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Al-Battani ( Albategnius ) (868—929)
Abdallah Muhammad Ibn Jabir Ibn Sinan al-Battani al-Harrani was born around 858 C.E. in Harran, and according to one account, in Battan, a State of Harran. Battani was first educated by his father Jabir Ibn San'an al-Battani, who was also a well-known scientist. He then moved to Raqqa, situated on the bank of the Euphrates, where he received advanced education and later on flourished as a scholar. At the beginning of the 9th century, he migrated to Samarra, where he worked till the end of his life in 929 C.E. He was of Sabian origin, but was himself a Muslim
- Discovered the increase of the suns apogee(He found that the longitude of the sun's apogee had increased by 16° , 47' since Ptolemy.)
- responsible for the discovery motion of the solar apsides
- Best known is ' On the Science of Stars ' (Kitab al-Zij)
- achievements in Kitab Al-Zij: He catalogued 489 stars, refined the existing values for the solar year's length (as 365 days, 5 hours, 48 minutes and 24 seconds), calculated 54.5" per year for the precession of the equinoxes, and obtained the value of 23.35' for the inclination of the ecliptic,.
- Rather than using geometrical methods, as Ptolemy had done, al-Battani used trigonometrical methods, constituting an important advance. For example, he provided important trigonometric formulas for right-angled triangles such as: b sin(A) = a sin(90-A).
Al-Biruni (973-1050)
Abu Raihan Mohammed Ibn Ahmad Al-Biruni was born in Khwarazm about 365 AH and dead 440, He applied his talents in many fields of knowledge, excelling particularly in astronomy, mathematics, chronology, physics, medicine, and history. He corresponded with the great philosopher Ibn Sīnā .Sometime after 1017 he went to India and made a comprehensive study of its culture. Later he settled at Ghazna (now Ghaznī) in Afghanistan, he died in 1048 CE at the age of 75
- He discussed with approval the theory of the Earth’s rotation on its axis and made accurate calculations of latitudes and longitudes, He calculated the earth circumference, and fixed scientifically the direction of Makkah (Mecca) from any point of the globe. Al-Biruni wrote in total 150 works, including 35 treatises on pure astronomy, of which only six have survived, he also Determine geodetic measurements. - Biruni also criticized Aristotle's view of heavenly bodies only moving in circular orbits, and considered the possibility of the heavenly bodies moving in elliptic orbits:[41] - Best known of his books:
1. Qanun-i-Masoodi which discusses several theories of astronomy, trigonometry, solar, lunar, and planetary movements, and other related topics.
2. Al-Athar al-Baqia, he attempted a connected account of ancient history of nations and the related geographical knowledge, discussed the rotation of the earth and had given correct values of latitudes and longitudes of various places. He has also made many contributions to several topics of physical and economic geography in this book. At that time people believed in the geocentric theory that is they believed that the earth was in the center and the planets, stars, and sun revolved around it. He clearly knew, 600 years before Galileo, that the earth rotates on its axis daily and moves yearly around the sun. And for the first time in history, he made a scientific explanation of why the sun never sets in the North or South Pole.
Abd Al-Rahman Al Sufi (December 7, 903 - May 25, 986)
- He lived in Isfahan, Persia, and worked on translating and expanding Greek astronomical works, especially the Almagest of Ptolemy. He contributed several corrections to Ptolemy's star list and did his own brightness and magnitude estimates which frequently deviated from those in Ptolemy's work. He was the first to attempt to relate the Greek with the traditional Arabic star names and constellations, which were completely unrelated and overlapped in complicated ways.
