Alhazen

Muslim scientist
Ibn al-Haytham.png
Name: Abū ‘Alī al-Ḥasan ibn al-Ḥasan ibn al-Haytham
Title: Ibn al-Haytham and Alhacen
Birth: 965 CE[1] (354 AH)[2]
Death: c. 1040 CE[1] (430 AH)[3]
Region: Basra in present-day Iraq, a part of Buyid Persia at that time[1]
Main interests: Anatomy, Astronomy, Engineering, Mathematics, Mechanics, Medicine, Optics, Ophthalmology, Philosophy, Physics, Psychology, Science
Notable ideas: Pioneer in optics, scientific method, experimental science, experimental physics, experimental psychology, visual perception, analytic geometry, non-Ptolemaic astronomy, celestial mechanics
Works: Book of Optics, Doubts Concerning Ptolemy, On the Configuration of the World, The Model of the Motions, Treatise on Light, Treatise on Place
Influences: Aristotle, Euclid, Ptolemy, Galen, Muhammad, Banū Mūsā, Thabit ibn Qurra, al-Kindi, Ibn Sahl, al-Qūhī
Influenced: Khayyam, al-Khazini, Averroes, Roger Bacon, Witelo, Pecham, Farisi, Theodoric, Gersonides, Alfonso, von Peuerbach, Taqi al-Din, Risner, Clavius, Kepler, John Wallis, Saccheri

Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham (Arabic: ابو علي، الحسن بن الحسن بن الهيثم, Persian: ابن هیثم, Latinized: Alhacen or (deprecated)[4] Alhazen) (965 in Basra - c. 1039 in Cairo) was a Persian[5][6] or Arab[7][8][9][10] scientist and polymath.[11] He made significant contributions to the principles of optics, as well as to physics, anatomy, astronomy, engineering, mathematics, medicine, ophthalmology, philosophy, psychology, visual perception, and to science in general with his early application of the scientific method. He is sometimes called al-Basri (Arabic: البصري), after his birthplace in the city of Basra.[12] He was also nicknamed Ptolemaeus Secundus ("Ptolemy the Second")[13] or simply "The Physicist"[14] in medieval Europe. Alhazen wrote insightful commentaries on works by Aristotle, Ptolemy, and the Greek mathematician Euclid.[15]

Born circa 965, in Basra, Iraq and part of Buyid Persia at that time,[1] he lived mainly in Cairo, Egypt, dying there at age 76.[13] Over-confident about practical application of his mathematical knowledge, he assumed that he could regulate the floods of the Nile.[16] After being ordered by Al-Hakim bi-Amr Allah, the sixth ruler of the Fatimid caliphate, to carry out this operation, he quickly perceived the impossibility of what he was attempting to do, and retired from engineering. Fearing for his life, he feigned madness[1][17] and was placed under house arrest, during and after which he devoted himself to his scientific work until his death.[13]

Contents

Overview

Biography

Head of a bearded man with bushy eyebrows, wearing a turban.
Alhazen, the great Islamic polymath.

Alhazen was born in Basra, in the Iraq province of the Buyid Persian Empire.[1] He probably died in Cairo, Egypt. During the Islamic Golden Age, Basra was a "key beginning of learning",[18] and he was educated there and in Baghdad, the capital of the Abbasid Caliphate, and the focus of the "high point of Islamic civilization".[18] During his time in Buyid Iran, he worked as a civil servant and read many theological and scientific books.[12][19]

One account of his career has him called to Egypt by Al-Hakim bi-Amr Allah, ruler of the Fatimid Caliphate, to regulate the flooding of the Nile, a task requiring an early attempt at building a dam at the present site of the Aswan Dam.[20] After his field work made him aware of the impracticality of this scheme,[13] and fearing the caliph's anger, he feigned madness. He was kept under house arrest from 1011 until al-Hakim's death in 1021.[21] During this time, he wrote his influential Book of Optics.

Although there are tall tales that Ibn al-Haitham fled to Syria, ventured into Baghdad later in his life, or was even in Basra when he pretended to be insane, it is certain that he was in Egypt by 1038 at the latest.[12] During his time in Cairo, he became associated with Al-Azhar University, as well the city's "House of Wisdom",[22] known as Dar Al-Hekma (House of Knowledge), which was a library "first in importance" to Baghdad's House of Wisdom.[12] After his house arrest ended, he wrote scores of other treatises on physics, astronomy and mathematics. He later traveled to Islamic Spain. During this period, he had ample time for his scientific pursuits, which included optics, mathematics, physics, medicine, and the development of scientific methods; he left several outstanding books on these subjects.

Among his students we know only two of them, Sorkhab (Sohrab), his Persian student who was one of the greatest people of Iran's Semnan and was his student for over 3 years, and Abu al-Wafa Mubashir ibn Fatek a famous Egyptian scientist who learned mathematics from him.[19]

Legacy

Front page of a Latin edition of Alhazen's Thesaurus opticus, showing how Archimedes set on fire the Roman ships before Syracuse with the help of parabolic mirrors.

Ibn al-Haythem made significant improvements in optics, physical science, and the scientific method which influenced the development of science for over five hundred years after his death. 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.[23] The scientific method is considered to be so fundamental to modern science that some—especially philosophers of science and practising scientists—consider earlier inquiries into nature to be pre-scientific.

