In this article, some aspects of Kitab Nūr hadaqat al-ibsār wa-nūr haqīqat al-anzār (Book of the Light of the Pupil of Vision and the Light of the Truth of the Sights) of the renowned Ottoman astronomer Taqī al-Dīn ibn Ma‘rūf, who lived in Istanbul in the 16th century, is discussed in detail in order to show the high level and quality of the scientific research carried out during the reign of the Ottoman Empire.
Dr. Hüseyin Gazi Topdemir*
Table of contents
This article is extracted from the long study Takîyüddîn'in Optik Kitabi  (Taqī al-Dīn's Book of Optics), carried out by the author on the important volume Taqī al-Dīn b. Ma‘rūf devoted to the science of optics and the problems of vision. The study consists in a translation and interpretation of the Taqī al-Dīn's book on optics Kitab Nūr hadaqat al-ibsār wa-nūr haqīqat al-anzār (henceforth Kitāb Nūr) by the renowned Ottoman mathematician and astronomer Taqī al-Dīn b. Ma‘rūf.
The interpretation part of the essay Takîyüddîn'in Optik Kitabi has three chapters. The first one is reserved to the topic of direct sight in parallel with Kitāb Nūr. Here light, sight, and the effect of light on the eye and sight are thoroughly discussed. The second chapter is about sight through reflection. Here the variations to which light is subject on mirrors and how an image is created on different mirrors are explored. The third chapter deals with the topic of refraction. Here the changes to which light go through as it travels in mediums different in density.
In the present article we discuss in detail all aspects of Kitāb Nūr in order to show the level and quality of the scientific research and studies carried out during the reign of the Ottoman Empire.
Figure 2: The colophon and first two pages of Kitāb Nūr hadaqat al-ibsār wa-nūr haqīqat al-anzār. Süleymaniye Library, Collection Laleli, MS 2558, folio 1b-2a.
One of the many gifted and renowned Muslim scientists, Taqī al-Dīn b. Ma‘rūf was born around 1521 in Damascus. He was an eminent astronomer, mathematician and physicist. In contrast to our lack of knowledge of the lives of many Ottoman and Turkish scientists, we have plenty of details about Taqī al-Dīn b. Ma‘rūf's life. Our knowledge is nourished by numerous bio-bibliographical notes devoted to him in books of history .
Taqī al-Dīn b. Ma‘rūf was a prolific writer on all aspects of science and natural philosophy. More than fifty works are attributed to him. The main topics on which he wrote were astronomy, optics, including the theory of light and a theory of vision, and mathematics, including geometry and number theory. On all those subjects, he wrote more than ninety books, few of which have survived. But his contributions have been immense. His ideas brought forth a new era in theoretical and experimental astronomical and optical research. The extant works of our scholar in astronomy, mathematics and optics, are the following:
- Al-Dur (or: al-‘iqd) al-nazīm fī tashīl al-taqwīm (Pearl of ordered simplification of the calendar);
- Al-Turuq al-saniyya fī al-ālāt al-rūhāniyya (on mechanics and machines);
- Sidratu muntahā ‘l-afkār fī malakūt al-falak al-dawwār (book of astronomy);
- Buǧyat al-tullāb min ‘ilm al-hisāb (on arithmetics)
- Jarīdat al-durar wa-kharīdat al-fikar (book of trigonometry)
- Kitāb al-nisab al-mutashākala (book of mathematics, on ratios)
- Kitab Nūr hadaqat al-ibsār wa-nūr haqīqat al-anzār (book of optics);
- Rajaz fī rub‘ al-dastūr al-ma‘rūf bi-‘l-mujayyab (on an astronomical instrument);
- Al-Dastūr al-rajīh li qawā‘id al-tastīh (on geometry);
- Risāla al-tawārikh (on chronology);
- Risāla fī samt al-qibla (on finding the direction of the qibla);
- Sharhu kitāb al-tajnīs fī al-hisāb li-‘l-Sakhāwandī (commentary on Sakhāwandī's book of arithmetics Kitāb al-tajnīs fī al-hisāb);
- Risāla fī al-tasyīr (article on astrology);
- Risāla dar bayān-i usturlāb (article on the astrolabe);
- Risāla fī al-jabr wa al-muqābala (article on algebra);
- Kitāb ma‘rifat awqāt al-salāt (on finding the prayer times);
- Khulāsat al-a‘māl fī mawāqīt al-ayyām wa-‘l-layl (On daytime and night);
- Al-Kawākib al-durriyya fī waz‘ al-bankāmāt al-dawriyya (on making periodical clocks);
- Rayhānat al-rūh fī sasm al-sā‘āt ‘alā mustawā ‘l-sutūh (on gnomons);
- Kitāb al-simār al-yāni‘a (on a universal astronomical instrument);
- Risāla fī'l-‘amal bi'l-rub‘ al-shikāzī (on an astronomical quadrant);
- Al-Mizwalat al-shimāliyya bi-fadli dā'iri ufuqi al-Qustantīniyya (gnomons for Constantinople's latitude);
- Al-Ālāt al-rasadiyya bi zīj al-Shāhinshāhiyya (observational instruments in the Shāhinshāhiyya astronomical table);
- Risāla fī sababi ta'akhuri gurūb al-shams (on the reason of sunset delay).
