Menu
Home Explore People Places Arts History Plants & Animals Science Life & Culture Technology
On this page
Ibn al-Haytham
Arab physicist, mathematician and astronomer (c. 965 – c. 1040)

Ḥasan Ibn al-Haytham (Latinized as Alhazen; c. 965–c. 1040) was a medieval mathematician, astronomer, and physicist from the Islamic Golden Age, renowned as "the father of modern optics." His seminal work, the Kitāb al-Manāẓir ("Book of Optics"), profoundly influenced later scientists like Isaac Newton and Kepler. Ibn al-Haytham correctly explained vision theory, emphasizing its brain-based nature, and introduced principles foundational to Fermat's principle of least time. A pioneer of the scientific method, he advocated experimental validation centuries before the Renaissance. Born in Basra, he worked mainly in Cairo, earning titles like the "Second Ptolemy" and profoundly shaping physical optics.

Related Image Collections Add Image
Profiles
1 Image
We don't have any YouTube videos related to Ibn al-Haytham yet.
We don't have any PDF documents related to Ibn al-Haytham yet.
We don't have any Books related to Ibn al-Haytham yet.

Biography

Ibn al-Haytham (Alhazen) was born c. 965 to a family of Arab272829303132 or Persian3334353637 origin in Basra, Iraq, which was at the time part of the Buyid emirate. His initial influences were in the study of religion and service to the community. At the time, society had a number of conflicting views of religion that he ultimately sought to step aside from religion. This led to him delving into the study of mathematics and science.38 He held a position with the title of vizier in his native Basra, and became famous for his knowledge of applied mathematics, as evidenced by his attempt to regulate the flooding of the Nile.39

Upon his return to Cairo, he was given an administrative post. After he proved unable to fulfill this task as well, he contracted the ire of the caliph Al-Hakim,40 and is said to have been forced into hiding until the caliph's death in 1021, after which his confiscated possessions were returned to him.41 Legend has it that Alhazen feigned madness and was kept under house arrest during this period.42 During this time, he wrote his influential Book of Optics. Alhazen continued to live in Cairo, in the neighborhood of the famous University of al-Azhar, and lived from the proceeds of his literary production43 until his death in c. 1040.44 (A copy of Apollonius' Conics, written in Ibn al-Haytham's own handwriting exists in Aya Sofya: (MS Aya Sofya 2762, 307 fob., dated Safar 415 A.H. [1024]).)45: Note 2 

Among his students were Sorkhab (Sohrab), a Persian from Semnan, and Abu al-Wafa Mubashir ibn Fatek, an Egyptian prince.46[verification needed]

Book of Optics

Main article: Book of Optics

Alhazen's most famous work is his seven-volume treatise on optics Kitab al-Manazir (Book of Optics), written from 1011 to 1021.47 In it, Ibn al-Haytham was the first to explain that vision occurs when light reflects from an object and then passes to one's eyes,48 and to argue that vision occurs in the brain, pointing to observations that it is subjective and affected by personal experience.49

Optics was translated into Latin by an unknown scholar at the end of the 12th century or the beginning of the 13th century.5051

This work enjoyed a great reputation during the Middle Ages. The Latin version of De aspectibus was translated at the end of the 14th century into Italian vernacular, under the title De li aspecti.52

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 (English: Treasury of Optics: seven books by the Arab Alhazen, first edition; by the same, on twilight and the height of clouds).53 Risner is also the author of the name variant "Alhazen"; before Risner he was known in the west as Alhacen.54 Works by Alhazen on geometric subjects were discovered in the Bibliothèque nationale in Paris in 1834 by E. A. Sedillot. In all, A. Mark Smith has accounted for 18 full or near-complete manuscripts, and five fragments, which are preserved in 14 locations, including one in the Bodleian Library at Oxford, and one in the library of Bruges.55

Theory of optics

See also: Horopter

Two major theories on vision prevailed in classical antiquity. The first theory, the emission theory, was supported by such thinkers as Euclid and Ptolemy, who believed that sight worked by the eye emitting rays of light. The second theory, the intromission theory supported by Aristotle and his followers, had physical forms entering the eye from an object. Previous Islamic writers (such as al-Kindi) had argued essentially on Euclidean, Galenist, or Aristotelian lines. The strongest influence on the Book of Optics was from Ptolemy's Optics, while the description of the anatomy and physiology of the eye was based on Galen's account.56 Alhazen's achievement was to come up with a theory that successfully combined parts of the mathematical ray arguments of Euclid, the medical tradition of Galen, and the intromission theories of Aristotle. Alhazen's intromission theory followed al-Kindi (and broke with Aristotle) in asserting that "from each point of every colored body, illuminated by any light, issue light and color along every straight line that can be drawn from that point".57 This left him with the problem of explaining how a coherent image was formed from many independent sources of radiation; in particular, every point of an object would send rays to every point on the eye.

What Alhazen needed was for each point on an object to correspond to one point only on the eye.58 He attempted to resolve this by asserting that the eye would only perceive perpendicular rays from the object – for any one point on the eye, only the ray that reached it directly, without being refracted by any other part of the eye, would be perceived. He argued, using a physical analogy, that perpendicular rays were stronger than oblique rays: in the same way that a ball thrown directly at a board might break the board, whereas a ball thrown obliquely at the board would glance off, perpendicular rays were stronger than refracted rays, and it was only perpendicular rays which were perceived by the eye. As there was only one perpendicular ray that would enter the eye at any one point, and all these rays would converge on the centre of the eye in a cone, this allowed him to resolve the problem of each point on an object sending many rays to the eye; if only the perpendicular ray mattered, then he had a one-to-one correspondence and the confusion could be resolved.59 He later asserted (in book seven of the Optics) that other rays would be refracted through the eye and perceived as if perpendicular.60 His arguments regarding perpendicular rays do not clearly explain why only perpendicular rays were perceived; why would the weaker oblique rays not be perceived more weakly?61 His later argument that refracted rays would be perceived as if perpendicular does not seem persuasive.62 However, despite its weaknesses, no other theory of the time was so comprehensive, and it was enormously influential, particularly in Western Europe. Directly or indirectly, his De Aspectibus (Book of Optics) inspired much activity in optics between the 13th and 17th centuries. Kepler's later theory of the retinal image (which resolved the problem of the correspondence of points on an object and points in the eye) built directly on the conceptual framework of Alhazen.63

Alhazen showed through experiment that light travels in straight lines, and carried out various experiments with lenses, mirrors, refraction, and reflection.64 His analyses of reflection and refraction considered the vertical and horizontal components of light rays separately.65

Alhazen studied the process of sight, the structure of the eye, image formation in the eye, and the visual system. Ian P. Howard argued in a 1996 Perception article that Alhazen should be credited with many discoveries and theories previously attributed to Western Europeans writing centuries later. For example, he described what became in the 19th century Hering's law of equal innervation. He wrote a description of vertical horopters 600 years before Aguilonius that is actually closer to the modern definition than Aguilonius's – and his work on binocular disparity was repeated by Panum in 1858.66 Craig Aaen-Stockdale, while agreeing that Alhazen should be credited with many advances, has expressed some caution, especially when considering Alhazen in isolation from Ptolemy, with whom Alhazen was extremely familiar. Alhazen corrected a significant error of Ptolemy regarding binocular vision, but otherwise his account is very similar; Ptolemy also attempted to explain what is now called Hering's law.67 In general, Alhazen built on and expanded the optics of Ptolemy.68

In a more detailed account of Ibn al-Haytham's contribution to the study of binocular vision based on Lejeune69 and Sabra,70 Raynaud71 showed that the concepts of correspondence, homonymous and crossed diplopia were in place in Ibn al-Haytham's optics. But contrary to Howard, he explained why Ibn al-Haytham did not give the circular figure of the horopter and why, by reasoning experimentally, he was in fact closer to the discovery of Panum's fusional area than that of the Vieth-Müller circle. In this regard, Ibn al-Haytham's theory of binocular vision faced two main limits: the lack of recognition of the role of the retina, and obviously the lack of an experimental investigation of ocular tracts.

Alhazen's most original contribution was that, after describing how he thought the eye was anatomically constructed, he went on to consider how this anatomy would behave functionally as an optical system.72 His understanding of pinhole projection from his experiments appears to have influenced his consideration of image inversion in the eye,73 which he sought to avoid.74 He maintained that the rays that fell perpendicularly on the lens (or glacial humor as he called it) were further refracted outward as they left the glacial humor and the resulting image thus passed upright into the optic nerve at the back of the eye.75 He followed Galen in believing that the lens was the receptive organ of sight, although some of his work hints that he thought the retina was also involved.76

Alhazen's synthesis of light and vision adhered to the Aristotelian scheme, exhaustively describing the process of vision in a logical, complete fashion.77

His research in catoptrics (the study of optical systems using mirrors) was centred on spherical and parabolic mirrors and spherical aberration. He made the observation that the ratio between the angle of incidence and refraction does not remain constant, and investigated the magnifying power of a lens.78

Law of reflection

Main article: Specular reflection

Alhazen was the first physicist to give complete statement of the law of reflection.798081 He was first to state that the incident ray, the reflected ray, and the normal to the surface all lie in a same plane perpendicular to reflecting plane.8283

Alhazen's problem

Main article: Alhazen's problem

His work on catoptrics in Book V of the Book of Optics contains a discussion of what is now known as Alhazen's problem, first formulated by Ptolemy in 150 AD. It comprises drawing lines from two points in the plane of a circle meeting at a point on the circumference and making equal angles with the normal at that point. This is equivalent to finding the point on the edge of a circular billiard table at which a player must aim a cue ball at a given point to make it bounce off the table edge and hit another ball at a second given point. Thus, its main application in optics is to solve the problem, "Given a light source and a spherical mirror, find the point on the mirror where the light will be reflected to the eye of an observer." This leads to an equation of the fourth degree.84 This eventually led Alhazen to derive a formula for the sum of fourth powers, where previously only the formulas for the sums of squares and cubes had been stated. His method can be readily generalized to find the formula for the sum of any integral powers, although he did not himself do this (perhaps because he only needed the fourth power to calculate the volume of the paraboloid he was interested in). He used his result on sums of integral powers to perform what would now be called an integration, where the formulas for the sums of integral squares and fourth powers allowed him to calculate the volume of a paraboloid.85 Alhazen eventually solved the problem using conic sections and a geometric proof. His solution was extremely long and complicated and may not have been understood by mathematicians reading him in Latin translation. Later mathematicians used Descartes' analytical methods to analyse the problem.86 An algebraic solution to the problem was finally found in 1965 by Jack M. Elkin, an actuarian.87 Other solutions were discovered in 1989, by Harald Riede88 and in 1997 by the Oxford mathematician Peter M. Neumann.8990 Recently, Mitsubishi Electric Research Laboratories (MERL) researchers solved the extension of Alhazen's problem to general rotationally symmetric quadric mirrors including hyperbolic, parabolic and elliptical mirrors.91

Camera Obscura

The camera obscura was known to the ancient Chinese, and was described by the Han Chinese polymath Shen Kuo in his scientific book Dream Pool Essays, published in the year 1088 C.E. Aristotle had discussed the basic principle behind it in his Problems, but Alhazen's work contained the first clear description of camera obscura.92 and early analysis93 of the device.

Ibn al-Haytham used a camera obscura mainly to observe a partial solar eclipse.94 In his essay, Ibn al-Haytham writes that he observed the sickle-like shape of the sun at the time of an eclipse. The introduction reads as follows: "The image of the sun at the time of the eclipse, unless it is total, demonstrates that when its light passes through a narrow, round hole and is cast on a plane opposite to the hole it takes on the form of a moonsickle."

It is admitted that his findings solidified the importance in the history of the camera obscura95 but this treatise is important in many other respects.

