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In the Golden Age of Islam, Muslim scholars and scientists wrote a lot of books and manuscripts in many sciences such as medicine.

My question is, are there any books which have had some longer (or future) influence on the development modern theories?

What books have been translated into other languages?

As an example, I know that Avicenna's (Ibn Sina) book about Medicine "The Canon of Medicine القانون في الطب‎ al-Qānūn fī aṭ-Ṭibb) was used as a medical textbook through the 18th century in Europe!

Well, if I need to focus my question, my focus here could be on Medicine!

If i don't need to focus this would be great!

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Islamic science and mathematics experienced a boom during middle ages, contributions in mathematics, mechanics, astronomy and medicine were especially prominent, and had a deep impact on Renaissance Europe. There are many historical articles on Muslim Heritage: Science, see also links on Muslim Philosophers, Mathematicians & Scientists.

In mathematics aside from Khwarizmi's famous Hisab Al-Jabr wal Muqabala we have Omar Khayyam's Treatise on the Demonstration of Problems of Algebra, that has complete classification and geometric solution of all cubics. His also Explanations of the Difficulties in the Postulates of Euclid is considered the first work on the parallel postulate that avoids circular attempts to prove it, and anticipates a path to the hyperbolic geometry using a quadrilateral, later rediscovered by Saccheri and named after him in the West. Al-Karaji's s Al-Fakhri Fil-Jabr wal-Muqabala (Glorious on Algebra) introduced notations for all positive and negative powers of a variable and gave laws of exponents among them. Al-Samawal's Shining Book on Calculation gave the first version of long/synthetic division of polynomials. Al-Tusi's Treatise On The Quadrilateral was the most authoritative medieval work on trigonometry, and the first one to treat it independently of astronomy. See Kadyrov's Muslim Contributions to Mathematics for more.

Meragha school reformed epicyclic astronomy of Ptolemy making it consistent with (Aristotelian) dynamics, improving its precision and computational techniques. Al-Tusi’s Tadhkira i ilm al-Haya (Memoir on Astronomy) was a thorough critique of Ptolemy, especially of eccentrics and equants that appeared as ad hoc tricks. Al-Tusi found a way to model oscillatory linear motion with epicycles (the so-called Tusi couple), and used it in place of equants. In the Final Quest Concerning the Rectification of Principles al-Shatir eliminated eccenters and equants completely, without sacrificing precision, by mounting epicycles on epicycles. Although there is no direct confirmation, numerical coincidences strongly suggest that Copernicus used al-Shatir's models in his heliocentric reformulation.

In his influential commentary on Aristotle's physics Avempace revived the impetus theory of Philoponus (Avicenna discussed it as well), an alternative to Aristotle's theory of projectile motion, and an inspiration for momentum in modern dynamics. His commentary made its way to Europe, where the impetus theory was taken up by Buridan, Oresme and the merton school, who eventually influenced Galileo and Descartes.

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In mathematics, perhaps the best known is "The Compendious Book on Calculation by Completion and Balancing" by the Persian scholar Muḥammad ibn Mūsā al-Khwārizmī.

The English words "algebra" and "algorithm" derive from this.

The date is around 820.

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  • $\begingroup$ Well as i wasn't sure i if such a braod question would be accepted here i focused in my Question on medicine, but of course i know al-Khawarizmi and his book on algebra he called the way to solve equations: al-jabr (algebra) wal muqabala (My own transliteration) which in Arabic means " the arrangement and confrontation". There were also several -to me- less known mathematicians like al-Kashi and of course 'Omar al-Khiyyam ... $\endgroup$ – Medi1Saif Oct 19 '15 at 6:46
  • $\begingroup$ @MediSaif: Mathematics certainly played a large role in the development of science. Algebra was what allowed Newton to formalize his notions on laws of nature and ushered a golden age of empirical science. Today, some would consider science done without mathematics as not really scientific. $\endgroup$ – slebetman Oct 21 '15 at 7:03
  • $\begingroup$ @slebetman i know this for sure as i studied mathematics. My point is that in Historie SE a Question without a focus would have been canceled or at least put on holdi was not sure if it's the same here! $\endgroup$ – Medi1Saif Oct 21 '15 at 7:10
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I would like to mention:

