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Ibn al-Haytham

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This article is about the scientist. For the crater on the Moon named after him, see Alhazen (crater). For the asteroid, see 59239 Alhazen.
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Abū ‘Alī al-Ḥasan ibn al-Ḥasan ibn al-Haytham
TitleIbn al-Haytham and Alhacen
Personal
EraIslamic Golden Age
JurisprudenceSunni or Shia
Main interest(s)Anatomy, Astronomy, Engineering, Mathematics, Mechanics, Medicine, Optics, Ophthalmology, Philosophy, Physics, Psychology, Science
Notable work(s)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
Senior posting
Influenced by
Influenced

Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham (Arabic: ابو علی، حسن بن حسن بن هيثم, Latinized: Alhacen or (deprecated) Alhazen) (965– c. 1039), was an Arab[2][3][4] or Persian[5] polymath[6] who made significant contributions to the principles of optics, as well as to anatomy, astronomy, engineering, mathematics, medicine, ophthalmology, philosophy, physics, psychology, 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, Iraq.[7] He was also nicknamed Ptolemaeus Secundus in Europe.[8]

Though born in Iraq around the year 965[1], he spent most of his life in Cairo, Egypt, dying there at the age of 76.[8] In his over-confidence about the practical application of his mathematical knowledge, he assumed that he could regulate the floods caused by the overflow of the Nile.[9] Ordered by the sixth Fatimid caliph, al-Hakim, to carry out this operation, he quickly perceived the inanity of what he was attempting to do, and retired from engineering. Fearing for his life, he feigned madness[1][2] and was placed under house arrest, during and after which he devoted himself to his scientific work until his death.[8]

Ibn al-Haytham is regarded as the "father of modern optics"[10] for his influential Book of Optics (written while he was under house arrest), 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.[11] He studied binocular vision and the Moon illusion, described the finite speed[12][13] and rectilinear propagation of light,[13] and argued that rays of light are streams of corpuscular energy particles[14] travelling in straight lines.[15] 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[16][17] and the originator of experimental science[18] and experimental physics,[19] and some have described him as the "first scientist" for these reasons.[20] He is also considered by some to be the founder of experimental psychology[21] for his experimental approach to the psychology of visual perception and optical illusions,[22] 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,[23] for initiating a revolution in optics[24] and visual perception.[25]

Among his other achievements, Ibn al-Haytham gave the first clear description[26] and correct analysis[27] of the camera obscura, enunciated Fermat's principle of least time and the concept of inertia (Newton's first law of motion),[28] developed the concept of momentum,[29] described the attraction between masses and was aware of the magnitude of acceleration due to gravity at-a-distance,[30] stated 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 the Lambert quadrilateral[31] and a concept similar to Playfair's axiom[3] now used in non-Euclidean geometry, formulated and solved Alhazen's problem geometrically using early ideas related to calculus and mathematical induction,[32] and in his optical research laid the foundations for the later development of telescopic astronomy,[33] as well as for the microscope and the use of optical aids in Renaissance art.[34]

Overview

Biography

Abū ‘Alī al-Hasan ibn al-Hasan ibn al-Haytham was born in Basra, Iraq, then under the rule of the Buyid dynasty of Persia,[7] and he probably died in Cairo, Egypt. Known in the West as Alhacen or Alhazen, Ibn al-Haytham was born in circa 965 in Basra, and was educated there and in Baghdad. During his time in Iraq, he worked as a civil servant and read many theological and scientific books.[35]

One account of his career has him summoned to Egypt by the mercurial Fatimid caliph al-Hakim to regulate the flooding of the Nile. After his field work made him aware of the impracticality of this scheme,[8] and fearing the caliph's anger, he feigned madness. He was kept under house arrest from 1011 until al-Hakim's death in 1021.[36] During this time, he wrote his influential Book of Optics. After his house arrest ended, he wrote scores of other treatises on physics, astronomy and mathematics. He later traveled to Islamic 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 a number of outstanding books.

