Islamic astronomy comprises the astronomical developments made in the Islamic world, particularly during the Islamic Golden Age (9th–13th centuries), and mostly written in the Arabic language. These developments mostly took place in the Middle East, Central Asia, Al-Andalus, and North Africa, and later in the Far East and India. It closely parallels the genesis of other Islamic sciences in its assimilation of foreign material and the amalgamation of the disparate elements of that material to create a science with Islamic characteristics. These included Greek, Sassanid, and Indian works in particular, which were translated and built upon.
After the Islamic conquest of Persia, the province of Mesopotamia came to be known as Iraq in the Arabic language. During the Abbasid period of the region's history, Baghdad was the capital of the Arab Empire, and for centuries, remained the centre of astronomical activity throughout the Islamic world. Astronomy was also studied in Basra and other Iraqi cities. During the Islamic period, Arabic was adopted as the language of scholarship, and Iraq continued to make numerous contributions to the field of astronomy, up until the 1258 sack of Baghdad, when many libraries were destroyed and scientific activity in Iraq came to a halt. Despite this, the work that did survive had an impact on the subsequent development of astronomy, through the medieval Arabic-Latin translation movement in Europe and Maragheh observatory in Persia.
Islamic astronomy played a significant role in the revival of Byzantine and European astronomy following the loss of knowledge during the early medieval period, notably with the production of Latin translations of Arabic works during the 12th century. Islamic astronomy also had an influence on Chinese astronomy and Malian astronomy. A significant number of stars in the sky, such as Aldebaran, Altair and Deneb, and astronomical terms such as alidade, azimuth, and nadir, are still referred to by their Arabic names. A large corpus of literature from Islamic astronomy remains today, numbering approximately 10,000 manuscripts scattered throughout the world, many of which have not been read or catalogued. Even so, a reasonably accurate picture of Islamic activity in the field of astronomy can be reconstructed.
The period throughout the ninth, tenth and early eleventh centuries was one of vigorous investigation, in which the superiority of the Ptolemaic system of astronomy was accepted and significant contributions made to it. Astronomical research was greatly supported by the Abbasid caliph al-Mamun. Baghdad and Damascus became the centers of such activity. The caliphs not only supported this work financially, but endowed the work with formal prestige.
Early observational astronomyEdit
In observational astronomy, the first major original Muslim work of astronomy was Zij al-Sindh by Al-Khwarizimi in 830. The work contains tables for the movements of the sun, the moon and the five planets known at the time. The work is significant as it introduced Indian and Ptolemaic concepts into Islamic sciences. This work also marked the turning point in Islamic astronomy. Hitherto, Muslim astronomers had adopted a primarily research approach to the field, translating works of others and learning already discovered knowledge. Al-Khwarizmi's work marked the beginning of non-traditional methods of study and calculations.
Between 825 to 835, Habash al-Hasib al-Marwazi conducted various observations at the Al-Shammisiyyah observatory in Baghdad, where he estimated a number of geographic and astronomical values. He compiled his results in The Book of Bodies and Distances, in which many of his estimates come closer to modern values than any of his predecessors. For example, he estimated the Moon's diameter as 3,037 km (equivalent to 1,519 km radius) and its distance from the Earth as 215,209 miles, which come close to the currently accepted values of 1,735 km radius and 238,857 miles distance, respectively.
In 850, Al-Farghani wrote Kitab fi Jawani ("A compendium of the science of stars"). The book primarily gave a summary of Ptolemic cosmography. However, it also corrected Ptolemy's Almagest based on findings of earlier Iranian astronomers. Al-Farghani gave revised values for the obliquity of the ecliptic, the precessional movement of the apogees of the sun and the moon, and the circumference of the earth. The books were widely circulated through the Muslim world, and even translated into Latin.
Muhammad ibn Jābir al-Harrānī al-Battānī (Albatenius) (853-929) produced "improved tables of the orbits of the sun and the moon" that "comprise his discovery that the direction of the sun's eccentric as recorded by Ptolemy was changing," which in modern astronomy is equivalent to the Earth moving in an elliptical orbit around the Sun. His times for the new moon, lengths for the solar year and sidereal year, prediction of eclipses, and work on the phenomenon of parallax, carried astronomers "to the verge of relativity and the space age." Around the same time, Yahya Ibn Abi Mansour carried out extensive observations and tests, and wrote the Al-Zij al-Mumtahan, in which he completely revised the Almagest values.
Ibn Yunus observed more than 10,000 entries for the sun's position for many years using a large astrolabe with a diameter of nearly 1.4 meters. His observations on eclipses were still used centuries later in Simon Newcomb's investigations on the motion of the moon, while his other observations inspired Laplace's Obliquity of the Ecliptic and Inequalities of Jupiter and Saturn. Abu-Mahmud al-Khujandi relatively accurately computed the axial tilt to be 23°32'19" (23.53°).
Early heliocentric modelsEdit
- See also: Islamic cosmology
The Babylonian astronomer, Seleucus of Seleucia developed a heliocentric model in the 2nd century BC, wrote a work that was later translated into Arabic. A fragment of his work has survived only in Arabic translation, which was later referred to by the Persian philosopher Muhammad ibn Zakariya al-Razi (865-925).
In the late ninth century, Ja'far ibn Muhammad Abu Ma'shar al-Balkhi (Albumasar) developed a planetary model which some have interpreted as a heliocentric model. This is due to his orbital revolutions of the planets being given as heliocentric revolutions rather than geocentric revolutions, and the only known planetary theory in which this occurs is in the heliocentric theory. His work on planetary theory has not survived, but his astronomical data was later recorded by al-Hashimi, Abū Rayhān al-Bīrūnī and al-Sijzi. In the tenth century, the Brethren of Purity wrote the Encyclopedia of the Brethren of Purity, in which some verses have been interpreted as implying a heliocentric model, particularly a verse in the Rasa'il (II, 30) which states:
"...in so far as the sun is to the heavens what the king is to his kingdom and the planets are to it what soldiers, auxiliaries, and subjects generally are to the king, and the spheres are like regions and the constellations like countries and the degrees and minutes like towns, it was enjoined by divine wisdom that it should be located at the center of the universe."
"God has placed the Sun at the center of the Universe just as the capital of a country is placed in its middle and the ruler's palace at the center of the city."
