Ibn al-Haytham

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Muslim scientist
Ibn al-Haytham depicted in an Iraqi 10,000-dinar note.
Name: Abū ‘Alī al-Ḥasan ibn al-Ḥasan ibn al-Haytham
Title: Ibn al-Haytham and Alhacen
Birth: 965
Death: 1039
Ethnicity: Arab or Persian
Region: Iraq (Mesopotamia) and Egypt
School tradition: Ash'ari
Main interests: Anatomy, Astronomy, Engineering, Mathematics, Mechanics, Medicine, Optics, Ophthalmology, Philosophy, Physics, Psychology, Science
Notable ideas: Pioneer in optics, scientific method, scientific skepticism, experimental science, experimental physics, experimental psychology, psychophysics, phenomenology, visual perception, analytic geometry, elliptical geometry, hyperbolic geometry, non-Euclidean geometry, non-Ptolemaic astronomy, astrophysics and celestial mechanics
Works: Book of Optics, Analysis and Synthesis, Balance of Wisdom, Discourse on Place, Doubts Concerning Ptolemy, Maqala fi'l-qarastun, On the Configuration of the World, Opuscula, The Model of the Motions, The Resolution of Doubts, Treatise on Light, Treatise on Place
Influences: Aristotle, Euclid, Ptolemy, Galen, Muhammad, Abu al-Hasan al-Ash'ari, Banū Mūsā, Thabit ibn Qurra, al-Kindi, Ibn Sahl, Abū Sahl al-Qūhī
Influenced: Khayyam, al-Khazini, Sharaf al-Dīn al-Tūsī, Urdi, Tusi, Qutb al-Din al-Shirazi, Farisi, Ibn al-Shatir, Roger Bacon, Peckham, Witelo, Gersonides, Alfonso, da Vinci, Cardano, Francis Bacon, Fermat, Kepler, Willebrord Snellius, Descartes, Christiaan Huygens, James Gregory, Guillaume de l'Hôpital, Isaac Barrow, John Wallis, Isaac Newton, Saccheri

Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham (Arabic: أبو علي الحسن بن الحسن بن الهيثم, Latinized: Alhacen or (deprecated) Alhazen) (965 – 1039), was an Arab[1][2][3] or Persian[4] Muslim polymath[5][6] who made significant contributions to the principles of optics, as well as to anatomy, astronomy, engineering, mathematics, medicine, ophthalmology, philosophy, physics, psychology, Ash'ari theology, visual perception, and to science in general with his introduction of the scientific method. He is sometimes called al-Basri (Arabic: البصري), after his birthplace in the city of Basra in Iraq (Mesopotamia), then ruled by the Buyid dynasty of Persia.[7]

Ibn al-Haytham is regarded as the father of optics for his influential Book of Optics, which correctly explained and proved the modern intromission theory of vision, and for his experiments on optics, including experiments on lenses, mirrors, refraction, reflection, and the dispersion of light into its constituent colours.[8] He studied binocular vision and the moon illusion, speculated on the finite speed, and rectilinear propagation of light,[9] and argued for the corpuscular theory. Due to his formulation of a modern quantitative, empirical and experimental approach to physics and science, he is considered the pioneer of the modern scientific method[10][11] and the originator of experimental science[12] and experimental physics,[13] and some have described him as the "first scientist" for these reasons.[14] He is also considered by some to be the founder of experimental psychology[15] for his experimental approach to the psychology of visual perception and optical illusions,[16] and a pioneer of the philosophical field of phenomenology. His Book of Optics has been ranked alongside Isaac Newton's Philosophiae Naturalis Principia Mathematica as one of the most influential books in the history of physics,[17] for initiating a revolution in optics[18] and visual perception.[19]

Among his other achievements, Ibn al-Haytham gave the first clear description[20] and correct analysis[21] of the camera obscura, discovered Fermat's principle of least time and the law of inertia (known as Newton's first law of motion),[22] discovered the concept of momentum (part of Newton's second law of motion),[23] described the attraction between masses and was aware of the magnitude of acceleration due to gravity at a distance,[24] discovered that the heavenly bodies were accountable to the laws of physics, presented a critique and reform of Ptolemaic astronomy, first stated Wilson's theorem in number theory, formulated and solved Alhazen's problem geometrically using early ideas related to calculus and mathematical induction,[25] and in his optical research laid the foundations for the later development of telescopic astronomy,[26] as well as for the microscope and the use of optical aids in Renaissance art.[27]

Contents

[edit] Overview

[edit] Biography

Abū ‘Alī al-Hasan ibn al-Hasan ibn al-Haytham was born in the Arab city of Basra, Iraq (Mesopotamia), then part of the Buyid dynasty of Persia,[7] and he probably died in Cairo, Egypt.[4] Known in the West as Alhacen or Alhazen, Ibn al-Haytham was born in 965 in Basra, and was educated there and in Baghdad.

One account of his career has him summoned to Egypt by the mercurial caliph Hakim to regulate the flooding of the Nile. After his field work made him aware of the impracticality of this scheme, and fearing the caliph's anger, he feigned madness. He was kept under house arrest until Hakim's death in 1021. During this time, he wrote his influential Book of Optics and scores of other important treatises on physics and mathematics. He later traveled to Spain and, during this period, he had ample time for his scientific pursuits, which included optics, mathematics, physics, medicine, and the development of scientific methods — on all of which he has left several outstanding books.

[edit] Works

Ibn al-Haytham was a pioneer in optics, astronomy, engineering, mathematics, physics, and psychology. His optical writings influenced many Western intellectuals such as Roger Bacon, John Pecham, Witelo, Johannes Kepler.[28] His pioneering work on number theory, analytic geometry, and the link between algebra and geometry, also had an influence on René Descartes's geometric analysis and Isaac Newton's calculus.[29]

According to medieval biographers, Ibn al-Haytham wrote more than 200 works on a wide range of subjects,[30] of which at least 96 of his scientific works are known. Most of his works are now lost, but more than 50 of them have survived to some extent. Nearly half of his surviving works are on mathematics, 23 of them are on astronomy, and 14 of them are on optics, with a few on other areas of science.[31] Not all of his surviving works have yet been studied, but some of his most important ones are described below. These include:

  • Book of Optics (1021)
  • Analysis and Synthesis
  • Balance of Wisdom
  • Discourse on Place
  • Maqala fi'l-qarastun
  • Doubts Concerning Ptolemy (1028)
  • On the Configuration of the World
  • Opuscula
  • The Model of the Motions of Each of the Seven Planets (1038)
  • The Resolution of Doubts
  • Treatise on Light
  • Treatise on Place