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.[11] 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.[37]

Due to its importance in the history of science, Richard Powers considers his development of the scientific method to be the most important scientific development of the second millennium.[34] Nobel Prize winning physicist Abdus Salam considered Ibn-al-Haitham "one of the greatest physicists of all time."[28] 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."[38][39] Robert S. Elliot considered Ibn al-Haytham to be "one of the ablest students of optics of all times."[40] 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."[41]

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,[42] 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 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.

The list of his books runs to 200 or so, yet very few of the books have survived. 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 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, and moreover Iran's largest laser research facility, located in the Atomic Energy Organization of Iran headquarters in Tehran, is named after him as well.

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),[43] which has been ranked alongside Isaac Newton's Philosophiae Naturalis Principia Mathematica as one of the most influential books in physics,[23] for introducing an early scientific method and for initiating a revolution in optics[24] and visual perception.[25]

Optics was translated into Latin by an unknown scholar at the end of the 12th century or the beginning of the 13th century.[44] 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.[45] 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.[46] 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,[33] as well as of the modern camera, the microscope, and the use of optical aids in Renaissance art.[34]

Optics

Ibn al-Haytham proved that light travels in straight lines using the scientific method in his Book of Optics (1021).

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.[47]

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.[11] 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 also discovered a result similar to Snell's law of sines, but did not quantify it and derive the law mathematically.[49] Ibn al-Haytham also gave the first clear description[26] and correct analysis[27] of the camera obscura, though the underlying principles of the camera oscura or pinhole camera were earlier known to Mozi and Aristotle.[26]

Scientific method

Rosanna Gorini notes that "according to the majority of the historians al-Haytham was the pioneer of the modern scientific method."[16][50] Ibn al-Haytham developed rigorous experimental methods of controlled scientific testing in order to verify theoretical hypotheses and substantiate inductive conjectures.[30] Ibn al-Haytham's scientific method was very similar to the modern scientific method and consisted of the following procedures:[51]

  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. 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).[52][53][22]

The concept of Ockam'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 superflous and useless."[54]

Alhazen's problem

His work on catoptrics in Book V of the Book of Optics contains the 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. He used his result on sums of integral powers to perform an integration, in order to find the volume of a paraboloid. 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.[32]

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,[3] until it was eventually solved by the end of the 20th century.[22]

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."[55]

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.[56]

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.[57] He also made several improvements to eye surgery and described the process of sight.[58]

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.[59]

In Islamic psychology, Ibn al-Haytham is considered the founder of experimental psychology,[21] for his pioneering work on the psychology of visual perception and optical illusions.[22] 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.[22]

Omar Khaleefa has argued that Ibn al-Haytham should also be considered the founder of psychophysics, a subdiscipline and precursor to modern psychology.[21] 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.[60]

Other works on physics

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.[30]

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.[11]

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".[61] 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.[30] 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.[62] 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 earliest attempt at applying the experimental method to astronomy and astrophysics. He disproved the universally held opinion that the Moon reflects sunlight like a mirror and correctly concluded that it "emits light from those portions of its surface which the sun's light strikes." In order to prove that "light is emitted from every point of the Moon's illuminated surface," he built an "ingenious experimental device." 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.[63]

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.[30] This was similar to the concept of inertia, but was largely a hypotheses 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 then formulated as Newton's first law of motion.[28]

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.[64]

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).[29]

Astronomical works

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:[65]

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.[66][67]

Ibn al-Haytham further criticized Ptolemy's model on other empirical, observational and experimental grounds,[68] 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.[69]

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…[70]

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.[70]

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,[71] 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.[72]

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 during the European Middle Ages and Renaissance.[73][74]

The Model of the Motions

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.[75]

His reformed empirical model was the first to reject the equant[76] and eccentrics,[77] 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,[78] and the centres of motion were geometrical points without any physical significance, like Johannes Kepler's model centuries later.[79]

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.[80]

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.[81]

Ibn al-Haytham also wrote a treatise entitled On the Milky Way,[82] in which he dealt with problems regarding the Milky Way galaxy and parallax.[83] 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."[84] 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."[85] He wrote that if the Milky Way were located around the Earth's atmosphere, "one must find a difference in position relative to the fixed stars." He described two methods in order 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.[86]