Ancient optics and medieval optics were divided into optics and burning mirrors. Optics proper mainly focused on the study of vision, while burning mirrors focused on the properties of light and luminous rays. On the shape of the eclipse is probably one of the first attempts made by Ibn al-Haytham to articulate these two sciences.

Very often Ibn al-Haytham's discoveries benefited from the intersection of mathematical and experimental contributions. This is the case with On the shape of the eclipse. Besides the fact that this treatise allowed more people to study partial eclipses of the sun, it especially allowed to better understand how the camera obscura works. This treatise is a physico-mathematical study of image formation inside the camera obscura. Ibn al-Haytham takes an experimental approach, and determines the result by varying the size and the shape of the aperture, the focal length of the camera, the shape and intensity of the light source.96

In his work he explains the inversion of the image in the camera obscura,97 the fact that the image is similar to the source when the hole is small, but also the fact that the image can differ from the source when the hole is large. All these results are produced by using a point analysis of the image.98

Refractometer

Main article: Refractometer

In the seventh tract of his book of optics, Alhazen described an apparatus for experimenting with various cases of refraction, in order to investigate the relations between the angle of incidence, the angle of refraction and the angle of deflection. This apparatus was a modified version of an apparatus used by Ptolemy for similar purpose.99100101

Unconscious inference

Main article: Unconscious inference

Alhazen basically states the concept of unconscious inference in his discussion of colour before adding that the inferential step between sensing colour and differentiating it is shorter than the time taken between sensing and any other visible characteristic (aside from light), and that "time is so short as not to be clearly apparent to the beholder." Naturally, this suggests that the colour and form are perceived elsewhere. Alhazen goes on to say that information must travel to the central nerve cavity for processing and:

the sentient organ does not sense the forms that reach it from the visible objects until after it has been affected by these forms; thus it does not sense color as color or light as light until after it has been affected by the form of color or light. Now the affectation received by the sentient organ from the form of color or of light is a certain change; and change must take place in time; .....and it is in the time during which the form extends from the sentient organ's surface to the cavity of the common nerve, and in (the time) following that, that the sensitive faculty, which exists in the whole of the sentient body will perceive color as color...Thus the last sentient's perception of color as such and of light as such takes place at a time following that in which the form arrives from the surface of the sentient organ to the cavity of the common nerve.102

Color constancy

Main article: Color constancy

Alhazen explained color constancy by observing that the light reflected from an object is modified by the object's color. He explained that the quality of the light and the color of the object are mixed, and the visual system separates light and color. In Book II, Chapter 3 he writes:

Again the light does not travel from the colored object to the eye unaccompanied by the color, nor does the form of the color pass from the colored object to the eye unaccompanied by the light. Neither the form of the light nor that of the color existing in the colored object can pass except as mingled together and the last sentient can only perceive them as mingled together. Nevertheless, the sentient perceives that the visible object is luminous and that the light seen in the object is other than the color and that these are two properties.103

Other contributions

The Kitab al-Manazir (Book of Optics) describes several experimental observations that Alhazen made and how he used his results to explain certain optical phenomena using mechanical analogies. He conducted experiments with projectiles and concluded that only the impact of perpendicular projectiles on surfaces was forceful enough to make them penetrate, whereas surfaces tended to deflect oblique projectile strikes. For example, to explain refraction from a rare to a dense medium, he used the mechanical analogy of an iron ball thrown at a thin slate covering a wide hole in a metal sheet. A perpendicular throw breaks the slate and passes through, whereas an oblique one with equal force and from an equal distance does not.104 He also used this result to explain how intense, direct light hurts the eye, using a mechanical analogy: Alhazen associated 'strong' lights with perpendicular rays and 'weak' lights with oblique ones. The obvious answer to the problem of multiple rays and the eye was in the choice of the perpendicular ray, since only one such ray from each point on the surface of the object could penetrate the eye.105

Sudanese psychologist Omar Khaleefa has argued that Alhazen should be considered the founder of experimental psychology, for his pioneering work on the psychology of visual perception and optical illusions.106 Khaleefa has also argued that Alhazen should also be considered the "founder of psychophysics", a sub-discipline and precursor to modern psychology.107 Although Alhazen made many subjective reports regarding vision, there is no evidence that he used quantitative psychophysical techniques and the claim has been rebuffed.108

Alhazen offered an explanation of the Moon illusion, an illusion that played an important role in the scientific tradition of medieval Europe.109 Many authors repeated explanations that attempted to solve the problem of the Moon appearing larger near the horizon than it does when higher up in the sky. Alhazen argued against Ptolemy's refraction theory, and defined the problem in terms of perceived, rather than real, enlargement. He said that judging the distance of an object depends on there being an uninterrupted sequence of intervening bodies between the object and the observer. When the Moon is high in the sky there are no intervening objects, so the Moon appears close. The perceived size of an object of constant angular size varies with its perceived distance. Therefore, the Moon appears closer and smaller high in the sky, and further and larger on the horizon. Through works by Roger Bacon, John Pecham and Witelo based on Alhazen's explanation, the Moon illusion gradually came to be accepted as a psychological phenomenon, with the refraction theory being rejected in the 17th century.110 Although Alhazen is often credited with the perceived distance explanation, he was not the first author to offer it. Cleomedes (c. 2nd century) gave this account (in addition to refraction), and he credited it to Posidonius (c. 135–50 BCE).111 Ptolemy may also have offered this explanation in his Optics, but the text is obscure.112 Alhazen's writings were more widely available in the Middle Ages than those of these earlier authors, and that probably explains why Alhazen received the credit.

Scientific method

Further information: Scientific method

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. 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 ... 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.

— Alhazen113

An aspect associated with Alhazen's optical research is related to systemic and methodological reliance on experimentation (i'tibar)(Arabic: اختبار) 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). This mathematical-physical approach to experimental science supported most of his propositions in Kitab al-Manazir (The Optics; De aspectibus or Perspectivae)114 and grounded his theories of vision, light and colour, as well as his research in catoptrics and dioptrics (the study of the reflection and refraction of light, respectively).115

According to Matthias Schramm,116 Alhazen "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."117 G. J. Toomer expressed some skepticism regarding Schramm's view,118 partly because at the time (1964) the Book of Optics had not yet been fully translated from Arabic, and Toomer was concerned that without context, specific passages might be read anachronistically. While acknowledging Alhazen's importance in developing experimental techniques, Toomer argued that Alhazen should not be considered in isolation from other Islamic and ancient thinkers.119 Toomer concluded his review by saying that it would not be possible to assess Schramm's claim that Ibn al-Haytham was the true founder of modern physics without translating more of Alhazen's work and fully investigating his influence on later medieval writers.120

Other works on physics

Optical treatises

Besides the Book of Optics, Alhazen wrote several other treatises on the same subject, including his Risala fi l-Daw' (Treatise on Light). He investigated the properties of luminance, the rainbow, eclipses, twilight, and moonlight. Experiments with mirrors and the refractive interfaces between air, water, and glass cubes, hemispheres, and quarter-spheres provided the foundation for his theories on catoptrics.121

Celestial physics

Alhazen discussed the physics of the celestial region in his Epitome of Astronomy, arguing that Ptolemaic models must be understood in terms of physical objects rather than abstract hypotheses – in other words that it should be possible to create physical models where (for example) none of the celestial bodies would collide with each other. The suggestion of mechanical models for the Earth centred Ptolemaic model "greatly contributed to the eventual triumph of the Ptolemaic system among the Christians of the West". Alhazen's determination to root astronomy in the realm of physical objects was important, however, because it meant astronomical hypotheses "were accountable to the laws of physics", and could be criticised and improved upon in those terms.122

He also wrote Maqala fi daw al-qamar (On the Light of the Moon).

Mechanics

In his work, Alhazen discussed theories on the motion of a body.123

Astronomical works

On the Configuration of the World

In his On the Configuration of the World Alhazen presented a detailed description of the physical structure of the earth:

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.124

The book is a non-technical explanation of Ptolemy's Almagest, which was eventually translated into Hebrew and Latin in the 13th and 14th centuries and subsequently had an influence on astronomers such as Georg von Peuerbach125 during the European Middle Ages and Renaissance.126

Doubts Concerning Ptolemy

In his Al-Shukūk ‛alā Batlamyūs, variously translated as Doubts Concerning Ptolemy or Aporias against Ptolemy, published at some time between 1025 and 1028, Alhazen criticized Ptolemy's Almagest, Planetary Hypotheses, and Optics, pointing out various contradictions he found in these works, particularly in astronomy. Ptolemy's Almagest concerned mathematical theories regarding the motion of the planets, whereas the Hypotheses concerned what Ptolemy thought was the actual configuration of the planets. Ptolemy himself acknowledged that his theories and configurations did not always agree with each other, arguing that this was not a problem provided it did not result in noticeable error, but Alhazen was particularly scathing in his criticism of the inherent contradictions in Ptolemy's works.127 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 noted the absurdity of relating actual physical motions to imaginary mathematical points, lines and circles:128

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.129

Having pointed out the problems, Alhazen appears to have intended to resolve the contradictions he pointed out in Ptolemy in a later work. Alhazen believed there was a "true configuration" of the planets that Ptolemy had failed to grasp. He intended to complete and repair Ptolemy's system, not to replace it completely.130 In the Doubts Concerning Ptolemy Alhazen set out his views on the difficulty of attaining scientific knowledge and the need to question existing authorities and theories:

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...131

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

Model of the Motions of Each of the Seven Planets

Alhazen's The Model of the Motions of Each of the Seven Planets was written c. 1038. Only one damaged manuscript has been found, with only the introduction and the first section, on the theory of planetary motion, surviving. (There was also a second section on astronomical calculation, and a third section, on astronomical instruments.) Following on from his Doubts on Ptolemy, Alhazen described a new, geometry-based planetary model, describing the motions of the planets in terms of spherical geometry, infinitesimal geometry and trigonometry. He kept a geocentric universe and assumed that celestial motions are uniformly circular, which required the inclusion of epicycles to explain observed motion, but he managed to eliminate Ptolemy's equant. In general, his model didn't try to provide a causal explanation of the motions, but concentrated on providing a complete, geometric description that could explain observed motions without the contradictions inherent in Ptolemy's model.132

Other astronomical works

Alhazen wrote a total of twenty-five astronomical works, some concerning technical issues such as Exact Determination of the Meridian, a second group concerning accurate astronomical observation, a third group concerning various astronomical problems and questions such as the location of the Milky Way; Alhazen made the first systematic effort of evaluating the Milky Way's parallax, combining Ptolemy's data and his own. He concluded that the parallax is (probably very much) smaller than Lunar parallax, and the Milky way should be a celestial object. Though he was not the first who argued that the Milky Way does not belong to the atmosphere, he is the first who did quantitative analysis for the claim.133 The fourth group consists of ten works on astronomical theory, including the Doubts and Model of the Motions discussed above.134

Mathematical works

In mathematics, Alhazen built on the mathematical works of Euclid and Thabit ibn Qurra and worked on "the beginnings of the link between algebra and geometry". Alhazen made developments in conic sections and number theory.135

He developed a formula for summing the first 100 natural numbers, using a geometric proof to prove the formula.136

Geometry

Alhazen explored what is now known as the Euclidean parallel postulate, the fifth postulate in Euclid's Elements, using a proof by contradiction,137 and in effect introducing the concept of motion into geometry.138 He formulated the Lambert quadrilateral, which Boris Abramovich Rozenfeld names the "Ibn al-Haytham–Lambert quadrilateral".139 He was criticised by Omar Khayyam who pointed that Aristotle had condemned the use of motion in geometry.140

In elementary geometry, Alhazen attempted to solve the problem of squaring the circle using the area of lunes (crescent shapes), but later gave up on the impossible task.141 The two lunes formed from a right triangle by erecting a semicircle on each of the triangle's sides, inward for the hypotenuse and outward for the other two sides, are known as the lunes of Alhazen; they have the same total area as the triangle itself.142

Number theory

Alhazen's contributions to number theory include his work on perfect numbers. In his Analysis and Synthesis, he may have been the first to state 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; Euler later proved it in the 18th century, and it is now called the Euclid–Euler theorem.143

Alhazen solved problems involving congruences using what is now called Wilson's theorem. In his Opuscula, Alhazen 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.144

Calculus

Alhazen discovered the sum formula for the fourth power, using a method that could be generally used to determine the sum for any integral power. He used this to find the volume of a paraboloid. He could find the integral formula for any polynomial without having developed a general formula.145

Other works

Influence of Melodies on the Souls of Animals

Alhazen also wrote a Treatise on the Influence of Melodies on the Souls of Animals, although no copies have survived. It appears to have been concerned with the question of whether animals could react to music, for example whether a camel would increase or decrease its pace.