Of course, his best-known and most influential works are the book of astronomy Sidratu muntahā ‘l-afkār the book of optics Kitab Nūr hadaqat al-ibsār wa-nūr haqīqat al-anzār and the work of mechanics Al-Turuq al-saniyya fī al-ālāt al-rūhaniyya. A discussion of all these works goes beyond the scope of this article. Thus, we concentrate our effort on the matters dealt with in optics as they are disclosed in Kitāb Nūr.
Figure 3: Ottoman astronomers studying the moon and the stars in a miniature dating from the 17th century at Istanbul University Library. (Source).
The treatise is extant in four different copies. One of them is held at the Süleymaniye Library in Istanbul, Laleli Collections, MS 2558. We refer hereafter to this copy with the symbol ‘S'. This copy consists of 72 folios. Each folio contains 27 lines. In its introduction it is said that this edition of Kitāb Nūr was dedicated to al-Karîm ibn al-Karîm ibn al-Karîm Molla Çelebî Efendi Abd al-Karîm. It was not possible for us to determine the identity of this person.
Another copy is recorded at Oxford, Bodleian Library, MS Marsh 119; we refer to it with the letter ‘O' . It contains in total 83 folios. In its introduction, it is stated that this copy is dedicated to Sultan Murad Han III. In the last paragraph of the colophon, Taqī al-Dīn b. Marūf's authorship of the book is recorded in detail as "Taqī al-Dīn Muhammad ibn Zain al-Dīn, the glory of the sect and religion and the last of the investigators, Ma‘rūf ibn al-Shaikh Shihāb al-Dīn Ahmad ibn Muhammad ibn Muhammad ibn Ahmad ibn Yūsuf ibn Ahmad ibn al-Amīr Nasr al-Dīn Menqubars ibn al-Amir Naskh al-Dīn Khumar Takin al-Arīn, the prince of virility".
The third copy (referred to as ‘M') is conserved in the Mehmet Nuri Efendi Collection, MS 163/3, at Süleymaniye Library in Istanbul.
The fourth copy (referred to as ‘C') is at Dār al-Kutūb, in Cairo, in the section Riyāza, MS 893.
The treatise is composed of three main parts or books (in Arabic mirsad) as listed below:
Book I: Direct Vision:
1. Inquiry into the Properties of Direct Vision
2. Inquiry into the Properties of Lights and into the Manner of Radiation of Lights
3. The Effect of Light upon Sight
4. The Structure of the Eye
5. The Formation and the Nature of Vision
6. The Causes of Errors of Sight
Book II: Catoptrics:
1. Inquiry into the Properties of Reflected Lights
2. Inquiry into the Properties of Reflection
3. Inquiry into the Properties of Reflective Objects
4. On the Formation of Images by Reflection
5. On the Properties of Images by Reflection
6. On the Causes of Errors of Images by Reflection
Book III: Dioptrics:
1. Inquiry into the Properties of Refracted Lights
2. Inquiry into the Properties of Refraction
3. On the Formation of Images by Refraction
4. On the Causes of Errors of Images by Refraction
5. On the Properties of Images by Refraction
6. On the Ratio of Refracted Angels
Figure 4: Extract from Kitāb Nūr, presenting the title and beginning of the first chapter. Süleymaniye Library, MS Laleli 2558, folio 3v.