In contrast to ancient Greek philosophers who believed that the universe had an infinite past with no beginning, medieval philosophers and theologians developed the concept of the universe having a finite past with a beginning (see Temporal finitism). This view was inspired by the creation myth shared by the three Abrahamic religions: Judaism, Christianity and Islam. The Christian philosopher, John Philoponus, presented the first such argument against the ancient Greek notion of an infinite past. His arguments were adopted by many most notably; early Muslim philosopher, Al-Kindi (Alkindus); the Jewish philosopher, Saadia Gaon (Saadia ben Joseph); and the Muslim theologian, Al-Ghazali (Algazel). They used two logical arguments against an infinite past, the first being the "argument from the impossibility of the existence of an actual infinite", which states:
- "An actual infinite cannot exist."
- "An infinite temporal regress of events is an actual infinite."
- ".•. An infinite temporal regress of events cannot exist."
The second argument, the "argument from the impossibility of completing an actual infinite by successive addition", states:
- "An actual infinite cannot be completed by successive addition."
- "The temporal series of past events has been completed by successive addition."
- ".•. The temporal series of past events cannot be an actual infinite."
Both arguments were adopted by later Christian philosophers and theologians, and the second argument in particular became more famous after it was adopted by Immanuel Kant in his thesis of the first antimony concerning time.
Experimental astronomy, astrophysics, celestial mechanicsEdit
In the 9th century, the eldest Banū Mūsā brother, Ja'far Muhammad ibn Mūsā ibn Shākir, made significant contributions to astrophysics and celestial mechanics. He was the first to hypothesize that the heavenly bodies and celestial spheres are subject to the same laws of physics as Earth, unlike the ancients who believed that the celestial spheres followed their own set of physical laws different from that of Earth. In his Astral Motion and The Force of Attraction, Muhammad ibn Musa also proposed that there is a force of attraction between heavenly bodies, foreshadowing Newton's law of universal gravitation.
In the 10th century, Muhammad ibn Jābir al-Harrānī al-Battānī (Albatenius) (853-929) introduced the idea of testing "past observations by means of new ones". This led to the use of exacting empirical observations and experimental techniques by Muslim astronomers from the eleventh century onwards.
In the early 11th century, Ibn al-Haytham (Alhazen) wrote the Maqala fi daw al-qamar (On the Light of the Moon) some time before 1021. This was the first attempt successful at combining mathematical astronomy with physics and the earliest attempt at applying the experimental method to astronomy and astrophysics. He disproved the universally held opinion that the moon reflects sunlight like a mirror and correctly concluded that it "emits light from those portions of its surface which the sun's light strikes." In order to prove that "light is emitted from every point of the moon's illuminated surface," he built an "ingenious experimental device." Ibn al-Haytham had "formulated a clear conception of the relationship between an ideal mathematical model and the complex of observable phenomena; in particular, he was the first to make a systematic use of the method of varying the experimental conditions in a constant and uniform manner, in an experiment showing that the intensity of the light-spot formed by the projection of the moonlight through two small apertures onto a screen diminishes constantly as one of the apertures is gradually blocked up."
Ibn al-Haytham, in his Book of Optics (1021), was also the first to discover that the celestial spheres do not consist of solid matter, and he also discovered that the heavens are less dense than the air. These views were later repeated by Witelo and had a significant influence on the Copernican and Tychonic systems of astronomy.
Ibn al-Haytham also refuted Aristotle's view on the Milky Way galaxy. Aristotle believed the Milky Way to be caused by "the ignition of the fiery exhalation of some stars which were large, numerous and close together" and that the "ignition takes place in the upper part of the atmosphere, in the region of the world which is continuous with the heavenly motions." Ibn al-Haytham refuted this by making the first attempt at observing and measuring the Milky Way's parallax, and he thus "determined that because the Milky Way had no parallax, it was very remote from the earth and did not belong to the atmosphere."
During this period, a distinctive Islamic system of astronomy flourished. It was Greek tradition to separate mathematical astronomy (as typified by Ptolemy) from philosophical cosmology (as typified by Aristotle). Muslim scholars developed a program of seeking a physically real configuration (hay'a) of the universe, that would be consistent with both mathematical and physical principles. Within the context of this hay'a tradition, Muslim astronomers began questioning technical details of the Ptolemaic system of astronomy. Most of these criticisms, however, continued to follow the Ptolemaic astronomical paradigm, remaining within the geocentric framework. As the historian of astronomy, A. I. Sabra, noted:
"All Islamic astronomers from Thabit ibn Qurra in the ninth century to Ibn al-Shatir in the fourteenth, and all natural philosophers from al-Kindi to Averroes and later, are known to have accepted what Kuhn has called the "two-sphere universe" ...—the Greek picture of the world as consisting of two spheres of which one, the celestial sphere made up of a special element called aether, concentrically envelops the other, where the four elements of earth, water, air, and fire reside."
Refutations of astrologyEdit
The first semantic distinction between astronomy and astrology was given by the Persian astronomer Abu Rayhan al-Biruni in the 11th century, though he himself refuted astrology in another work. The study of astrology was also refuted by other Muslim astronomers at the time, including al-Farabi, Ibn al-Haytham, Avicenna and Averroes. Their reasons for refuting astrology were often due to both scientific (the methods used by astrologers being conjectural rather than empirical) and religious (conflicts with orthodox Islamic scholars) reasons.
Beginning of hay'a programEdit
Between 1025 and 1028, Ibn al-Haytham (Latinized as Alhazen), began the hay'a tradition of Islamic astronomy with his Al-Shuku ala Batlamyus (Doubts on Ptolemy). While maintaining the physical reality of the geocentric model, he was the first to criticize Ptolemy's astronomical system, which he criticized on empirical, observational and experimental grounds, and for relating actual physical motions to imaginary mathematical points, lines and circles:
"Ptolemy assumed an arrangement that cannot exist, and the fact that this arrangement produces in his imagination the motions that belong to the planets does not free him from the error he committed in his assumed arrangement, for the existing motions of the planets cannot be the result of an arrangement that is impossible to exist."
Ibn al-Haytham developed a physical structure of the Ptolemaic system in his Treatise on the configuration of the World, or Maqâlah fî hay'at al-‛âlam, which became an influential work in the hay'a tradition. In his Epitome of Astronomy, he insisted that the heavenly bodies "were accountable to the laws of physics."
