Taqi al-Din Ibn Ma’ruf: Survey on his Works and Scientific Method

by Ihsan Fazlioglu Published on: 4th July 2008

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Being in form a bio-bibliographical essay on the life and works of Taqī al-Dīn Ibn Ma'rūf, a well known scholar of 16th-century Istanbul, this article presents the contents of his books and compares his scientific method with his predecessors. This investigation leads in turn to a description of the originality of his achievement and shows the novel aspects of his work.


İhsan Fazlioǧlu*

Taqī al-Dīn Abu Bakr Muhammad b. Zayn al-Dīn Marūf al-Dimashqî, al-Hanafî, known as Taqī al-Dīn al-Rasid, was a mathematician, astronomer, optician and mechanical scholar. He is famous as founder and the director of the Istanbul observatory. He made various astronomical instruments and for the first time he used automatic-mechanic clock in his astronomical observations. He advanced the arithmetic of decimal fraction and used decimal fractions in the calculation of astronomical tables.

Taqī al-Dīn first studied basic religious sciences and Arabic within the paradigm he lived in. Later on he learned transmitted (naqlī) and exact (‘aqlī) sciences from the scholars in Damascus and Egypt and especially from his father. It is probable that Taqī al-Dīn’s teacher in mathematics was Shihāb al-Dīn al-Ghāzzī while the one in astronomy was Muhammad b. Abī al-Fath al-Sūfī. Taqī al-Dīn himself states in the forewords of his various books that he assigned a special interest in mathematical sciences during his education.

After completing his education, Taqī al-Dīn worked in the capacity of mudarris for a short while at the madrasas in Damascus. Together with his father Marūf Efendi, he came to Istanbul around the year 1550. There, he participated to and benefited from the circles of scholars such as Chivī-zāda, Abū al-Su‘ūd, Qutb al-Dīn-zāda Mahmad and Sajlī Amīr. Then he returned to Egypt (circa 1550) and taught at Shayhuniyya and Surgatmishiyya madrasas in Cairo. He once again returned to Istanbul for a short time. He worked in the capacity of mudarris at Edirnekapi Madrasa during the time of grand vizier Samīz Alī Pāshā. In this period he used Ali Pasha’s private library and clock collection. Then he returned to Egypt since his family was there and Ali Pasha was appointed the governor to Egypt. He worked in the capacity of mudarris and qadi (judge) in Egypt. During the reign of Selim II, he deputized Chivi-zada and later Nishanci-zada after their successive appointments to the post of the judge of Egypt. Following Nishanci-zada, Kazasker Abd al-Karīm Efendī became judge to Egypt. Kazasker Abd al-Karīm Efendī and his father Qutb al-Dīn encouraged Taqī al-Dīn to deal with mathematics and astronomy. Qutb al-Dīn gave his collection of works, including various astronomical instruments, inherited from Alī Kushjū, Jamshīd al-Kāshī and Bursālī Qādī-zāda to Taqī al-Dīn to increase his knowledge of astronomy. From then on, Taqī al-Dīn dealt constantly with astronomy and mathematics. He made astronomical observations via an astronomical instrument which he mounted, a 25 meter deep-well when he was a judge in Tinnin.

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Figure 1: Astronomer observing the comet of 1577 above Istanbul with a wooden quadrant. Mustafa Ali, Nusratnāme, Topkapi Palace Museum Library, Hazine 1365, folio 5v.

Taqī al-Dīn came to Istanbul in 1570. On the death of Chief Astronomer Mustafā b. Alī al-Muwaqqit in 1571, the Sultan Murad III appointed him chief astronomer. He entered into the circle of with Hoca Sad al-Dīn Efendi who was supported by him. He continued his observations in a building situated on a height overlooking Tophane or in Galata Tower. His study drew the attentions of Hoca Sa‘d al-Dīn, one time instructor of Sultan Murad III, and Sadrazam Sokullu Mahmad Pasha. It was decided to build an observatory in the early 1579. After issuing an imperial edict by Sultan Murad III, the construction was started on a height overlooking Tophane where French Palace is located today. Important astronomical books and instruments were collected there. In a monograph entitled Al-Ālāt al-rasadiya li-zīj al-shāhinshāhiyya, written by a scholar within Taqī al-Dīn’s entourage (İstanbul Univesity, TY, no. 1993), and in ‘Alā’ al-Dīn Mansūr al-Shīrāzī’s Shahinshāhnāma (İstanbul University, TY, no. 1404), the pictures of the scholars and astronomical instruments used in observation are given. The information about the place and shape of the observatory is not certain. Apart from the observatory building, a well called “çah-i rasad” which was used by Taqī al-Dīn is also mentioned.