  • J. L. Berggren, Mathematik im mittelalterlichen Islam, 2010
  • M. Paty, Rationalités comparées des contenus mathématiques, 2002, Colloque des sciences arabes
  • Michael Morgan: Lost History: The Enduring Legacy of Muslim Scientists, Thinkers, and Artists, 2008
  • and especially the Encyclopedia of the History of Arabic Science, edited by R. Rashed, with three volumes
    • Volume 1: "Astronomy--Theoretical and applied"
    • Volume 2: "Mathematics and the Physical Sciences"
    • Volume 3: "Technology, Alchemy, and the Life Sciences".

The works of Roshdi Rashed deserve a lot of attention. I recently heard from him through a collection of talks by François Nicolas, who draw relationships between IXth-XIIth century "arabic" mathematics toward modern category theory. Some of his works might be in French. Yet, some of his books are in arabic on one page, and translated (at least in French) on the other pages, which is quite interesting.

  • "Al-Bahir in Algebra As-Samaw'al", with S. Ahmad, University Press of Damascus, Damascus, 1972.
  • "The Work algebraic al-Khayyam", in collaboration with A. Djebbar, University Press of Aleppo, Aleppo, 1981.
  • "Between Arithmetic and Algebra. Research on the History of Arabic Mathematics", Collection "Arabic Sciences and Philosophy. Studies and included", Les Belles Lettres, Paris 1984. (ISBN 2251355316) "Studies on Avicenna", directed by J. Jolivet and R. Rashed, collection "Arabic Sciences and Philosophy - Studies and included", Les Belles Lettres, Paris, 1984.
  • "Mathematics of Sharaf al-Din al-Tusi. Algebra and Geometry in the twelfth century", Vol. II Collection "Arabic Sciences and Philosophy - Texts and Studies", Les Belles Lettres, Paris, 1986. Arabic translation: Beirut, 1998 .
  • "Optics and Mathematics: Research on the history of scientific thought in Arabic," Variorum reprints, Aldershot, 1992.
  • "Geometry and Dioptrics the tenth century: Ibn Sahl al-Quhi and Ibn al-Haytham," Les Belles Lettres, Paris, 1993.
  • "Al-Khayyam mathematician", in collaboration with B. Vahabzadeh, Bookstore Blanchard, Paris, 1999.
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Another great contribution to astronomy came from al-Sūfī (903-986, better known as Azophi in the West) with his book Book on the Constellations (Here is a copy of his book). In his book, he gave details of more than a thousand stars based on Ptolemy's Almagest and his own observations and provided beautiful illustrations of constellations.

Book on the Constellations was very influential in especially the naming of the stars. It was translated into Latin and used by many Muslim scholars as well as Europeans, such as Albrecht Dürer (1515), Peter Apian, J.A. Colom (1635), Thomas Hyde, Giuseppe Piazzi, Giovanni Riccioli (1651), V. Coronelli (1665).

See The Biographical Encyclopedia of Astronomers, p 1110.

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From Wikipedia:

Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham (Arabic: أبو علي، الحسن بن الحسن بن الهيثم‎; c. 965 – c. 1040 CE), better known by the Latinization Alhazen or Alhacen or as Ibn al-Haytham (ابن الهيثم), was an Arab Muslim polymath and philosopher who is widely considered as one of the most influential scientists of all time. Referred to as the father of experimental physics and modern optics and scientific methodology, he made significant contributions to the principles of optics, astronomy, mathematics, meteorology, visual perception and the scientific method.

His most famous work is his Book of Optics.

The Book of Optics (Arabic: Kitāb al-Manāẓir‎ (كتاب المناظر); Latin: De Aspectibus or Perspectiva; Italian: Deli Aspecti) is a seven-volume treatise on optics and other fields of study composed by the medieval Arab scholar Ibn al-Haytham, known in the West as Alhazen (965–c. 1040 AD).

The Book of Optics presented experimentally founded arguments against the widely held extramission theory of vision (as held by Euclid in his Optica) and in favor of intromission theory, as supported by thinkers such as Aristotle, the now accepted model that vision takes place by light entering the eye. Alhazen's work extensively affected the development of optics in Europe between 1260 and 1650.

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