In the first book, the nature of light, the source of light, the nature of the propagation of light, the formation of sight, and the effect of light on the eye and sight are thoroughly discussed.
The second book is about sight through reflection. In this chapter, the variations that light are subject to on mirrors, formation of an image on different mirrors and the nature of reflected light, are explored.
The third and the last book deals with the topic of refraction. In particular, it analyses the important question of the variations light undergoes while travelling in mediums having different densities, i.e. the nature of refracted light, the formation of refraction, the nature of images formed by refracted light. The relevant chapter also includes a sub-section that concentrates on the variations that light is subject to in the atmosphere.
Figure 5: Reflection and refraction at the interface between air and water: a ray of light hitting a surface between two isotropic media will generally give rise to a reflected ray and a refracted ray. (Source).
Kitāb Nūr begins with an introduction in which Taqī al-Dīn b. Ma‘rūf argues that he begins his study by inquiring the first principles and premises of optics. His method involves criticizing premises and exercising caution in drawing conclusions while he aims to employ justice, not to follow prejudice, and take care in all that we judge and criticize that we seek the truth and not be influenced by opinions.
In Book I, he makes it clear that his investigation of light is based on experimental evidence rather than on abstract theory. He notes that light is the same irrespective of the source, and gives the examples of sunlight, light from a fire, or light reflected from a mirror, all of which are of the same nature. Departing from Ibn al-Haytham's theory, he produces a correct explanation of vision, showing that light is reflected from an object into the eye. Most of the rest of Book I is devoted to the structure of the eye and the errors of direct vision and their causes. However, in this part he seems to be in error since he does not have the concept of lens which is necessary to understand the way the eye functions. Further, he discusses in this Book I visual perception and examines conditions necessary for a good vision. Moreover, the author examines how errors in vision are caused.
Figure 6: Front cover of a study on Ibn al-Haytham's optics in Turkish by Hüseyin G. Topdemir, Modern Optigin Kurucusu: Ibnü'l Heysem Hayati, Eserleri ve Teorileri (Ankara, 2002).
Despite the importance of the topics dealt with in Book I, however, from a mathematical point of view, Book II is more important since it discusses the theory of reflection. Taqī al-Dīn b. Ma‘rūf provides the experimental proof of the specular reflection of accidental as well as essential light, a complete formulation of the laws of reflection, and a description of the construction and use of a copper instrument for measuring reflections from plane, spherical, cylindrical, and conical mirrors, whether convex or concave. Further, in this second book II, our scholar inquires into errors in vision due to reflection.
The third and final book is devoted to refraction. Taqī al-Dīn b. Ma‘rūf does not give the impression that he sought for a law but he failed to discover. In fact, his "explanation" of refraction certainly forms part of the history of the formulation of the refraction law. The explanation is based on the idea that light is a movement, which admits a variable speed (being less in denser bodies). His research in dioptrics yielded knowledge of the changing ratio between the angle of incidence and refraction. He came very close to developing a theory on magnifying lenses when he carried out experiments with glass vessels filled with water.
Concerning the methodological level, Taqī al-Dīn b. Ma‘rūf used and applied the experimental method in his optical researches. He conducted experiments on the propagation of light and colour, optic illusions, as well as reflections. He also conducted the first experiments on the dispersion of light into its constituent colours.
In addition, he contributed to the knowledge on the description of vision and the eye, though he thought the lens was the receptor of light. He realized the nature of the reflection of light off objects into our eye, rather than anything originating within the organ itself. Taqī al-Dīn b. Ma‘rūf described accurately the parts of the eye, and provided scientific explanations for the process of vision. He explained binocular vision and correctly explained the apparent increase in size of the Sun and Moon when they are near the horizon.
Taqī al-Dīn b. Ma‘rūf's Kitāb Nūr, is probably the only work written on optics under the reign of the Ottoman Empire, with a large array of comprehensive content. In the book, traditional optical problems are dealt with and most of the arguments related to those problems are experimentally proven and explained by analogy.