Engineering

In engineering, one account of his career as a civil engineer has him summoned to Egypt by the Fatimid Caliph, Al-Hakim bi-Amr Allah, to regulate the flooding of the Nile River. He carried out a detailed scientific study of the annual inundation of the Nile River, and he drew plans for building a dam, at the site of the modern-day Aswan Dam. His field work, however, later made him aware of the impracticality of this scheme, and he soon feigned madness so he could avoid punishment from the Caliph.146

Philosophy

In his Treatise on Place, Alhazen disagreed with Aristotle's view that nature abhors a void, and he used geometry in an attempt to demonstrate that place (al-makan) is the imagined three-dimensional void between the inner surfaces of a containing body.147 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.148

Alhazen also discussed space perception and its epistemological implications in his Book of Optics. In "tying the visual perception of space to prior bodily experience, Alhazen 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."149

Theology

Alhazen was a Muslim and most sources report that he was a Sunni and a follower of the Ash'ari school.150151152153 Ziauddin Sardar says that some of the greatest Muslim scientists, such as Ibn al-Haytham and Abū Rayhān al-Bīrūnī, who were pioneers of the scientific method, were themselves followers of the Ashʿari school of Islamic theology.154 Like other Ashʿarites who believed that faith or taqlid should apply only to Islam and not to any ancient Hellenistic authorities,155 Ibn al-Haytham's view that taqlid should apply only to prophets of Islam and not to any other authorities formed the basis for much of his scientific skepticism and criticism against Ptolemy and other ancient authorities in his Doubts Concerning Ptolemy and Book of Optics.156

Alhazen wrote a work on Islamic theology in which he discussed prophethood and developed a system of philosophical criteria to discern its false claimants in his time.157 He also wrote a treatise entitled Finding the Direction of Qibla by Calculation in which he discussed finding the Qibla, where prayers (salat) are directed towards, mathematically.158

There are occasional references to theology or religious sentiment in his technical works, e.g. in Doubts Concerning Ptolemy:

Truth is sought for its own sake ... Finding the truth is difficult, and the road to it is rough. For the truths are plunged in obscurity. ... God, however, has not preserved the scientist from error and has not safeguarded science from shortcomings and faults. If this had been the case, scientists would not have disagreed upon any point of science...159

In The Winding Motion:

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.160

Regarding the relation of objective truth and 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.161

Legacy

Alhazen made significant contributions to optics, number theory, geometry, astronomy and natural philosophy. Alhazen's work on optics is credited with contributing a new emphasis on experiment.

His main work, Kitab al-Manazir (Book of Optics), was known in the Muslim world mainly, but not exclusively, through the thirteenth-century commentary by Kamāl al-Dīn al-Fārisī, the Tanqīḥ al-Manāẓir li-dhawī l-abṣār wa l-baṣā'ir.162 In al-Andalus, it was used by the eleventh-century prince of the Banu Hud dynasty of Zaragossa and author of an important mathematical text, al-Mu'taman ibn Hūd. A Latin translation of the Kitab al-Manazir was made probably in the late twelfth or early thirteenth century.163 This translation was read by and greatly influenced a number of scholars in Christian Europe including: Roger Bacon,164 Robert Grosseteste,165 Witelo, Giambattista della Porta,166 Leonardo da Vinci,167 Galileo Galilei,168 Christiaan Huygens,169 René Descartes,170 and Johannes Kepler.171 Meanwhile, in the Islamic world, Alhazen's work influenced Averroes' writings on optics, and his legacy was further advanced through the 'reforming' of his Optics by Persian scientist Kamal al-Din al-Farisi (died c. 1320) in the latter's Kitab Tanqih al-Manazir (The Revision of [Ibn al-Haytham's] Optics).172 Alhazen wrote as many as 200 books, although only 55 have survived. 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.

H. J. J. Winter, a British historian of science, summing up the importance of Ibn al-Haytham in the history of physics wrote:

After the death of Archimedes no really great physicist appeared until Ibn al-Haytham. If, therefore, we confine our interest only to the history of physics, there is a long period of over twelve hundred years during which the Golden Age of Greece gave way to the era of Muslim Scholasticism, and the experimental spirit of the noblest physicist of Antiquity lived again in the Arab Scholar from Basra.173

Although only one commentary on Alhazen's optics has survived the Islamic Middle Ages, Geoffrey Chaucer mentions the work in The Canterbury Tales:174

"They spoke of Alhazen and Vitello, And Aristotle, who wrote, in their lives, On strange mirrors and optical instruments."

The impact crater Alhazen on the Moon is named in his honour,175 as was the asteroid 59239 Alhazen.176 In honour of Alhazen, the Aga Khan University (Pakistan) named its Ophthalmology endowed chair as "The Ibn-e-Haitham Associate Professor and Chief of Ophthalmology".177

The 2015 International Year of Light celebrated the 1000th anniversary of the works on optics by Ibn Al-Haytham.178

In 2014, the "Hiding in the Light" episode of Cosmos: A Spacetime Odyssey, presented by Neil deGrasse Tyson, focused on the accomplishments of Ibn al-Haytham. He was voiced by Alfred Molina in the episode.

Over forty years previously, Jacob Bronowski presented Alhazen's work in a similar television documentary (and the corresponding book), The Ascent of Man. In episode 5 (The Music of the Spheres), Bronowski remarked that in his view, Alhazen was "the one really original scientific mind that Arab culture produced", whose theory of optics was not improved on till the time of Newton and Leibniz.

UNESCO declared 2015 the International Year of Light and its Director-General Irina Bokova dubbed Ibn al-Haytham 'the father of optics'.179 Amongst others, this was to celebrate Ibn Al-Haytham's achievements in optics, mathematics and astronomy. An international campaign, created by the 1001 Inventions organisation, titled 1001 Inventions and the World of Ibn Al-Haytham featuring a series of interactive exhibits, workshops and live shows about his work, partnering with science centers, science festivals, museums, and educational institutions, as well as digital and social media platforms.180 The campaign also produced and released the short educational film 1001 Inventions and the World of Ibn Al-Haytham.

Ibn al-Haytham appears on the 10,000 dinar banknote of the Iraqi dinar, series 2003.181

List of works

According to medieval biographers, Alhazen wrote more than 200 works on a wide range of subjects, of which at least 96 of his scientific works are known. Most of his works are now lost, but more than 50 of them have survived to some extent. Nearly half of his surviving works are on mathematics, 23 of them are on astronomy, and 14 of them are on optics, with a few on other subjects.182 Not all his surviving works have yet been studied, but some of the ones that have are given below.183

  1. Book of Optics (كتاب المناظر)
  2. Analysis and Synthesis (مقالة في التحليل والتركيب)
  3. Balance of Wisdom (ميزان الحكمة)
  4. Corrections to the Almagest (تصويبات على المجسطي)
  5. Discourse on Place (مقالة في المكان)
  6. Exact Determination of the Pole (التحديد الدقيق للقطب)
  7. Exact Determination of the Meridian (رسالة في الشفق)
  8. Finding the Direction of Qibla by Calculation (كيفية حساب اتجاه القبلة)
  9. Horizontal Sundials (المزولة الأفقية)
  10. Hour Lines (خطوط الساعة)
  11. Doubts Concerning Ptolemy (شكوك على بطليموس)
  12. Maqala fi'l-Qarastun (مقالة في قرسطون)
  13. On Completion of the Conics (إكمال المخاريط)
  14. On Seeing the Stars (رؤية الكواكب)
  15. On Squaring the Circle (مقالة فی تربیع الدائرة)
  16. On the Burning Sphere (المرايا المحرقة بالدوائر)
  17. On the Configuration of the World (تكوين العالم)
  18. On the Form of Eclipse (مقالة فی صورة ‌الکسوف)
  19. On the Light of Stars (مقالة في ضوء النجوم)184
  20. On the Light of the Moon (مقالة في ضوء القمر)
  21. On the Milky Way (مقالة في درب التبانة)
  22. On the Nature of Shadows (كيفيات الإظلال)
  23. On the Rainbow and Halo (مقالة في قوس قزح)
  24. Opuscula (Minor Works)
  25. Resolution of Doubts Concerning the Almagest (تحليل شكوك حول الجست)
  26. Resolution of Doubts Concerning the Winding Motion
  27. The Correction of the Operations in Astronomy (تصحيح العمليات في الفلك)
  28. The Different Heights of the Planets (اختلاف ارتفاع الكواكب)
  29. The Direction of Mecca (اتجاه القبلة)
  30. The Model of the Motions of Each of the Seven Planets (نماذج حركات الكواكب السبعة)
  31. The Model of the Universe (نموذج الكون)
  32. The Motion of the Moon (حركة القمر)
  33. The Ratios of Hourly Arcs to their Heights
  34. The Winding Motion (الحركة المتعرجة)
  35. Treatise on Light (رسالة في الضوء)185
  36. Treatise on Place (رسالة في المكان)
  37. Treatise on the Influence of Melodies on the Souls of Animals (تأثير اللحون الموسيقية في النفوس الحيوانية)
  38. كتاب في تحليل المسائل الهندسية (A book in engineering analysis)
  39. الجامع في أصول الحساب (The whole in the assets of the account)
  40. قول فی مساحة الکرة (Say in the sphere)
  41. القول المعروف بالغریب فی حساب المعاملات (Saying the unknown in the calculation of transactions)
  42. خواص المثلث من جهة العمود (Triangle properties from the side of the column)
  43. رسالة فی مساحة المسجم المکافی (A message in the free space)
  44. شرح أصول إقليدس (Explain the origins of Euclid)
  45. المرايا المحرقة بالقطوع (The burning mirrors of the rainbow)
  46. مقالة في القرصتن (Treatise on Centers of Gravity)

Lost works

  1. A Book in which I have Summarized the Science of Optics from the Two Books of Euclid and Ptolemy, to which I have added the Notions of the First Discourse which is Missing from Ptolemy's Book186
  2. Treatise on Burning Mirrors
  3. Treatise on the Nature of [the Organ of] Sight and on How Vision is Achieved Through It

See also

Notes

Sources

Further reading

Primary

Secondary

References

  1. Also Alhacen, Avennathan, Avenetan, etc.; the identity of "Alhazen" with Ibn al-Haytham al-Basri "was identified towards the end of the 19th century". (Vernet 1996, p. 788) - Vernet, J. (1996) [1960], "Ibn al-Haytham", in Gibb, H. A. R.; Bearman, P. (eds.), Encyclopaedia of Islam (First ed.), Leiden: Brill Publishers, ISBN 978-9004161214, archived from the original on 9 January 2012, retrieved 11 February 2016 http://referenceworks.brillonline.com/entries/encyclopaedia-of-islam-2/ibn-al-haytham-SIM_3195 ↩

  2. "Ibn al-Haytham". The American Heritage Dictionary of the English Language (5th ed.). HarperCollins. Retrieved 23 June 2019. https://www.ahdictionary.com/word/search.html?q=Ibn+al-Haytham ↩

  3. Esposito, John L. (2000). The Oxford History of Islam. Oxford University Press. p. 192.: "Ibn al-Haytham (d. 1039), known in the West as Alhazan, was a leading Arab mathematician, astronomer, and physicist. His optical compendium, Kitab al-Manazir, is the greatest medieval work on optics." ↩