[edit] Legacy

Ibn al-Haytham was one of the most eminent physicists, whose developments in optics and the scientific method were particularly outstanding. Ibn al-Haytham's work on optics is credited with contributing a new emphasis on experiment. His influence on physical sciences in general, and on optics in particular, has been held in high esteem and, in fact, ushered in a new era in optical research, both in theory and practice.[8] The scientific method is considered to be so fundamental to modern science that some — especially philosophers of science and practicing scientists — consider earlier inquiries into nature to be pre-scientific.[32]

Due to its importance in the history of science, some have considered his development of the scientific method to be the most important scientific development of the second millennium.[27] Nobel Prize winning physicist Abdus Salam considered Ibn-al-Haitham "one of the greatest physicists of all time."[22] George Sarton, the father of the history of science, wrote that "Ibn Haytham's writings reveal his fine development of the experimental faculty" and considered him "not only the greatest Muslim physicist, but by all means the greatest of mediaeval times."[33][34] Robert S. Elliot considered Ibn al-Haytham to be "one of the ablest students of optics of all times."[35] The Biographical Dictionary of Scientists wrote that Ibn al-Haytham was "probably the greatest scientist of the Middle Ages" and that "his work remained unsurpassed for nearly 600 years until the time of Johannes Kepler."[36]

The Latin translation of his main work, Kitab al-Manazir, exerted a great influence upon Western science: for example, on the work of Roger Bacon, who cites him by name,[37] and on Kepler. It brought about a great progress in experimental methods. His research in catoptrics centered on spherical and parabolic mirrors and spherical aberration. He made the important observation that the ratio between the angle of incidence and refraction does not remain constant, and investigated the magnifying power of a lens. His work on catoptrics also contains the important problem known as Alhazen's problem.

The list of his books runs to 200 or so, yet very few of the books have survived. Even his monumental treatise on optics survived only through its Latin translation. During the Middle Ages his books on cosmology were translated into Latin, Hebrew and other languages.

The Alhazen crater on the Moon was named in his honour. Ibn al-Haytham is also featured on the obverse of the Iraqi 10,000 dinars banknote issued in 2003. The asteroid "59239 Alhazen" was also named in his honour, while Iran's largest laser research facility, located in the Atomic Energy Organization of Iran headquarters in Tehran, is named after him as well.

[edit] Book of Optics

Main article: Book of Optics

Ibn al-Haytham's most famous work is his seven volume treatise on optics, Kitab al-Manazir (Book of Optics) (written from 1011 to 1021),[38] which has been ranked alongside Isaac Newton's Philosophiae Naturalis Principia Mathematica as one of the most influential books in physics,[17] for introducing an early scientific method and for initiating a revolution in optics[18] and visual perception.[19]

Optics was translated into Latin by an unknown scholar at the end of the 12th century or the beginning of the 13th century.[39] It was printed by Friedrich Risner in 1572, with the title Opticae thesaurus: Alhazeni Arabis libri septem, nuncprimum editi; Eiusdem liber De Crepusculis et nubium ascensionibus.[40] Risner is also the author of the name variant "Alhazen"; before Risner he was known in the west as Alhacen, which is the correct transcription of the Arabic name.[41] This work enjoyed a great reputation during the Middle Ages. Works by Alhacen on geometrical subjects were discovered in the Bibliothèque nationale in Paris in 1834 by E. A. Sedillot. Other manuscripts are preserved in the Bodleian Library at Oxford and in the library of Leiden. Ibn al-Haytham's optical studies were influential in a number of later developments, including the telescope, which laid the foundations of telescopic astronomy,[26] as well as of the modern camera, the microscope, and the use of optical aids in Renaissance art.[27]

[edit] Optics

In classical antiquity, there were two major theories on vision. The first theory, the emission theory, was supported by such thinkers as Euclid and Ptolemy, who believed that sight worked by the eye emitting rays of light. The second theory, the intromission theory, supported by Aristotle and his followers, had physical forms entering the eye from an object. Ibn al-Haytham argued on the basis of common observations (such as the eye being dazzled or even injured if we look at a very bright light) and logical arguments (such as how a ray could proceeding from the eyes reach the distant stars the instant after we open our eye) to maintain that we cannot see by rays being emitted from the eye, nor through physical forms entering the eye. He instead developed a highly successful theory which explained the process of vision as rays of light proceeding to the eye from each point on an object, which he proved through the use of experimentation.[42]

Ibn al-Haytham proved that rays of light travel in straight lines, and carried out a number of experiments with lenses, mirrors, refraction, and reflection.[8] He was also the first to reduce reflected and refracted light rays into vertical and horizontal components, which was a fundamental development in geometric optics.[43] He also discovered a result similar to Snell's law of sines, but did not quantify it and derive the law mathematically.[44] Ibn al-Haytham also gave the first clear description[20] and correct analysis[21] of the camera obscura, though the underlying principles of the camera oscura or pinhole camera were earlier known to Mozi and Aristotle.[20]

[edit] Scientific method

Rosanna Gorini notes that "according to the majority of the historians al-Haytham was the pioneer of the modern scientific method."[10][45] Ibn al-Haytham developed rigorous experimental methods of controlled scientific testing in order to verify theoretical hypotheses and substantiate inductive conjectures.[24] Ibn al-Haytham's scientific method was very similar to the modern scientific method and consisted of the following procedures:[30]

  1. Observation
  2. Statement of problem
  3. Formulation of hypothesis
  4. Testing of hypothesis using experimentation
  5. Analysis of experimental results
  6. Interpretation of data and formulation of conclusion
  7. Publication of findings

[edit] Alhazen's problem

His work on catoptrics in Book V of the Book of Optics contains the important problem known as Alhazen's problem. It comprises drawing lines from two points in the plane of a circle meeting at a point on the circumference and making equal angles with the normal at that point. This leads to an equation of the fourth degree. This eventually led Ibn al-Haytham to derive the earliest formula for the sum of fourth powers; and by using an early proof by mathematical induction, he developed a method that is readily generalizable to finding the formula for the sum of any integral powers. This was fundamental to the development of infinitesimal and integral calculus.[25] Ibn al-Haytham eventually solved the problem using conic sections and a geometric proof, though many after him attempted to find an algebraic solution to the problem,[1] until the end of the 20th century.[16]