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.[87]

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.[88]

Geometry

In geometry, Ibn al-Haytham developed analytical geometry and established a link between algebra and geometry.[88] 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.[89]

Ibn al-Haytham made the first attempt at proving the Euclidean parallel postulate using a proof by contradiction,[90] where he introduced the concept of motion and transformation into geometry.[91] He formulated the Lambert quadrilateral, which Boris Abramovich Rozenfeld refers to as the "Ibn al-Haytham–Lambert quadrilateral",[31] and his attempted proof also shows similarities to Playfair's axiom.[3] 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 Persian 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.[92]

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.[35] 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.[70]

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).[35]

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.[35]

Other works

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.[93]

According to al-Khazini, Ibn al-Haytham also wrote a treatise providing a description on the construction of a water clock.[94]

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 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.[64]

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."[95]

Theology

Ibn al-Haytham was a devout Muslim,[96] who is said to have been a follower of the orthodox Ash'ari school of Sunni Islamic theology,[97][98] and opposed to the views of the Mu'tazili school,[98] though it has been argued that he may have been a supporter of Mu'tazili theology[99] or Shia Islam (specifically the Ismaili branch).[100][101]

Ibn al-Haytham 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.[102] He also wrote a treatise entitled Finding the Direction of Qibla by Calculation, in which he mathematically dealt with finding the Qibla, where Salah prayers are directed towards.[82]

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.[103][104][105] 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.[51] 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.[70]

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.[106]

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.[107]

List of 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.[108] 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.[88]

According to medieval biographers, Ibn al-Haytham wrote more than 200 works on a wide range of subjects,[51] 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.[109] Not all of his surviving works have yet been studied, but some of the ones that have are given below.[110][82]

  • Book of Optics (1021)
  • Analysis and Synthesis
  • Balance of Wisdom
  • Corrections to the Almagest
  • Discourse on Place
  • Exact Determination of the Pole
  • Exact Determination of the Meridian
  • Finding the Direction of Qibla by Calculation
  • Horizontal Sundials
  • Hour Lines
  • Doubts Concerning Ptolemy (1028)
  • Maqala fi'l-Qarastun
  • On Completion of the Conics
  • On Seeing the Stars
  • On Squaring the Circle
  • On the Burning Sphere
  • On the Configuration of the World
  • On the Form of Eclipse
  • On the Light of Stars
  • On the Light of the Moon
  • On the Milky Way
  • On the Nature of Shadows
  • On the Rainbow and Halo
  • Opuscula
  • Resolution of Doubts Concerning the Almagest
  • Resolution of Doubts Concerning the Winding Motion
  • The Correction of the Operations in Astronomy
  • The Different Heights of the Planets
  • The Direction of Mecca
  • The Model of the Motions of Each of the Seven Planets (1038)
  • The Model of the Universe
  • The Motion of the Moon
  • The Ratios of Hourly Arcs to their Heights
  • The Winding Motion
  • Treatise on Light
  • Treatise on Place

See also

Notes

  1. ^ a b c d "Ibn al-Haytham". Encyclopædia Britannica. 2008. Retrieved 2008-08-06. Cite error: The named reference "Britannica" was defined multiple times with different content (see the help page).
  2. ^ a b "Alhazen," Microsoft® Encarta® Online Encyclopedia 2007 http://encarta.msn.com © 1997-2007 Microsoft Corporation. All Rights Reserved. [1]
  3. ^ a b c d (Smith 1992)
  4. ^
  5. ^
    • Understanding History by John Child, Paul Shuter, David Taylor - Page 70
    • 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
  6. ^ (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.
  7. ^ a b "Electromagnetic Theory and Light". Retrieved 2008-01-23.
  8. ^ a b c d Corbin (1993), p.149
  9. ^ "Vita: Ibn al-Haytham". Harvard Magazine. September–October 2003. Retrieved 2008-08-06.{{cite web}}: CS1 maint: date format (link)
  10. ^ R. L. Verma (1969). Al-Hazen: father of modern optics.
  11. ^ a b c d Dr. Mahmoud Al Deek. "Ibn Al-Haitham: Master of Optics, Mathematics, Physics and Medicine", Al Shindagah, November-December 2004.
  12. ^ MacKay, R. J.; Oldford, R. W. (August 2000), "Scientific Method, Statistical Method and the Speed of Light", Statistical Science, 15 (3): 254–78, doi:10.1214/ss/1009212817
  13. ^ a b (Hamarneh 1972, p. 119)
  14. ^ (Rashed 2007, p. 19):