  4. For the description of his main fields, see e.g. Vernet 1996, p. 788 ("He is one of the principal Arab mathematicians and, without any doubt, the best physicist.") Sabra 2008, Kalin, Ayduz & Dagli 2009 ("Ibn al-Ḥaytam was an eminent eleventh-century Arab optician, geometer, arithmetician, algebraist, astronomer, and engineer."), Dallal 1999 ("Ibn al-Haytham (d. 1039), known in the West as Alhazan, was a leading Arab mathematician, astronomer, and physicist. His optical compendium, Kitab al-Manazir, is the greatest medieval work on optics.") - Vernet, J. (1996) [1960], "Ibn al-Haytham", in Gibb, H. A. R.; Bearman, P. (eds.), Encyclopaedia of Islam (First ed.), Leiden: Brill Publishers, ISBN 978-9004161214, archived from the original on 9 January 2012, retrieved 11 February 2016 http://referenceworks.brillonline.com/entries/encyclopaedia-of-islam-2/ibn-al-haytham-SIM_3195 ↩

  5. Masic, Izet (2008). "Ibn al-Haitham--father of optics and describer of vision theory". Medicinski Arhiv. 62 (3): 183–188. PMID 18822953. https://www.researchgate.net/publication/23286650 ↩

  6. "International Year of Light: Ibn al Haytham, pioneer of modern optics celebrated at UNESCO". UNESCO. Archived from the original on 18 September 2015. Retrieved 2 June 2018. https://en.unesco.org/news/international-year-light-ibn-al-haytham-pioneer-modern-optics-celebrated-unesco ↩

  7. Al-Khalili, Jim (4 January 2009). "The 'first true scientist'". BBC News. Archived from the original on 26 April 2015. Retrieved 2 June 2018. http://news.bbc.co.uk/2/hi/science/nature/7810846.stm ↩

  8. Selin 2008: "The three most recognizable Islamic contributors to meteorology were: the Alexandrian mathematician/ astronomer Ibn al-Haytham (Alhazen 965–1039), the Arab-speaking Persian physician Ibn Sina (Avicenna 980–1037), and the Spanish Moorish physician/jurist Ibn Rushd (Averroes; 1126–1198)." He has been dubbed the "father of modern optics" by the UNESCO. "Impact of Science on Society". UNESCO. 26–27: 140. 1976. Archived from the original on 5 February 2023. Retrieved 12 September 2019.. "International Year of Light – Ibn Al-Haytham and the Legacy of Arabic Optics". www.light2015.org. Archived from the original on 1 October 2014. Retrieved 9 October 2017.. "International Year of Light: Ibn al Haytham, pioneer of modern optics celebrated at UNESCO". UNESCO. Archived from the original on 18 September 2015. Retrieved 9 October 2017.. Specifically, he was the first to explain that vision occurs when light bounces on an object and then enters an eye. Adamson, Peter (2016). Philosophy in the Islamic World: A History of Philosophy Without Any Gaps. Oxford University Press. p. 77. ISBN 978-0-19-957749-1. Archived from the original on 5 February 2023. Retrieved 3 October 2016. 978-0-19-957749-1 ↩

  9. Adamson, Peter (2016). Philosophy in the Islamic World: A History of Philosophy Without Any Gaps. Oxford University Press. p. 77. ISBN 978-0-19-957749-1. Archived from the original on 5 February 2023. Retrieved 3 October 2016. 978-0-19-957749-1 ↩

  10. Baker 2012, p. 445. - Baker, David B., ed. (2012), The Oxford Handbook of the History of Psychology: Global Perspectives, Oxford University Press, ISBN 978-0-19-536655-6 ↩

  11. Rashed, Roshdi (1 April 2019). "Fermat et le principe du moindre temps". Comptes Rendus Mécanique. 347 (4): 357–364. Bibcode:2019CRMec.347..357R. doi:10.1016/j.crme.2019.03.010. ISSN 1631-0721. S2CID 145904123. https://doi.org/10.1016%2Fj.crme.2019.03.010 ↩

  12. Selin 2008, p. 1817. - Selin, Helaine, ed. (2008), "M", Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures, vol. 1, Springer, p. 1667, ISBN 978-1-4020-4559-2 ↩

  13. Boudrioua, Azzedine; Rashed, Roshdi; Lakshminarayanan, Vasudevan (2017). Light-Based Science: Technology and Sustainable Development, The Legacy of Ibn al-Haytham. CRC Press. ISBN 978-1-351-65112-7. Archived from the original on 6 March 2023. Retrieved 22 February 2023. 978-1-351-65112-7 ↩

  14. Haq, Syed (2009). "Science in Islam". Oxford Dictionary of the Middle Ages. ISSN 1703-7603. Retrieved 22 October 2014. /wiki/Nomanul_Haq ↩

  15. G. J. Toomer. JSTOR 228328?pg=464, Toomer's 1964 review of Matthias Schramm (1963) Ibn Al-Haythams Weg Zur Physik] Archived 26 March 2017 at the Wayback Machine Toomer p. 464: "Schramm sums up [Ibn Al-Haytham's] achievement in the development of scientific method." /wiki/G._J._Toomer ↩

  16. "International Year of Light – Ibn Al-Haytham and the Legacy of Arabic Optics". Archived from the original on 1 October 2014. Retrieved 4 January 2015. https://web.archive.org/web/20141001171116/http://www.light2015.org/Home/ScienceStories/1000-Years-of-Arabic-Optics.html ↩

  17. Gorini, Rosanna (October 2003). "Al-Haytham the man of experience. First steps in the science of vision" (PDF). Journal of the International Society for the History of Islamic Medicine. 2 (4): 53–55. Archived (PDF) from the original on 9 October 2022. Retrieved 25 September 2008. http://www.ishim.net/ishimj/4/10.pdf ↩

  18. Al-Khalili, Jim (4 January 2009). "The 'first true scientist'". BBC News. Archived from the original on 26 April 2015. Retrieved 2 June 2018. http://news.bbc.co.uk/2/hi/science/nature/7810846.stm ↩

  19. Roshdi Rashed, Ibn al-Haytham's Geometrical Methods and the Philosophy of Mathematics: A History of Arabic Sciences and Mathematics, Volume 5, Routledge (2017), p. 635 /wiki/Roshdi_Rashed ↩

  20. According to Al-Qifti. O'Connor & Robertson 1999. /wiki/Al-Qifti ↩

  21. O'Connor & Robertson 1999 - O'Connor, J. J.; Robertson, E. F., eds. (November 1999), "Abu Ali al-Hasan ibn al-Haytham", MacTutor History of Mathematics archive, Scotland: School of Mathematics and Statistics, University of St Andrews, archived from the original on 19 April 2009, retrieved 20 September 2008 http://www-history.mcs.st-andrews.ac.uk/Biographies/Al-Haytham.html ↩

  22. O'Connor & Robertson 1999 - O'Connor, J. J.; Robertson, E. F., eds. (November 1999), "Abu Ali al-Hasan ibn al-Haytham", MacTutor History of Mathematics archive, Scotland: School of Mathematics and Statistics, University of St Andrews, archived from the original on 19 April 2009, retrieved 20 September 2008 http://www-history.mcs.st-andrews.ac.uk/Biographies/Al-Haytham.html ↩

  23. Disputed: Corbin 1993, p. 149. - Corbin, Henry (1993) [Original French 1964], History of Islamic Philosophy, translated by Sherrard, Liadain; Sherrard, Philip, London: Kegan Paul International in association with Islamic Publications for The Institute of Ismaili Studies, ISBN 0-7103-0416-1, OCLC 22109949 https://search.worldcat.org/oclc/22109949 ↩

  24. Noted by Abu'l-Hasan Bayhaqi (c. 1097–1169), and by Sabra 1994 Archived 5 February 2023 at the Wayback Machine p. 197 Carl Boyer 1959 p. 80 /wiki/Abu%27l-Hasan_Bayhaqi ↩

  25. Lindberg 1967, p. 331:"Peckham continually bows to the authority of Alhazen, whom he cites as "the Author" or "the Physicist"." - Lindberg, David C. (1967), "Alhazen's Theory of Vision and Its Reception in the West", Isis, 58 (3): 321–341, doi:10.1086/350266, PMID 4867472, S2CID 10792576 https://doi.org/10.1086%2F350266 ↩

  26. A. Mark Smith (1996). Ptolemy's Theory of Visual Perception: An English Translation of the Optics. American Philosophical Society. p. 57. ISBN 978-0-87169-862-9. Archived from the original on 5 February 2023. Retrieved 16 August 2019. 978-0-87169-862-9 ↩

  27. For the description of his main fields, see e.g. Vernet 1996, p. 788 ("He is one of the principal Arab mathematicians and, without any doubt, the best physicist.") Sabra 2008, Kalin, Ayduz & Dagli 2009 ("Ibn al-Ḥaytam was an eminent eleventh-century Arab optician, geometer, arithmetician, algebraist, astronomer, and engineer."), Dallal 1999 ("Ibn al-Haytham (d. 1039), known in the West as Alhazan, was a leading Arab mathematician, astronomer, and physicist. His optical compendium, Kitab al-Manazir, is the greatest medieval work on optics.") - Vernet, J. (1996) [1960], "Ibn al-Haytham", in Gibb, H. A. R.; Bearman, P. (eds.), Encyclopaedia of Islam (First ed.), Leiden: Brill Publishers, ISBN 978-9004161214, archived from the original on 9 January 2012, retrieved 11 February 2016 http://referenceworks.brillonline.com/entries/encyclopaedia-of-islam-2/ibn-al-haytham-SIM_3195 ↩

  28. Simon 2006 - Simon, G (2006), "The gaze in Ibn al-Haytham.", The Medieval History Journal, 9 (1): 89–98, doi:10.1177/097194580500900105, S2CID 170628785 https://doi.org/10.1177%2F097194580500900105 ↩

  29. Gregory, Richard Langton (2004). The Oxford Companion to the Mind. Oxford University Press. p. 24. ISBN 978-0-19-866224-2. Archived from the original on 4 December 2023. Retrieved 28 June 2023. 978-0-19-866224-2 ↩

  30. "Alhazen Arab mathematician and physicist who was born around 965 in what is now Iraq." Critical Companion to Chaucer: A Literary Reference to His Life and Work ↩

  31. Esposito (2000)، The Oxford History of Islam، Oxford University Press، p. 192. : "Ibn al-Haytham (d. 1039), known in the West as Alhazan, was a leading Arab mathematician, astronomer, and physicist. His optical compendium, Kitab al-Manazir, is the greatest medieval work on optics" ↩

  32. "Ibn al-Haytham – Arab Scientist, Mathematician & Optics Pioneer". Encyclopædia Britannica. Encyclopædia Britannica. Retrieved 3 June 2025. The term "Arab" appears in the article's subtitle: "Ibn al-Haytham – Arab Scientist, Mathematician & Optics Pioneer." https://www.britannica.com/biography/Ibn-al-Haytham ↩

  33. Varvoglis, Harry (29 January 2014). History and Evolution of Concepts in Physics. Springer. p. 24. ISBN 978-3-319-04292-3. Archived from the original on 20 June 2023. Retrieved 13 March 2023. 978-3-319-04292-3 ↩

  34. "Chemical News and Journal of Industrial Science". 6 January 1876. p. 59. Archived from the original on 26 March 2023. Retrieved 13 March 2023. https://books.google.com/books?id=3nBJAAAAYAAJ&dq=alhazen&pg=PA59 ↩

  35. Hendrix, John Shannon; Carman, Charles H. (5 December 2016). Renaissance Theories of Vision edited by John Shannon Hendrix, Charles. Routledge. p. 77. ISBN 978-1-317-06640-8. Archived from the original on 20 June 2023. Retrieved 13 March 2023. 978-1-317-06640-8 ↩