The main texture of the book is formed by arguments and problems, which were the results of the detailed and successful optical studies that started 800 years before that book in the Islamic world. The creative Islamic tradition in optics have also formed the base for the studies in this field in the West until the 17th century. At first glance, this fact may seem very fascinating, and numerous recent historiographical studies have showed that Ibn al-Haytham's (in Latin Alhazen) (965-1039) arguments had formed the very basis and tradition in optics in pre-modern Europe until the 17th century.
There are two aspects of Ibn al-Haytham's arguments: The evaluation of the optical problems geometrically, and the explanation of the problems by causal analysis. These two aspects are supported by sophisticated and well-organized experiments.
This approach dominated the Western field of optics for about 600 years, until 17th century. Roger Bacon (1214-1294), Witelo (1230-1275), John Pecham (1220-1292) and Johannes Kepler (1571-1630) used this model of study for solving optical problems. Only Kepler made new achievements. He succeeded in putting new arguments that are fundamental for handling lenses in the branch of dioptrics. Historians consider these studies as a milestone in optics; thus, they acknowledge that the modern period of optics starts with Kepler .
This conclusion is partly acceptable because the main subject of modern optics is the colour. Hence, Newton's studies made the colour one of the major subject to be dealt with in optics. In his book of Opticks, Newton (1642-1724) dealt with all aspects of colour. Even though, the full name of the book is Opticks or Treatise of the Reflections, Refractions, Inflections and Colours of Light , he only briefly gave principles of reflection and refraction and in the rest of the book he only dealt with analysis of colour.
While the West had been making progress in optical studies, studies in the East were not consistent. For instance, Nasr al-Dīn Tūsī (1201-1274) chose the Aristotelian approach to explain the optical problems instead of Ibn al-Haytham's approach, although he lived two hundred years after him. In contrary to that, Kamāl al-Dīn al-Fārisī (d. 1320), a Persian scholar who lived almost three centuries after Ibn al-Haytham, followed his tradition and put forward the correct solutions for optical problems. Consequently, the West was successful in making use of Ibn al-Haytham's studies and, therefore, was able to start the modern period of optics.
Since the translation activities from Arabic into Latin, so called the 12th century Renaissance, ended in the 12th-13th centuries, apparently the developments brought about by Kamāl al-Dīn al-Fārisī could not have been transferred to the West and therefore Islamic optics after Ibn al-Haytham was not known in Europe.
Meanwhile, in the East, the situation was reverse. Ibn al-Haytham's book Kitāb al-manāzir and Kamāl al-Dīn al-Fārisī's book Tanqīh al-manāzir were in widespread use. During that time it was very common to read commentary (šarh) books instead of original books, and it would not be wrong to say that the earlier books of manāzir were commonly known because the commentary books on the Tanqīh of al-Fārisī were numerous and widespread.
In this context, if we go back to Taqī al-Dīn's book, his Kitāb Nūr benefited from the contributions of earlier Muslim scholars, mainly Ibn al-Haytham and Kamāl al-Dīn al-Fārisī, whose influence can easily be observed in this treatise. For instance, for an object to be seen, the size of the object is as important as the distance between the eye and object. If the distance is sufficient for a clear vision, then it is called "moderate distance" (bu‘d mu‘tadil); and for the reverse situation, it is called "excess distance" (bu‘d musrif) . These terms were defined by Ibn al-Haytam. However, Kamāl al-Dīn al-Fārisī added another term for the explanation of the distance between the eye and the object. That term is varying distance (bu‘d -mutafāwit) .
The concept of varying distance seems much more explicative than moderate and excess distance, because there are upper and lower limits for the visibility of objects. It is the size of the object that defines the limits. Because of that, there has to be varying distances for visibility of each different object size. Taqī al-Dīn recognized this truth and established his arguments on this basis. In fact, in the introduction to Kitāb Nūr, he stated that Kamāl al-Dīn al-Fārisī was his major rival in this subject. He also stated that Ibn al-Haytam's arguments were much more developed by al-Fārisī, claiming that his aim in writing his book was to make the arguments clear and show the differences among his two eminent predecessors.