Richard Powers nominated Ibn al-Haytham's scientific method and scientific skepticism as the most influential idea of the second millennium.[24] 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."[25] Robert S. Elliot considers Ibn al-Haytham to be "one of the ablest students of optics of all times."[26] Professor Jim Al-Khalili also considers him the "world's first true scientist".[27] 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."[28] At a scientific conference in February 2007 as a part of the Hockney-Falco thesis, 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."[29] The Latin translation of his main work, Kitab al-Manazir (Book of Optics), exerted a great influence on Western science: for example, on the work of Roger Bacon, who cites him by name,[30] and on Johannes Kepler. It brought about a great progress in experimental methods. His research in catoptrics (the study of optical systems using mirrors) centred on spherical and parabolic mirrors and spherical aberration. He made the 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 problem known as "Alhazen's problem".[23] Meanwhile in the Islamic world, Ibn al-Haytham's work influenced Averroes' writings on optics,[31] and his legacy was further advanced through the 'reforming' of his Optics by Persian scientist Kamal al-Din al-Farisi (d. ca. 1320) in the latter's Kitab Tanqih al-Manazir (The Revision of [Ibn al-Haytham's] Optics).[32] The correct explanations of the rainbow phenomenon given by al-Fārisī and Theodoric of Freiberg in the 14th century depended on Ibn al-Haytham's Book of Optics.[33] The work of Ibn al-Haytham and al-Fārisī was also further advanced in the Ottoman Empire by polymath Taqi al-Din in his Book of the Light of the Pupil of Vision and the Light of the Truth of the Sights (1574).[34] He wrote as many as 200 books, although only 55 have survived, and many of those have not yet been translated from Arabic. Even some of his treatises on optics survived only through Latin translation. During the Middle Ages his books on cosmology were translated into Latin, Hebrew and other languages. The crater Alhazen on the Moon is named in his honour[35], as was the asteroid "59239 Alhazen".[36] In honour of Ibn al-Haytham, the Aga Khan University (Pakistan) named its Ophthalmology endowed chair as "The Ibn-e-Haitham Associate Professor and Chief of Ophthalmology".[37]

Ibn al-Haytham is featured on the obverse of the Iraqi 10,000 dinars banknote issued in 2003,[38] and on 10 dinar notes from 1982. A research facility that UN weapons inspectors suspected of conducting chemical and biological weapons research in Saddam Hussein's Iraq was also named after him.[38][39]

Book of Optics

Ibn al-Haytham's most famous work is his seven volume Arabic treatise on optics, Kitab al-Manazir (Book of Optics), written from 1011 to 1021. It has been ranked alongside Isaac Newton's Philosophiae Naturalis Principia Mathematica as one of the most influential books in physics[40] for introducing an early scientific method, and for initiating a revolution in optics[41] and visual perception.[42]

Optics was translated into Latin by an unknown scholar at the end of the 12th century or the beginning of the 13th century.[43] 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.[44] 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.[45] This work enjoyed a great reputation during the Middle Ages. Works by Ibn al-Haytham on geometric 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.

Theory of Vision

Photo of a symphony orchestra under stage lighting, showing lines of light fanning out.
Ibn al-Haytham proved that light travels in straight lines using the scientific method in his Book of Optics (1021).

Two major theories on vision prevailed in classical antiquity. 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 that the process of vision occurs neither by rays emitted from the eye, nor through physical forms entering it. He reasoned that a ray could not proceed from the eyes and reach the distant stars the instant after we open our eyes. He also appealed to common observations such as the eye being dazzled or even injured if we look at a very bright light. 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.[46] His unification of geometrical optics with philosophical physics forms the basis of modern physical optics.[47]

Ibn al-Haytham proved that rays of light travel in straight lines, and carried out various experiments with lenses, mirrors, refraction, and reflection.[23] 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.[48] He proposed a causal model for the refraction of light that could have been extended to yield a result similar to Snell's law of sines, however Alhazen did not develop his model sufficiently to attain that result.[49]

Ibn al-Haytham also gave the first clear description[50] and correct analysis[51] of the camera obscura and pinhole camera. While Aristotle, Theon of Alexandria, Al-Kindi (Alkindus) and Chinese philosopher Mozi had earlier described the effects of a single light passing through a pinhole, none of them suggested that what is being projected onto the screen is an image of everything on the other side of the aperture. Ibn al-Haytham was the first to demonstrate this with his lamp experiment where several different light sources are arranged across a large area. He was thus the first to successfully project an entire image from outdoors onto a screen indoors with the camera obscura.

