars during the Middle Ages.
Both th ...
References
* http://www.jphogendijk.nl/publ.html
List of Muslim rulers
External links
{{DEFAULTSORT:Mutaman Hud, Yusuf Ahmad
11th-century Arab people
Mathematicians from al-Andalus
11th-century mathematicians
Emirs of Zaragoza
11th-century monarchs in Al-Andalus
Banu Hud
1085 deaths