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).
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Abū ‘Alī al-Ha ṣan ibn al-Ha ṣan ibn al-Haytham
TitleIbn al-Haytham and Alhacen
Personal
EraIslamic Golden Age
RegionMuslim scientist
Main interest(s)Anatomy, Astronomy, Engineering, Mathematics, Medicine, Optics, Ophthalmology, Physics, Psychology, Science
Notable work(s)Book of Optics, Analysis and Synthesis, Aporias against Ptolemy, Discourse on Place, Doubts on Ptolemy, Maqala fi'l-qarastun, Mizan al-Hikmah, On the Configuration of the World, Opuscula, The Resolution of Doubts, Treatise on Light, Treatise on Place

Abū ‘Alī al-Ha

ṣan ibn al-Ha

ṣan ibn al-Haytham (965–1039) (Arabic: أبو علي الحسن بن الحسن بن الهيثم, Latinized: Alhacen or (deprecated) Alhazen), was a Arab Muslim polymath, anatomist, astronomer, engineer, mathematician, ophthalmologist, physician, physicist, psychologist, and scientist, who made significant contributions to the principles of optics, as well as mechanics, motion, astronomy, analytical geometry, infinitesimal and integral calculus, and number theory, and pioneered the use of the experimental scientific method. He is sometimes called al-Basri (Arabic: البصري), after his birthplace of Basra in Iraq (Mesopotamia). Ibn al-Haytham is considered the "father of optics" for his empirical experiments on light and optics, including experiments with lenses, mirrors, refraction, and reflection, and for correctly explaining and proving the intromission theory of vision. He is also considered the pioneer of the modern scientific method,[1][2] and some have described him as the "first scientist" for this reason.[3]

Among his other achievements, Ibn al-Haytham invented the camera obscura and pinhole camera,[4] discovered Fermat's principle of least time and Newton's first law of motion,[5] formulated Alhazen's problem, developed and proved the earliest general formula for integral calculus,[6] and in his optical research, laid the foundations for the later development of telescopic astronomy.[7]

Biography

He was born in the Arab city of Basra, Iraq, and he died in Cairo, Egypt.[2]

Abū ‘Alī al-Hasan ibn al-Hasan ibn al-Haytham was one of the most eminent physicists, whose contributions to optics and the scientific method are outstanding. Known in the West as Alhacen or Alhazen, Ibn al-Haytham was born in 965 A. D. in Basrah, and was educated there and in Baghdad. One account of his career has him summoned to Egypt by the mercurial caliph Hakim to regulate the flooding of the Nile. After his field work made him aware of the impracticality of this scheme, and fearing the caliph's anger, he feigned madness. He was kept under house arrest until Hakim's death in 1021. During this time he wrote scores of important mathematical treatises. He later traveled to Spain and, during this period, he had ample time for his scientific pursuits, which included optics, mathematics, physics, medicine and development of scientific methods on each of which he has left several outstanding books.

Legacy

Ibn al-Haytham's work on optics is credited with contributing a new emphasis on experiment. His influence on physical sciences in general, and optics in particular, has been held in high esteem and, in fact, it ushered in a new era in optical research, both in theory and practice.[8]

Rosanna Gorini wrote the following on Ibn al-Haytham's development of the scientific method:

"According to the majority of the historians al-Haytham was the pioneer of the modern scientific method. With his book he changed the meaning of the term optics and established experiments as the norm of proof in the field. His investigations are based not on abstract theories, but on experimental evidences and his experiments were systematic and repeatable."[2]

Roshdi Rashed wrote the following on Ibn al-Haytham's early use of experimentation:

"By promoting the use of experiments in scientific research, al-Haytham played an important part in setting the scene for modern science."[9]

Nobel Prize winning physicist Abdus Salam wrote:

"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 tlie 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."[5]

George Sarton, the "father of the history of science", described Ibn al-Haytham as:

"The greatest Muslim physicist and student of optics of all times."[7]