  36. Suhail Zubairy, M. (6 January 2024). Quantum Mechanics for Beginners: With Applications to Quantum Communication By M. Suhail Zubairy. Oxford University Press. p. 81. ISBN 978-0-19-885422-7. Archived from the original on 20 June 2023. Retrieved 13 March 2023. 978-0-19-885422-7 ↩

  37. (Child, Shuter & Taylor 1992, p. 70), (Dessel, Nehrich & Voran 1973, p. 164), Understanding History by John Child, Paul Shuter, David Taylor, p. 70. "Alhazen, a Persian scientist, showed that the eye saw light from other objects. This started optics, the science of light. The Arabs also studied astronomy, the study of the stars. " - Child, John; Shuter, Paul; Taylor, David (1992). Understanding history. Oxford: Heinemann Educational. ISBN 0435312111. OCLC 27338645. https://search.worldcat.org/oclc/27338645 ↩

  38. Tbakhi, Abdelghani; Amr, Samir S. (2007). "Ibn Al-Haytham: Father of Modern Optics". Annals of Saudi Medicine. 27 (6): 464–467. doi:10.5144/0256-4947.2007.464. ISSN 0256-4947. PMC 6074172. PMID 18059131. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6074172 ↩

  39. Corbin 1993, p. 149. - Corbin, Henry (1993) [Original French 1964], History of Islamic Philosophy, translated by Sherrard, Liadain; Sherrard, Philip, London: Kegan Paul International in association with Islamic Publications for The Institute of Ismaili Studies, ISBN 0-7103-0416-1, OCLC 22109949 https://search.worldcat.org/oclc/22109949 ↩

  40. The Prisoner of Al-Hakim. Clifton, NJ: Blue Dome Press, 2017. ISBN 1682060160 /wiki/ISBN_(identifier) ↩

  41. Carl Brockelmann, Geschichte der arabischen Litteratur, vol. 1 (1898), p. 469. /wiki/Carl_Brockelmann ↩

  42. "the Great Islamic Encyclopedia". Cgie.org.ir. Archived from the original on 30 September 2011. Retrieved 27 May 2012.[verification needed] https://web.archive.org/web/20110930153427/http://www.cgie.org.ir/shavad.asp?id=123&avaid=1917 ↩

  43. For Ibn al-Haytham's life and works, Smith 2001, p. cxix recommends Sabra 1989, pp. vol. 2, xix–lxxiii - Smith, A. Mark, ed. (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, Transactions of the American Philosophical Society, vol. 91–4, 91–5, translated by Smith, A. Mark, Philadelphia: American Philosophical Society & Diane Publishing, ISBN 978-0-87169-914-5, OCLC 163278528 https://search.worldcat.org/oclc/163278528 ↩

  44. Corbin 1993, p. 149. - Corbin, Henry (1993) [Original French 1964], History of Islamic Philosophy, translated by Sherrard, Liadain; Sherrard, Philip, London: Kegan Paul International in association with Islamic Publications for The Institute of Ismaili Studies, ISBN 0-7103-0416-1, OCLC 22109949 https://search.worldcat.org/oclc/22109949 ↩

  45. "A. I. Sabra encyclopedia.com Ibn Al-Haytham, Abū". Archived from the original on 26 March 2023. Retrieved 4 November 2018. https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/ibn-al-haytham-abu ↩

  46. Sajjadi, Sadegh, "Alhazen", Great Islamic Encyclopedia, Volume 1, Article No. 1917 ↩

  47. Al-Khalili 2015. - Al-Khalili, Jim (12 February 2015), "In retrospect: Book of Optics", Nature, 518 (7538), Nature Publishing Group: 164–165, Bibcode:2015Natur.518..164A, doi:10.1038/518164a https://ui.adsabs.harvard.edu/abs/2015Natur.518..164A ↩

  48. Adamson, Peter (2016). Philosophy in the Islamic World: A History of Philosophy Without Any Gaps. Oxford University Press. p. 77. ISBN 978-0-19-957749-1. Archived from the original on 5 February 2023. Retrieved 3 October 2016. 978-0-19-957749-1 ↩

  49. Baker 2012, p. 445. - Baker, David B., ed. (2012), The Oxford Handbook of the History of Psychology: Global Perspectives, Oxford University Press, ISBN 978-0-19-536655-6 ↩

  50. Crombie 1971, p. 147, n. 2. - Crombie, A. C. (1971), Robert Grosseteste and the Origins of Experimental Science, 1100–1700, Clarendon Press, University of Oxford ↩

  51. A. Mark Smith has determined that there were at least two translators, based on their facility with Arabic; the first, more experienced scholar began the translation at the beginning of Book One, and handed it off in the middle of Chapter Three of Book Three. Smith 2001 91 Volume 1: Commentary and Latin text pp.xx–xxi. See also his 2006, 2008, 2010 translations. - Smith, A. Mark, ed. (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, Transactions of the American Philosophical Society, vol. 91–4, 91–5, translated by Smith, A. Mark, Philadelphia: American Philosophical Society & Diane Publishing, ISBN 978-0-87169-914-5, OCLC 163278528 https://search.worldcat.org/oclc/163278528 ↩

  52. Enrico Narducci (1871). "Nota intorno ad una traduzione italiana fatta nel secolo decimoquarto del trattato d'ottica d'Alhazen". Bollettino di Bibliografia e di Storia delle Scienze Matematiche e Fisiche. 4: 1–40.. On this version, see Raynaud 2020, pp. 139–153. /wiki/Enrico_Narducci ↩

  53. Alhazen (965–1040): Library of Congress Citations, Malaspina Great Books, archived from the original on 27 September 2007, retrieved 23 January 2008[verification needed] https://web.archive.org/web/20070927190009/http://www.mala.bc.ca/~mcneil/cit/citlcalhazen1.htm ↩

  54. Smith 2001, p. xxi. - Smith, A. Mark, ed. (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, Transactions of the American Philosophical Society, vol. 91–4, 91–5, translated by Smith, A. Mark, Philadelphia: American Philosophical Society & Diane Publishing, ISBN 978-0-87169-914-5, OCLC 163278528 https://search.worldcat.org/oclc/163278528 ↩

  55. Smith 2001, p. xxii. - Smith, A. Mark, ed. (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, Transactions of the American Philosophical Society, vol. 91–4, 91–5, translated by Smith, A. Mark, Philadelphia: American Philosophical Society & Diane Publishing, ISBN 978-0-87169-914-5, OCLC 163278528 https://search.worldcat.org/oclc/163278528 ↩

  56. Smith 2001, p. lxxix. - Smith, A. Mark, ed. (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, Transactions of the American Philosophical Society, vol. 91–4, 91–5, translated by Smith, A. Mark, Philadelphia: American Philosophical Society & Diane Publishing, ISBN 978-0-87169-914-5, OCLC 163278528 https://search.worldcat.org/oclc/163278528 ↩

  57. Lindberg 1976, p. 73. - Lindberg, David C. (1976), Theories of Vision from al-Kindi to Kepler, University of Chicago Press, Chicago, ISBN 0-226-48234-0, OCLC 1676198 https://search.worldcat.org/oclc/1676198 ↩

  58. Lindberg 1976, p. 73. - Lindberg, David C. (1976), Theories of Vision from al-Kindi to Kepler, University of Chicago Press, Chicago, ISBN 0-226-48234-0, OCLC 1676198 https://search.worldcat.org/oclc/1676198 ↩

  59. Lindberg 1976, p. 74 - Lindberg, David C. (1976), Theories of Vision from al-Kindi to Kepler, University of Chicago Press, Chicago, ISBN 0-226-48234-0, OCLC 1676198 https://search.worldcat.org/oclc/1676198 ↩

  60. Lindberg 1976, p. 76 - Lindberg, David C. (1976), Theories of Vision from al-Kindi to Kepler, University of Chicago Press, Chicago, ISBN 0-226-48234-0, OCLC 1676198 https://search.worldcat.org/oclc/1676198 ↩

  61. Lindberg 1976, p. 75 - Lindberg, David C. (1976), Theories of Vision from al-Kindi to Kepler, University of Chicago Press, Chicago, ISBN 0-226-48234-0, OCLC 1676198 https://search.worldcat.org/oclc/1676198 ↩

  62. Lindberg 1976, pp. 76–78 - Lindberg, David C. (1976), Theories of Vision from al-Kindi to Kepler, University of Chicago Press, Chicago, ISBN 0-226-48234-0, OCLC 1676198 https://search.worldcat.org/oclc/1676198 ↩

  63. Lindberg 1976, p. 86. - Lindberg, David C. (1976), Theories of Vision from al-Kindi to Kepler, University of Chicago Press, Chicago, ISBN 0-226-48234-0, OCLC 1676198 https://search.worldcat.org/oclc/1676198 ↩

  64. Al Deek 2004. - Al Deek, Mahmoud (2004), "Ibn Al-Haitham: Master of Optics, Mathematics, Physics and Medicine", Al Shindagah (November–December 2004), archived from the original on 17 June 2008, retrieved 21 September 2008 https://web.archive.org/web/20080617021504/http://www.alshindagah.com/novdec2004/ibn.html ↩

  65. Heeffer 2003. - Heeffer, Albrecht (14–15 September 2003), "Kepler's near discovery of the sine law: A qualitative computational model", Third International workshop: Computer models of scientific reasoning and applications (PDF), Buenos Aires: National Library of the Argentine Republic, archived (PDF) from the original on 9 October 2022, retrieved 23 January 2008 http://logica.ugent.be/albrecht/thesis/Heeffer-CMSRAfinal.pdf ↩

  66. Howard 1996. - Howard, Ian P. (1996), "Alhazen's neglected discoveries of visual phenomena", Perception, 25 (10): 1203–1217, doi:10.1068/p251203, PMID 9027923, S2CID 20880413 https://doi.org/10.1068%2Fp251203 ↩

  67. Aaen-Stockdale 2008 - Aaen-Stockdale, C. R. (2008), "Ibn al-Haytham and psychophysics", Perception, 37 (4): 636–638, doi:10.1068/p5940, PMID 18546671, S2CID 43532965 https://doi.org/10.1068%2Fp5940 ↩

  68. Wade 1998, pp. 240, 316, 334, 367; Howard & Wade 1996, pp. 1195, 1197, 1200. - Wade, Nicholas J. (1998), A Natural History of Vision, Cambridge, MA: MIT Press ↩

  69. Lejeune 1958. - Lejeune, Albert (1958), "Les recherches de Ptolémée sur la vision binoculaire", Janus, 47: 79–86 ↩

  70. Sabra 1989. - Sabra, A. I., ed. (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, translated by Sabra, A. I., London: The Warburg Institute, University of London, ISBN 0-85481-072-2, OCLC 165564751 https://search.worldcat.org/oclc/165564751 ↩

  71. Raynaud 2003. - Raynaud, Dominique (2003), "Ibn al-Haytham sur la vision binoculaire: un précurseur de l'optique physiologique", Arabic Sciences and Philosophy, 13 (1), Cambridge University Press: 79–99, doi:10.1017/S0957423903003047, S2CID 231735113 https://doi.org/10.1017%2FS0957423903003047 ↩

  72. Russell 1996, p. 691. - Russell, Gül A. (1996), "Emergence of Physiological Optics", in Rāshid, Rushdī; Morelon, Régis (eds.), Encyclopedia of the History of Arabic Science, Routledge, pp. 672–716, ISBN 0-415-12410-7, OCLC 34731151 https://search.worldcat.org/oclc/34731151 ↩

  73. Russell 1996, p. 689. - Russell, Gül A. (1996), "Emergence of Physiological Optics", in Rāshid, Rushdī; Morelon, Régis (eds.), Encyclopedia of the History of Arabic Science, Routledge, pp. 672–716, ISBN 0-415-12410-7, OCLC 34731151 https://search.worldcat.org/oclc/34731151 ↩

