1521:
416:, 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.
382:
340:, 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.
530:. 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
329:, 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.
368:
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
317:
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.
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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
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314:, 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.
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336:, Abu Bakr, through marriage alliances. But Valencia was entangled in a complex game of alliances. Alfonso VI, skilfully using diplomacy, got al-Kadir, the
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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
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465:. 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
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637:
Glick, Thomas F.; Livesey, Steven John; Wallis, Faith (2005). Medieval
Science, Technology, and Medicine: An Encyclopedia. Psychology Press. p. 243.
1799:
652:
Hogendijk, Jan, P. (1986). "Discovery of an 11th-century geometrical compilation: The Istikmāl of Yūsuf al-Mu'taman ibn Hūd, King of
Saragossa".
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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
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El Cid contained the attacks of the
Aragonese until 1083, when Sancho managed to take the line of fortifications that protected Zaragoza like
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As king, Al-Mu'taman was a patron of science, philosophy and arts, and was himself a scholar of considerable accomplishment. He knew
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was at its peak. Al-Muqtadir divided his lands between his two sons: al-Mu'taman received the western part of the taifa with
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dynasty, reigning from 1081 to 1085, at the height of power of Muslim
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was not completed but it was still seen as an important work from the eleventh-century king. The encyclopedist
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and al-Mu'taman offered their own input and original contributions beyond their transmission of ancient ideas.
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Yusuf was born on an unknown date, certainly in
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The first external concern of the king was the threat posed by the
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dedicated to the translation of ancient Greek texts, ranging from
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603:{\displaystyle {\frac {AF}{FB}}={\frac {EA}{CE}}{\frac {DC}{BD}}}
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The
Compendious Book on Calculation by Completion and Balancing
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Al-Mu'taman also tried to strengthen relations with his vassal
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should be read by mathematicians alongside such works as the
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400:). This book was a compendium of the Greek mathematics of
163:. The name al-Mu'taman is itself a shortening of his full
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Book on the Measurement of Plane and Spherical Figures
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received the coastal zone of the kingdom, including
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al-Mu'taman Billah Abu Amir Yusuf ibn Ahmad ibn Hud
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678:: CS1 maint: multiple names: authors list (
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1583:Encyclopedia of the Brethren of Purity
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200:Al-Mu'taman was the third king of the
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392:The main work of al-Mu'taman was his
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620:List of Arab scientists and scholars
212:, nicknamed as "the palace of joy".
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716:http://www.jphogendijk.nl/publ.html
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231:region in the 11th century, the
197:'Trustee through God').
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872:Al-Musta'in II, Ahmad ibn Yusuf
695:Geometry: Our Cultural Heritage
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735:Rediscovering Arabic Science
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134:أبو عامر يوسف بن أحمد بن هود
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1769:History of trigonometry
1764:Trigonometric functions
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721:List of Muslim rulers
693:Holme, Audun (2010).
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1642:Al-Azhar University
1569:The Book of Healing
975:Al-Ḥajjāj ibn Yūsuf
733:Richard Covington,
507:and two others for
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435:suggested that the
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1729:Indian mathematics
1703:Indian mathematics
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427:said that had the
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233:Kitab al-Istikmal
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176:المؤتمن بالله
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68:Al-Mustain II
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19:
1602:
1595:
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1560:
1553:
1546:
1539:
1530:Mathematical
1485:16th century
1436:Ibn al-Majdi
1429:15th century
1393:14th century
1312:13th century
1266:12th century
1252:Omar Khayyam
1241:
1185:11th century
1081:Aṣ-Ṣaidanānī
1049:10th century
1010:Al-Khwarizmi
866:
753:
734:
694:
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657:
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156:
125:
124:
1825:1085 deaths
1548:De Gradibus
1502:Taqi ad-Din
1492:Al-Birjandi
1466:al-Qalaṣādī
1247:Al-Isfizari
1212:Ibn al-Samh
1141:Al-Isfahani
1121:al-Uqlidisi
1091:al-Khojandi
1056:Abu al-Wafa
995:al-Dinawari
953:9th century
509:stereometry
476:deals with
377:Mathematics
225:mathematics
165:regnal name
157:al-Mu'taman
153: 1085
54:Predecessor
1789:Categories
1712:Influenced
1686:Influences
1456:Ali Qushji
1415:Al-Khalili
1283:Al-Khazini
1278:Al-Kharaqī
1237:al-Zarqālī
1227:al-Jayyānī
1171:al-Majriti
1156:Abu al-Jud
1126:Al-Battani
1101:Al-Saghani
1096:Al-Nayrizi
1035:al-Marwazi
970:al-Jawharī
890:Almoravids
816:Banu Tujib
806:rulers of
759:1081-1085
626:References
501:arithmetic
486:quadrature
467:Maimonides
463:Apollonius
455:Archimedes
406:Archimedes
354:philosophy
229:al-Andalus
221:philosophy
1461:al-Wafa'i
1451:Ulugh Beg
1354:al-Abhari
1339:Ibn Adlan
1329:Ibn Munim
1293:al-Hassar
1232:al-Nasawī
1207:Al-Biruni
1176:al-Jabali
1166:Al-Karaji
1116:Ibn Yunus
1071:Abu Kamil
1066:Al-Qabisi
1061:al-Khazin
990:Al-Mahani
895:Aragonese
660:: 43–52.
490:parabolic
433:Ibn Aknin
371:Ibn Qurra
366:Banu Musa
362:astronomy
300:Castilian
265:Calatayud
245:Aljaferia
217:astrology
210:Aljafería
181:romanized
139:romanized
64:Successor
49:1081–1085
38:Ruler of
1820:Banu Hud
1614:Concepts
1446:al-Kāshī
1420:al-Umawi
1222:Avicenna
1161:Al-Sijzi
1111:Ibn Sahl
980:Al-Kindi
849:Banu Hud
808:Zaragoza
614:See also
505:geometry
442:Elements
437:Istikmal
429:Istikmal
358:medicine
350:movement
267:, while
253:Zaragoza
202:Banu Hud
118:Banu Hud
81:Zaragoza
40:Zaragoza
1738:Related
1667:Madrasa
1635:Centers
1441:al-Rūmī
1344:al-Urdi
1242:ibn Hud
1197:Alhazen
1151:al-Qūhī
497:tangent
493:segment
488:of the
281:Tortosa
269:Mundhir
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459:Conics
457:, and
447:Euclid
402:Euclid
327:Ayerbe
304:El Cid
277:Monzón
273:Lérida
261:Huesca
257:Tudela
172:Arabic
130:Arabic
1532:works
360:, to
356:, to
323:Graus
302:lord
285:Dénia
113:House
98:Names
46:Reign
699:ISBN
680:link
514:The
472:The
419:The
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283:and
263:and
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