Ibn al-Haytham made a thorough examination of the passage of light through various media and discovered the laws of refraction. He also carried out the first experiments on the dispersion of light into its constituent colours.[8] His book Kitab al-Manazir (Book of Optics) was translated into Latin in the Middle Ages, as also was his book dealing with the colours of sunset. He dealt at length with the theory of various physical phenomena such as shadows, eclipses, and the rainbow, and speculated on the physical nature of light. He is the first to describe accurately the various parts of the eye and give a scientific explanation of the process of vision. He also attempted to explain binocular vision and the apparent increase in size of the Sun and the Moon when near the horizon. He is known for the earliest use of the camera obscura. He contradicted Ptolemy's and Euclid's theory of vision that objects are seen by rays of light emanating from the eyes; according to him the rays originate in the object of vision and not in the eye. Through these extensive researches on optics, he has been considered as the father of modern optics.

The Latin translation of his main work, Kitab al-Manazir, exerted a great influence upon Western science e.g. on the work of Roger Bacon who cites him by name[10] and Kepler. It brought about a great progress in experimental methods. His research in catoptrics centered on spherical and parabolic mirrors and spherical aberration. He made the important observation that the ratio between the angle of incidence and refraction does not remain constant and investigated the magnifying power of a lens. His catoptrics contain the important problem known as Alhazen's problem. It comprises drawing lines from two points in the plane of a circle meeting at a point on the circumference and making equal angles with the normal at that point. This leads to an equation of the fourth degree.

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

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

Major works

Alhacen was a pioneer in optics, astronomy, engineering, mathematics and physics. His contribution to mathematics and physics was also extensive. Alhacen taught that vision does not result from the emission of rays from the eye, and wrote on the refraction of light, especially on atmospheric refraction, for example, the cause of morning and evening twilight. He solved the problem of finding the point on a convex mirror at which a ray coming from one point is reflected to another point.

Alhacen's optical writings influenced many Western intellectuals such as Roger Bacon, John Pecham, Witelo, and Johannes Kepler.[11]

According to medieval biographers, Ibn al-Haytham wrote at least 96 scientific works. Most of his works are now lost, but more than 50 of them have survived to some extent. Nearly half of his surviving works are on mathematics, 23 of them are on astronomy, and 14 of them are on optics, with a few on other areas of science.[9] Not all of his surviving works have yet been studied, but some of his most important ones are described below.

Book of Optics

The title page of a 1572 Latin manuscript of Ibn al-Haytham's Book of Optics

His seven volume treatise on optics, Kitab al-Manazir (Book of Optics) (written from 1011 to 1021),[12] drastically transformed the ancient understanding of vision. 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 particles entering the eye. Alhacen 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 particles entering the eye. Alhacen instead developed a highly successful theory which explained the process of vision by rays of light proceeding to the eye from each point on an object, which he proved through the use of experimentation.[13]

Ibn al-Haytham proved that rays of light travel in straight lines, and carried out a number of experimnts with lenses, mirrors, refraction, and reflection.[8] He was also the first to reduce reflected and refracted light rays into vertical and horizontal components, which was a fundamental development in geometric optics.[14] He also discovered a result similar to Snell's law of sines, but did not quantify it and derive the law mathematically.[15] Ibn al-Haytham is also credited with the invention of the camera obscura and pinhole camera.[4]

In his work on optics, Alhacen described sight as the inference of distinct properties of two similar and dissimilar objects. The eye perceives the size, shape, transparency (color and light), position, and motion from cognitive distinction which is entirely different from perceiving by mere sensation the characteristics of the object. The faculty of the mind, for Alhacen, includes perceiving through judgement and inference of distinct properties of similar objects outline and structure. Alhacen continues this body of work by concluding that the discrimination performed by the faculty of judgment and inference is in addition to sensing the objects visible form and not by pure sensation alone. We recognize visible objects that we frequently see. Recognition of an object is not pure sensation because we do not recognize everything we see. Ultimately, recognition does not take place without remembering. Recognition is due to the inference because of our mental capacity to conclude what objects are. Alhacen uses our ability to recognize species and likening their characteristics to that of similar individuals to support recognition associated and processed by inference. Alhacen further concludes that we are processing visual stimuli in very short intervals which allows us to recognize and associate objects through inference but we do not need syllogism to recognize it. These premises are stored infinitely in our souls.