Therefore, we could say that Taqī al-Dīn's Kitāb Nūr is in a way a sort of commentary book on Kitāb al-manāzir and Tanqih al-manāzir. In fact, the author arranged the chapters in a similar form to theirs. For instance, Kitāb al-Manāzir is divided into seven chapters. The first three deal with direct vision, the second three chapters treat of reflection, while the last one is on refraction. On the other hand, Tanqīh al-Manāzir has a similar arrangement, as it consists of seven chapters (in Arabic maqāla). And finally, Kitāb Nūr has three chapters or books (in Arabic mirsad) dealing with direct vision, reflection and refraction respectively.
As for the content of Taqī al-Dīn's book, no doubt he had achieved the target of making the subject clear and understandable for the matters he discussed, namely direct vision, reflection and refraction. For example, to prove the rule that light emerges from object not from eye, Ibn al-Haytham and Kamāl al-Dīn al-Fārisī gave too many examples in their books which were boring and pages long. Taqī al-Dīn, on the other hand, gave only one example from astronomy but proved the rule better. According to him, if the ray of light had emerged from the eye, it would take too much time for us to see in the sphere of fixed stars. As known, however, there is a distance of millions of kilometres between the star and eye. Since the velocity of light is constant, it would take too much time for it to travel to the star and come back to the eye. But this is not the case, since we see the star as soon as we open our eyes. Therefore the light must emerge from the object not from the eyes .
Kitāb Nūr contains following assertions:
A. First Book (al-mirsad al-awwal):
- The source of light is the object and the end of light is the eye.
- The images coming to the eyes with the light contain also the colour of the object.
- Eyes can only detect the objects which are illuminated or which emits light.
- The sight is a geometrical fact, because the propagated light has a conical form of which the top is the source of light and its base is on the eye.
- The light is corporeal, but it can be approached as a geometrical object in optical treatment.
- The rays of light propagate in spherical forms, but this propagation occurs through rectilinear lines.
- The colour occurs with the reflection and refraction of light.
From the explanations given before, it is obvious that all the above assertions were not put forward by Taqī al-Dīn for the first time. But his priority holds in what concerns the propagation of light and the formation of colour. Ibn al-Haytham had put forward the idea that light propagated from source to all directions in straight lines. This means that light propagates in a spherical form . However, Taqī al-Dīn developed this idea and proved that the spherical propagation of light is also true for all forms of light propagation, i.e. rectilinear, reflected and refracted light. Therefore, Ibn al-Haytham's idea of propagation of light in spherical forms has turned with Taqī al-Dīn into a proven knowledge from an ordinary idea .
The formation of colour, on the other hand, was satisfactorily explained by Taqī al-Dīn for the first time in the Islamic world. He clearly stated that colour formed as a result of reflection and refraction of light. Considering that in the West, the formation of colour was truly finalized by Newton only at the end of the 17th century, Taqī al-Dīn's determination of the same fact around two hundred years before him is very valuable from the historical view point .
B. Second Book (al-mirsad al-thānī):
- The reflected lights also form a conical form whose top is on the reflecting surface, and the base is the place where it ends.
- The reflected light has the colour of the reflecting surface.
- The reflection of light is also a geometrical problem.
- The rays of the reflected light propagate in a spherical form.
- The incident ray, the reflected ray and the normal to the reflecting surface, lie in the same plane.
- The angle of incidence (between the incident ray and the normal at the point of incidence) is equal to the angle of reflection (between the reflected ray and the normal at the point of incidence).
The fact of reflection is an early developed branch of optics with respect to refraction. For that reason, its rules were also found out earlier. As one can easily realize, the rules of reflection have been known ever since the Ancient times and all those rules are parallel to that of direct vision.
Therefore, Taqī al-Dīn, naturally focused his attention on proving the validity of the above mentioned rules for all different types of mirrors, i.e. plain, spherical, cylindrical, paraboloidal, and he succeeded to do so geometrically and experimentally. When the rules of reflection and direct vision are compared, it can be easily seen that the only difference between them is the source of light. For the former, it is the reflecting surface, and for the latter, it is the object itself.
C. Third Book (al-mirsad al-thālith):
- The refracted light propagates in a spherical form, like the reflected light.
- The refracted light has the colour of the object through which it penetrates.
- When a ray of light passes obliquely from a medium of lesser to one of greater optical density, it is bent toward the normal; conversely, a ray of light passing obliquely from an optically denser medium to an optically rarer medium is bent from the normal to the surface.