    "In his optics ‘‘the smallest parts of light’’, as he calls them, retain only properties that can be treated by geometry and verified by experiment; they lack all sensible qualities except energy."
  15. ^ O'Connor, John J.; Robertson, Edmund F., "Light through the ages: Ancient Greece to Maxwell", MacTutor History of Mathematics Archive, University of St Andrews
  16. ^ a b (Gorini 2003)
  17. ^ David Agar (2001). "Essay Two: Arabic Studies in Physics and Astronomy During 800–1400 AD". University of Jyväskylä. Retrieved 2008-01-23.
  18. ^ (Omar 1977)
  19. ^ Rüdiger Thiele (2005). "In Memoriam: Matthias Schramm", Arabic Sciences and Philosophy 15, p. 329–331. Cambridge University Press.
  20. ^ (Steffens 2006)
  21. ^ a b c (Khaleefa 1999)
  22. ^ a b c d e (Steffens 2006), Chapter 5
  23. ^ a b (Salih, Al-Amri & El Gomati 2005)
  24. ^ a b Sabra, A. I.; Hogendijk, J. P. (2003), The Enterprise of Science in Islam: New Perspectives, MIT Press, pp. 85–118, ISBN 0262194821
  25. ^ a b Hatfield, Gary (1996), "Was the Scientific Revolution Really a Revolution in Science?", in Ragep, F. J.; Ragep, Sally P.; Livesey, Steven John (eds.), Tradition, Transmission, Transformation: Proceedings of Two Conferences on Pre-modern Science held at the University of Oklahoma, Brill Publishers, p. 500, ISBN 9004091262
  26. ^ 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."
  27. ^ 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."
  28. ^ 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.
  29. ^ 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.
  30. ^ a b c d e (El-Bizri 2006)
  31. ^ a b Boris Abramovich Rozenfeld (1988), A History of Non-Euclidean Geometry: Evolution of the Concept of a Geometric Space, p. 65. Springer, ISBN 0387964584.
  32. ^ a b (Katz 1995, pp. 165-9 & 173-4)
  33. ^ a b (Marshall 1950)
  34. ^ a b c Powers, Richard (April 18, 1999), "Best Idea; Eyes Wide Open", [[New York Times]] (PDF), retrieved 2008-01-23 {{citation}}: URL–wikilink conflict (help)
  35. ^ a b c d O'Connor, John J.; Robertson, Edmund F., "Abu Ali al-Hasan ibn al-Haytham", MacTutor History of Mathematics Archive, University of St Andrews
  36. ^ "به گفتۀ قفطی... ابن هیثم اندکی بعد در رأس گروهی از مهندسان به بررسی نیل و مجرای آن در بخش مرتفع جنوب مصر پرداخت، اما با مشاهدۀ آثار و ابنیه‌ای که مصریان براساس طرحهای دقیق هندسی ساخته بودند، دریافت که اگر اجرای طرحی که او در اندیشه داشت، ممکن بود، این مصریان فرهیختۀ دانا به هندسه و ریاضیات، البته پیش‌تر به آن دست می‌زدند. بررسی چگونگی مرتفعات اسوان که نیل از آن می‌گذرد، نیز این نتیجه‌گیری را تأیید کرد. از این‌رو نزد خلیفه به ناکامی خود اعتراف کرد. ظاهراً خلیفه واکنش تندی از خود نشان نداد، اما چنین می‌نماید که از این ناکامی چندان خشمناک شده بود که ابن هیثم را به جای آنکه در جایی چون دارالحکمۀ قاهره، در کنار کسانی مانند ابن یونس منجم به کار بگمارد، به شغلی دیوانی گماشت. ابن هیثم با آنکه از بیم این فرمانروای خونریز، به این شغل گردن نهاد، ولی برای رهایی از آن چاره در این دید که باز تظاهر به جنون کند. از این‌رو خلیفه اموال او را مصادره کرد و کسی را به قیمومتش گماشت و در خانه‌اش محبوس کرد. چون الحاکم درگذشت (411ق/1020م)، ابن هیثم نیز از تظاهر به جنون دست برداشت و آزاد شد و اموالش را باز پس گرفت. " the Great Islamic Encyclopedia
  37. ^ (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.
  38. ^ 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.
  39. ^ Dr. A. Zahoor and Dr. Z. Haq (1997). "Quotations from Famous Historians of Science". Cyberistan. Retrieved 2008-01-23.
  40. ^ (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.
  41. ^ "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.
  42. ^ (Lindberg 1996, p. 11), passim
  43. ^ (Steffens 2006) (cf. "Review of Ibn al-Haytham: First Scientist". The Critics. Barnes & Noble. Retrieved 2008-01-23.)
  44. ^ (Crombie 1971, p. 147, n. 2)
  45. ^ "Alhazen (965-1040): Library of Congress Citations". Retrieved 2008-01-23.
  46. ^ (Smith 2001) harv error: multiple targets (2×): CITEREFSmith2001 (help)
  47. ^ (Lindberg 1976, pp. 60–7)
  48. ^ Albrecht Heeffer. "Kepler's near discovery of the sine law: A qualitative computational model" (PDF). Ghent University, Belgium. Retrieved 2008-01-23.
  49. ^ (Sabra 1981) (cf. Pavlos Mihas. "Use of History in Developing ideas of refraction, lenses and rainbow" (PDF). Demokritus University, Thrace, Greece. p. 5. Retrieved 2008-01-23.)
  50. ^ (Rashed 2002, p. 773)
  51. ^ a b c (Steffens 2006) (cf. Steffens, Bradley, Who Was the First Scientist?, Ezine Articles)
  52. ^ Nader El-Bizri, "A Philosophical Perspective on Alhazen’s Optics," Arabic Sciences and Philosophy, Vol. 15, Issue 2 (2005), pp. 189-218 (Cambridge University Press)
  53. ^ Nader El-Bizri, "Ibn al-Haytham," in Medieval Science, Technology, and Medicine: An Encyclopedia, eds. Thomas F. Glick, Steven J. Livesey, and Faith Wallis (New York — London: Routledge, 2005), pp. 237-240.