  74. Lindberg 1976, pp. 80–85 - Lindberg, David C. (1976), Theories of Vision from al-Kindi to Kepler, University of Chicago Press, Chicago, ISBN 0-226-48234-0, OCLC 1676198 https://search.worldcat.org/oclc/1676198 ↩

  75. Smith 2004, pp. 186, 192. - Smith, A. Mark (June 2004), "What is the History of Medieval Optics Really About?" (PDF), Proceedings of the American Philosophical Society, 148 (2): 180–194, JSTOR 1558283, PMID 15338543, archived from the original (PDF) on 18 October 2011 https://web.archive.org/web/20111018045417/http://www.amphilsoc.org/sites/default/files/480202.pdf ↩

  76. Wade 1998, p. 14 - Wade, Nicholas J. (1998), A Natural History of Vision, Cambridge, MA: MIT Press ↩

  77. 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 "Kitāb al-Manāẓir": Volume Two". Transactions of the American Philosophical Society. 91 (5): 339–819. doi:10.2307/3657357. JSTOR 3657357. Archived from the original on 30 June 2015. Retrieved 12 January 2015. http://www.jstor.org/stable/3657357 ↩

  78. Al Deek 2004. - Al Deek, Mahmoud (2004), "Ibn Al-Haitham: Master of Optics, Mathematics, Physics and Medicine", Al Shindagah (November–December 2004), archived from the original on 17 June 2008, retrieved 21 September 2008 https://web.archive.org/web/20080617021504/http://www.alshindagah.com/novdec2004/ibn.html ↩

  79. Stamnes, J. J. (2017). Waves in Focal Regions: Propagation, Diffraction and Focusing of Light, Sound and Water Waves. Routledge. ISBN 978-1-351-40468-6. Archived from the original on 31 March 2023. Retrieved 22 February 2023. 978-1-351-40468-6 ↩

  80. Mach, Ernst (2013). The Principles of Physical Optics: An Historical and Philosophical Treatment. Courier Corporation. ISBN 978-0-486-17347-4. Archived from the original on 31 March 2023. Retrieved 22 February 2023. 978-0-486-17347-4 ↩

  81. Iizuka, Keigo (2013). Engineering Optics. Springer Science & Business Media. ISBN 978-3-662-07032-1. Archived from the original on 31 March 2023. Retrieved 22 February 2023. 978-3-662-07032-1 ↩

  82. Selin 2008, p. 1817. - Selin, Helaine, ed. (2008), "M", Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures, vol. 1, Springer, p. 1667, ISBN 978-1-4020-4559-2 ↩

  83. Mach, Ernst (2013). The Principles of Physical Optics: An Historical and Philosophical Treatment. Courier Corporation. ISBN 978-0-486-17347-4. Archived from the original on 31 March 2023. Retrieved 22 February 2023. 978-0-486-17347-4 ↩

  84. O'Connor & Robertson 1999, Weisstein 2008. - O'Connor, J. J.; Robertson, E. F., eds. (November 1999), "Abu Ali al-Hasan ibn al-Haytham", MacTutor History of Mathematics archive, Scotland: School of Mathematics and Statistics, University of St Andrews, archived from the original on 19 April 2009, retrieved 20 September 2008 http://www-history.mcs.st-andrews.ac.uk/Biographies/Al-Haytham.html ↩

  85. Katz 1995, pp. 165–169, 173–174. - Katz, Victor J. (1995), "Ideas of Calculus in Islam and India", Mathematics Magazine, 68 (3): 163–174, doi:10.2307/2691411, JSTOR 2691411 https://doi.org/10.2307%2F2691411 ↩

  86. Smith 1992. - Smith, John D. (1 March 1992), "The Remarkable Ibn al-Haytham", The Mathematical Gazette, 76 (475), Mathematical Association: 189–198, doi:10.2307/3620392, ISSN 0025-5572, JSTOR 3620392, S2CID 118597450 https://doi.org/10.2307%2F3620392 ↩

  87. Elkin, Jack M. (1965), "A deceptively easy problem", Mathematics Teacher, 58 (3): 194–199, doi:10.5951/MT.58.3.0194, JSTOR 27968003 /wiki/Doi_(identifier) ↩

  88. Riede, Harald (1989), "Reflexion am Kugelspiegel. Oder: das Problem des Alhazen", Praxis der Mathematik (in German), 31 (2): 65–70 ↩

  89. Neumann, Peter M. (1998), "Reflections on Reflection in a Spherical Mirror", American Mathematical Monthly, 105 (6): 523–528, doi:10.1080/00029890.1998.12004920, JSTOR 2589403, MR 1626185 /wiki/Peter_M._Neumann ↩

  90. Highfield, Roger (1 April 1997), "Don solves the last puzzle left by ancient Greeks", Electronic Telegraph, 676, archived from the original on 23 November 2004 /wiki/Roger_Highfield ↩

  91. Agrawal, Taguchi & Ramalingam 2011. - Agrawal, Amit; Taguchi, Yuichi; Ramalingam, Srikumar (2011), Beyond Alhazen's Problem: Analytical Projection Model for Non-Central Catadioptric Cameras with Quadric Mirrors, IEEE Conference on Computer Vision and Pattern Recognition, CiteSeerX 10.1.1.433.9727, archived from the original on 7 March 2012 https://web.archive.org/web/20120307040949/http://www.umiacs.umd.edu/~aagrawal/cvpr11/fp/fp.html ↩

  92. Kelley, Milone & Aveni 2005, p. 83: "The first clear description of the device appears in the Book of Optics of Alhazen." - Kelley, David H.; Milone, E. F.; Aveni, A. F. (2005), Exploring Ancient Skies: An Encyclopedic Survey of Archaeoastronomy, Birkhäuser, ISBN 0-387-95310-8, OCLC 213887290, archived from the original on 5 February 2023, retrieved 7 April 2014 https://books.google.com/books?id=zNkgyyPr7kwC ↩

  93. 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." - Wade, Nicholas J.; Finger, Stanley (2001), "The eye as an optical instrument: from camera obscura to Helmholtz's perspective", Perception, 30 (10): 1157–1177, doi:10.1068/p3210, PMID 11721819, S2CID 8185797 https://doi.org/10.1068%2Fp3210 ↩

  94. German physicist Eilhard Wiedemann first provided an abridged German translation of On the shape of the eclipse: Eilhard Wiedemann (1914). "Über der Camera obscura bei Ibn al Haiṭam". Sitzungsberichte phys.-med. Sozietät in Erlangen. 46: 155–169. The work is now available in full: Raynaud 2016. - Raynaud, Dominique (2016), A Critical Edition of Ibn al-Haytham's On the Shape of the Eclipse. The First Experimental Study of the Camera Obscura, New York: Springer International, ISBN 978-3-319-47991-0 ↩

  95. Eder, Josef (1945). History of Photography. New York: Columbia University Press. p. 37. ↩

  96. Raynaud 2016, pp. 130–160 - Raynaud, Dominique (2016), A Critical Edition of Ibn al-Haytham's On the Shape of the Eclipse. The First Experimental Study of the Camera Obscura, New York: Springer International, ISBN 978-3-319-47991-0 ↩

  97. Raynaud 2016, pp. 114–116 - Raynaud, Dominique (2016), A Critical Edition of Ibn al-Haytham's On the Shape of the Eclipse. The First Experimental Study of the Camera Obscura, New York: Springer International, ISBN 978-3-319-47991-0 ↩

  98. Raynaud 2016, pp. 91–94 - Raynaud, Dominique (2016), A Critical Edition of Ibn al-Haytham's On the Shape of the Eclipse. The First Experimental Study of the Camera Obscura, New York: Springer International, ISBN 978-3-319-47991-0 ↩

  99. History Of Science And Technology In Islam Fuat Sezgin. 2011. http://archive.org/details/history-of-science-and-technology-in-islam-fuat-sezgin ↩

  100. Gaukroger, Stephen (1995). Descartes: An Intellectual Biography. Clarendon Press. ISBN 978-0-19-151954-3. 978-0-19-151954-3 ↩

  101. Newton, Isaac (1984). The Optical Papers of Isaac Newton. Vol. 1: The Optical Lectures 1670–1672. Cambridge University Press. ISBN 978-0-521-25248-5. 978-0-521-25248-5 ↩

  102. Boudrioua, Azzedine; Rashed, Roshdi; Lakshminarayanan, Vasudevan (2017). Light-Based Science: Technology and Sustainable Development, The Legacy of Ibn al-Haytham. CRC Press. ISBN 978-1-4987-7940-1. 978-1-4987-7940-1 ↩

  103. Boudrioua, Azzedine; Rashed, Roshdi; Lakshminarayanan, Vasudevan (2017). Light-Based Science: Technology and Sustainable Development, The Legacy of Ibn al-Haytham. CRC Press. ISBN 978-1-4987-7940-1. 978-1-4987-7940-1 ↩

  104. Russell 1996, p. 695. - Russell, Gül A. (1996), "Emergence of Physiological Optics", in Rāshid, Rushdī; Morelon, Régis (eds.), Encyclopedia of the History of Arabic Science, Routledge, pp. 672–716, ISBN 0-415-12410-7, OCLC 34731151 https://search.worldcat.org/oclc/34731151 ↩

  105. Russell 1996. - Russell, Gül A. (1996), "Emergence of Physiological Optics", in Rāshid, Rushdī; Morelon, Régis (eds.), Encyclopedia of the History of Arabic Science, Routledge, pp. 672–716, ISBN 0-415-12410-7, OCLC 34731151 https://search.worldcat.org/oclc/34731151 ↩

  106. Khaleefa 1999 - Khaleefa, Omar (1999), "Who Is the Founder of Psychophysics and Experimental Psychology?", American Journal of Islamic Social Sciences, 16 (2) ↩

  107. Khaleefa 1999 - Khaleefa, Omar (1999), "Who Is the Founder of Psychophysics and Experimental Psychology?", American Journal of Islamic Social Sciences, 16 (2) ↩

  108. Aaen-Stockdale 2008. - Aaen-Stockdale, C. R. (2008), "Ibn al-Haytham and psychophysics", Perception, 37 (4): 636–638, doi:10.1068/p5940, PMID 18546671, S2CID 43532965 https://doi.org/10.1068%2Fp5940 ↩

  109. Ross & Plug 2002. - Ross, H .E.; Plug, C. (2002), The mystery of the moon illusion: Exploring size perception, Oxford University Press, Bibcode:2002mmi..book.....R, ISBN 978-0-19-850862-5 https://ui.adsabs.harvard.edu/abs/2002mmi..book.....R ↩

  110. Hershenson 1989, pp. 9–10. - Hershenson, Maurice (1989), The Moon Illusion, Lawrence Erlbaum Associates, ISBN 0-8058-0121-9, OCLC 20091171, archived from the original on 22 March 2016, retrieved 22 September 2008 https://web.archive.org/web/20160322052547/https://books.google.com/books?id=x1qcL4CTwlIC ↩

  111. Ross 2000. - Ross, H.E. (2000), "Cleomedes c. 1st century AD) on the celestial illusion, atmospheric enlargement and size-distance invariance", Perception, 29 (7): 853–861, doi:10.1068/p2937, PMID 11064807, S2CID 24967431 https://doi.org/10.1068%2Fp2937 ↩

  112. Ross & Ross 1976. - Ross, H .E.; Ross, G .M. (1976), "Did Ptolemy understand the moon illusion?", Perception, 5 (4): 377–385, doi:10.1068/p050377, PMID 794813, S2CID 23948158 https://doi.org/10.1068%2Fp050377 ↩

  113. Sabra 1989. - Sabra, A. I., ed. (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, translated by Sabra, A. I., London: The Warburg Institute, University of London, ISBN 0-85481-072-2, OCLC 165564751 https://search.worldcat.org/oclc/165564751 ↩