In addition to physical optics, The Book of Optics also gave rise to the field of "physiological optics".[52] Ibn al-Haytham discussed the topics of medicine, ophthalmology, anatomy and physiology, which included commentaries on Galenic works. He described the process of sight,[53] the structure of the eye, image formation in the eye, and the visual system. He also described what became known as Hering's law of equal innervation, vertical horopters, and binocular disparity,[54] and improved on the theories of binocular vision, motion perception and horopters previously discussed by Aristotle, Euclid and Ptolemy.[55][56]

His most original anatomical contribution was his description of the functional anatomy of the eye as an optical system,[57] or optical instrument. His experiments with the camera obscura provided sufficient empirical grounds for him to develop his theory of corresponding point projection of light from the surface of an object to form an image on a screen. It was his comparison between the eye and the camera obscura which brought about his synthesis of anatomy and optics, which forms the basis of physiological optics. As he conceptualized the essential principles of pinhole projection from his experiments with the pinhole camera, he considered image inversion to also occur in the eye,[52] and viewed the pupil as being similar to an aperture.[58] Regarding the process of image formation, he incorrectly agreed with Avicenna that the lens was the receptive organ of sight, but correctly hinted at the retina being involved in the process.[55]

Scientific method

Frontispiece of book showing two persons in robes, one holding a geometrical diagram, the other holding a telescope.
Hevelius's Selenographia, showing Alhasen [sic] representing reason, and Galileo representing the senses.

Neuroscientist Rosanna Gorini notes that "according to the majority of the historians al-Haytham was the pioneer of the modern scientific method."[35][59] Ibn al-Haytham developed rigorous experimental methods of controlled scientific testing to verify theoretical hypotheses and substantiate inductive conjectures.[60] Ibn al-Haytham's scientific method was very similar to the modern scientific method and consisted of the following procedures:

  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

An aspect associated with Ibn al-Haytham's optical research is related to systemic and methodological reliance on experimentation (i'tibar) and controlled testing in his scientific inquiries. Moreover, his experimental directives rested on combining classical physics ('ilm tabi'i) with mathematics (ta'alim; geometry in particular) in terms of devising the rudiments of what may be designated as a hypothetico-deductive procedure in scientific research. This mathematical-physical approach to experimental science supported most of his propositions in Kitab al-Manazir (The Optics; De aspectibus or Perspectivae) and grounded his theories of vision, light and colour, as well as his research in catoptrics and dioptrics (the study of the refraction of light). His legacy was further advanced through the 'reforming' of his Optics by Kamal al-Din al-Farisi (d. ca. 1320) in the latter's Kitab Tanqih al-Manazir (The Revision of [Ibn al-Haytham's] Optics).[32]

The concept of Occam's razor is also present in the Book of Optics. For example, after demonstrating that light is generated by luminous objects and emitted or reflected into the eyes, he states that therefore "the extramission of [visual] rays is superfluous and useless."[61]

Alhazen's problem

His work on catoptrics in Book V of the Book of Optics contains a discussion of what is now known as Alhazen's problem, first formulated by Ptolemy in 150 AD. 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 is equivalent to finding the point on the edge of a circular billiard table at which a cue ball at a given point must be aimed in order to carom off the edge of the table and hit another ball at a second given point. Thus, its main application in optics is to solve the problem, "Given a light source and a spherical mirror, find the point on the mirror where the light will be reflected to the eye of an observer." This leads to an equation of the fourth degree.[12][62] This eventually led Ibn al-Haytham to derive the earliest formula for the sum of fourth powers; by using an early proof by mathematical induction, he developed a method that can be readily generalized to find the formula for the sum of any integral powers. He applied his result of sums on integral powers to find the volume of a paraboloid through integration. He was thus able to find the integrals for polynomials up to the fourth degree, and came close to finding a general formula for the integrals of any polynomials. This was fundamental to the development of infinitesimal and integral calculus.[63] 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,[64] which was finally found in 1997 by the Oxford mathematician Peter M. Neumann.[65]

Other contributions

The Book of Optics describes several early experimental observations that Ibn al-Haytham made in mechanics and how he used his results to explain certain optical phenomena using mechanical analogies. He conducted experiments with projectiles, and concluded that "it was only the impact of perpendicular projectiles on surfaces which was forceful enough to enable them to penetrate whereas the oblique ones were deflected. For example, to explain refraction from a rare to a dense medium, he used the mechanical analogy of an iron ball thrown at a thin slate covering a wide hole in a metal sheet. A perpendicular throw would break the slate and pass through, whereas an oblique one with equal force and from an equal distance would not." He used this result to explain explained how intense direct light hurts the eye: "Applying mechanical analogies to the effect of light rays on the eye, lbn al-Haytham associated 'strong' lights with perpendicular rays and 'weak' lights with oblique ones. The obvious answer to the problem of multiple rays and the eye was in the choice of the perpendicular ray since there could only be one such ray from each point on the surface of the object which could penetrate the eye."[66]

Chapters 15–16 of the Book of Optics covered astronomy. Ibn al-Haytham was the first to discover that the celestial spheres do not consist of solid matter. 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.[67]

Sudanese psychologist Omar Khaleefa has argued that Ibn al-Haytham should be considered be the "founder of experimental psychology", for his pioneering work on the psychology of visual perception and optical illusions.[68] 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.[69] Khaleefa has also argued that Ibn al-Haytham should also be considered the "founder of psychophysics", a subdiscipline and precursor to modern psychology.[68] Although Ibn al-Haytham made many subjective reports regarding vision, there is no evidence that he used quantitative psychophysical techniques and the claim has been rebuffed.[70]