In 1038, Ibn al-Haytham described the first non-Ptolemaic configuration in The Model of the Motions. His reform was not concerned with cosmology, as he developed a systematic study of celestial kinematics that was completely geometric. This in turn led to innovative developments in infinitesimal geometry. His reformed model was the first to reject the equant and eccentrics, separate natural philosophy from astronomy, free celestial kinematics from cosmology, and reduce physical entities to geometrical entities. The model also propounded the Earth's rotation about its axis, and the centres of motion were geometrical points without any physical significance, like Johannes Kepler's model centuries later. Ibn al-Haytham also describes an early version of Occam's razor, where he employs only minimal hypotheses regarding the properties that characterize astronomical motions, as he attempts to eliminate from his planetary model the cosmological hypotheses that cannot be observed from Earth.
Abu Said al-Sijzi, a contemporary of al-Biruni, suggested the possible heliocentric movement of the Earth around the Sun, which al-Biruni did not reject. Al-Biruni agreed with the Earth's rotation about its own axis, and while he was initially neutral regarding the heliocentric and geocentric models, he considered heliocentrism to be a philosophical problem. He remarked that if the Earth rotates on its axis and moves around the Sun, it would remain consistent with his astronomical parameters:
"Rotation of the earth would in no way invalidate astronomical calculations, for all the astronomical data are as explicable in terms of the one theory as of the other. The problem is thus difficult of solution."
In 1031, Al-Biruni completed his extensive astronomical encyclopaedia Kitab al-Qanun al-Mas'udi (Latinized as Canon Mas’udicus), in which he recorded his astronomical findings and formulated astronomical tables. In it he presented a geocentric model, tabulating the distance of all the celestial spheres from the central Earth, computed according to the principles of Ptolemy's Almagest. The book introduces the mathematical technique of analysing the acceleration of the planets, and first states that the motions of the solar apogee and the precession are not identical. Al-Biruni also discovered that the distance between the Earth and the Sun is larger than Ptolemy's estimate, on the basis that Ptolemy disregarded annular eclipses.
In the 11th-12th centuries, astronomers in al-Andalus took up the challenge earlier posed by Ibn al-Haytham, namely to develop an alternate non-Ptolemaic configuration that evaded the errors found in the Ptolemaic model. Like Ibn al-Haytham's critique, the anonymous Andalusian work, al-Istidrak ala Batlamyus (Recapitulation regarding Ptolemy), included a list of objections to Ptolemic astronomy. This marked the beginning of the Andalusian school's revolt against Ptolemaic astronomy, otherwise known as the "Andalusian Revolt".
The "Maragha Revolution" refers to the Maragheh school's revolution against Ptolemaic astronomy. The "Maragha school" was an astronomical tradition beginning in the Maragheh observatory and continuing with astronomers from the Damascus mosque and Samarkand observatory. Like their Andalusian predecessors, the Maragha astronomers attempted to solve the equant problem and produce alternative configurations to the Ptolemaic model. They were more successful than their Andalusian predecessors in producing non-Ptolemaic configurations which eliminated the equant and eccentrics, were more accurate than the Ptolemaic model in numerically predicting planetary positions, and were in better agreement with empirical observations. The most important of the Maragha astronomers included Mo'ayyeduddin Urdi (d. 1266), Nasīr al-Dīn al-Tūsī (1201–1274), Najm al-Dīn al-Qazwīnī al-Kātibī (d. 1277), Qotb al-Din Shirazi (1236–1311), Sadr al-Sharia al-Bukhari (c. 1347), Ibn al-Shatir (1304–1375), Ali al-Qushji (c. 1474), al-Birjandi (d. 1525) and Shams al-Din al-Khafri (d. 1550).
Mo'ayyeduddin Urdi (d. 1266) was the first of the Maragheh astronomers to develop a non-Ptolemaic model, and he proposed a new theorem, the "Urdi lemma". Nasīr al-Dīn al-Tūsī (1201–1274) resolved significant problems in the Ptolemaic system by developing the Tusi-couple as an alternative to the physically problematic equant introduced by Ptolemy, and conceived a plausible model for elliptical orbits. Tusi's student Qotb al-Din Shirazi (1236–1311), in his The Limit of Accomplishment concerning Knowledge of the Heavens, discussed the possibility of heliocentrism. Al-Qazwīnī al-Kātibī (d. 1277), who also worked at the Maragheh observatory, in his Hikmat al-'Ain, wrote an argument for a heliocentric model, though he later abandoned the idea.
Ibn al-Shatir (1304–1375) of Damascus, in A Final Inquiry Concerning the Rectification of Planetary Theory, incorporated the Urdi lemma, and eliminated the need for an equant by introducing an extra epicycle (the Tusi-couple), departing from the Ptolemaic system in a way that was mathematically identical to what Nicolaus Copernicus did in the 16th century. Unlike previous astronomers before him, Ibn al-Shatir was not concerned with adhering to the theoretical principles of natural philosophy or Aristotelian cosmology, but rather to produce a model that was more consistent with empirical observations. For example, it was Ibn al-Shatir's concern for observational accuracy which led him to eliminate the epicycle in the Ptolemaic solar model and all the eccentrics, epicycles and equant in the Ptolemaic lunar model. His model was thus in better agreement with empirical observations than any previous model, and was also the first that permitted empirical testing. His work thus marked a turning point in astronomy, which may be considered a "Scientific Revolution before the Renaissance". His rectified model was later adapted into a heliocentric model by Copernicus, which was mathematically achieved by reversing the direction of the last vector connecting the Earth to the Sun. In the published version of his masterwork, De revolutionibus orbium coelestium, Copernicus also cites the theories of al-Battani, Arzachel and Averroes as influences, while the works of Ibn al-Haytham and al-Biruni were also known in Europe at the time.
The astronomical tradition established by the Maragha school continued at the Ulugh Beg Observatory at Samarkand, in modern-day Uzbekistan. Founded by Ulugh Beg in the early 15th century, the observatory made considerable progress in observational astronomy. In the Zij-i Sultani, Beg determined the length of the sidereal year as 365d 5h 49m 15s, which has an error of +25s, making it more accurate than Nicolaus Copernicus' estimate which had an error of +30s. Beg also determined the Earth's axial tilt as 23.52 degrees, which remains the most accurate measurement to date. It was more accurate than later measurements by Copernicus and Tycho Brahe, and matches the currently accepted value precisely.