Robert S. Elliot writes:

"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."[16]

Optics was translated into Latin by an unknown scholar at the end of the 12th century or the beginning of the 13th century.[17] 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 [3]. Risner is also the author of the name variant "Alhazen", before him he was known in the west as Alhacen, which is correct transcription of the Arabic name.[18] 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, such as the telescope, which laid the foundations of telescopic astronomy.[7]

Book I

In Book I of the treatise, Ibn al-Haytham begins by writing an introduction to the systematic approach he will use for his investigations on optics, and correctly explains how vision is perceived by rays of light travelling in straight lines from an object to the eye:[19]

"We should distinguish the properties of particulars, and gather by induction what pertains to the eye when vision takes place and what is found in the manner of sensation to be uniform, unchanging, manifest, and not subject to doubt. After which we should ascend in our inquiry and reasonings, gradually and orderly, criticizing premises and exercising caution in regard to conclusions—our aim in all that we make subject to inspection and review being to employ justice, not to follow prejudice, and to take care in all that we judge and criticize that we seek the truth and not be swayed by opinion."

"Straight lines [exist between] the surface of the eye [and] each point on the seen surface of the object. An accurate experimental examination of this fact may be easily made with the help of rulers and tubes. [...] If…he covers any part of the opening, then there will be screened off only that portion…that lies on a straight line with the eye and the screening body—this straightness being secured by the ruler and the straightness of the tube, [...] It follows from this experiment, with a necessity that dispels doubt, that sight does not perceive any visible object existing with it in the same atmosphere, this perception being not by reflection, except through straight lines alone that can be imagined to extend between the surface of the object and the surface of the eye. Sight does not perceive any visible object unless there exists in the object some light, which the object possesses of itself or which radiates upon it from another object."

He also states that his investigation of light will be based on experimental evidence rather than on abstract theory, and notes that light is always the same from every source, using sunlight, fire, and a mirror as examples. He then examines the anatomical structure of the eye, and proposes the first use of a camera obscura.

Books II-III

Book II of the treatise contains a discussion on visual perception.[8] In Book III, he pioneered the psychology of visual perception, being the first scientist to argue that vision occurs in the brain, rather than the eyes. He pointed out that personal experience has an affect on what people see and how they see, and that vision and perception are subjective. He explained possible errors in vision in detail, and as an example, describes how a small child with less experience may have more difficulty interpreting what he/she sees. He also gives an example of an adult that can make mistakes in vision because of how one's experience suggests that he/she is seeing one thing, when he/she is really seeing something else.[19]

Books IV-VII

Book IV deals with the theory of reflection mathematically, while Book V deals with the influential Alhazen's problem. Book VI examines errors in vision due to reflection, while the final volume, Book VII, examines refraction.[8]

Treatise on Light

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, the 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.[20]

Analysis and Synthesis

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).[21]

Opuscula

In number theory, 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.[21]

On the Configuration of the World

In his On the Configuration of the World, Ibn al-Haytham 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:[22]

"Ptolemy assumed an arrangement that cannot exist, and the fact that this arrangement produces in his imagination the motions that belong to the planets does not free him from the error he committed in his assumed arrangement, for the existing motions of the planets cannot be the result of an arrangement that is impossible to exist."[23]

Despite his criticisms directed towards Ptolemy, Ibn al-Haytham continued to accept the physical reality of the geocentric model of the universe,[24] 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."[25]

According to Giambattista della Porta, Alhacen was the first to give a correct explanation of the apparent increase in the size of the Moon and Sun when near Earth's horizon.[26] (Ptolemy made earlier attempts at explaining it, according to Roger Bacon.)