- He observed that the ecliptic plane is inclined with respect to the celestial equator and more accurately calculated the length of the solar year. He observed and described the stars, their positions, their magnitudes (brightness) and their color, setting out his results constellation by constellation. For each constellation, he provided two drawings, one from the outside of a celestial globe, and the other from the inside (as seen from the sky). Al Sufi also wrote on the astrolabe, finding numerous additional uses for it. *Best known is "Book of Fixed Stars" ("Kitab al-Kawatib al-Thabit al-Musawwar")in 964
Ibn Yunus(950 – 1009)
He was born in Egypt between 950 and 952 * Best known is al-Zij al-Kabir al-Hakimi_was a handbook of astronomical tables which contained very accurate observations, many of which may have been obtained with very large astronomical instruments
- Ibn Yunus described 40 planetary conjunctions and 30 lunar eclipses which were used by Simon Newcomb in his lunar theory,in the 19th century For example, he accurately describes the planetary conjunction that occurred in the year 1000 as follows: A conjunction of Venus and Mercury in Gemini, observed in the western sky: The two planets were in conjunction after sunset on the night [of Sunday 19 May 1000]. The time was approximately eight equinoctial hours after midday on Sunday . Mercury was north of Venus and their latitude difference was a third of of a degree.

- Ibn Yunus' other observations also inspired Laplace's Obliquity of the Ecliptic and Inequalities of Jupiter and Saturn's. Ibn Yunus also observed more than 10,000 entries for the sun's position for many years using a large monument Monumental astrolabe with a diameter of nearly 1.4 metres.
- Solved the problems of spherical trigonometry
- First to study the isometric oscillatory motion of a pendulum
Abu Ja'far Muhammad ibn Musa Al-Khwarizmi(about 790 - about 850)
- Al-Khwārizmī lived in Baghdad, where he worked at the “House of Wisdom” (Dār al-Ḥikma) - His major works introduced Hindu-Arabic numerals and the concepts of algebra into European mathematics.
- Achievements:
1. al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr waʾl-muqābala (“The Compendious Book on Calculation by Completion and Balancing”) which is about elementary algebra.
2. In the 12th century a second work by al-Khwārizmī introduced Hindu-Arabic numerals and their arithmetic to the West. It is preserved only in a Latin translation, Algoritmi de numero Indorum (“Al-Khwārizmī Concerning the Hindu Art of Reckoning”).
3. A third major book was his Kitāb ṣūrat al-arḍ (“The Image of the Earth”; translated as Geography), which presented the coordinates of localities in the known world based, ultimately, on those in the Geography of Ptolemy but with improved values for the length of the Mediterranean Sea and the location of cities in Asia and Africa. He also assisted in the construction of a world map for al-Ma2mūn and participated in a project to determine the circumference of the Earth, which had long been known to be spherical, by measuring the length of a degree of a meridian through the plain of Sinjār in Iraq.
4. Finally, al-Khwārizmī also compiled a set of astronomical tables (Zīj), based on a variety of Hindu and Greek sources. This work included a table of sines, evidently for a circle of radius 150 units. Like his treatises on algebra and Hindu-Arabic numerals, this astronomical work (or an Andalusian revision thereof) was translated into Latin.
Ibn al-Haytham
Born Basra (Iraq), 965 Died Cairo (Egypt), circa 1040 Ibn al‐Haytham (often referred to in the literature as Alhazen, the Latin version of al‐Ḥasan) was one of the most important and influential figures in the history of science. He wrote on topics that included logic, ethics, politics, poetry, music, and theology (kalām), and produced summaries of Aristotle and Galen. His extant works are mostly on mathematics, optics, and astronomy. As a young man, Ibn al‐Haytham moved to Egypt from Iraq and was involved in an abortive engineering project in Egypt on regulating the flow of the Nile.

The sources do not agree on the details of the story; however, it is clear that after this brief try at government work, Ibn l‐Haytham chose a life of quiet scholarship. He earned his living copying scientific manuscripts, and carried out extensive research and correspondence in philosophy and the sciences. In his youth Ibn al‐Haytham inquired into the different religions and came to the conclusion that the truth is one. At least since Aristotle, it has been taken for a fact that the motions of the celestial bodies are uniform and circular, and that the stars are embedded within a set of concentric spheres. However, astronomy had progressed much in the intervening centuries; in particular, the Almagest, Ptolemy's landmark text, had set out a theory far more detailed and complex than anything Aristotle had proposed. True, Ptolemy himself had tried to give a physical account in his Planetary Hypotheses. However, no one was quite sure how all the pieces fit together. Moreover, some of the mathematical devices that Ptolemy had employed, for example, the equant or lunar prosneusis, were in direct violation of the principle of uniform circular motion about a fixed center.