  114. See, for example,De aspectibus Book 7 Archived 18 August 2018 at the Wayback Machine, for his experiments in refraction http://perspectiva.biblhertz.it/doc01.VII.html ↩

  115. El-Bizri 2005a, 2005b. - El-Bizri, Nader (2005a), "A Philosophical Perspective on Alhazen's Optics", Arabic Sciences and Philosophy, 15 (2), Cambridge University Press: 189–218, doi:10.1017/S0957423905000172, S2CID 123057532 https://doi.org/10.1017%2FS0957423905000172 ↩

  116. "see Schramm's Habilitationsschrift, Ibn al-Haythams Weg zur Physik (Steiner, Wiesbaden, 1963) as cited by Rüdiger Thiele (2005) Historia Mathematica 32, 271–274. "In Memoriam: Matthias Schramm, 1928–2005"" (PDF). Archived (PDF) from the original on 25 October 2017. Retrieved 25 October 2017. https://core.ac.uk/download/pdf/82356023.pdf ↩

  117. Toomer 1964, pp. 463–464 - Toomer, G. J. (December 1964), "Review: Ibn al-Haythams Weg zur Physik by Matthias Schramm", Isis, 55 (4): 463–465, doi:10.1086/349914 https://doi.org/10.1086%2F349914 ↩

  118. Toomer 1964, p. 465 - Toomer, G. J. (December 1964), "Review: Ibn al-Haythams Weg zur Physik by Matthias Schramm", Isis, 55 (4): 463–465, doi:10.1086/349914 https://doi.org/10.1086%2F349914 ↩

  119. Toomer 1964, p. 465 - Toomer, G. J. (December 1964), "Review: Ibn al-Haythams Weg zur Physik by Matthias Schramm", Isis, 55 (4): 463–465, doi:10.1086/349914 https://doi.org/10.1086%2F349914 ↩

  120. G. J. Toomer. Review at Toomer's 1964 review of Matthias Schramm (1963) Ibn Al-Haythams Weg Zur Physik Archived 26 March 2017 at the Wayback Machine Toomer p. 464: "Schramm sums up [Ibn Al-Haytham's] achievement in the development of scientific method.", p. 465: "Schramm has demonstrated .. beyond any dispute that Ibn al-Haytham is a major figure in the Islamic scientific tradition, particularly in the creation of experimental techniques." p. 465: "Only when the influence of ibn al-Haytam and others on the mainstream of later medieval physical writings has been seriously investigated can Schramm's claim that ibn al-Haytam was the true founder of modern physics be evaluated." /wiki/G._J._Toomer ↩

  121. El-Bizri 2006. - El-Bizri, Nader (2006), "Ibn al-Haytham or Alhazen", in Meri, Josef W. (ed.), Medieval Islamic Civilization: An Encyclopaedia, vol. II, New York & London: Routledge, pp. 343–345, ISBN 0-415-96692-2, OCLC 224371638 https://search.worldcat.org/oclc/224371638 ↩

  122. Duhem 1969, p. 28. - Duhem, Pierre (1969) [First published 1908], To Save the Phenomena: An Essay on the Idea of Physical theory from Plato to Galileo, University of Chicago Press, Chicago, ISBN 0-226-16921-9, OCLC 12429405 https://search.worldcat.org/oclc/12429405 ↩

  123. El-Bizri 2006. - El-Bizri, Nader (2006), "Ibn al-Haytham or Alhazen", in Meri, Josef W. (ed.), Medieval Islamic Civilization: An Encyclopaedia, vol. II, New York & London: Routledge, pp. 343–345, ISBN 0-415-96692-2, OCLC 224371638 https://search.worldcat.org/oclc/224371638 ↩

  124. Langermann 1990, chap. 2, sect. 22, p. 61 - Langermann, Y. Tzvi (1990), Ibn al Haytham's on the Configuration of the World ↩

  125. Lorch 2008. - Lorch, Richard (2008), "Ibn al-Haytham", Encyclopædia Britannica, archived from the original on 12 June 2008, retrieved 6 August 2008 https://www.britannica.com/EBchecked/topic/738111/Ibn-al-Haytham ↩

  126. Langermann 1990, pp. 34–41; Gondhalekar 2001, p. 21. - Langermann, Y. Tzvi (1990), Ibn al Haytham's on the Configuration of the World ↩

  127. Sabra 1998. - Sabra, A. I. (1998), "Configuring the Universe: Aporetic, Problem Solving, and Kinematic Modeling as Themes of Arabic Astronomy", Perspectives on Science, 6 (3): 288–330, doi:10.1162/posc_a_00552, S2CID 117426616 http://www.accessmylibrary.com/article-1G1-56027684/configuring-universe-aporetic-problem.html ↩

  128. Langermann 1990, pp. 8–10 - Langermann, Y. Tzvi (1990), Ibn al Haytham's on the Configuration of the World ↩

  129. Sabra 1978b, p. 121, n. 13 - 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 ↩

  130. Sabra 1998. - Sabra, A. I. (1998), "Configuring the Universe: Aporetic, Problem Solving, and Kinematic Modeling as Themes of Arabic Astronomy", Perspectives on Science, 6 (3): 288–330, doi:10.1162/posc_a_00552, S2CID 117426616 http://www.accessmylibrary.com/article-1G1-56027684/configuring-universe-aporetic-problem.html ↩

  131. Sabra 1989. - Sabra, A. I., ed. (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, translated by Sabra, A. I., London: The Warburg Institute, University of London, ISBN 0-85481-072-2, OCLC 165564751 https://search.worldcat.org/oclc/165564751 ↩

  132. Rashed 2007. - Rashed, Roshdi (2007), "The Celestial Kinematics of Ibn al-Haytham", Arabic Sciences and Philosophy, 17, Cambridge University Press: 7–55, doi:10.1017/S0957423907000355, S2CID 170934544 https://doi.org/10.1017%2FS0957423907000355 ↩

  133. Eckart 2018 - Eckart, Andreas (March 2018), "The Early Great Debate: A Comment on Ibn Al-Haytham's Work on the Location of the Milky Way with Respect to the Earth", Arabic Sciences and Philosophy, 28 (1): 1–30, doi:10.1017/S0957423917000078, S2CID 171746839 https://doi.org/10.1017%2FS0957423917000078 ↩

  134. Rashed 2007, pp. 8–9. - Rashed, Roshdi (2007), "The Celestial Kinematics of Ibn al-Haytham", Arabic Sciences and Philosophy, 17, Cambridge University Press: 7–55, doi:10.1017/S0957423907000355, S2CID 170934544 https://doi.org/10.1017%2FS0957423907000355 ↩

  135. Faruqi 2006, pp. 395–396: 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. - Faruqi, Yasmeen M. (2006), "Contributions of Islamic scholars to the scientific enterprise", International Education Journal, 7 (4): 391–396 ↩

  136. Rottman 2000, Chapter 1. - Rottman, J. (2000). A first course in Abstract Algebra. Prentice Hall. ISBN 0-13-011584-3. OCLC 42960682. https://search.worldcat.org/oclc/42960682 ↩

  137. Eder 2000. - Eder, Michelle (2000), Views of Euclid's Parallel Postulate in Ancient Greece and in Medieval Islam, Rutgers University, archived from the original on 19 August 2016, retrieved 23 January 2008 http://www.math.rutgers.edu/~cherlin/History/Papers2000/eder.html ↩

  138. Katz 1998, p. 269: "In effect, this method characterised parallel lines as lines always equidistant from one another and also introduced the concept of motion into geometry." - Katz, Victor J. (1998), History of Mathematics: An Introduction, Addison-Wesley, ISBN 0-321-01618-1, OCLC 38199387 https://archive.org/details/historyofmathema00katz ↩

  139. Rozenfeld 1988, p. 65. - Rozenfeld, Boris A. (1988), A History of Non-Euclidean Geometry: Evolution of the Concept of a Geometric Space, Springer Science+Business Media, ISBN 0-387-96458-4, OCLC 15550634 https://search.worldcat.org/oclc/15550634 ↩

  140. Boyer, Carl B.; Merzbach, Uta C. (2011). A History of Mathematics. John Wiley & Sons. ISBN 978-0-470-63056-3. Archived from the original on 7 September 2023. Retrieved 19 March 2023. 978-0-470-63056-3 ↩

  141. O'Connor & Robertson 1999. - O'Connor, J. J.; Robertson, E. F., eds. (November 1999), "Abu Ali al-Hasan ibn al-Haytham", MacTutor History of Mathematics archive, Scotland: School of Mathematics and Statistics, University of St Andrews, archived from the original on 19 April 2009, retrieved 20 September 2008 http://www-history.mcs.st-andrews.ac.uk/Biographies/Al-Haytham.html ↩

  142. Alsina & Nelsen 2010. - Alsina, Claudi; Nelsen, Roger B. (2010), "9.1 Squarable lunes", Charming Proofs: A Journey into Elegant Mathematics, Dolciani mathematical expositions, vol. 42, Mathematical Association of America, pp. 137–144, ISBN 978-0-88385-348-1 https://books.google.com/books?id=mIT5-BN_L0oC ↩

  143. O'Connor & Robertson 1999. - O'Connor, J. J.; Robertson, E. F., eds. (November 1999), "Abu Ali al-Hasan ibn al-Haytham", MacTutor History of Mathematics archive, Scotland: School of Mathematics and Statistics, University of St Andrews, archived from the original on 19 April 2009, retrieved 20 September 2008 http://www-history.mcs.st-andrews.ac.uk/Biographies/Al-Haytham.html ↩

  144. O'Connor & Robertson 1999. - O'Connor, J. J.; Robertson, E. F., eds. (November 1999), "Abu Ali al-Hasan ibn al-Haytham", MacTutor History of Mathematics archive, Scotland: School of Mathematics and Statistics, University of St Andrews, archived from the original on 19 April 2009, retrieved 20 September 2008 http://www-history.mcs.st-andrews.ac.uk/Biographies/Al-Haytham.html ↩

  145. Katz, Victor J. (1995). "Ideas of Calculus in Islam and India". Mathematics Magazine. 68 (3): 163–174 [165–169, 173–174]year=1995. doi:10.2307/2691411. JSTOR 2691411. /wiki/Victor_J._Katz ↩

  146. Plott 2000, Pt. II, p. 459. - Plott, C. (2000), Global History of Philosophy: The Period of Scholasticism, Motilal Banarsidass, ISBN 8120805518 ↩

  147. El-Bizri 2007. - El-Bizri, Nader (2007), "In Defence of the Sovereignty of Philosophy: Al-Baghdadi's Critique of Ibn al-Haytham's Geometrisation of Place", Arabic Sciences and Philosophy, 17, Cambridge University Press: 57–80, doi:10.1017/S0957423907000367, S2CID 170960993 https://doi.org/10.1017%2FS0957423907000367 ↩

  148. El-Bizri 2007. - El-Bizri, Nader (2007), "In Defence of the Sovereignty of Philosophy: Al-Baghdadi's Critique of Ibn al-Haytham's Geometrisation of Place", Arabic Sciences and Philosophy, 17, Cambridge University Press: 57–80, doi:10.1017/S0957423907000367, S2CID 170960993 https://doi.org/10.1017%2FS0957423907000367 ↩

  149. Smith 2005, pp. 219–240. - Smith, A. Mark (2005), "The Alhacenian Account of Spatial Perception And Its Epistemological Implications", Arabic Sciences and Philosophy, 15 (2), Cambridge University Press: 219–240, doi:10.1017/S0957423905000184, S2CID 171003284 https://doi.org/10.1017%2FS0957423905000184 ↩

  150. Ishaq, Usep Mohamad, and Wan Mohd Nor Wan Daud. "Tinjauan biografi-bibliografi Ibn al-haytham." Historia : Jurnal Program Studi Pendidikan Sejarah 5.2 (2017): 107–124. ↩