[edit] Hockney-Falco thesis

Main article: Hockney-Falco thesis

At a scientific conference in February 2007, Charles M. Falco argued that Ibn al-Haytham's work on optics may have influenced the use of optical aids by Renaissance artists. Falco said that his and David Hockney's examples of Renaissance art "demonstrate a continuum in the use of optics by artists from circa 1430, arguably initiated as a result of Ibn al-Haytham's influence, until today."[46]

[edit] Other contributions

Chapters 15–16 of the Book of Optics dealt with astronomy. Ibn al-Haytham was 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.[47]

Ibn al-Haytham discussed the topics of medicine, ophthalmology and eye surgery in the anatomical and physiological portions of the Book of Optics and in his commentaries on Galenic works.[48] He also made several improvements to eye surgery and described the process of sight.[49]

In philosophy, Ibn al-Haytham is considered a pioneer of phenomenology. He articulated a relationship between the physical and observable world and that of intuition, psychology and mental functions. His theories regarding knowledge and perception, linking the domains of science and religion, led to a philosophy of existence based on the direct observation of reality from the observer's point of view.[50]

In Islamic psychology, Ibn al-Haytham is considered the founder of experimental psychology,[15] for his pioneering work on the psychology of visual perception and optical illusions.[16] In the Book of Optics, Ibn al-Haytham was the first scientist to argue that vision occurs in the brain, rather than the eyes. He pointed out that personal experience has an effect on what people see and how they see, and that vision and perception are subjective.[16]

[edit] Other works on physics

[edit] Optical treatises

Besides the Book of Optics, Ibn al-Haytham wrote a number of other treatises on optics. His Risala fi l-Daw’ (Treatise on Light) is a supplement to his Kitab al-Manazir (Book of Optics). The text contained further investigations on the properties of luminance and its radiant dispersion through various transparent and translucent media. He also carried out further observations, investigations and examinations on the anatomy of the eye, the camera obscura and pinhole camera, illusions in visual perception, the meteorology of the rainbow and the density of the atmosphere, various celestial phenomena (including the eclipse, twilight, and moonlight), refraction, catoptrics, dioptrics, spherical and parabolic mirrors, and magnifying lenses.[24]

In his treatise, Mizan al-Hikmah (Balance of Wisdom), Ibn al-Haytham discussed the density of the atmosphere and related it to altitude. He also studied atmospheric refraction. He discovered that the twilight only ceases or begins when the Sun is 19° below the horizon and attempted to measure the height of the atmosphere on that basis.[8]

[edit] Astrophysics

In astrophysics and the celestial mechanics field of physics, Ibn al-Haytham, in his Epitome of Astronomy, discovered that the heavenly bodies "were accountable to the laws of physics".[51]

Ibn al-Haytham's Mizan al-Hikmah (Balance of Wisdom) dealt with statics, astrophysics, and celestial mechanics. He discussed the theory of attraction between masses, and it seems that he was also aware of the magnitude of acceleration due to gravity at a distance.[24]

His Maqala fi'l-qarastun is a treatise on centers of gravity. Little is currently known about the work, except for what is known through the later works of al-Khazini in the 12th century. In this treatise, Ibn al-Haytham formulated the theory that the heaviness of bodies varies with their distance from the center of the Earth.[52]

[edit] Mechanics

In the dynamics and kinematics fields of mechanics, Ibn al-Haytham's Risala fi’l-makan (Treatise on Place) discussed theories on the motion of a body. He maintained that a body moves perpetually unless an external force stops it or changes its direction of motion.[24] This was a precursor to the law of inertia later stated by Galileo Galilei in the 16th century and now known as Newton's first law of motion.[22]

Ibn al-Haytham also discovered the concept of momentum, part of Newton's second law of motion, around the same time as his contemporary, Avicenna.[23]

[edit] Astronomical works

[edit] Doubts Concerning Ptolemy

In his Al-Shukūk ‛alā Batlamyūs, variously translated as Doubts Concerning Ptolemy or Aporias against Ptolemy, written between 1025 and 1028, Ibn al-Haytham criticized many of Ptolemy's works, including the Almagest, Planetary Hypotheses, and Optics, pointing out various contradictions he found in these works. He considered that some of the mathematical devices Ptolemy introduced into astronomy, especially the equant, failed to satisfy the physical requirement of uniform circular motion, and wrote a scathing critique of the physical reality of Ptolemy's astronomical system, noting the absurdity of relating actual physical motions to imaginary mathematical points, lines and circles:[53]

Ptolemy assumed an arrangement (hay'a) 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… [F]or a man to imagine a circle in the heavens, and to imagine the planet moving in it does not bring about the planet's motion.[54][55]

Ibn al-Haytham further criticized Ptolemy's model on other empirical, observational and experimental grounds,[56] such as Ptolemy's use of conjectural undemonstrated theories in order to "save appearances" of certain phenomena, which Ibn al-Haytham did not approve of due to his insistence on scientific demonstration. Unlike some later astronomers who criticized the Ptolemaic model on the grounds of being incompatible with Aristotelian natural philosophy, Ibn al-Haytham was mainly concerned with empirical observation and the internal contradictions in Ptolemy's works.[57]

In his Aporias against Ptolemy, Ibn al-Haytham commented on the difficulty of attaining scientific knowledge:

Truth is sought for itself [but] the truths, [he warns] are immersed in uncertainties [and the scientific authorities (such as Ptolemy, whom he greatly respected) are] not immune from error…[58]

He held that the criticism of existing theories — which dominated this book — holds a special place in the growth of scientific knowledge:

Therefore, the seeker after the truth is not one who studies the writings of the ancients and, following his natural disposition, puts his trust in them, but rather the one who suspects his faith in them and questions what he gathers from them, the one who submits to argument and demonstration, and not to the sayings of a human being whose nature is fraught with all kinds of imperfection and deficiency. Thus the duty of the man who investigates the writings of scientists, if learning the truth is his goal, is to make himself an enemy of all that he reads, and, applying his mind to the core and margins of its content, attack it from every side. He should also suspect himself as he performs his critical examination of it, so that he may avoid falling into either prejudice or leniency.[58]

[edit] On the Configuration of the World

In his On the Configuration of the World, despite his criticisms directed towards Ptolemy, Ibn al-Haytham continued to accept the physical reality of the geocentric model of the universe,[59] presenting a detailed description of the physical structure of the celestial spheres in his On the Configuration of the World:

The earth as a whole is a round sphere whose center is the center of the world. It is stationary in its [the world's] middle, fixed in it and not moving in any direction nor moving with any of the varieties of motion, but always at rest.[60]