Ibn al‐Haytham addressed these issues in a number of his writings. In his al‐Shukūk ʿalā Baṭlamyūs (Doubts concerning Ptolemy), a thoroughgoing critique of the Almagest, Planetary Hypotheses, and Optics, he showed in great detail where and how Ptolemy had violated the principles of natural philosophy. An early monograph, which does not survive but which is mentioned in a later defense of his views and is summarized by Naṣīr al‐Dīn al‐Ṭūsī, attempts to provide a physical solution for one of the knottiest problems, the motion called iltifāf, which was produced by Ptolemy's models for the motion in latitude of the planets.

The conflicts between astronomy and optics were far less serious, affecting only some specific problems. The so called Moon illusion, i. e., the apparent enlargement of celestial bodies and the distances between them when they lie low on the horizon, occupied Ibn al‐Haytham's attention throughout his career. In his youthful commentary to the Almagest, he endorsed and even provided with “proof” Ptolemy's remarks that the enlargement is produced by refraction through the Earth's “vapors” (i. e., atmosphere), similar to the way bodies immersed in water are magnified. In a later monograph devoted exclusively to this topic, Fī Ruʾyat al‐kawākib (On seeing the stars), he distanced himself somewhat from Ptolemy's explanation. In his masterful compendium al‐Manāẓir (Optics) Ibn al‐Haytham correctly identified the problem as one belonging to the psychology of perception, though he did allow that thick vapors could sometimes be a secondary factor.
Al-Marrākushī
Flourished (Egypt), second half of the 13th century Marrākushī was one of the major astronomers in 13th‐century Egypt. As his name indicates, he was originally from Maghrib, but his major astronomical activities took place in Cairo during the second half of the 13th century. It is not too surprising, given the turmoil affecting al‐Andalus and Maghrib at that time, that a scholar from the westernmost part of the Islamic world would decide to emigrate to Egypt, whose capital Cairo was already established as the major cultural center of the Islamic world. Unfortunately, Marrākushī does not figure in any biographical sources, so we must rely on the scanty evidence provided by his own work in order to shed some light on his life.
Marrākushī is best known for his remarkable summa devoted to spherical astronomy and astronomical instrumentation, entitled Jāmiʿ al‐mabādiʾ wa‐ʾl‐ghāyāt fī ʿilm al‐mīqāt (Collection of the principles and objectives in the science of timekeeping), which is intended as a comprehensive encyclopedia of practical astronomy. This work is the single most important source for the history of astronomical instrumentation in Islam. It was the standard reference work for Mamluk Egyptian and Syrian, Rasūlid Yemeni, and Ottoman Turkish specialists of the subject .
Al-Tusi
Born Ṭūs (northeast Iran), 17 February 1201 Died Baghdad (Iraq), 25 June 1274 Naṣīr al‐Dīn al‐Ṭūsī's major scientific writings in astronomy, in which he worked to reform Ptolemaic theoretical astronomy, had an enormous influence upon late medieval Islamic astronomy as well as the work of early‐modern European astronomers, including Nicholas Copernicus. Ṭūsī wrote over 150 works, in Arabic and Persian, that dealt with the ancient mathematical sciences, the Greek philosophical tradition, and the religious sciences (law [fiqh], dialectical theology [kalām], and Sufism).