- The angle of refraction is less than the angle of incidence.
- The incident ray, the refracted ray and the normal to the surface at the point of incidence are all in the same plane.
- The perpendicular ray does not refract.
- The difference between the refraction angles of different incident rays is less than the difference between the angles of incidence.
- The ratio of the angle of the larger incident to its refraction angle is larger than the ratio of the angle of the smaller incident to its refraction angle.
It is obvious that most of the principles stated above are the current refraction rules. Yet, we have to mention that Taqī al-Dīn did not formulate them all; in particular, he did develop only the last two rules whilst he asserted the first six without going deep in their analysis. However, in his study of the last two principles about refraction angles, Taqī al-Dīn tried to formulate the law that we call today Snell's law. Actually, Willebrord Snell (1580-1626) found out the constant ratio between the sine of incidences and refraction angles; on his part, Taqī al-Dīn formulated the relationship between the incident and refraction angles formed by different incident rays. In other words, he certainly concentrated his attention on the densities of medium and set forth the mentioned relations accordingly .
Taqī al-Dīn could not be considered as unsuccessful for not setting forth the so-called Snell's law before him. The main reason for this is that, as it is known, the refraction is the most difficult and complex branch of optics which, therefore, could have only been advanced after the other branches of the optics.
To compensate this relative "failure", Taqī al-Dīn evokes in his book Kitāb Nūr an important discovery that was never mentioned before. This regards an instrument that makes the objects located far away appear closer to the observer. He says: "I made a crystal (billawr) that has two lenses displaying in details the objects from long distances. When they look from one of its edges, people can see the sail of the ship in far. My instrument is similar to that of ancient Greeks which had made and placed on the Tower of Alexandria" .
Taqī al-Dīn's assertion evokes no less than a kind of spectacles, the instrument that had beginning from 1609 the tremendous fortune we know of, when Galileo directed it to the skies and used it as a telescope. As he describes it, Taqi al-Din's instrument helps to see the objects in detail by bringing them very close. In addition, he stated that he wrote an article explaining the way of making and using this instrument. Yet, there is confusion concerning a part of his explanation, when he claims that his apparatus has similar properties to one used by ancient Greeks in Alexandria penthouse. Obviously, this derives from the tales and narrations that surrounded this mysterious monument, like burning mirrors.
At any rate, this is a topic that needs to be investigated carefully, to state whether such an invention was really made in Ottoman lands, if Taqi al-Din's instrument attracted the attention of his contemporaries, and most of all, if it was transmitted in a way or another to Western Europe by the end of the 16th century. According to the known and available information, spectacles were used in Europe at the beginning of the 17th century. It was in this context that Galileo used them in astronomical investigation from the summer of 1609. Now, Taqī al-Dīn's book had been written nearly 30-35 years before. What conclusions could be drawn from these dates? Only a thorough research in the original archives can attain a conclusion. What we can state for the moment is that this is an area of research worth a deep investigation, and that it may reveal some hidden secrets.
In the light of all of the explanations above, Taqī al-Dīn's book could be considered as a valuable book of optics with respect to the way of handling optical problems, their analysis and the level of optical knowledge he discloses. In addition, the book is one of the fundamental sources for a good evaluation of the scientific scene in the Ottoman Empire in the 16th century.
Taqī al-Dīn's book has two significant dimensions to be mentioned:
1. The book was probably a unique textbook of optics that was written during the Ottoman Empire in the 16th century.
2. Researches of optics of the preceding Islamic tradition of optics became popular through this tremendous book.
At that time, the intensive efforts of Ibn al-Haytham and his arguments in Kitāb al-Manāzir made the subject of optics as the best known and mostly devoted subject in the Islamic World. It has become the only reference book in both the Eastern and Western Worlds after it was translated into Latin in the 12th century. The same impact on the Islamic World was achieved by Kamāl al-Dīn al-Fārisī's book Tanqih al-Manāzir in 1320, approximately three hundreds years later. While there had been no attempt to clarify the value of al-Fārisī's book and to determine to what extent it has spread out, small-scale studies on its different parts showed that this book, whose title means the corrections of the optics, was the most significant work ever since Kitāb al-Manāzir in the Islamic World.