While he attempted to discover the physical reality behind Ptolemy's mathematical model, he developed the concept of a single orb (falak) for each component of Ptolemy's planetary motions. This work was eventually translated into Hebrew and Latin in the 13th and 14th centuries and subsequently had an important influence during the European Middle Ages and Renaissance.[61][62]

[edit] The Model of the Motions

Ibn al-Haytham's The Model of the Motions of Each of the Seven Planets, written in 1038, was an important book on astronomy. The surviving manuscript of this work has only recently been discovered, with much of it still missing, hence the work has not yet been published in modern times. Following on from his Doubts on Ptolemy and The Resolution of Doubts, Ibn al-Haytham described the first non-Ptolemaic model 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.[63]

His reformed empirical model was the first to reject the equant[64] and eccentrics,[65] 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,[66] and the centres of motion were geometrical points without any physical significance, like Johannes Kepler's model centuries later.[67]

In the text, 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 the Earth.[68]

[edit] Refutation of astrology

Ibn al-Haytham distinguished astrology from astronomy, and he refuted the study of astrology, due to the methods used by astrologers being conjectural rather than empirical, and also due to the views of astrologers conflicting with orthodox Islam.[69]

[edit] Mathematical works

In mathematics, Ibn al-Haytham builds on the mathematical works of Euclid and Thabit ibn Qurra. He goes on to systemize conic sections and number theory, carries out some early work on analytic geometry, and works on "the beginnings of the link between algebra and geometry." This in turn had an influence on the development of René Descartes's geometric analysis and Isaac Newton's calculus.[29]

[edit] Geometry

In geometry, Ibn al-Haytham developed analytical geometry and established a link between algebra and geometry.[29] Ibn al-Haytham also discovered a formula for adding the first 100 natural numbers (which may later have been intuited by Carl Friedrich Gauss as a youth). Ibn al-Haytham used a geometric proof to prove the formula.[70]

Ibn al-Haytham made the first attempt at proving the Euclidean parallel postulate using a proof by contradiction,[71] where he introduced the concept of motion and transformation into geometry.[72] His proof was also the first to employ the Lambert quadrilateral and Playfair's axiom, both of which were not known in Europe until the 18th century.[1] Some have referred to the Lambert quadrilateral as the "Ibn al-Haytham–Lambert quadrilateral" as a result.[73] His theorems on quadrilaterals, including the Lambert quadrilateral, were the first theorems on elliptical geometry and hyperbolic geometry, and along with his alternative postulates, such as Playfair's axiom, his work marked the beginning of non-Euclidean geometry and had a considerable influence on its development among later Muslim geometers such as Omar Khayyám and Nasīr al-Dīn al-Tūsī and European geometers such as Witelo, Gersonides, Alfonso, John Wallis and Giovanni Girolamo Saccheri.[74]

In elementary geometry, Ibn al-Haytham attempted to solve the problem of squaring the circle using the area of lunes, but later gave up on the impossible task.[4] Ibn al-Haytham also tackled other problems in elementary (Euclidean) and advanced (Apollonian and Archimedean) geometry, some of which he was the first to solve.[58]

[edit] Number theory

His contributions to number theory includes his work on perfect numbers. In his Analysis and Synthesis, Ibn al-Haytham was the first to realize that every even perfect number is of the form 2n−1(2n − 1) where 2n − 1 is prime, but he was not able to prove this result successfully (Euler later proved it in the 18th century).[4]

Ibn al-Haytham solved problems involving congruences using what is now called Wilson's theorem. In his Opuscula, Ibn al-Haytham considers the solution of a system of congruences, and gives two general methods of solution. His first method, the canonical method, involved Wilson's theorem, while his second method involved a version of the Chinese remainder theorem.[4]

[edit] Other works

[edit] Engineering

In engineering, one account of his career as a civil engineer has him summoned to Egypt by the Fatimid Caliph al-Hakim bi-Amr Allah to regulate the flooding of the Nile River. He carried out a detailed scientific study of the annual inundation of the Nile River, and he drew plans for building a dam, at the site of the modern-day Aswan Dam. His field work, however, later made him aware of the impracticality of this scheme, and he soon feigned madness in order to avoid punishment from the Caliph.[75]

According to al-Khazini, Ibn al-Haytham also wrote a treatise providing a description on the construction of a water clock.[76]

[edit] Philosophy

In early Islamic philosophy, Ibn al-Haytham's Risala fi’l-makan (Treatise on Place) presents a critique of Aristotle's concept of place (topos). Aristotle's Physics stated that the place of something is the two-dimensional boundary of the containing body that is at rest and is in contact with what it contains. Ibn al-Haytham disagreed and demonstrated that place (al-makan) is the imagined three-dimensional void between the inner surfaces of the containing body. He showed that place was akin to space, foreshadowing René Descartes's concept of place in the Extensio in the 17th century.

Following on from his Treatise on Place, Ibn al-Haytham's Qawl fi al-Makan (Discourse on Place) was an important treatise which presents geometrical demonstrations for his geometrization of place, in opposition to Aristotle's philosophical concept of place, which Ibn al-Haytham rejected on mathematical grounds. Abd-el-latif, a supporter of Aristotle's philosophical view of place, later criticized the work in Fi al-Radd ‘ala Ibn al-Haytham fi al-makan (A refutation of Ibn al-Haytham’s place) for its geometrization of place.[77]

[edit] Theology

Ibn al-Haytham was a devout Muslim,[78] who is said to have been a follower of the orthodox Ash'ari school of Sunni Islamic theology,[79] and opposed to the views of the Mu'tazili school,[80] though he may have been a supporter of Mu'tazili theology[81] or Shia Islam[82] at some point in his life.