He came up with a theory to explain the Moon illusion, which played an important role in the scientific tradition of medieval Europe. It was an attempt to the solve the problem of the Moon appearing larger near the horizon than it does while higher up in the sky, a debate that is unresolved to this day. Arguing against Ptolemy's refraction theory, he redefined the problem in terms of perceived, rather than real, enlargement. He said that judging the distance of an object depends on there being an uninterrupted sequence of intervening bodies between the object and the observer. With the Moon however, there are no intervening objects. Therefore, since the size of an object depends on its observed distance, which is in this case inaccurate, the Moon appears larger on the horizon. Through works by Roger Bacon, John Pecham and Witelo based on Ibn al-Haytham's explanation, the Moon illusion gradually came to be accepted as a psychological phenomenon, with Ptolemy's theory being rejected in the 17th century.[71]

Some have suggested that Ibn al-Haythams views on pain and sensation may have been influenced by Buddhist philosophy. He writes that every sensation is a form of 'suffering' and that what people call pain is only an exaggerated perception; that there is no qualitative difference but only a quantitative difference between pain and ordinary sensation.[72]

Other works on physics

Optical treatises

Besides the Book of Optics, Ibn al-Haytham wrote several 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 examinations into anatomy of the eye and illusions in visual perception. He built the first camera obscura and pinhole camera[51], and investigated the meteorology of the rainbow and the density of the atmosphere. Various celestial phenomena (including the eclipse, twilight, and moonlight) were also examined by him. He also made investigations into refraction, catoptrics, dioptrics, spherical mirrors, and magnifying lenses.[60]

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.[23]

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".[73] Ibn al-Haytham's Mizan al-Hikmah (Balance of Wisdom) covered 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.[60] His Maqala fi'l-qarastun is a treatise on centres of gravity. Little is 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 centre of the Earth.[74]

Another treatise, Maqala fi daw al-qamar (On the Light of the Moon), which he wrote some time before his famous Book of Optics, was the first successful attempt 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." To prove that "light is emitted from every point of the Moon's illuminated surface", he built an "ingenious experimental device."[75] According to Matthias Schramm, 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.[75]

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.[60] This was similar to the concept of inertia, but was largely a hypothesis that was not verified by experimentation. The key breakthrough in classical mechanics, the introduction of frictional force, was eventually made centuries later by Galileo Galilei, and later formulated as Newton's first law of motion.

Also in his Treatise on Place, Ibn al-Haytham disagreed with Aristotle's view that nature abhors a void, and he thus used geometry to demonstrate that place (al-makan) is the imagined three-dimensional void between the inner surfaces of a containing body.[76]

Ibn al-Haytham also discovered the concept of momentum (now part of Newton's second law of motion) around the same time as his contemporary, Avicenna (Ibn Sina).[77]

Astronomical works

Doubts Concerning Ptolemy

In his Al-Shukūk ‛alā Batlamyūs, variously translated as Doubts Concerning Ptolemy or Aporias against Ptolemy, published at some time 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:[78]

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.[79][80]

Ibn al-Haytham further criticized Ptolemy's model on other empirical, observational and experimental grounds,[81] 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.[82]

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...[16]

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.[16]

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,[83] 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.[84]

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 influence on astronomers such as Georg von Peuerbach[1] during the European Middle Ages and Renaissance.[85][86]

Model of the Motions of Each of the Seven Planets

Ibn al-Haytham's The Model of the Motions of Each of the Seven Planets, written in 1038, was a 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.[87]

His reformed empirical model was the first to reject the equant[88] and eccentrics,[89] separate natural philosophy from astronomy, free celestial kinematics from cosmology, and reduce physical entities to geometric entities. The model also propounded the Earth's rotation about its axis,[90] and the centres of motion were geometric points without any physical significance, like Johannes Kepler's model centuries later.[91]

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.[92]

Other astronomical works

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 that of orthodox Islam.[93]

Ibn al-Haytham also wrote a treatise entitled On the Milky Way,[94] in which he solved problems regarding the Milky Way galaxy and parallax.[87] In antiquity, 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."[95] Ibn al-Haytham refuted this and "determined that because the Milky Way had no parallax, it was very remote from the earth and did not belong to the atmosphere."[96] He wrote that if the Milky Way was located around the Earth's atmosphere, "one must find a difference in position relative to the fixed stars." He described two methods to determine the Milky Way's parallax: "either when one observes the Milky Way on two different occasions from the same spot of the earth; or when one looks at it simultaneously from two distant places from the surface of the earth." He made the first attempt at observing and measuring the Milky Way's parallax, and determined that since the Milky Way had no parallax, then it does not belong to the atmosphere.[97]

In 1858, Muhammad Wali ibn Muhammad Ja'far, in his Shigarf-nama, claimed that Ibn al-Haytham wrote a treatise Maratib al-sama in which he conceived of a planetary model similar to the Tychonic system where the planets orbit the Sun which in turn orbits the Earth. However, the "verification of this claim seems to be impossible", since the treatise is not listed among the known bibliography of Ibn al-Haytham.[98]

Mathematical works

In mathematics, Ibn al-Haytham built on the mathematical works of Euclid and Thabit ibn Qurra. He systemized conic sections and number theory, carried out some early work on analytic geometry, and worked 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.[99]

Geometry

In geometry, Ibn al-Haytham developed analytical geometry and established a link between algebra and geometry.[99] Ibn al-Haytham also discovered a formula for adding the first 100 natural numbers. Ibn al-Haytham used a geometric proof to prove the formula.[100]