He thereby acquired the honorific titles of khwāja (distinguished scholar and teacher), ustādh al‐bashar (teacher of mankind), and al‐muʿallim al‐thālith (the third teacher, the first two being Aristotle and Fārābī). In addition, Ṭūsī was the director of the first major astronomical observatory, which was located in Marāgha (Iran). In the early 1230s, after completing his education, Ṭūsī found patrons at the Ismāʿīlī courts in eastern Iran; he eventually relocated to Alamūt, the Ismāʿīlī capital, and witnessed its fall to the Mongols in 1256. Ṭūsī then served under the Mongols as an advisor to Īlkhānid ruler Hūlāgū Khan, becoming court astrologer as well as minister of religious endowments (awqāf). One major outcome was that Ṭūsī oversaw the construction of an astronomical observatory and its instruments in Marāgha, the Mongol headquarters in Azerbaijan, and he became its first director. The Marāgha Observatory also comprised a library and school. It was one of the most ambitious scientific institutions established up to that time and may be considered the first full‐scale observatory. It attracted many famous and talented scientists and students from the Islamic world and even from as far away as China. The observatory lasted only about 50 years, but its intellectual legacy would have repercussions from China to Europe for centuries to come.

Indeed, it is said that Ulugh Beg's childhood memory of visiting the remnants of the Marāgha Observatory as a youth contributed to his decision to build the Samarqand Observatory. Mughal observatories in India, such as those built by Jai Singh in the 18th century, clearly show the influence of these earlier observatories, and it has been suggested that Tycho Brahe might have been influenced by them as well. In 1274 Ṭūsī left Marāgha with a group of his students for Baghdad. Ṭūsī's writings are both synthetic and original. His recensions (taḥārīr) of Greek and early Islamic scientific works, which included his original commentaries, became the standard in a variety of disciplines. included Euclid's Elements, Ptolemy's Almagest, and the so called mutawassiṭāt (the Intermediate Books” that were to be studied between Euclid's Elements and Ptolemy's Almagest) with treatises by Euclid, Theodosius, Hypsicles, Autolycus, Aristarchus, Archimedes, Menelaus, Thābit ibn Qurra, and the Banū Mūsā. In mathematics, Ṭūsī published a sophisticated “proof” of Euclid's parallels postulate that was important for the development of non‐Euclidian geometry, and he treated trigonometry as a discipline independent of astronomy, which was in many ways similar to what was accomplished later in Europe by Johann Müller (Regiomontanus). Other important and influential works include books on logic, ethics, and a famous commentary on aphilosophical work of Ibn Sīnā.

In astronomy, Ṭūsī wrote several treatises on practical astronomy (taqwīm), instruments, astrology, and cosmography/theoretical astronomy (ʿilm al‐hayʾa). He also compiled a major astronomical handbook (in Persian) entitled Zīj‐i Īlkhānī for his Mongol patrons in Marāgha. Virtually all these works were the subject of commentaries and supercommentaries, and many of his Persian works were translated into Arabic. They were influential for centuries, some still being used into the 20th century. Ṭūsī's work in practical astronomy, as well as his Zīj‐i Īlkhānī, were not particularly original or innovative. This was not the case with his work in planetary theory. There he sought to rid the Ptolemaic system of its inconsistencies, in particular its violations of the fundamental principle of uniform circular motion in the heavens. Ṭūsī also influenced his astronomical and cosmological successors with his discussion of the Earth's motion. Although he remained committed to a geocentric universe, Ṭūsī criticized Ptolemy's reliance on observational proofs to demonstrate the Earth's stasis, noting that such proofs were not decisive. Recent research has revealed a striking similarity between Ṭūsī's arguments and those of Copernicus.
Ibn al-Shatir
Born Damascus (Syria), circa 1305 Died Damascus (Syria), circa 1375 Ibn al‐Shāṭir was the most distinguished Muslim astronomer of the 14th century. Although he was head muwaqqit at the Umayyad mosque in Damascus, responsible for the regulation of the astronomically defined times of prayer, his works on astronomical timekeeping are considerably less significant than those of his colleague Khalīlī. On the other hand, Ibn al‐Shāṭir, continuing the tradition of Ibn al‐Sarrāj, made substantial advances in the design of astronomical instruments. Nevertheless, his most significant contribution to astronomy was his planetary theory.
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