Ibn al-Haytham also wrote a work on Islamic theology, in which he discusses prophethood and develops a system of philosophical criteria to discern true prophethood from false claimants in his time.[83]

Ibn al-Haytham attributed his experimental scientific method and scientific skepticism to his Islamic faith. The Qur'an, for example, placed a strong emphasis on empiricism.[84][85][86] He also believed that human beings are inherently flawed and that only God is perfect. He reasoned that to discover the truth about nature, it is necessary to eliminate human opinion and error, and allow the universe to speak for itself.[30] He wrote in his Doubts Concerning Ptolemy:

Therefore, the seeker after the truth is not one who studies the writings of the ancients and, following his natural disposition, puts his trust in them, but rather the one who suspects his faith in them and questions what he gathers from them, the one who submits to argument and demonstration, and not to the sayings of a human being whose nature is fraught with all kinds of imperfection and deficiency. Thus the duty of the man who investigates the writings of scientists, if learning the truth is his goal, is to make himself an enemy of all that he reads, and, applying his mind to the core and margins of its content, attack it from every side. He should also suspect himself as he performs his critical examination of it, so that he may avoid falling into either prejudice or leniency.[58]

In The Winding Motion, Ibn al-Haytham further wrote that faith should only apply to prophets of Islam and not to any other authorities, in the following comparison between the Islamic prophetic tradition and the demonstrative sciences:

From the statements made by the noble Shaykh, it is clear that he believes in Ptolemy's words in everything he says, without relying on a demonstration or calling on a proof, but by pure imitation (taqlid); that is how experts in the prophetic tradition have faith in Prophets, may the blessing of God be upon them. But it is not the way that mathematicians have faith in specialists in the demonstrative sciences.[87]

Ibn al-Haytham described his search for truth and knowledge as a way of leading him closer to God:

I constantly sought knowledge and truth, and it became my belief that for gaining access to the effulgence and closeness to God, there is no better way than that of searching for truth and knowledge.[88]

[edit] See also

[edit] Notes

  1. ^ a b c (Smith 1992)
  2. ^ "Ibn al-Haytham", Columbia Encyclopedia (Sixth ed.), 2007, <http://www.encyclopedia.com/doc/1E1-IbnalHay.html>. Retrieved on 23 January 2008
    "Ibn al-Haytham", Columbia Encyclopedia (Sixth ed.), Columbia University Press, 2006, <http://education.yahoo.com/reference/encyclopedia/entry/IbnalHay>. Retrieved on 23 January 2008
  3. ^ Alhazen, Ibn al-Haytham (c. 965-1038). Retrieved on 2008-01-23.
  4. ^ a b c d e O'Connor, John J; Edmund F. Robertson "Abu Ali al-Hasan ibn al-Haytham". MacTutor History of Mathematics archive.  
  5. ^ (Hamarneh 1972):

    A great man and a universal genius, long neglected even by his own people.

  6. ^ (Bettany 1995):

    Ibn ai-Haytham provides us with the historical personage of a versatile universal genius.

  7. ^ a b Electromagnetic Theory and Light. Retrieved on 2008-01-23.
  8. ^ a b c d Dr. Mahmoud Al Deek. "Ibn Al-Haitham: Master of Optics, Mathematics, Physics and Medicine", Al Shindagah, November-December 2004.
  9. ^ (Hamarneh 1972, p. 119)
  10. ^ a b (Gorini 2003)
  11. ^ David Agar (2001). Arabic Studies in Physics and Astronomy During 800 - 1400 AD. University of Jyväskylä. Retrieved on 2008-01-23.
  12. ^ (Omar 1977)
  13. ^ Rüdiger Thiele (2005). "In Memoriam: Matthias Schramm", Arabic Sciences and Philosophy 15, p. 329–331. Cambridge University Press.
  14. ^ (Steffens 2006)
  15. ^ a b (Khaleefa 1999)
  16. ^ a b c d (Steffens 2006), Chapter 5
  17. ^ a b (Salih, Al-Amri & El Gomati 2005)
  18. ^ a b Sabra, A. I. & Hogendijk, J. P. (2003), The Enterprise of Science in Islam: New Perspectives, MIT Press, pp. 85-118, ISBN 0262194821
  19. ^ a b Hatfield, Gary (1996), "Was the Scientific Revolution Really a Revolution in Science?", in Ragep, F. J.; Ragep, Sally P. & Livesey, Steven John, Tradition, Transmission, Transformation: Proceedings of Two Conferences on Pre-modern Science held at the University of Oklahoma, Brill Publishers, p. 500, ISBN 9004091262
  20. ^ a b c David H. Kelley, Exploring Ancient Skies: An Encyclopedic Survey of Archaeoastronomy:

    "The first clear description of the device appears in the Book of Optics of Alhazen."

  21. ^ a b (Wade & Finger 2001):

    "The principles of the camera obscura first began to be correctly analysed in the eleventh century, when they were outlined by Ibn al-Haytham."

  22. ^ a b c (Salam 1984):

    Ibn-al-Haitham (Alhazen, 965–1039 CE) was one of the greatest physicists of all time. He made experimental contributions of the highest order in optics. He enunciated that a ray of light, in passing through a medium, takes the path which is the easier and 'quicker'. In this he was anticipating Fermat's Principle of Least Time by many centuries. He enunciated the law of inertia, later to become Newton's first law of motion. Part V of Roger Bacon's "Opus Majus" is practically an annotation to Ibn al Haitham's Optics.

  23. ^ a b Seyyed Hossein Nasr, "The achievements of Ibn Sina in the field of science and his contributions to its philosophy", Islam & Science, December 2003.
  24. ^ a b c d e (El-Bizri 2006)
  25. ^ a b (Katz 1995)
  26. ^ a b (Marshall 1950)
  27. ^ a b c Power, Richard (University of Illinois) (April 18, 1999), "Best Idea; Eyes Wide Open", New York Times, <http://online.physics.uiuc.edu/courses/phys199epp/fall06/Powers-NYTimes.pdf>. Retrieved on 23 January 2008
  28. ^ (Lindberg 1967)
  29. ^ a b c (Faruqi 2006, pp. 395–6):

    In seventeenth century Europe the problems formulated by Ibn al-Haytham (965–1041) became known as 'Alhazen's problem'. […] Al-Haytham’s contributions to geometry and number theory went well beyond the Archimedean tradition. Al-Haytham also worked on analytical geometry and the beginnings of the link between algebra and geometry. Subsequently, this work led in pure mathematics to the harmonious fusion of algebra and geometry that was epitomised by Descartes in geometric analysis and by Newton in the calculus. Al-Haytham was a scientist who made major contributions to the fields of mathematics, physics and astronomy during the latter half of the tenth century.