Ibn al-Haytham made the first attempt at proving the Euclidean parallel postulate, the fifth postulate in Euclid's Elements, using a proof by contradiction,[101] where he introduced the concept of motion and transformation into geometry.[102] He formulated the Lambert quadrilateral, which Boris Abramovich Rozenfeld names the "Ibn al-Haytham–Lambert quadrilateral",[103] and his attempted proof also shows similarities to Playfair's axiom.[64] His theorems on quadrilaterals, including the Lambert quadrilateral, were the first theorems on elliptical geometry and hyperbolic geometry. These theorems, along with his alternative postulates, such as Playfair's axiom, can be seen as marking the beginning of non-Euclidean geometry. His work had a considerable influence on its development among the later Persian geometers Omar Khayyám and Nasīr al-Dīn al-Tūsī, and the European geometers Witelo, Gersonides, Alfonso, John Wallis, Giovanni Girolamo Saccheri[104] and Christopher Clavius.[105]

In elementary geometry, Ibn al-Haytham attempted to solve the problem of squaring the circle using the area of lunes (crescent shapes), but later gave up on the impossible task.[12] 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.[16]

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).[12]

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.[12]

Other works

Influence of Melodies on the Souls of Animals

In psychology and musicology, Ibn al-Haytham's Treatise on the Influence of Melodies on the Souls of Animals was the earliest treatise dealing with the effects of music on animals. In the treatise, he demonstrates how a camel's pace could be hastened or retarded with the use of music, and shows other examples of how music can affect animal behaviour and animal psychology, experimenting with horses, birds and reptiles. Through to the 19th century, a majority of scholars in the Western world continued to believe that music was a distinctly human phenomenon, but experiments since then have vindicated Ibn al-Haytham's view that music does indeed have an effect on animals.[106]

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 so he could avoid punishment from the Caliph.[107]

According to Al-Khazini, Ibn al-Haytham also wrote a treatise providing a description on the construction of a water clock.[108]

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 a treatise which presents geometric 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.[76]

Ibn al-Haytham also discussed space perception and its epistemological implications in his Book of Optics. His experimental proof of the intromission model of vision led to changes in the way the visual perception of space was understood, contrary to the previous emission theory of vision supported by Euclid and Ptolemy. In "tying the visual perception of space to prior bodily experience, Alhacen unequivocally rejected the intuitiveness of spatial perception and, therefore, the autonomy of vision. Without tangible notions of distance and size for correlation, sight can tell us next to nothing about such things."[109]

Theology

Ibn al-Haytham was a devout Muslim, though it is uncertain which branch of Islam he followed. He may have been either a follower of the orthodox Ash'ari school of Sunni Islamic theology according to Ziauddin Sardar[110] and Lawrence Bettany[111] (and opposed to the views of the Mu'tazili school),[111] a follower of the Mu'tazili school of Islamic theology according to Peter Edward Hodgson,[112] or a follower of Shia Islam possibly according to A. I. Sabra.[113]

Ibn al-Haytham wrote a work on Islamic theology, in which he discussed prophethood and developed a system of philosophical criteria to discern its false claimants in his time.[114] He also wrote a treatise entitled Finding the Direction of Qibla by Calculation, in which he discussed finding the Qibla, where Salah prayers are directed towards, mathematically.[94]

Ibn al-Haytham attributed his experimental scientific method and scientific skepticism to his Islamic faith. The Islamic holy book, the Qur'an, for example, places a strong emphasis on empiricism.[115] 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. He wrote in his Doubts Concerning Ptolemy:

Truth is sought for its own sake ... Finding the truth is difficult, and the road to it is rough. For the truths are plunged in obscurity. ... God, however, has not preserved the scientist from error and has not safeguarded science from shortcomings and faults. If this had been the case, scientists would not have disagreed upon any point of science...[116]
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.[16]

In The Winding Motion, Ibn al-Haytham further wrote that faith (or taqlid or "imitation") applied to prophets of Islam especially with respect to worship (ibadah), but should not be applied to scientists (natural philosophers) investigating the material world and mathematics (the fallacy of argumentum ad verecundiam). For example, in the following comparison between the Islamic prophetic tradition and the demonstrative sciences he writes:

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.[117]

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.[118]

Works

Ibn al-Haytham was a pioneer in many areas of science, making significant contributions in varying disciplines. His optical writings influenced many Western intellectuals such as Roger Bacon, John Pecham, Witelo, Johannes Kepler.[119] 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.[99]

According to medieval biographers, Ibn al-Haytham wrote more than 200 works on a wide range of subjects, 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 subjects.[59] Not all his surviving works have yet been studied, but some of the ones that have are given below.[94][120]