Doubts on Ptolemy

In his Doubts on Ptolemy, Ibn al-Haytham argued that the equant introduced by Ptolemy failed to satisfy the Ptolemaic model's requirement of uniform circular motion. While he attempted to discover the physical reality behind Ptolemy's mathematical model, he developed the concept of a single celestial sphere for each component of Ptolemy's planetary motions. This work was eventually translated into Latin by the 14th century and subsequently had an important influence during the European Renaissance.[27]

Aporias against Ptolemy

Due to controversies with contemporaries about truth and authority and the role of criticism in scientific research later in his life, Ibn al-Haytham wrote sophisticated arguments on the practice of science and the growth of scientific knowledge in his Aporias against Ptolemy:

"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..."[28]

He also extended his argument to human nature itself:

"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."[28]

The Resolution of Doubts

Ibn al-Haytham's The Resolution of Doubts, written in 1029, was an important book on astronomy, which has not yet been published. Following on from his Doubts on Ptolemy, The Resolution of Doubts contains Ibn al-Haytham's reform of the Ptolemaic model. His reform excluded cosmology, as he developed a systematic study of celestial kinematics that was completely geometric. This in turn led to innovative developments in infinitesimal geometry.[29]

Maqala fi'l-qarastun

The 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 vary with their distance from the center of the Earth.[30]

Mizan al-Hikmah

In his book Mizan al-Hikmah, Ibn al-Haytham has discussed the density of the atmosphere and related it to altitude. He also studied atmospheric refraction. He discovered that the twilight only ceases or begins when the Sun is 19° below the horizon and attempted to measure the height of the atmosphere on that basis.[8] He also discussed the theory of attraction between masses, and it seems that he was aware of the magnitude of acceleration due to gravity.[20]

Treatise on Place

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 Rene Descartes’ concept of place in the Extensio in the 17th century. Ibn al-Haytham also builds on the mathematical works of Euclid and Thabit ibn Qurra, and goes on to systemize infinitesimal calculus, conic sections, number theory, and analytic geometry after linking algebra to geometry. Ibn al-Haytham also studied the mechanics of the motion of a body and maintained that a body moves perpetually unless an external force stops it or changes its direction of motion.[20] This was similar to the law of inertia later stated by Galileo Galilei in the 16th century and now known as Newton's first law of motion.[5]

Discourse on Place

Following on from his Treatise on Place, Ibn al-Haytham's Qawl fi al-Makan (Discourse on Place) was an important treatise which presents geometrical demonstrations for his geometrization of place, in opposition to Aristotle's philosophical concept of place, which Ibn al-Haytham rejected on mathematical grounds. Abd-el-latif, a supporter of Aristotle's philosophical view of place, later criticized the work in Fi al-Radd ‘ala Ibn al-Haytham fi al-makan (A refutation of Ibn al-Haytham’s place) for its geometrization of place.[31]

Other contributions

Yasmeen M. Faruqi writes:

"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."[32]

Alhazen's problem

His work on catoptrics in Book V of the Book of Optics contains the important problem known as Alhazen's problem. It comprises drawing lines from two points in the plane of a circle meeting at a point on the circumference and making equal angles with the normal at that point. This leads to an equation of the fourth degree. This eventually led Ibn al-Haytham to derive the earliest formula for the sum of the fourth powers, and using an early proof by mathematical induction, he developed a method for determining the general formula for the sum of any integral powers, which was fundamental to the development of infinitesimal and integral calculus.[6]

Ibn al-Haytham solved the problem using conic sections and a geometric proof, but Alhazen's problem remained influential in Europe, when later mathematicians such as Christiaan Huygens, James Gregory, Guillaume de l'Hôpital, Isaac Barrow, and many others, attempted to find an algebraic solution to the problem, using various methods, including analytic methods of geometry and derivation by complex numbers.[33] Mathematicians were not able to find an algebraic solution to the problem until the end of the 20th century.[19]

Geometry

In mathematics, Ibn al-Haytham developed analytical geometry by establishing linkage between algebra and geometry. Ibn al-Haytham also discovered a formula for adding the first 100 natural numbers, which was later often attributed to Carl Friedrich Gauss. Ibn al-Haytham had used a geometric proof to prove the formula.[34] His attempted proof of the parallel postulate was also similar to the Lambert quadrilateral and Playfair's axiom in the 18th century.[33]

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.[21] 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.[28]

Hockney-Falco thesis

Main article: Hockney-Falco thesis

At a scientific conference in February 2007, Charles M. Falco speculated that Ibn al-Haytham did work on optics that 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 c. 1430, arguably initiated as a result of Ibn al-Haytham's influence, until today."[35]