  30. ^ a b c (Steffens 2006) (cf. Steffens, Bradley, Who Was the First Scientist?, Ezine Articles)
  31. ^ (Rashed 2002, p. 773)
  32. ^ (Briffault 1928, p. 190–202):

    What we call science arose as a result of new methods of experiment, observation, and measurement, which were introduced into Europe by the Arabs. […] Science is the most momentous contribution of Arab civilization to the modern world, but its fruits were slow in ripening. Not until long after Moorish culture had sunk back into darkness did the giant to which it had given birth, rise in his might. It was not science only which brought Europe back to life. Other and manifold influences from the civilization of Islam communicated its first glow to European life. […] The debt of our science to that of the Arabs does not consist in startling discoveries or revolutionary theories; science owes a great deal more to Arab culture, it owes its existence…The ancient world was, as we saw, pre-scientific. The astronomy and mathematics of Greeks were a foreign importation never thoroughly acclimatized in Greek culture. The Greeks systematized, generalized and theorized, but the patient ways of investigations, the accumulation of positive knowledge, the minute methods of science, detailed and prolonged observation and experimental inquiry were altogether alien to the Greek temperament. […] What we call science arose in Europe as a result of new spirit of enquiry, of new methods of experiment, observation, measurement, of the development of mathematics, in a form unknown to the Greeks. That spirit and those methods were introduced into the European world by the Arabs.

  33. ^ George Sarton, Introduction to the History of Science, "The Time of Al-Biruni":

    [Ibn al-Haytham] was not only the greatest Muslim physicist, but by all means the greatest of mediaeval times.

    Ibn Haytham's writings reveal his fine development of the experimental faculty. His tables of corresponding angles of incidence and refraction of light passing from one medium to another show how closely he had approached discovering the law of constancy of ratio of sines, later attributed to Snell. He accounted correctly for twilight as due to atmospheric refraction, estimating the sun's depression to be 19 degrees below the horizon, at the commencement of the phenomenon in the mornings or at its termination in the evenings.

  34. ^ Dr. A. Zahoor and Dr. Z. Haq (1997). Quotations from Famous Historians of Science. Cyberistan. Retrieved on 2008-01-23.
  35. ^ (Elliott 1966), Chapter 1:

    Alhazen was one of the ablest students of optics of all times and published a seven-volume treatise on this subject which had great celebrity throughout the medieval period and strongly influenced Western thought, notably that of Roger Bacon and Kepler. This treatise discussed concave and convex mirrors in both cylindrical and spherical geometries, anticipated Fermat's law of least time, and considered refraction and the magnifying power of lenses. It contained a remarkably lucid description of the optical system of the eye, which study led Alhazen to the belief that light consists of rays which originate in the object seen, and not in the eye, a view contrary to that of Euclid and Ptolemy.

  36. ^ "Alhazen", in (Abbott 1983, p. 75):

    He was probably the greatest scientist of the Middle Ages and his work remained unsurpassed for nearly 600 years until the time of Johannes Kepler.

  37. ^ (Lindberg 1996, p. 11), passim
  38. ^ (Steffens 2006) (cf. Review of Ibn al-Haytham: First Scientist. Barnes & Noble. Retrieved on 2008-01-23.)
  39. ^ (Crombie 1971, p. 147, n. 2)
  40. ^ Alhazen (965-1040): Library of Congress Citations. Retrieved on 2008-01-23.
  41. ^ (Smith 2001)
  42. ^ (Lindberg 1976, pp. 60–7)
  43. ^ Albrecht Heeffer. Kepler’s near discovery of the sine law: A qualitative computational model. Ghent University, Belgium. Retrieved on 2008-01-23.
  44. ^ (Sabra 1981) (cf. Pavlos Mihas. Use of History in Developing ideas of refraction, lenses and rainbow. Demokritus University, Thrace, Greece. Retrieved on 2008-01-23.)
  45. ^ (Rashed 2002, p. 773)
  46. ^ (Falco 2007)
  47. ^ Edward Rosen (1985), "The Dissolution of the Solid Celestial Spheres", Journal of the History of Ideas 46 (1), p. 13–31 [19–20, 21].
  48. ^ (Steffens 2006) (cf. Review by Sulaiman Awan. Retrieved on 2008-01-23.)
  49. ^ Bashar Saad, Hassan Azaizeh, Omar Said (October 2005). "Tradition and Perspectives of Arab Herbal Medicine: A Review", Evidence-based Complementary and Alternative Medicine 2 (4), p. 475–479 [476], Oxford University Press
  50. ^ Dr Valérie Gonzalez, "Universality and Modernity", The Ismaili United Kingdom, December 2002, p. 50–53.
  51. ^ (Duhem 1969, p. 28)
  52. ^ Professor Mohammed Abattouy (2002). "The Arabic Science of weights: A Report on an Ongoing Research Project", The Bulletin of the Royal Institute for Inter-Faith Studies 4, p. 109–130.
  53. ^ (Langerman 1990, pp. 8–10)
  54. ^ (Sabra 1978b, p. 121, n. 13)
  55. ^ Stanford Encyclopedia of Philosophy (2004-2005). Retrieved on 2008-01-23.
  56. ^ A. I. Sabra (1998), "Configuring the Universe: Aporetic, Problem Solving, and Kinematic Modeling as Themes of Arabic Astronomy", Perspectives on Science 6 (3), p. 288–330 [300].
  57. ^ Shlomo Pines (1986), Studies in Arabic Versions of Greek Texts and in Mediaeval Science, p. 438–439. Brill Publishers, ISBN 9652236268.
  58. ^ a b c d (Sabra 2003)
  59. ^ Some writers, however, argue that Alhazen's critique constituted a form of heliocentricity (see (Qadir 1989, p. 5–6 & 10)).
  60. ^ (Langerman 1990), chap. 2, sect. 22, p. 61
  61. ^ (Langerman 1990, pp. 34–41)
  62. ^ (Gondhalekar 2001, p. 21)
  63. ^ (Rashed 2007)
  64. ^ (Rashed 2007, p. 20 & 53)
  65. ^ (Rashed 2007, pp. 33–4)
  66. ^ (Rashed 2007, pp. 20 & 32–33)
  67. ^ (Rashed 2007, pp. 51–2)
  68. ^ (Rashed 2007, pp. 35–6)
  69. ^ George Saliba (1994), A History of Arabic Astronomy: Planetary Theories During the Golden Age of Islam, p. 60, 67–69. New York University Press, ISBN 0814780237.
  70. ^ J. Rottman. A first course in Abstract Algebra, Chapter 1.
  71. ^ Michelle Eder (2000). Views of Euclid's Parallel Postulate in Ancient Greece and in Medieval Islam. Rutgers University. Retrieved on 2008-01-23.
  72. ^ Victor J. Katz (1998), History of Mathematics: An Introduction, p. 269, Addison-Wesley, ISBN 0321016181:

    In effect, this method characterized parallel lines as lines always equidisant from one another and also introduced the concept of motion into geometry.