Allusions to heliocentrism also can be found in the works of Muslim theologians and philosophers such as Fakhr al-Din al-Razi (b. 1149), Al-Zamakhshari (b. 1075), and Ottoman Sheikh ul-Islam Ebussuud Efendi (b.1490). In his major work Tafsir al-Kabir, Fakhr al-Din al-Razi defends ideas of heliocentrism, with the only difference that the Sun is not mentioned as a static object or as a centre of the Universe:
Even though the Earth is described as a bed in this verse, in the other verse it is portrayed as a sphere. Spherical earth is revolving around the Sun. If questioned "How people and objects can stand on the Earth if the Earth, as a sphere, revolving around the Sun?", my answer will be that the Earth is such a huge sphere where flat surfaces appear."
Influence in Christian EuropeEdit
During this period, Islamic-ruled regions of Europe, such as Al-Andalus, the Emirate of Sicily, and southern Italy, were slowly being reconquered by Christians. This led to the Arabic-Latin translation movement, which saw the assimilation of knowledge from the Islamic world by Western European science, including astronomy.
One of the most productive translators in Spain was Gerard of Cremona, who translated 87 books from Arabic to Latin. The astronomical texts he translated include Jabir ibn Aflah's Elementa astronomica, Ahmad ibn Muhammad ibn Kathīr al-Farghānī's On Elements of Astronomy on the Celestial Motions, the works of Thabit ibn Qurra and Hunayn ibn Ishaq, and the works of Arzachel, the Banū Mūsā brothers, Abū Kāmil Shujā ibn Aslam, Abu al-Qasim, and Ibn al-Haytham (including the Book of Optics). The astronomical works translated by Plato of Tivoli included Al-Battani's astronomical and trigonometrical work De motu stellarum. Al-Khwarizmi's Astronomical tables (also containing trigonometric tables) were translated by Robert of Chester and by Adelard of Bath (fl. 1116-1142), who also translated the Introduction to Astrology of Abū Ma'shar. Adelard associated with other scholars in Western England such as Peter Alfonsi and Walcher of Malvern who translated and developed the astronomical concepts brought from Islamic Spain. Other Arabic astronomical texts translated into Latin include Muhammad al-Fazari's Great Sindhind (based on the Surya Siddhanta and the works of Brahmagupta).
Islamic astronomers had based their work largely on actual observations of the heavens, far more so than earlier Greek astronomers who relied heavily upon abstract calculation. This led to the emergence of the modern astronomical observatory as a research institute (as opposed to a private observation post as was the case in ancient times) being first introduced by medieval Muslim astronomers, who produced accurate Zij treatises using these observatories. The Islamic observatory was the first specialized astronomical institution with its own scientific staff, director, astronomical program, large astronomical instruments, and building where astronomical research and observations are carried out. Islamic observatories were also the first to employ enormously large astronomical instruments in order to greatly improve the accuracy of their observations.
The medieval Islamic observatories were also the earliest institutions to emphasize group research (as opposed to individual research) and where "theoretical investigations went hand in hand with observations." In this sense, they were similar to modern scientific research institutions.
The first systematic observations in Islam are reported to have taken place under the patronage of al-Ma'mun, and the first Islamic observatories were built in 9th century Iraq under his patronage. In many private observatories from Damascus to Baghdad, meridian degrees were measured, solar parameters were established, and detailed observations of the Sun, Moon, and planets were undertaken. One of these early observatories in Baghdad was the Al-Shammisiyyah observatory, where between 825 to 835, Habash al-Hasib al-Marwazi conducted various observations and estimated a number of geographic and astronomical values.
In the 10th century, the Buwayhid dynasty encouraged the undertaking of extensive works in Astronomy, such as the construction of a large scale instrument with which observations were made in the year 950. We know of this by recordings made in the zij of astronomers such as Ibn al-Alam. The great astronomer Abd Al-Rahman Al Sufi was patronised by prince 'Adud al-Dawla, who systematically revised Ptolemy's catalogue of stars. Abu-Mahmud al-Khujandi also constructed an observatory in Ray, Iran where he is known to have constructed the first huge mural sextant in 994 AD. Sharaf al-Daula also established a similar observatory in Baghdad. Reports by Ibn Yunus and al-Zarqall in Toledo and Cordoba indicate the use of sophisticated instruments for their time.
- See also: Inventions in the Muslim world
Modern knowledge of the instruments used by Muslim astronomers primarily comes from two sources. First the remaining instruments in private and museum collections today, and second the treatises and manuscripts preserved from the Middle Ages.
Muslims both made many improvements to instruments already in use before their time, such as adding new scales or details and significantly enlarging them to improve accuracy, and invented many of their own new instruments. Islamic astronomers were also the first to build enormously large scientific instruments in order to greatly improve the accuracy of observations. Their contributions to astronomical instrumentation are abundant. Many of these instruments were often invented or designed for Islamic purposes, such as the determination of the Qibla (direction to Mecca) or the times of Salah prayers.
Brass astrolabes were developed in much of the Islamic world, often as an aid to finding the qibla. The earliest known example is dated 315 AH, (927/8 CE). The first person credited for building the Astrolabe in the Islamic world is reportedly Fazari. Though the first astrolabe to chart the stars was invented in the Hellenistic civilization, Fazari made several improvements to the device, such as the introduction of angular scales to the astrolabe, adding circles indicating azimuths on the horizon. The Arabs then took it during the Abbasid Caliphate and perfected it to be used to find the beginning of Ramadan, the hours of prayer (Salah), the direction of Mecca (Qibla), and over a thousand other uses.
In the 10th century, Al-Sufi first described over 1,000 different uses of an astrolabe, in areas as diverse as astronomy, astrology, horoscopes, navigation, surveying, timekeeping, Qibla, Salah, etc.
- Mechanical geared astrolabe
The first mechanical astrolabes with gears were invented in the Muslim world, and were perfected by Ibn Samh (c. 1020). One such device with eight gear-wheels was also constructed by Abū Rayhān al-Bīrūnī in 996. These can be considered as an ancestor of the mechanical clocks developed by later Muslim engineers.
- Navigational astrolabe
- Universal astrolabe (Saphaea)
The first astrolabe instruments were used to read the rise of the time of rise of the Sun and fixed stars. The first universal astrolabes were later constructed in the Islamic world and which, unlike their predecessors, did not depend on the latitude of the observer and could be used anywhere on the Earth. The basic idea for a latitude-independent astrolabe was conceived in the 9th century by Habash al-Hasib al-Marwazi in Baghdad and the topic was later discussed in the early 11th century by Al-Sijzi in Persia.