  54. ^ Alhazen; 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, DIANE Publishing, pp. 372 & 408, ISBN 0871699141
  55. ^ (Falco 2007) harv error: multiple targets (2×): CITEREFFalco2007 (help)
  56. ^ Edward Rosen (1985), "The Dissolution of the Solid Celestial Spheres", Journal of the History of Ideas 46 (1), p. 13–31 [19–20, 21].
  57. ^ (Steffens 2006) (cf. "Review by Sulaiman Awan". Retrieved 2008-01-23.)
  58. ^ 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
  59. ^ Dr Valérie Gonzalez, "Universality and Modernity", The Ismaili United Kingdom, December 2002, p. 50–53.
  60. ^ Aaen-Stockdale, C.R. (2008). "Ibn al-Haytham and psychophysics". Perception. 37 (4): 636–638. doi:10.1068/p5940.
  61. ^ (Duhem 1969, p. 28)
  62. ^ 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.
  63. ^ Toomer, G. J. (December 1964), "Review: Ibn al-Haythams Weg zur Physik by Matthias Schramm", Isis, 55 (4): 463–465 [463–4], doi:10.1086/349914
  64. ^ a b (El-Bizri 2007)
  65. ^ (Langerman 1990, pp. 8–10)
  66. ^ (Sabra 1978b, p. 121, n. 13)
  67. ^ "[[Stanford Encyclopedia of Philosophy]]". 2004–2005. Retrieved 2008-01-23. {{cite web}}: |contribution= ignored (help); URL–wikilink conflict (help)CS1 maint: date format (link)
  68. ^ 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].
  69. ^ Shlomo Pines (1986), Studies in Arabic Versions of Greek Texts and in Mediaeval Science, p. 438–439. Brill Publishers, ISBN 9652236268.
  70. ^ a b c d (Sabra 2003)
  71. ^ Some writers, however, argue that Alhazen's critique constituted a form of heliocentricity (see (Qadir 1989, p. 5–6 & 10)).
  72. ^ (Langerman 1990), chap. 2, sect. 22, p. 61
  73. ^ (Langerman 1990, pp. 34–41)
  74. ^ (Gondhalekar 2001, p. 21)
  75. ^ (Rashed 2007)
  76. ^ (Rashed 2007, p. 20 & 53)
  77. ^ (Rashed 2007, pp. 33–4)
  78. ^ (Rashed 2007, pp. 20 & 32–33)
  79. ^ (Rashed 2007, pp. 51–2)
  80. ^ (Rashed 2007, pp. 35–6)
  81. ^ 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.
  82. ^ a b c Huseyin Gazi Topdemir (July 18, 2007). "Ibn al-Haytham (965-1039) His Life and Works". Retrieved 2008-07-08.
  83. ^ (Rashed 2007)
  84. ^ Josep Puig Montada (September 28, 2007). "Ibn Bajja". Stanford Encyclopedia of Philosophy. Retrieved 2008-07-11.
  85. ^ Hamid-Eddine Bouali, Mourad Zghal, Zohra Ben Lakhdar (2005). "Popularisation of Optical Phenomena: Establishing the First Ibn Al-Haytham Workshop on Photography" (PDF). The Education and Training in Optics and Photonics Conference. Retrieved 2008-07-08.{{cite web}}: CS1 maint: multiple names: authors list (link)
  86. ^ Mohamed, Mohaini (2000), Great Muslim Mathematicians, Penerbit UTM, pp. 49–50, ISBN 9835201579
  87. ^ Arjomand, Kamran (1997), "The emergence of scientific modernity in Iran: controversies surrounding astrology and modern astronomy in the mid-nineteenth century", Iranian Studies, 30 (1): 5–24
  88. ^ 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.
  89. ^ J. Rottman. A first course in Abstract Algebra, Chapter 1.
  90. ^ Michelle Eder (2000). "Views of Euclid's Parallel Postulate in Ancient Greece and in Medieval Islam". Rutgers University. Retrieved 2008-01-23.
  91. ^ 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.
  92. ^ 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 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.
  93. ^ C. Plott (2000), Global History of Philosophy: The Period of Scholasticism, Pt. II, p. 459. ISBN 8120805518, Motilal Banarsidass Publ.
  94. ^ (Hassan 2007)
  95. ^ Smith, A. Mark (2005), "The Alhacenian Account Of Spatial Perception And Its Epistemological Implications", Arabic Sciences and Philosophy, 15, Cambridge University Press: 219–40
  96. ^ (Steffens 2006) (cf. "Review of Ibn al-Haytham: First Scientist". Kirkus Reviews. 2006-12-01. Retrieved 2008-01-23.)
  97. ^ Sardar, Ziauddin (1998), "Science in Islamic philosophy", Islamic Philosophy, Routledge Encyclopedia of Philosophy, retrieved 2008-02-03
  98. ^ a b (Bettany 1995, p. 251)
  99. ^ (Hodgson 2006, p. 53)
  100. ^ (Sabra 1978a, p. 54)
  101. ^ "The Ismaili Community". Institute of Ismaili Studies. 2007-07-18. Retrieved 2008-08-06. {{cite web}}: Check date values in: |date= (help)
  102. ^ C. Plott (2000), Global History of Philosophy: The Period of Scholasticism, Pt. II, p. 464. ISBN 8120805518, Motilal Banarsidass Publ.
  103. ^ 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))
  104. ^ "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."[Quran 17:36]
  105. ^ "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."[Quran 2:164]
  106. ^ (Rashed 2007, p. 11)
  107. ^ C. Plott (2000), Global History of Philosophy: The Period of Scholasticism, Pt. II, p. 465. ISBN 8120805518, Motilal Banarsidass Publ.
  108. ^ (Lindberg 1967)
  109. ^ (Rashed 2002, p. 773)
  110. ^ (Rashed 2007, pp. 8–9)