  73. ^ Boris Abramovich Rozenfelʹd (1988), A History of Non-Euclidean Geometry: Evolution of the Concept of a Geometric Space, p. 65. Springer, ISBN 0387964584.
  74. ^ Boris A. Rosenfeld and Adolf P. Youschkevitch (1996), "Geometry", in Roshdi Rashed, ed., Encyclopedia of the History of Arabic Science, Vol. 2, p. 447-494 [470], Routledge, London and New York:

    Three scientists, Ibn al-Haytham, Khayyam and al-Tusi, had made the most considerable contribution to this branch of geometry whose importance came to be completely recognized only in the nineteenth century. In essence their propositions concerning the properties of quadrangles which they considered assuming that some of the angles of these figures were acute of obtuse, embodied the first few theorems of the hyperbolic and the elliptic geometries. Their other proposals showed that various geometric statements were equivalent to the Euclidean postulate V. It is extremely important that these scholars established the mutual connection between tthis postulate and the sum of the angles of a triangle and a quadrangle. By their works on the theory of parallel lines Arab mathematicians directly influenced the relevant investiagtions of their European couterparts. The first European attempt to prove the postulate on parallel lines - made by Witelo, the Polish scientists of the thirteenth century, while revising Ibn al-Haytham's Book of Optics (Kitab al-Manazir) - was undoubtedly prompted by Arabic sources. The proofs put forward in the fourteenth century by the Jewish scholar Gersonides, who lived in southern France, and by the above-mentioned Alfonso from Spain directly border on Ibn al-Haytham's demonstration. Above, we have demonstrated that Pseudo-Tusi's Exposition of Euclid had stimulated borth J. Wallis's and G. Saccheri's studies of the theory of parallel lines.

  75. ^ C. Plott (2000), Global History of Philosophy: The Period of Scholasticism, Pt. II, p. 459. ISBN 8120805518, Motilal Banarsidass Publ.
  76. ^ (Hassan 2007)
  77. ^ (El-Bizri 2007)
  78. ^ (Steffens 2006) (cf. Review of Ibn al-Haytham: First Scientist (December 1, 2006). Retrieved on 2008-01-23.)
  79. ^ Sardar, Ziauddin (1998), "Science in Islamic philosophy", Islamic Philosophy, Routledge Encyclopedia of Philosophy, <http://www.muslimphilosophy.com/ip/rep/H016.htm>. Retrieved on 3 February 2008
  80. ^ (Bettany 1995, p. 251)
  81. ^ (Hodgson 2006, p. 53)
  82. ^ (Sabra 1978a)[page # needed]
  83. ^ C. Plott (2000), Global History of Philosophy: The Period of Scholasticism, Pt. II, p. 464. ISBN 8120805518, Motilal Banarsidass Publ.
  84. ^ C. A. Qadir (1990), Philosophy and Science in the lslumic World, pp. 24-5, Routledge, London:

    "Muslims are inspired in the first instance by the numerous verses of the Quran which invite believers to observe nature and reflect over it."

    (cf. (Bettany 1995, p. 247))
  85. ^ “You shall not accept any information, unless you verify it for yourself. I have given you the hearing, the eyesight, and the brain, and you are responsible for using them.”[Qur'an 17:36]
  86. ^ “Behold! In the creation of the heavens and the earth; in the alternation of the night and the day; in the sailing of the ships through the ocean for the benefit of mankind; in the rain which Allah Sends down from the skies, and the life which He gives therewith to an earth that is dead; in the beasts of all kinds that He scatters through the earth; in the change of the winds, and the clouds which they trail like their slaves between the sky and the earth – (Here) indeed are Signs for a people that are wise.”[Qur'an 2:164]
  87. ^ (Rashed 2007, p. 11)
  88. ^ C. Plott (2000), Global History of Philosophy: The Period of Scholasticism, Pt. II, p. 465. ISBN 8120805518, Motilal Banarsidass Publ.