  151. Kaminski, Joseph J. "The Trajectory of the Development of Islamic Thought – A Comparison Between Two Earlier and Two Later Scholars." The Contemporary Islamic Governed State. Palgrave Macmillan, Cham, 2017. 31–70. "For example, Ibn al-Haytham and Abū Rayhān al-Bīrūnī were among the most important medieval scholars who used the scientific method in their approach to natural science, and they were both Ash'arites" ↩

  152. Sardar 1998 - Sardar, Ziauddin (1998), "Science in Islamic philosophy", Islamic Philosophy, Routledge Encyclopedia of Philosophy, archived from the original on 26 May 2018, retrieved 3 February 2008 http://www.muslimphilosophy.com/ip/rep/H016.htm ↩

  153. Bettany 1995, p. 251 - Bettany, Laurence (1995), "Ibn al-Haytham: an answer to multicultural science teaching?", Physics Education, 30 (4): 247–252, Bibcode:1995PhyEd..30..247B, doi:10.1088/0031-9120/30/4/011, S2CID 250826188 https://ui.adsabs.harvard.edu/abs/1995PhyEd..30..247B ↩

  154. Sardar 1998 - Sardar, Ziauddin (1998), "Science in Islamic philosophy", Islamic Philosophy, Routledge Encyclopedia of Philosophy, archived from the original on 26 May 2018, retrieved 3 February 2008 http://www.muslimphilosophy.com/ip/rep/H016.htm ↩

  155. Anwar, Sabieh (October 2008), "Is Ghazālī really the Halagu of Science in Islam?", Monthly Renaissance, 18 (10), retrieved 14 October 2008 /wiki/Al-Mawrid ↩

  156. Rashed, Roshdi (2007), "The Celestial Kinematics of Ibn al-Haytham", Arabic Sciences and Philosophy, Cambridge University Press, 17 (1): 7–55 [11], doi:10.1017/S0957423907000355 /wiki/Cambridge_University_Press ↩

  157. Plott 2000, Pt. II, p. 464 - Plott, C. (2000), Global History of Philosophy: The Period of Scholasticism, Motilal Banarsidass, ISBN 8120805518 ↩

  158. Topdemir 2007, pp. 8–9. - Topdemir, Huseyin Gazi (18 July 2007), Ibn al-Haytham (965–1039): His Life and Works ↩

  159. Translated by S. Pines, as quoted in Sambursky 1974, p. 139. - Sambursky, Samuel (1974), Physical Thought from the Presocratics to the Quantum Physicists, Pica Press, pp. 51, ISBN 0-87663-712-8 https://archive.org/details/physicalthoughtf0000unse/page/139 ↩

  160. Rashed 2007, p. 11. - Rashed, Roshdi (2007), "The Celestial Kinematics of Ibn al-Haytham", Arabic Sciences and Philosophy, 17, Cambridge University Press: 7–55, doi:10.1017/S0957423907000355, S2CID 170934544 https://doi.org/10.1017%2FS0957423907000355 ↩

  161. Plott 2000, Pt. II, p. 465 - Plott, C. (2000), Global History of Philosophy: The Period of Scholasticism, Motilal Banarsidass, ISBN 8120805518 ↩

  162. Sabra 2007. - Sabra, A. I. (2007), "The 'Commentary' That Saved the Text: The Hazardous Journey of Ibn al-Haytham's Arabic "Optics"", Early Science and Medicine, 12 (2): 117–133, doi:10.1163/157338207x194668, JSTOR 20617660, retrieved 22 January 2014 https://www.researchgate.net/publication/233484584 ↩

  163. Sabra 2007, pp. 122, 128–129. & Grant 1974, p. 392 notes the Book of Optics has also been denoted as Opticae Thesaurus Alhazen Arabis, as De Aspectibus, and also as Perspectiva - Sabra, A. I. (2007), "The 'Commentary' That Saved the Text: The Hazardous Journey of Ibn al-Haytham's Arabic "Optics"", Early Science and Medicine, 12 (2): 117–133, doi:10.1163/157338207x194668, JSTOR 20617660, retrieved 22 January 2014 https://www.researchgate.net/publication/233484584 ↩

  164. Lindberg 1996, p. 11, passim. - Lindberg, David C. (1996), Roger Bacon and the Origins of Perspectiva in the Middle Ages, Clarendon Press ↩

  165. Authier 2013, p. 23: "Alhazen's works in turn inspired many scientists of the Middle Ages, such as the English bishop, Robert Grosseteste (c. 1175–1253), and the English Franciscan, Roger Bacon (c. 1214–1294), Erazmus Ciolek Witelo, or Witelon (c. 1230* 1280), a Silesian-born Polish friar, philosopher and scholar, published in c. 1270 a treatise on optics, Perspectiva, largely based on Alhazen's works." - Authier, André (2013), "3: The Dual Nature of Light", Early Days of X-ray Crystallography, Oxford University Press, ISBN 978-0-19-965984-5 ↩

  166. Magill & Aves 1998, p. 66: "Roger Bacon, John Peckham, and Giambattista della Porta are only some of the many thinkers who were influenced by Alhazen's work." - Magill, Frank Northen; Aves, Alison (1998), "The Middles Ages: Alhazen", Dictionary of World Biography, vol. 2, Routledge, ISBN 978-1-57958-041-4 ↩

  167. Zewail & Thomas 2010, p. 5: "The Latin translation of Alhazen's work influenced scientists and philosophers such as (Roger) Bacon and da Vinci, and formed the foundation for the work by mathematicians like Kepler, Descartes and Huygens..." - Zewail, Ahmed H.; Thomas, John Meurig (2010), 4D Electron Microscopy: Imaging in Space and Time, World Scientific, ISBN 978-1-84816-390-4 ↩

  168. El-Bizri 2010, p. 12: "This [Latin] version of Ibn al-Haytham's Optics, which became available in print, was read and consulted by scientists and philosophers of the caliber of Kepler, Galileo, Descartes, and Huygens as discussed by Nader El-Bizri." - El-Bizri, Nader (2010). "Classical Optics and the Perspectiva Traditions Leading to the Renaissance". In Hendrix, John Shannon; Carman, Charles H. (eds.). Renaissance Theories of Vision (Visual Culture in Early Modernity). Farnham, Surrey: Ashgate Publishing. pp. 11–30. ISBN 978-1-4094-0024-0. ↩

  169. Magill & Aves 1998, p. 66: "Sabra discusses in detail the impact of Alhazen's ideas on the optical discoveries of such men as Descartes and Christiaan Huygens; see also El-Bizri 2005a." - Magill, Frank Northen; Aves, Alison (1998), "The Middles Ages: Alhazen", Dictionary of World Biography, vol. 2, Routledge, ISBN 978-1-57958-041-4 ↩

  170. El-Bizri 2010, p. 12. - El-Bizri, Nader (2010). "Classical Optics and the Perspectiva Traditions Leading to the Renaissance". In Hendrix, John Shannon; Carman, Charles H. (eds.). Renaissance Theories of Vision (Visual Culture in Early Modernity). Farnham, Surrey: Ashgate Publishing. pp. 11–30. ISBN 978-1-4094-0024-0. ↩

  171. Magill & Aves 1998, p. 66: "Even Kepler, however, used some of Alhazen's ideas, for example, the one-to-one correspondence between points on the object and points in the eye. It would not be going too far to say that Alhazen's optical theories defined the scope and goals of the field from his day to ours." - Magill, Frank Northen; Aves, Alison (1998), "The Middles Ages: Alhazen", Dictionary of World Biography, vol. 2, Routledge, ISBN 978-1-57958-041-4 ↩

  172. El-Bizri 2005a, 2005b. - El-Bizri, Nader (2005a), "A Philosophical Perspective on Alhazen's Optics", Arabic Sciences and Philosophy, 15 (2), Cambridge University Press: 189–218, doi:10.1017/S0957423905000172, S2CID 123057532 https://doi.org/10.1017%2FS0957423905000172 ↩

  173. Winter, H. J. J. (September 1953). "The Optical Researches of Ibn Al-Haitham". Centaurus. 3 (1): 190–210. Bibcode:1953Cent....3..190W. doi:10.1111/j.1600-0498.1953.tb00529.x. ISSN 0008-8994. PMID 13209613. /wiki/Bibcode_(identifier) ↩

  174. "Ibn al-Haytham's scientific method". UNESCO. 14 May 2018. Archived from the original on 25 October 2021. Retrieved 25 October 2021. https://en.unesco.org/courier/news-views-online/ibn-al-haytham-s-scientific-method ↩

  175. Chong, Lim & Ang 2002 Appendix 3, p. 129. - Chong, S.M.; Lim, A.C.H.; Ang, P.S (2002), Photographic Atlas of the Moon, Cambridge University Press, ISBN 978-0-521-81392-1 https://books.google.com/books?id=vIcFxgAs-C8C ↩

  176. NASA 2006. - NASA (22 March 2006), "59239 Alhazen (1999 CR2)", JPL Small-Body Database Browser, NASA Jet Propulsion Laboratory, archived from the original on 7 August 2011, retrieved 20 September 2008 https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=59239+Alhazen ↩

  177. "AKU Research Publications 1995–98". Archived from the original (PDF) on 4 January 2015. https://web.archive.org/web/20150104215931/http://www.aku.edu/res-office/pdfs/AKU_Research_Publications_1995 ↩

  178. "Ibn Al-Haytham and the Legacy of Arabic Optics". 2015 International Year of Light. 2015. Archived from the original on 1 October 2014. Retrieved 4 January 2015. https://web.archive.org/web/20141001171116/http://www.light2015.org/Home/ScienceStories/1000-Years-of-Arabic-Optics.html ↩

  179. "2015, International Year of Light" (PDF). Archived (PDF) from the original on 15 April 2017. Retrieved 10 October 2017. http://www.unesco.org/fileadmin/MULTIMEDIA/HQ/SC/pdf/Programme-Opening_IYL2015.pdf ↩

  180. "1000 Years of Arabic Optics to be a Focus of the International Year of Light in 2015". United Nations. Archived from the original on 21 November 2014. Retrieved 27 November 2014. http://www.unesco.org/new/en/media-services/single-view/news/1000_years_of_arabic_optics_to_be_a_focus_of_the_international_year_of_light_in_2015 ↩

  181. "10 Dinars, Iraq". en.numista.com. Retrieved 28 May 2024. https://en.numista.com/catalogue/note203100.html ↩

  182. Rashed 2002a, p. 773. - Rashed, Roshdi (August 2002a), "A Polymath in the 10th century", Science, 297 (5582): 773, doi:10.1126/science.1074591, ISSN 0036-8075, PMID 12161634 https://doi.org/10.1126%2Fscience.1074591 ↩

  183. Rashed 2007, pp. 8–9; Topdemir 2007 - Rashed, Roshdi (2007), "The Celestial Kinematics of Ibn al-Haytham", Arabic Sciences and Philosophy, 17, Cambridge University Press: 7–55, doi:10.1017/S0957423907000355, S2CID 170934544 https://doi.org/10.1017%2FS0957423907000355 ↩

  184. Ibn Al-Haytham, W. 'Arafat and H. J. J. Winter (1971) JSTOR 4025317 (c. 1027–1038) The Light of the Stars: A Short Discourse by Ibn Al-Haytham Archived 21 September 2022 at the Wayback Machine The British Journal for the History of Science Vol. 5, No. 3 (Jun., 1971), pp. 282–288 /wiki/JSTOR_(identifier) ↩

  185. Alhacen (c.1035) Treatise on Light (رسالة في الضوء) as cited in Shmuel Sambursky, ed. (1975) Physical thought from the Presocratics to the quantum physicists : an anthology, p.137 /wiki/Shmuel_Sambursky ↩

  186. From Ibn Abi Usaibia's catalog, as cited in Smith 2001 91(vol. 1), p. xv. /wiki/Ibn_Abi_Usaibia ↩