The first known universal astrolabe to be constructed was by Ali ibn Khalaf al-Shakkaz, an Arabic herbalist or apothecary in 11th century Al-Andalus. His instrument could solve problems of spherical astronomy for any geographic latitude, though in a somewhat more complicated fashion than the standard astrolabe. Another, more advanced and more famous, universal astrolabe was constructed by Abū Ishāq Ibrāhīm al-Zarqālī (Arzachel) soon after. His instrument became known in Europe as the "Saphaea". It was a universal lamina (plate) which "constituted a universal device representing a stereographic projection for the terrestrial equator and could be used to solve all the problems of spherical astronomy for any latitude."
Various analog computer devices were invented to compute the latitudes of the Sun, Moon, and planets, the ecliptic of the Sun, the time of day at which planetary conjunctions will occur, and for performing linear interpolation.
The volvelle, also called a wheel chart, is a type of slide chart, paper constructions with rotating parts. It is considered an early example of a paper analog computer. The volvelle can be traced back to "certain Arabic treateses on humoral medicine" and to Biruni (c. 1000) who made important contributions to the development of the volvelle. In the 20th century, the volvelle had many diverse uses.
- Castle clock with programmable analog computer
In 1206, Al-Jazari invented his largest astronomical clock, the "castle clock", which is considered to be the first programmable analog computer. It displayed the zodiac and the solar and lunar orbits. Another innovative feature of the clock was a pointer which traveled across the top of a gateway and caused automatic doors to open every hour.
- Water-powered astronomical clocks
Al-Jazari invented monumental water-powered astronomical clocks which displayed moving models of the Sun, Moon, and stars. His largest astronomical clock was the "castle clock", which is considered to be the first programmable analog computer (see Castle clock with programmable analog computer above).
Muslims made several important improvements to the theory and construction of sundials, which they inherited from their Indian and Hellenistic predecessors. Al-Khwarizmi made tables for these instruments which considerably shortened the time needed to make specific calculations. Muslim sundials could also be observed from anywhere on the Earth. Sundials were frequently placed on mosques to determine the time of prayer. One of the most striking examples was built in the 14th century by the muwaqqit (timekeeper) of the Umayyad Mosque in Damascus, Ibn al-Shatir. Muslim astronomers and engineers were the first to write instructions on the construction of horizontal sundials, vertical sundials, and polar sundials.
Since ancient dials were nodus-based with straight hour-lines, they indicated unequal hours — also called temporary hours — that varied with the seasons, since every day was divided into twelve equal segments; thus, hours were shorter in winter and longer in summer. The idea of using hours of equal time length throughout the year was the innovation of Abu'l-Hasan Ibn al-Shatir in 1371, based on earlier developments in trigonometry by Muhammad ibn Jābir al-Harrānī al-Battānī (Albategni). Ibn al-Shatir was aware that "using a gnomon that is parallel to the Earth's axis will produce sundials whose hour lines indicate equal hours on any day of the year." His sundial is the oldest polar-axis sundial still in existence. The concept later appeared in Western sundials from at least 1446.
- Navicula de Venetiis
This was a universal horary dial invented in 9th century Baghdad. It was used for accurate timekeeping by the Sun and Stars, and could be observed from any latitude. This was later known in Europe as the "Navicula de Venetiis", which was considered the most sophisticated timekeeping instrument of the Renaissance.
- Armillary sphere
- Spherical astrolabe
The spherical astrolabe was first produced in the Islamic world. It was an Islamic variation of the astrolabe and the armillary sphere, of which only one complete instrument, from the 14th century, has survived.
- Terrestrial globe
The first terrestrial globe of the Old World was constructed in the Muslim world during the Middle Ages, by Muslim geographers and astronomers working under the Abbasid caliph, Al-Ma'mun, in the 9th century. Another example was the terrestrial globe introduced to Beijing by the Persian astronomer Jamal ad-Din in 1267.
- Celestial globes
Celestial globes were used primarily for solving problems in celestial astronomy. Today, 126 such instruments remain worldwide, the oldest from the 11th century. The altitude of the sun, or the Right Ascension and Declination of stars could be calculated with these by inputting the location of the observer on the meridian ring of the globe.
- Observation tube
The first reference to an "observation tube" is found in the work of al-Battani (Albatenius) (853-929), and the first exact description of the observation tube was given by al-Biruni (973-1048), in a section of his work that is "dedicated to verifying the presence of the new crescent on the horizon." Though these early observation tubes did not have lenses, they "enabled an observer to focus on a part of the sky by eliminating light interference." These observation tubes were later adopted in Latin-speaking Europe, where they influenced the development of the telescope.
- Experimental device with apertures
In order to prove that "light is emitted from every point of the moon's illuminated surface," Ibn al-Haytham (Alhazen) built an "ingenious experimental device" showing "that the intensity of the light-spot formed by the projection of the moonlight through two small apertures onto a screen diminishes constantly as one of the apertures is gradually blocked up."
- Magnifying lens
The first optical research to describe a magnifying lens used in an instrument was found in a book called the Book of Optics (1021) written by Ibn al-Haytham (Alhazen). His descriptions were fundamental to the development of the telescope and helped set the parameters in Europe for the later advances in telescopic technology. His additional work in light refraction, parabolic mirrors, as well as the creation of other instruments such as the camera obscura, also helped spark the Scientific Revolution.
- Sine quadrant
The sine quadrant, invented by Muhammad ibn Mūsā al-Khwārizmī in 9th century Baghdad, was used for astronomical calculations. Also known as the "Sinecal Quadrant" (the Arabic term for it is "Rubul Mujayyab"), it was used for solving trigonometric problems and taking astronomical observations. It was developed by al-Khwarizmi in the 9th century and remained prevalent until the 19th century. Its defining feature is a graph paper like grid on one side that is divided into sixty equal intervals on each axis and is also bounded by a 90 degree graduated arc. A cord was attached to the apex of the quadrant with a bead at the end of it to act as a plumb bob. They were also sometimes drawn on the back of astrolabes.
- Horary quadrant
The first horary quadrant for specific latitudes, was invented by Muhammad ibn Mūsā al-Khwārizmī in 9th century Baghdad, center of the development of quadrants. It was used to determine time (especially the times of prayer) by observations of the Sun or stars. The horary quadrant could be used to find the time either in equal or unequal (length of the day divided by twelve) hours. Different sets of markings were created for either equal or unequal hours. For measuring the time in equal hours, the horary quadrant could only be used for one specific latitude while a quadrant for unequal hours could be used anywhere based on an approximate formula. One edge of the quadrant had to be aligned with the sun, and once aligned, a bead on the end of a plumbline attached to the centre of the quadrant showed the time of the day.