[edit] References

  • Abbott, David (1983), Biographical Dictionary of Scientists, vol. I
  • Bettany, Laurence (1995), "Ibn al-Haytham: an answer to multicultural science teaching?", Physics Education 30: 247–252
  • Briffault, Robert (1928), The Making of Humanity, G. Allen & Unwin Ltd.
  • Crombie, A. C. (1971), Robert Grosseteste and the Origins of Experimental Science, 1100 – 1700, Clarendon Press, Oxford University
  • Duhem, Pierre (1908, 1969), To Save the Phenomena: An Essay on the Idea of Physical theory from Plato to Galileo, University of Chicago Press, Chicago
  • El-Bizri, Nader (2006), "Ibn al-Haytham or Alhazen", in Meri, Josef W., Medieval Islamic Civilization: An Encyclopaedia, vol. II, Routledge, New York & London, pp. 343–345
  • El-Bizri, Nader (2007), "In Defence of the Sovereignty of Philosophy: Al-Baghdadi's Critique of Ibn al-Haytham's Geometrisation of Place", Arabic Sciences and Philosophy (Cambridge University Press) 17: 57–80
  • Elliott, Robert S. (1966), Electromagnetics, McGraw-Hill
  • Falco, Charles M. (12–15 February 2007), Ibn al-Haytham and the Origins of Modern Image Analysis, presented at a plenary session at the International Conference on Information Sciences, Signal Processing and its Applications, <http://www.optics.arizona.edu/ssd/FalcoPlenaryUAE.pdf>. Retrieved on 23 January 2008
  • Faruqi, Yasmeen M. (2006), "Contributions of Islamic scholars to the scientific enterprise", International Education Journal 7 (4): 391–396
  • Gondhalekar, Prabhakar M. (2001), The Grip of Gravity: The Quest to Understand the Laws of Motion and Gravitation, Cambridge University Press, ISBN 0521803160
  • Gorini, Rosanna (2003), "Al-Haytham the Man of Experience: First Steps in the Science of Vision", Journal of the International Society for the History of Islamic Medicine'' (Institute of Neurosciences, Laboratory of Psychobiology and Psychopharmacology, Rome, Italy)
  • Hamarneh, Sami (1972), "Review: Hakim Mohammed Said, Ibn al-Haitham", Isis 63 (1): 118–119
  • Hassan, Ahmad Y. (2007), Al-Jazari And the History of the Water Clock, <http://www.history-science-technology.com/Articles/articles%206.htm>. Retrieved on 23 January 2008
  • Hodgson, Peter Edward (2006), Theology And Modern Physics, Burlington, VT: Ashgate Publishing (published 2006-01-15), DDC: 201.653, LCC: BL265.P4 H63 2005, ISBN 9780754636229, OCLC 56876894
  • Katz, Victor J. (1995), "Ideas of Calculus in Islam and India", Mathematics Magazine 68 (3): 163–174
  • Khaleefa, Omar (1999), "Who Is the Founder of Psychophysics and Experimental Psychology?", American Journal of Islamic Social Sciences 16 (2)
  • Langerman, Y. Tzvi (1990), Ibn al Haytham's On the Configuration of the World
  • Lindberg, David C. (1967), "Alhazen's Theory of Vision and Its Reception in the West", Isis 58 (3): 321–341
  • Lindberg, David C. (1976), Theories of Vision from al-Kindi to Kepler, University of Chicago Press, Chicago, ISBN 0-226-48234-0
  • Lindberg, David C. (1996), Roger Bacon and the Origins of Perspectiva in the Middle Ages'', Clarendon Press
  • Marshall, O. S. (1950), "Alhazen and the Telescope", Astronomical Society of the Pacific Leaflets 6: 4
  • Omar, Saleh Beshara (1977), Ibn al-Haytham's Optics: A Study of the Origins of Experimental Science, Minneapolis: Bibliotheca Islamica, ISBN 0-88297-015-1
  • Qadir, Asghar (1989), Relativity: An Introduction to the Special Theory, World Scientific Publishing Co., Singapore
  • Rashed, Roshdi (2002), "A Polymath in the 10th century", Science 297 (5582): 773
  • Rashed, Roshdi (2007), "The Celestial Kinematics of Ibn al-Haytham", Arabic Sciences and Philosophy (Cambridge University Press) 17: 7–55
  • Sabra, A. I. (1971), "The astronomical origin of Ibn al-Haytham’s concept of experiment", Actes du XIIe congrès international d’histoire des sciences (Albert Blanchard, Paris) 3: 133–136. Reprinted in Sabra, A. I. (1994), Optics, Astronomy and Logic: Studies in Arabic Science and Philosophy, vol. 444, Collected Studies Series, Variorum, Aldershot, ISBN 0-86078-435-5.
  • Sabra, Abd al-Hamid (1978a), "Ibn al-Haytham and the Visual Ray Hypothesis", in Nasr, Seyyed Hossein, Ismaili Contributions to Islamic Culture, Boston: Shambhala Publications, pp. 178–216, ISBN 0-877-73731-2
  • Sabra, A. I. (1978b), "An Eleventh-Century Refutation of Ptolemy's Planetary Theory", Science and History: Studies in Honor of Edward Rosen, vol. XVI, Studia Copernicana, Ossolineum, Wrocław, pp. 117–131
  • Sabra, A. I. (1981), Theories of Light from Descartes to Newton, Cambridge University Press
  • Sabra, A. I. (October-December 2003), "Ibn al-Haytham: Brief life of an Arab mathematician", Harvard Magazine, <http://www.harvardmagazine.com/on-line/090351.html>. Retrieved on 23 January 2008
  • Salih, H.; Al-Amri, M. & El Gomati, M. (2005), "The Miracle of Light", A World of Science (UNESCO) 3 (3)
  • Salam, Abdus (1984), "Islam and Science" in Lai, C. H., ed. (1987), Ideals and Realities: Selected Essays of Abdus Salam (2nd ed.), World Scientific, Singapore, pp. 179–213
  • Smith, A. Mark (2001), Alhacen's theory of visual perception: a critical edition, with English translation and commentary, of the first three books of Alhacen's De aspectibus, the medieval Latin version of Ibn al-Haytham's Kitab al-Manazir, vol. 1, Philadelphia: American Philosophical Society, p. xxi, ISBN 9780871699145
  • Smith, John D. (1992), "The Remarkable Ibn al-Haytham", The Mathematical Gazette (Mathematical Association) 76 (475): 189–198
  • Steffens, Bradley (2006), Ibn al-Haytham: First Scientist, Morgan Reynolds Publishing, ISBN 1599350246
  • Wade, Nicholas J. & Finger, Stanley (2001), "The eye as an optical instrument: from camera obscura to Helmholtz's perspective", Perception 30 (10): 1157–1177

[edit] Further reading

[edit] Primary sources

  • Langermann, Y. Tzvi, ed. and trans. (1990), Ibn al-Haytham's On the Configuration of the World, Harvard Dissertations in the History of Science, New York: Garland, ISBN 0824000412
  • Sabra, A. I., ed. (1983), The Optics of Ibn al-Haytham, Books I-II-III: On Direct Vision. The Arabic text, edited and with Introduction, Arabic-Latin Glossaries and Concordance Tables, Kuwait: National Council for Culture, Arts and Letters
  • Sabra, A. I., ed. (2002), The Optics of Ibn al-Haytham. Edition of the Arabic Text of Books IV-V: On Reflection and Images Seen by Reflection. 2 vols., Kuwait: The National Council for Culture, Arts and Letters
  • Sabra, A. I., trans. (1989), The Optics of Ibn al-Haytham. Books I-II-III: On Direct Vision. English Translation and Commentary. 2 vols., Studies of the Warburg Institute, vol. 40, London: The Warburg Institute, University of London, ISBN 0-85481-072-2
  • Smith, A. Mark, ed. and trans. (2001), "Alhacen's Theory of Visual Perception: A Critical Edition, with English Translation and Commentary, of the First Three Books of Alhacen's De aspectibus, the Medieval Latin Version of Ibn al-Haytham's Kitāb al-Manāzir, 2 vols.", Transactions of the American Philosophical Society (Philadelphia) 91 (4–5), ISBN 0-87169-914-1
  • Smith, A. Mark, ed. and trans. (2006), "Alhacen on the Principles of Reflection: A Critical Edition, with English Translation and Commentary, of Books 4 and 5 of Alhacen's De Aspectibus, the Medieval Latin version of Ibn-al-Haytham's Kitāb al-Manāzir, 2 vols.", Transactions of the American Philosophical Society (Philadelphia) 96 (2–3), ISBN 0-87169-962-1

[edit] Secondary literature

[edit] External links


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Treatises The Compendious Book on Calculation by Completion and Balancing
Centers House of Wisdom  · Maragheh observatory
Influences Babylonian mathematics  · Egyptian mathematics  · Greek mathematics  · Indian mathematics
Influenced European mathematics  · Indian mathematics
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