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  • 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 {{citation}}: Italic or bold markup not allowed in: |journal= (help)
  • Hamarneh, Sami (1972), "Review: Hakim Mohammed Said, Ibn al-Haitham", Isis, 63 (1): 118–119, doi:10.1086/350861
  • Hassan, Ahmad Y. (2007), Al-Jazari And the History of the Water Clock, retrieved 2008-01-23
  • Hodgson, Peter Edward (2006), Theology And Modern Physics, Burlington, VT: Ashgate Publishing (published 2006-01-15), ISBN 9780754636229, OCLC 56876894, DDC: 201.653, LCC: BL265.P4 H63 2005 {{citation}}: Check date values in: |publication-date= (help)
  • 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, doi:10.1086/350266
  • 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
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  • Rashed, Roshdi (2007), "The Celestial Kinematics of Ibn al-Haytham", Arabic Sciences and Philosophy, 17, Cambridge University Press: 7–55, doi:10.1017/S0957423907000355
  • Sabra, A. I. (1971), "The astronomical origin of Ibn al-Haytham's concept of experiment", Actes du XIIe congrès international d’histoire des sciences, 3, Albert Blanchard, Paris: 133–136. Reprinted in Sabra, A. I. (1994), Optics, Astronomy and Logic: Studies in Arabic Science and Philosophy, Collected Studies Series, vol. 444, Variorum, Aldershot, ISBN 0-86078-435-5.
  • Sabra, Abd al-Hamid (1978a), "Ibn al-Haytham and the Visual Ray Hypothesis", in Nasr, Seyyed Hossein (ed.), 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", in Hilfstein, Erna; Czartoryski, Paweł; Grande, Frank D. (eds.), Science and History: Studies in Honor of Edward Rosen, Studia Copernicana, vol. XVI, Ossolineum, Wrocław, pp. 117–131
  • Sabra, A. I. (1981), Theories of Light from Descartes to Newton, Cambridge University Press
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  • 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
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Further reading