- Universal horary quadrant (Quadrans Novus)
The universal horary quadrant was an ingenious mathematical device invented by al-Khwarizmi in 9th century Baghdad and which was later known as the "Quadrans Vetus" (Old Quadrant) in medieval Europe from the 13th century. It could be used for any latitude on Earth and at any time of the year to determine the time in hours from the altitude of the Sun. This was the second most widely used astronomical instrument during the Middle Ages after the astrolabe. One of its main purposes in the Islamic world was to determine the times of Salah.
- Astrolabic/Almucantar quadrant (Quadrans Vetus)
The astrolabic or almucantar quadrant was invented in the medieval Islamic world, and it employed the use of trigonometry. The term "almucantar" is itself derived from Arabic. The almucantar quadrant was originally modified from the astrolabe. It was invented in Egypt in the 11th or 12th century, and was later known in Europe as the "Quadrans Vetus" (New Quadrant). It was intended as a simplified alternative to the astrolabe serving a specific latitude. According to David King:
"This was an invention of some consequence, for the astrolabe, fitted with a series of plates for different latitudes, was neither a practical device nor an accurate observational instrument. Also, being made of brass, it was expensive. The almucantar quadrant, on the other hand, could be made of wood and was an extremely practical device with which one could solve all the problems solvable with an astrolabe, for a particular latitude. The back of such a quandrant could carry a trigonometric grid called a sine quadrant for solving all manner of computational problems."
Various other astronomical instruments were also invented in the Islamic world:
- Alhidade: The alhidade was invented in the Islamic world, while the term "alhidade" is itself derived from Arabic.
- Orthogonal and regular grids: Islamic quadrants used for various astronomical and timekeeping purposes from the 10th century introduced orthogonal and regular grids and markings that are identical to modern graph paper.
- Qibla indicators: In 17th century Safavid Persia, two unique brass instruments with Mecca-centred world maps engraved on them were produced primarily for the purpose of finding the Qibla. These instruments were engraved with cartographic grids to make it more convenient to find the direction and distance to Mecca at the centre from anywhere on the Earth, which may be based on cartographic grids dating back to 10th century Baghdad. One of the two instruments, produced by Muhammad Husayn, also had a sundial and compass attached to it.
- Shadow square: The shadow square was an instrument used to determine the linear height of an object, in conjunction with the alidade, for angular observations. It was invented by Muhammad ibn Mūsā al-Khwārizmī in 9th century Baghdad.
List of notable treatisesEdit
- Zij treatises
- Ibrahim al-Fazari (d. 777) and Muhammad al-Fazari (d. 796/806)
- Az-Zij ‛alā Sinī al-‛Arab (c. 750)
- Yaqūb ibn Tāriq (d. 796)
- Az-Zij al-Mahlul min as-Sindhind li-Darajat Daraja
- Muhammad ibn Mūsā al-Khwārizmī (Latinized as Algorismi) (c. 780-850)
- Zij al-Sindhind (c. 830)
- Muhammad ibn Jābir al-Harrānī al-Battānī (Latinized as Albategni) (853-929)
- Az-Zij as-Sabi
- Other works
- Ja'far Muhammad ibn Mūsā ibn Shākir (Latinized as Mohammed Ben Musa) (800-873)
- Book on the motion of the orbs
- Astral Motion
- The Force of Attraction
- Ahmad ibn Muhammad ibn Kathīr al-Farghānī (Latinized as Alfraganus) (d. 850)
- Elements of astronomy on the celestial motions (c. 833)
- Kitab fi Jawami Ilm al-Nujum
- Ibn al-Haytham (Latinized as Alhacen) (965-1039)
- On the Configuration of the World
- Doubts concerning Ptolemy (c. 1028)
- The Resolution of Doubts (c. 1029)
- The Model of the Motions of Each of the Seven Planets (1029–1039)
- Al-Istidrak ala Batlamyus (Recapitulation regarding Ptolemy) (11th century)
- ↑ O'Connor, John J.; Robertson, Edmund F. (November 1999), "Abu Said Sinan ibn Thabit ibn Qurra", MacTutor History of Mathematics archive, University of St Andrews .
- ↑ (Dallal 1999, p. 163)
- ↑ 3.0 3.1 Langermann, Y. Tzvi (1985), "The Book of Bodies and Distances of Habash al-Hasib", Centaurus 28: 108–128 
- ↑ Langermann, Y. Tzvi (1985), "The Book of Bodies and Distances of Habash al-Hasib", Centaurus 28: 108–128 
- ↑ (Dallal 1999, p. 164)
- ↑ (Singer 1959, p. 151) (cf. (Zaimeche 2002))
- ↑ (Wickens 1976) (cf. (Zaimeche 2002))
- ↑ 23rd Annual Conference on the History of Arabic Science, Aleppo, Syria, October 2001 (cf. (Zaimeche 2002))
- ↑ 9.0 9.1 (Zaimeche 2002)
- ↑ Aulie, Richard P. (March 1994), "Al-Ghazali Contra Aristotle: An Unforeseen Overture to Science In Eleventh-Century Baghdad", Perspectives on Science and Christian Faith 45: 26–46 (cf. "References". 1001 Inventions. http://www.1001inventions.com/index.cfm?fuseaction=main.viewSection&intSectionID=441. Retrieved on 2008-01-22. )
- ↑ Cite error: Invalid
<ref>tag; no text was provided for refs named
- ↑ Bartel Leendert van der Waerden (1987). "The Heliocentric System in Greek, Persian and Hindu Astronomy", Annals of the New York Academy of Sciences 500 (1), 525–545 [534-537].