See also

Notes

  1. ↑ 1.0 1.1 1.2 1.3 1.4 1.5 1.6 (Lorch 2008)
  2. ↑ Charles M. Falco (November 27–29, 2007), Ibn al-Haytham and the Origins of Computerized Image Analysis, International Conference on Computer Engineering & Systems (ICCES), http://www.optics.arizona.edu/SSD/art-optics/papers/IEEECairo.pdf, retrieved 2010-01-30 
  3. ↑ Franz Rosenthal (1960-1961), "Al-Mubashshir ibn Fâtik. Prolegomena to an Abortive Edition", Oriens (Brill Publishers) 13: 132–158 [136–7], http://www.jstor.org/stable/1580309, retrieved 2010-01-30 
  4. ↑ Lindberg, 1996.
  5. ↑ (Child, Shuter & Taylor 1992, p. 70)
    (Dessel, Nehrich & Voran 1973, p. 164)
    (Samuelson Crookes, p. 497)
    Understanding History by John Child, Paul Shuter, David Taylor - Page 70.
  6. ↑ Science and Human Destiny by Norman F. Dessel, Richard B. Nehrich, Glenn I. Voran - Page 164.
    The Journal of Science, and Annals of Astronomy, Biology, Geology by James Samuelson, William Crookes - Page 497.
  7. ↑ (Smith 1992)
    (Grant 2008)
    (Vernet 2008)
    Paul Lagasse (2007), "Ibn al-Haytham", Columbia Encyclopedia (Sixth ed.), Columbia, ISBN 0-7876-5075-7, http://www.encyclopedia.com/doc/1E1-IbnalHay.html, retrieved 2008-01-23 
  8. ↑ [1]
    (Dessel, Nehrich & Voran 1973, p. 164)
    (Samuelson Crookes, p. 497)
  9. ↑ (Child, Shuter & Taylor 1992, p. 70)
    (Dessel, Nehrich & Voran 1973, p. 164)
    (Samuelson Crookes, p. 497)
    Understanding History by John Child, Paul Shuter, David Taylor - Page 70.
  10. ↑ Science and Human Destiny by Norman F. Dessel, Richard B. Nehrich, Glenn I. Voran - Page 164.
    The Journal of Science, and Annals of Astronomy, Biology, Geology by James Samuelson, William Crookes - Page 497.
  11. ↑ Review of Ibn al-Haytham: First Scientist, Kirkus Reviews, December 1, 2006:
    a devout, brilliant polymath
    (Hamarneh 1972):
    A great man and a universal genius, long neglected even by his own people.
    (Bettany 1995):
    Ibn ai-Haytham provides us with the historical personage of a versatile universal genius.
  12. ↑ 12.0 12.1 12.2 12.3 12.4 12.5 12.6 12.7 (O'Connor & Robertson 1999)
  13. ↑ 13.0 13.1 13.2 13.3 (Corbin 1993, p. 149)
  14. ↑ (Lindberg 1967, p. 331)
  15. ↑ "The rainbow bridge: rainbows in art, myth, and science". Raymond L. Lee, Alistair B. Fraser (2001). Penn State Press. p.142. ISBN 0271019778
  16. ↑ 16.0 16.1 16.2 16.3 16.4 (Sabra 2003)
  17. ↑ (Grant 2008)
  18. ↑ 18.0 18.1 (Whitaker 2004)
  19. ↑ 19.0 19.1 Sajjadi, Sadegh, "Alhazen", Great Islamic Encyclopedia, Volume 1, Article No. 1917;
  20. ↑ (Rashed 2002b)
  21. ↑ the Great Islamic Encyclopedia
  22. ↑ (Van Sertima 1992, p. 382)
  23. ↑ 23.0 23.1 23.2 23.3 (Dr. Al Deek 2004)
  24. ↑ (Powers 1999)
  25. ↑ (Sarton 1927), "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.
    (cf. (Dr. Zahoor & Dr. Haq 1997))
  26. ↑ (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.
  27. ↑ Al-Khalili, Jim (January 2008), "The 'first true scientist'", BBC, http://news.bbc.co.uk/2/hi/science/nature/7810846.stm, retrieved 2010-01-05 
  28. ↑ "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.
  29. ↑ (Falco 2007)
  30. ↑ (Lindberg 1996, p. 11), passim
  31. ↑ (Topdemir 2007a, p. 77)
  32. ↑ 32.0 32.1 (El-Bizri 2005a)
    (El-Bizri 2005b)
  33. ↑ (Topdemir 2007a, p. 83)
  34. ↑ (Topdemir 1999) (cf. (Topdemir 2008))
  35. ↑ 35.0 35.1 (Gorini 2003)
  36. ↑ 59239 Alhazen (1999 CR2), NASA, 2006-03-22, http://ssd.jpl.nasa.gov/sbdb.cgi?sstr=59239+Alhazen, retrieved 2008-09-20 
  37. ↑ www.aku.edu/res-office/pdfs/AKU_Research_Publications_1995-1998.pdf, www.aku.edu/Admissions/pdfs/AKU_Prospectus_2008.pdf
  38. ↑ 38.0 38.1 (Murphy 2003)
  39. ↑ (Burns 1999)
  40. ↑ (Salih, Al-Amri & El Gomati 2005)
  41. ↑ (Sabra & Hogendijk 2003, pp. 85–118)
  42. ↑ (Hatfield 1996, p. 500)
  43. ↑ (Crombie 1971, p. 147, n. 2)
  44. ↑ Alhazen (965-1040): Library of Congress Citations, Malaspina Great Books, http://www.mala.bc.ca/~mcneil/cit/citlcalhazen1.htm, retrieved 2008-01-23 
  45. ↑ (Smith 2001, p. xxi)
  46. ↑ (Lindberg 1976, pp. 60–7)
  47. ↑ (Toomer 1964)