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{{citation}}: CS1 maint: multiple names: authors list (link)
  • 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 {{citation}}: |first= has generic name (help)CS1 maint: multiple names: authors list (link)
  • 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 {{citation}}: |first= has generic name (help)CS1 maint: multiple names: authors list (link)
  • 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{{citation}}: CS1 maint: multiple names: authors list (link)
  • 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, 91 (4–5), Philadelphia, ISBN 0-87169-914-1{{citation}}: CS1 maint: multiple names: authors list (link)
  • 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, 96 (2–3), Philadelphia, ISBN 0-87169-962-1{{citation}}: CS1 maint: multiple names: authors list (link)

Secondary literature

  • Corbin, Henry (1993 (original French 1964)). History of Islamic Philosophy, Translated by Liadain Sherrard, Philip Sherrard. London; Kegan Paul International in association with Islamic Publications for The Institute of Ismaili Studies. ISBN 0710304161. {{cite book}}: Check date values in: |year= (help); Cite has empty unknown parameter: |coauthors= (help)
  • Falco, Charles M. (12–15 February 2007), Ibn al-Haytham and the Origins of Modern Image Analysis (PDF), presented at a plenary session at the International Conference on Information Sciences, Signal Processing and its Applications. In this lecture, Falco speculates that Ibn al-Haytham may have influenced the use of optical aids in Renaissance art (see Hockney-Falco thesis), retrieved 2008-01-23 {{citation}}: Unknown parameter |publication date= ignored (help)
  • Omar, Saleh Beshara (June 1975), Ibn al-Haytham and Greek optics: a comparative study in scientific methodology, PhD Dissertation, University of Chicago, Department of Near Eastern Languages and Civilizations

External links

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