- ↑ Eloise Hart (April–May 1973), "Pages of Medieval Mideastern History", Sunrise 22, http://www.theosociety.org/pasadena/sunrise/22-72-3/rel-elo2.htm, retrieved on 26 March 2010
- ↑ (Nasr 1993, p. 77)
- ↑ 15.0 15.1 15.2 Craig, William Lane (June 1979), "Whitrow and Popper on the Impossibility of an Infinite Past", The British Journal for the Philosophy of Science 30 (2): 165–170 [165–6], doi:10.1093/bjps/30.2.165
- ↑ (Saliba 1994a, p. 116)
- ↑ Waheed, K. A. (1978), Islam and The Origins of Modern Science, Islamic Publication Ltd., Lahore, p. 27
- ↑ (Briffault 1938, p. 191)
- ↑ (Huff 2003, p. 57)
- ↑ (Huff 2003, p. 326)
- ↑ 21.0 21.1 Toomer, G. J. (December 1964), "Review: Ibn al-Haythams Weg zur Physik by Matthias Schramm", Isis 55 (4): 463–465 [463–4], doi:10.1086/349914
- ↑ (Rosen 1985, pp. 19–20 & 21)
- ↑ Josep Puig Montada (September 28, 2007). "Ibn Bajja". Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/ibn-bajja. Retrieved on 2008-07-11.
- ↑ Mohamed, Mohaini (2000), Great Muslim Mathematicians, Penerbit UTM, pp. 49–50, ISBN 9835201579
- ↑ Hamid-Eddine Bouali, Mourad Zghal, Zohra Ben Lakhdar (2005). "Popularisation of Optical Phenomena: Establishing the First Ibn Al-Haytham Workshop on Photography" (PDF). The Education and Training in Optics and Photonics Conference. http://spie.org/etop/ETOP2005_080.pdf. Retrieved on 2008-07-08.
- ↑ (Sabra 1998, pp. 293–8)
- ↑ Dennis Duke. "Arabic Models for outer Planets and Venus". http://people.scs.fsu.edu/~dduke/arabmars.html. Retrieved on 2008-01-22.
- ↑ (Sabra 1998, pp. 317–18)
- ↑ S. Pines (September 1964). "The Semantic Distinction between the Terms Astronomy and Astrology according to al-Biruni", Isis 55 (3): 343-349.
- ↑ (Saliba 1994b, pp. 60 & 67–69)
- ↑ (Sabra 1998, p. 300)
- ↑ "Nicolaus Copernicus", Stanford Encyclopedia of Philosophy, 2004, http://setis.library.usyd.edu.au/stanford/entries/copernicus/index.html, retrieved on 22 January 2008
- ↑ (Langermann 1990, pp. 25–34)
- ↑ (Duhem 1969, p. 28)
- ↑ (Rashed 2007)
- ↑ (Rashed 2007, pp. 20 & 53)
- ↑ (Rashed 2007, pp. 33–4)
- ↑ (Rashed 2007, pp. 20 & 32–33)
- ↑ (Rashed 2007, pp. 51–2)
- ↑ (Rashed 2007, pp. 35–6)
- ↑ 41.0 41.1 (Baker & Chapter 2002)
- ↑ (Marmura 1965)
- ↑ 43.0 43.1 43.2 (Saliba 1999)
- ↑ 44.0 44.1 "Khwarizm". Foundation for Science Technology and Civilisation. http://muslimheritage.com/topics/default.cfm?ArticleID=482. Retrieved on 2008-01-22.
- ↑ G. Wiet, V. Elisseeff, P. Wolff, J. Naudu (1975). History of Mankind, Vol 3: The Great medieval Civilisations, p. 649. George Allen & Unwin Ltd, UNESCO.
- ↑ 46.0 46.1 46.2 (Covington 2007)
- ↑ (Nasr 1993, p. 134)
- ↑ (Saliba 1980, p. 249)
- ↑ (Saliba 1981, p. 219)
- ↑ Sabra, A. I., "The Andalusian Revolt Against Ptolemaic Astronomy: Averroes and al-Bitrûjî", in Mendelsohn, Everett, Transformation and Tradition in the Sciences: Essays in honor of I. Bernard Cohen, Cambridge University Press, pp. 233–53
- ↑ 51.0 51.1 51.2 (Saliba 1994b, pp. 233–234 & 240)
- ↑ (Dallal 1999, p. 171)
- ↑ (Saliba 1979)
- ↑ 54.0 54.1 (Gill 2005)
- ↑ Y. M. Faruqi (2006). "Contributions of Islamic scholars to the scientific enterprise", International Education Journal 7 (4): 395-396.
- ↑ 56.0 56.1 Hugh Thurston, Early Astronomy, (New York: Springer-Verlag), p. 194, ISBN 0-387-94107-X.
- ↑ Fakhr al-Din al-Razi, Tafsir al-Kabir 2/95
- ↑ Al-Zamakhshari, Al-Kashshaaf 1/125
- ↑ Ebussuud Efendi, Irshadu'l-Akli's-Selim 1/61
- ↑ 60.0 60.1 V. J. Katz, A History of Mathematics: An Introduction, p. 291.
- ↑ For a list of Gerard of Cremona's translations see: Edward Grant (1974) A Source Book in Medieval Science, (Cambridge: Harvard Univ. Pr.), pp. 35-8 or Charles Burnett, "The Coherence of the Arabic-Latin Translation Program in Toledo in the Twelfth Century," Science in Context, 14 (2001): at 249-288, at pp. 275-281.
- ↑ D. Campbell, Arabian Medicine and Its Influence on the Middle Ages, p. 6.
- ↑ Charles Burnett, ed. Adelard of Bath, Conversations with His Nephew, (Cambridge: Cambridge University Press, 1999), p. xi.
- ↑ M.-T. d'Alverny, "Translations and Translators," pp. 440-3
- ↑ G. G. Joseph, The Crest of the Peacock, p. 306
- ↑ Ute Ballay (November 1990), "The Astronomical Manuscripts of Naṣīr al-Dīn Ṭūsī", Arabica (Brill Publishers) 37 (3): 389–392 , http://www.jstor.org/stable/4057148, retrieved on 29 March 2010
- ↑ 67.0 67.1 67.2 67.3 (Kennedy 1962)
- ↑ 68.0 68.1 Micheau, Francoise, "The Scientific Institutions in the Medieval Near East", pp. 992–3 , in (Rashed & Morelon 1996, pp. 985–1007)
- ↑ Prof. Bakar, Osman (Georgetown University) (October 15, 2001), Islam's Contribution to Human Civilization: Science and Culture, CIC's annual Ottawa dinner, http://www.al-huda.com/Article_5%205.htm, retrieved on 22 January 2008
- ↑ O'Connor, John J.; Robertson, Edmund F., "Abu Mahmud Hamid ibn al-Khidr Al-Khujandi", MacTutor History of Mathematics archive, University of St Andrews .
- ↑ Richard Nelson Frye, Golden Age of Persia, p. 163.