See also

Notes

  1. ^ David Agar (2001). Arabic Studies in Physics and Astronomy During 800 - 1400 AD. University of Jyväskylä.
  2. ^ a b Rosanna Gorini (2003). "Al-Haytham the Man of Experience. First Steps in the Science of Vision", International Society for the History of Islamic Medicine. Institute of Neurosciences, Laboratory of Psychobiology and Psychopharmacology, Rome, Italy.
  3. ^ Bradley Steffens (2006). Ibn al-Haytham: First Scientist, Morgan Reynolds Publishing, ISBN 1599350246.
  4. ^ a b Nicholas J. Wade, Stanley Finger (2001), "The eye as an optical instrument: from camera obscura to Helmholtz's perspective", Perception 30 (10), p. 1157-1177.
  5. ^ a b c Abdus Salam (1984), "Islam and Science". In C. H. Lai (1987), Ideals and Realities: Selected Essays of Abdus Salam, 2nd ed., World Scientific, Singapore, p. 179-213.
  6. ^ a b Victor J. Katz (1995). "Ideas of Calculus in Islam and India", Mathematics Magazine 68 (3), p. 163-174.
  7. ^ a b c O. S. Marshall (1950). "Alhazen and the Telescope", Astronomical Society of the Pacific Leaflets 6, p. 4.
  8. ^ a b c d e f Dr. Mahmoud Al Deek. "Ibn Al-Haitham: Master of Optics, Mathematics, Physics and Medicine, Al Shindagah, November-December 2004.
  9. ^ a b Roshdi Rashed (August 2002). "A Polymath in the 10th Century", Science 297 (5582), p. 773.
  10. ^ David C. Lindberg. Roger Bacon and the Origins of Perspectiva in the Middle Ages. Clarendon Press 1996, p. 11, passim.
  11. ^ David C. Lindberg, "Alhazen's Theory of Vision and Its Reception in the West", Isis, 58 (1967): 321-341.
  12. ^ Bradley Steffens (2006), Ibn al-Haytham: First Scientist, Morgan Reynolds Publishing, ISBN 1599350246. (cf. Reviews of Ibn al-Haytham: First Scientist, The Critics, Barnes & Noble.)
  13. ^ D. C. Lindberg, Theories of Vision from al-Kindi to Kepler, (Chicago, Univ. of Chicago Pr., 1976), pp. 60-7.
  14. ^ Albrecht Heeffer. Kepler’s near discovery of the sine law: A qualitative computational model, Ghent University, Belgium.
  15. ^ A. I. Sabra (1981), Theories of Light from Descartes to Newton, Cambridge University Press. (cf. Pavlos Mihas, Use of History in Developing ideas of refraction, lenses and rainbow, p. 5, Demokritus University, Thrace, Greece.)
  16. ^ R. S. Elliott (1966). Electromagnetics, Chapter 1. McGraw-Hill.
  17. ^ A. C. Crombie, Robert Grosseteste and the Origins of Experimental Science, 1100 - 1700, (Oxford: Clarendon Press, 1971), p. 147, n. 2.
  18. ^ 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. pp. xxi. ISBN 9780871699145..
  19. ^ a b c Bradley Steffens (2006). Ibn al-Haytham: First Scientist, Chapter 5. Morgan Reynolds Publishing. ISBN 1599350246.
  20. ^ a b c Dr. Nader El-Bizri, "Ibn al-Haytham or Alhazen", in Josef W. Meri (2006), Medieval Islamic Civilization: An Encyclopaedia, Vol. II, p. 343-345, Routledge, New York, London.
  21. ^ a b c O'Connor, John J.; Robertson, Edmund F., "Abu Ali al-Hasan ibn al-Haytham", MacTutor History of Mathematics Archive, University of St Andrews
  22. ^ Y. Tzvi Langerman, Ibn al Haytham's On the Configuration of the World, p. 8-10
  23. ^ Nicolaus Copernicus. Stanford Encyclopedia of Philosophy (2004).
  24. ^ Some writers, however, argue that Alhazen's critique constituted a form of heliocentricity. (See Asghar Qadir, Relativity: An Introduction to the Special Theory, Singapore: World Scientific Publishing Co., 1989, pp. 5-6, 10.)
  25. ^ Y. Tzvi Langerman, Ibn al Haytham's On the Configuration of the World, chap. 2, sect.22, p. 61.
  26. ^ Vernon O. Georgia (2003). A History of the Muslim World to 1405: The Making of a Civilization, p. 200. Prentice Hall. ISBN 0-13-098389-6.
  27. ^ Prabhakar M. Gondhalekar (2001). The Grip of Gravity: The Quest to Understand the Laws of Motion and Gravitation, p. 21. Cambridge University Press. ISBN 0521803160.
  28. ^ a b c A. I. Sabra, Ibn al-Haytham: Brief life of an Arab mathematician, Harvard Magazine, October-December 2003.
  29. ^ Roshdi Rashed (2007). "The Celestial Kinematics of Ibn al-Haytham", Arabic Sciences and Philosophy 17, p. 7-55. Cambridge University Press.
  30. ^ 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.
  31. ^ Nader el-Bizri (2007). "In Defence of the Sovereignty of Philosophy: Al-Baghdadi's Critique of Ibn al-Haytham's Geometrisation of Place", Arabic Sciences and Philosophy 17, p. 57-80. Cambridge University Press.
  32. ^ Y. M. Faruqi (2006). "Contributions of Islamic scholars to the scientific enterprise", International Education Journal 7 (4), p. 395-396.
  33. ^ a b John D. Smith (1992). "The Remarkable Ibn al-Haytham", The Mathematical Gazette 76 (475), p. 189-198.
  34. ^ J. Rottman. A first course in Abstract Algebra, Chapter 1.
  35. ^ Falco, Charles M. "Ibn al-Haytham and the Origins of Modern Image Analysis", presented at a plenary session at the International Conference on Information Sciences, Signal Processing and its Applications, 12–15 February 2007. Sharjah, United Arab Emirates (U.A.E.). [1]