  48. ↑ (Heeffer 2003)
  49. ↑ (Sabra 1981, pp. 96-7) (cf. (Mihas 2005, p. 5))
  50. ↑ (Kelley, Milone & Aveni 2005):
    "The first clear description of the device appears in the Book of Optics of Alhazen."
  51. ↑ 51.0 51.1 (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."
  52. ↑ 52.0 52.1 Gul A. Russell, "Emergence of Physiological Optics", p. 689, in (Morelon & Rashed 1996)
  53. ↑ (Saad, Azaizeh & Said 2005, p. 476)
  54. ↑ (Howard 1996)
  55. ↑ 55.0 55.1 (Wade 1998)
  56. ↑ (Howard & Wade 1996)
  57. ↑ Gul A. Russell, "Emergence of Physiological Optics", p. 691, in (Morelon & Rashed 1996)
  58. ↑ Gul A. Russell, "Emergence of Physiological Optics", p. 695–8, in (Morelon & Rashed 1996)
  59. ↑ 59.0 59.1 (Rashed 2002a, p. 773)
  60. ↑ 60.0 60.1 60.2 60.3 (El-Bizri 2006)
  61. ↑ (Smith 2001, pp. 372 & 408)
  62. ↑ (Weisstein)
  63. ↑ (Katz 1995, pp. 165–9 & 173-4)
  64. ↑ 64.0 64.1 (Smith 1992)
  65. ↑ (Highfield 1997)
  66. ↑ Gul A. Russell, "Emergence of Physiological Optics", p. 695, in Morelon, Régis; Rashed, Roshdi (1996), Encyclopedia of the History of Arabic Science, 2, Routledge, ISBN 0415124107 
  67. ↑ (Rosen 1985, pp. 19–21)
  68. ↑ 68.0 68.1 (Khaleefa 1999)
  69. ↑ Bradley Steffens (2006). Ibn al-Haytham: First Scientist, Chapter 5. Morgan Reynolds Publishing. ISBN 1599350246.
  70. ↑ (Aaen-Stockdale 2008)
  71. ↑ (Hershenson 1989, pp. 9–10)
  72. ↑ Plott, C. (2000), Global History of Philosophy: The Period of Scholasticism, Motilal Banarsidass, p. 462, ISBN 8120805518 
  73. ↑ (Duhem 1969, p. 28)
  74. ↑ (Professor Abattouy 2002)
  75. ↑ 75.0 75.1 (Toomer 1964, pp. 463–4)
  76. ↑ 76.0 76.1 (El-Bizri 2007)
  77. ↑ (Nasr 2003)
  78. ↑ (Langerman 1990, pp. 8–10)
  79. ↑ (Sabra 1978b, p. 121, n. 13)
  80. ↑ Nicolaus Copernicus, Stanford Encyclopedia of Philosophy, 2005-04-18, http://plato.stanford.edu/entries/copernicus, retrieved 2008-01-23 
  81. ↑ (Sabra 1998, p. 300)
  82. ↑ (Pines 1986, pp. 438–9)
  83. ↑ Some writers, however, argue that Alhazen's critique constituted a form of heliocentricity (see (Qadir 1989, p. 5–6 & 10)).
  84. ↑ (Langerman 1990), chap. 2, sect. 22, p. 61
  85. ↑ (Langerman 1990, pp. 34–41)
  86. ↑ (Gondhalekar 2001, p. 21)
  87. ↑ 87.0 87.1 (Rashed 2007)
  88. ↑ (Rashed 2007, p. 20 & 53)
  89. ↑ (Rashed 2007, pp. 33–4)
  90. ↑ (Rashed 2007, pp. 20 & 32–33)
  91. ↑ (Rashed 2007, pp. 51–2)
  92. ↑ (Rashed 2007, pp. 35–6)
  93. ↑ (Saliba 1994, pp. 60 & 67–69)
  94. ↑ 94.0 94.1 94.2 (Topdemir 2007b)
  95. ↑ (Montada 2007)
  96. ↑ (Bouali, Zghal & Lakhdar 2005)
  97. ↑ (Mohamed 2000, pp. 49–50)
  98. ↑ (Arjomand 1997, pp. 5–24)
  99. ↑ 99.0 99.1 99.2 (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.
  100. ↑ (Rottman 2000), Chapter 1
  101. ↑ (Eder 2000)
  102. ↑ (Katz 1998, p. 269):
    In effect, this method characterized parallel lines as lines always equidisant from one another and also introduced the concept of motion into geometry.
  103. ↑ (Rozenfeld 1988, p. 65)
  104. ↑ (Rozenfeld & Youschkevitch 1996, p. 470):
    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 investigations of their European counterparts. 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.
  105. ↑ (Rozenfeld & Youschkevitch 1996, p. 93)
  106. ↑ 106.0 106.1 (Plott 2000, p. 461)
  107. ↑ (Plott 2000), Pt. II, p. 459
  108. ↑ (Hassan 2007)
  109. ↑ (Smith 2005, pp. 219–40)
  110. ↑ (Sardar 1998)
  111. ↑ 111.0 111.1 (Bettany 1995, p. 251)
  112. ↑ (Hodgson 2006, p. 53)
  113. ↑ (Sabra 1978a, p. 54)
  114. ↑ (Plott 2000), Pt. II, p. 464
  115. ↑ (Qadir 1990, pp. 24–5):
    "Muslims are inspired in the first instance by the numerous verses of the Quran which invite believers to observe nature and reflect over it."
  116. ↑ S. Pines (1962), Actes X Congrès internationale d'histoire des sciences, Vol I, Ithaca, as referenced in Sambursky, Shmuel (ed.) (1974), Physical Thought from the Presocratics to the Quantum Physicists, Pica Press, p. 139, ISBN 0-87663-712-8 
  117. ↑ (Rashed 2007, p. 11)
  118. ↑ (Plott 2000), Pt. II, p. 465
  119. ↑ (Lindberg 1967)
  120. ↑ (Rashed 2007, pp. 8–9)