- ↑ L. C. Martin (1923), Surveying and navigational instruments from the historical standpoint, 24, pp. 289–303 , doi:10.1088/1475-4878/24/5/302
- ↑ Victor J. Katz & Annette Imhausen (2007), The mathematics of Egypt, Mesopotamia, China, India, and Islam: a sourcebook, Princeton University Press, p. 519, ISBN 0691114854
- ↑ 74.0 74.1 Dr. Emily Winterburn (National Maritime Museum) (2005). "Using an Astrolabe". Foundation for Science Technology and Civilisation. http://www.muslimheritage.com/topics/default.cfm?ArticleID=529. Retrieved on 2008-01-22.
- ↑ "Islam, Knowledge, and Science". University of Southern California. http://www.usc.edu/dept/MSA/introduction/woi_knowledge.html. Retrieved on 2008-01-22.
- ↑ Robert Hannah (1997). "The Mapping of the Heavens by Peter Whitfield", Imago Mundi 49, pp. 161-162.
- ↑ John Brian Harley, David Woodward (1992), The history of cartography, 2, Oxford University Press, p. 29, ISBN 0226316351
- ↑ John Brian Harley, David Woodward (1992), The history of cartography, 2, Oxford University Press, pp. 28–9, ISBN 0226316351
- ↑ 79.0 79.1 (King 1983, p. 533)
- ↑ Nick Kanas. "VOLVELLES! Early Paper Astronomical Computers" (March–April 2005). Retrieved on 2009-10-13.</cite>
- ↑ <cite style="font-style:normal" class="Journal" id="harv">David Kahn (March 1980), "On the Origin of Polyalphabetic Substitution", Isis (University of Chicago Press) 71 (1): 122–127 , http://www.jstor.org/stable/230316, retrieved on 13 October 2009</cite> </li>
- ↑ <cite style="font-style:normal" class="Journal" id="harv">Bryan S. Turner (March 1987), "State, Science and Economy in Traditional Societies: Some Problems in Weberian Sociology of Science", British Journal of Sociology (Blackwell Publishing) 38 (1): 1–23 , http://www.jstor.org/stable/590576, retrieved on 13 October 2009</cite> </li>
- ↑ 83.0 83.1 <cite style="font-style:normal" class="Journal" id="harv">Ancient Discoveries, Episode 11: Ancient Robots, History Channel, http://www.youtube.com/watch?v=rxjbaQl0ad8, retrieved on 6 September 2008</cite> </li>
- ↑ (Hill 1991) </li>
- ↑ (Ajram 1992) </li>
- ↑ (King 1999a, pp. 168–9) </li>
- ↑ 87.0 87.1 <cite style="font-style:normal" class="Journal" id="harv">King, David A., "Astronomy and Islamic society", pp. 163–8</cite> , in (Rashed & Morelon 1996, pp. 128–184) </li>
- ↑ <cite style="font-style:normal" class="web" id="CITEREF">"History of the sundial". National Maritime Museum. http://www.nmm.ac.uk/server/show/conWebDoc.353. Retrieved on 2008-07-02.</cite> </li>
- ↑ <cite style="font-style:normal" class="Journal" id="harv">Jones, Lawrence (December 2005), "The Sundial And Geometry", North American Sundial Society 12 (4)</cite> </li>
- ↑ (King 2005) </li>
- ↑ (King 2003) </li>
- ↑ 92.0 92.1 (King 2004) </li>
- ↑ Emilie Savage-Smith (1993). "Book Reviews", Journal of Islamic Studies 4 (2): 296-299."There is no evidence for the Hellenistic origin of the spherical astrolabe, but rather evidence so far available suggests that it may have been an early but distinctly Islamic development with no Greek antecedents."
- ↑ Mark Silverberg. Origins of Islamic Intolerence. </li>
- ↑ <cite style="font-style:normal" class="Journal" id="harv">Covington, Richard (2007), , Saudi Aramco World, May–June 2007: 17–21, http://www.saudiaramcoworld.com/issue/200703/the.third.dimension.htm, retrieved on 6 July 2008</cite> </li>
- ↑ <cite style="font-style:normal" class="Journal" id="harv">David Woodward (1989), "The Image of the Spherical Earth", Perspecta (MIT Press) 25: 3–15 , http://www.jstor.org/stable/1567135, retrieved on 22 February 2010</cite> </li>
- ↑ <cite style="font-style:normal" class="web" id="CITEREF2001">"An overview of Muslim Astronomers". FSTC Limited. 26 December 2001. http://www.muslimheritage.com/topics/default.cfm?ArticleID=232. Retrieved on 2008-02-01.</cite> </li>
- ↑ Regis Morelon, "General Survey of Arabic Astronomy", pp. 9-10, in (Rashed & Morelon 1996, pp. 1–19) </li>
- ↑ 99.0 99.1 Sabra, A. I. & Hogendijk, J. P. (2003), The Enterprise of Science in Islam: New Perspectives, MIT Press, pp. 85-118, ISBN 0262194821 </li>
- ↑ O. S. Marshall (1950). "Alhazen and the Telescope", Astronomical Society of the Pacific Leaflets 6, p. 4 </li>
- ↑ Richard Powers (University of Illinois), Best Idea; Eyes Wide OpenNew York Times, April 18, 1999. </li>
- ↑ 102.0 102.1 102.2 (King 2002, pp. 237–238) </li>
- ↑ 103.0 103.1 <cite style="font-style:normal" class="Journal" id="harv">King, David A. (1987), Islamic Astronomical Instruments, London: Variorum</cite> </li>
- ↑ (King 1999a, pp. 167–8) </li>
- ↑ Elly Dekker (1995), "An unrecorded medieval astrolabe quadrant from c. 1300", Annals of Science 52 (1): 1-47 . </li>
- ↑ (King, Cleempoel & Moreno 2002, p. 333) </li>
- ↑ Josef W. Meri (2006), Medieval Islamic Civilization: An Encyclopedia, p. 75, Taylor and Francis, ISBN 0415966914. </li>
- ↑ (King 1999b, p. 17) </li>
- ↑ (Iqbal 2003) </li>
- ↑ (King 1997, p. 62) </li>
- ↑ <cite style="font-style:normal" class="web" id="CITEREF">"Shadow square". National Maritime Museum. http://www.nmm.ac.uk/collections/search/lightbox.cfm/category/90286. Retrieved on 2008-01-22.</cite> </li>
- ↑ (King 2002, pp. 238–239) </li></ol>
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