References

  • Lindberg, David C. Theories of Vision from al-Kindi to Kepler. Chicago: Univ. of Chicago Press, 1976. ISBN 0-226-48234-0
  • Sabra, A. I., "The astronomical origin of Ibn al-Haytham’s concept of experiment," pp. 133-136 in Actes du XIIe congrès international d’histoire des sciences, vol. 3. Paris: Albert Blanchard, 1971; reprinted in A. I. Sabra, Optics, Astronomy and Logic: Studies in Arabic Science and Philosophy. Collected Studies Series, 444. Aldershot: Variorum, 1994 ISBN 0-86078-435-5
  • Omar, Saleh Beshara. Ibn al-Haytham's Optics: A Study of the Origins of Experimental Science. Minneapolis: Bibliotheca Islamica, 1977. ISBN 0-88297-015-1

Further reading

Primary Sources

  • Langermann, Y. Tzvi, ed. and trans. Ibn al-Haytham's On the Configuration of the World, Harvard Dissertations in the History of Science. New York: Garland, 1990. ISBN 0824000412
  • Sabra, A. I., ed. 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, 1983.
  • Sabra, A. I., ed. 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, 2002.
  • Sabra, A. I., trans. 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, 1989. ISBN 0-85481-072-2
  • Smith, A. Mark, ed. and trans. 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, 2001. ISBN 0-87169-914-1
  • Smith, A. Mark, ed. and trans. 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, 2006. ISBN 0-87169-962-1

Secondary Literature

  • Falco, Charles M. "Ibn al-Haytham and the Origins of Modern Image Analysis" presented at a plenary session at the International Conference on Information Sciences, Signal Processing and its Applications, 12–15 February 2007. Sharjah, United Arab Emirates (U.A.E.).[4] In this lecture, Falco speculates that Ibn al-Haytham may have influenced the use of optical aids in Renaissance art. (See Hockney-Falco thesis.}
  • Omar, Saleh Beshara. Ibn al-Haytham and Greek optics: a comparative study in scientific methodology. PhD Dissertation, Univ. of Chicago, Dept. of Near Eastern Languages and Civilizations, June 1975.

External links

See also

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