The third important study on optics in the Islamic World we encountered after that time is, therefore, the work of Taqī al-Dīn Kitāb Nūr.
Accordingly, through this book we get some ideas about the general structure and content of scientific works in the Ottoman Empire, and more specifically, we observe the continuation and the value of the studies initiated by Ibn al-Haytham and developed by Kamāl al-Dīn al-Fārisī.
Kitāb Nūr includes an introduction and three main parts. The introductory part draws a background to the subject. The first part concerns the direct vision; the second one the reflection; and the third one the refraction. In the first part is included the subject of the relation between light and vision; in the second one the changes of light on the mirror and the relation between reflecting light and vision; and finally the third part is about the changes of the light in different media and about the differences emerging in vision resulting from those changes.
In the first part we observe that Taqī al-Dīn regards the source of light as the object itself. After this right contention, he puts his main epoch-making arguments, that light diffuses spherically through linear directions. This explanation is important in the sense that it makes the early references to the wave model of light before that of Huygens.
The second part of Kitāb Nūr is related to the reflection. In this part, Taqī al-Dīn explains the changes of the light on mirrors and the formation of vision on different mirrors.
The third part is dedicated to refraction. In this part, Taqī al-Dīn examines the changes of the light regarding its diffusion within the different media with different densities. Here, he did his important contribution to the optics by advocating a quite different approach to the law of refraction. He expressed the issue not trigonometrically but geometrically by defining the law of sinus as an inequality between angles.
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 Hüseyin Gazi Topdemir, Takîyüddîn'in Optik Kitabi, Ankara: Ministery of Culture Press, 1999.
 See A. Süheyl Ünver, Istanbul Rasathanesi, Ankara 1985, pp. 3-6; A. Adnan Adivar, Osmanli Türklerinde Ilim, Istanbul 1982, pp. 100-109; Ramazan Şeşen, "Meşhur Osmanli Astronomu Takîyüddîn el-Rasid'in Soyu Üzerine", Erdem, vol. 4, No. 10, 1988, pp. 165-171; E. Ihsanoǧlu, R. Şeşen, C. Izgi, C. Akpinar, I. Fazlioǧlu, Osmanli Astronomi Literatürü Tarihi, vol. I, Istanbul 1997, pp. 199-217; Muammer Dizer, Takiyüddin, Ankara 1990, pp. 24-34.
 H. J. J., Winter, "The Arabic Optical MSS in the British Isles", Centaurus, vol. 5, No. 1, 1956, p.
 Abraham Wolf, History of Science, Technology and Philosophy in the 16th and 17th Centuries, 2 vols., Vol. 1: (Gloucester, Mass., 1968), p. 246.
 See, Isaac Newton, Opticks, New York, 1952.
 See, Ibn al-Haytham, Kitāb al-manāzir, translated into English by A. I. Sabra, Book I, Chapter 2, Paragraph 25, London 1989, p. 12.
 See, Kamāl al-Dīn al-Fārisī, Tanqīh al-Manāzir, vol. I, Haydarabad 1928, p. 19.
 Taqī al-Dīn, Kitāb Nūr, Book I, Chapter 5, MS ‘O', folio 14b; MS ‘S', folio 12a-b.
 Ibn al-Haytham, Book I, Chapter 2, Paragraph 110, p. 43.
 Taqī al-Dīn, Kitāb Nūr, Book I, Chapter 2, MS ‘O', folio 7a-b; MS ‘S', folio 6a-b.
 Taqī al-Dīn, Kitāb Nūr, Book I, Chapter 2, MS ‘O', folio 10a-b; MS ‘S', folios 8b-9a.
 Taqī al-Dīn, Kitāb Nūr, Book III, Chapter 4, MS ‘O', folios 62a-63b; MS ‘S', folios 55b-57a.
 Taqī al-Dīn, Kitāb Nūr, Book III, Chapter 5, MS ‘O', folio no: 81b; MS ‘S', folio no: 72a. Emphasis by the author of the article.
* PhD, Department of Philosophy, Faculty of Letters, Ankara University, Ankara, Turkey. The article was heavily copy edited by the editorial board of www.MuslimHeritage.com (the Chief Editor).