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Mathematics in medieval Islam
Mathematicians
'Abd al-Hamīd ibn Turk · Abd al-Rahman al-Sufi · Abū al-Hasan ibn Alī al-Qalasādī · Abū al-Wafā' al-Būzjānī · Abū Ishāq Ibrāhīm al-Zarqālī · Abū Ja'far al-Khāzin · Abū Kāmil Shujā ibn Aslam · Sind ibn Ali · Abu'l-Hasan al-Uqlidisi · Abu-Mahmud al-Khujandi · Abu Nasr Mansur · Abū Rayhān al-Bīrūnī · Abū Sahl al-Qūhī · Ahmed ibn Yusuf · Al-Abbās ibn Said al-Jawharī · Al-Birjandi · Al-Hajjāj ibn Yūsuf ibn Matar · Al-Jayyani · Al-Karaji · Al-Khazini · Al-Kindi · Al-Mahani · Al-Nayrizi · Al-Saghani · Al-Sijzi · Al-Umawi · Alī ibn Ahmad al-Nasawī · Ali Qushji · Avicenna · Banū Mūsā · Brethren of Purity · Hunayn ibn Ishaq · Ibn al-Banna al-Marrakushi · Ibn al-Haytham · Ibn al-Shatir · Ibn Sahl · Ibn Tahir al-Baghdadi · Ibn Yahyā al-Maghribī al-Samaw'al · Ibn Yunus · Ibrahim ibn Sinan · Jamshīd al-Kāshī · Kamāl al-Dīn al-Fārisī · Kushyar ibn Labban · Muhammad Baqir Yazdi · Muhammad ibn Jābir al-Harrānī al-Battānī · Muhammad ibn Mūsā al-Khwārizmī · Muhyi al-Dīn al-Maghribī · Nasīr al-Dīn al-Tūsī · Omar Khayyám · Qāḍī Zāda al-Rūmī · Al-Khalili · Shams al-Dīn al-Samarqandī · Sharaf al-Dīn al-Tūsī · Sinan ibn Thabit · Taqi al-Din · Thābit ibn Qurra · Ulugh Beg · Yusuf al-Mu'taman ibn Hud
Treatises
Almanac · Book of Fixed Stars · Book of Optics · De Gradibus · Encyclopedia of the Brethren of Purity · Tables of Toledo · Tabula Rogeriana · The Compendious Book on Calculation by Completion and Balancing · The Book of Healing · Zij · Zij-i Ilkhani · Zij-i-Sultani
Centers
Al-Azhar University · Al-Mustansiriya University · House of Knowledge · House of Wisdom · Istanbul observatory of Taqi al-Din · Madrasah · Maktab · Maragheh observatory · University of Al-Karaouine
Influences
Babylonian mathematics · Greek mathematics · Indian mathematics
Influenced
Byzantine mathematics · European mathematics · Indian mathematics
Islamic philosophy
Fields
Alchemy · Aqidah · 'Aql · Cosmology (Astrology · Theoretical Astronomy) · Eschatology · Ethics · Kalam · Legal Philosophy · Logic · Metaphysics · Natural Philosophy · Peace · Philosophy of Education · Philosophy of Science · Psychology · Sociology (Medieval Sociology) · Sufism
Schools of Philosophy
Early Philosophy · Farabism · Avicennism · Averroism · Illuminationism · Sufi Philosophy (Cosmology · Metaphysics) · Transcendent Theosophy · Traditionalist School · Contemporary Philosophy
Philosophers
Al-Kindi · Al-Farabi · Muhammad ibn Zakariya al-Razi · Al Amiri · Ibn Miskawayh · Ibn Sina · Ikhwan al-Safa · Abu Sulayman al-Sijistani · Ayn-al-Quzat Hamadani · Ibn Masarrah · Ibn Hazm · Ibn Tufail · Ibn Rushd · Ibn Sab’in · Abu Yaqub al-Sijistani · Mu'ayyad fi'l-Din al-Shirazi  · Nasir Khusraw · Omar Khayyám · Suhrawardi  · Ibn Arabi · Afdal al-Din Kashani · al-Abharī · Nasir al-Din Tusi · Qutb al-Din al-Shirazi · Mir Damad · Mir Fendereski · Mulla Sadra · Mohsen Fayz Kashani · Imam Rabbani Mujaddid Alf-i-Sani · Shah Waliullah · Sabzevari · Allameh Tabatabaei · Muhammad Iqbal · Gohar Shahi · Mohammad Baqir al-Sadr · Abdul-Karim Ha'eri Yazdi · René Guénon · Frithjof Schuon · Hossein Nasr · Naquib al-Attas