Taqī al-Dīn started his observations when he was in Egypt and he wrote some books on astronomy. In these works he corrected the calculation errors in Ulugh Beg Astronomical Tables and decided to prepare a new zīj (astronomical table). The construction of Istanbul Observatory (Dār al-Rasad al-Jadīd) meant an opportunity for him to complete this book. But, because of some political reasons as well as Taqī al-Dīn’s wrong astrological interpretations, the observatory did not last long; it was demolished on 22 January, 1580. Because of this circumstance, Taqī al-Dīn’s astronomical observations remained incomplete.

In other scientific fields, Taqī al-Dīn composed a book on medicine and zoology, three on physics-mechanics, five on mathematics, besides the huge list of his writings in astronomy, amounting to twenty titles. Also he has a monograph entitled Risāla fī ‘amal al-mīzan al-tabī‘ī (Alexandria, Baladiya [Municipal] Library, Majāmi‘, MS 3762, 4 folios) on the specific gravity of substances and Archimedes’ hydrostatic experiments. All of his books are in Arabic. In the field of astronomy, there are eight books related to Taqī al-Dīn, five in Turkish, two in Arabic and one in Persian.

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Figure 2: The colophon of Tarjumān al-atibbā’ wa-lisān al-alibbā’. The National Library of Medicine in Bethesda, Maryland (MS A75, folio 2a). (Source).

Taqī al-Dīn has also a medical book entitled Tarjuman al-Atibba wa Lisan al-Alibba where simple (mufradat) medicines are examined in an alphabetical order. A treatise of zoology by him is entitled Al-Masābih al-muzhira fī ‘ilm al-bazdara (Berlin, Gotha, MS 2094, 44 folios), but this book hasn’t been examined yet. Taqī al-Dīn wrote his Al-Kawākib al-durriyya fi wadh‘ al-bankāmat al-dawriyya taking up mechanic-automatic clocks for the first time in Islamic and Ottoman world, in 1559 in Nablus. In the foreword, Taqī al-Dīn mentions that he benefited from Samiz Ali Pasha’s private library and from his collection of mechanical clocks brought from Europe. In this work, Taqī al-Dīn deals with mechanical clocks, their kinds and shapes and he takes up every clock in turn and examines it from geometrical and mechanical perspectives. The treatise was edited by Sevim Tekeli (Ankara 1966). His other book on mechanics is the one he wrote when he was 26, al-Turuq al-saniyya fī ‘l-ālāt al-rūhaniyya. In this work, Taqī al-Dīn focuses on the geometrical and mechanical analysis of the structures of the clocks, in he frame of the Islamic tradition of ‘ilm al-hiyal’ in which outstanding treatises were left by Banū Mūsā, Abū al-‘Izz al-Jazarī. Al-Turuq al-Saniyya was edited by Ahmed Yusuf al-Hassan (Aleppo 1976). In the field of physics and optics, Taqī al-Dīn examining Euclid, Ibn al-Haitam and Kamāl al-Dīn al-Fārīsī’ related books; his text in this area is Kitāb Nūr hadaqat al-ibsār wa-nūr haqīqat al-anzār, in which he took up the structure of light, its diffusion and global refraction and he examined the relations between light and colour.

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Figure 3: The colophon of Kitāb Nūr hadaqat al-ibsār wa-nūr haqīqat al-anzār. Süleymaniye Library, Collection Laleli, MS 2558, folio, 1b-2a.

In mathematics, Taqī al-Dīn studied the Arabic translation of Thedosius’ book entitled Ukar (Spheres). He wrote also a short monograph containing his answer to a question pertinent to the relation between the sides and angles of a triangle. As for algebra, he wrote a monograph entitled Kitāb al-nisab al-mutashākkala fī ‘l-jabr wa-‘l-muqābala. In his work on Jamshid al-Kashī’s al-Risāla al-Muhītiyya, he discussed the opinions that al-Kashī used decimal numbers for operations and examined circumference-diameter relations in a circle (Kandilli Observatory, MS 208/8). Taqī al-Dīn also prepared a handbook entitled Bughyat al-tullāb fī ‘ilm al-hisāb dedicated to the Indian calculus (hisāb-i hindī), hisāb-i sittīnī (sexagesimal system) and some other mathematical problems (Süleymaniye Library, Carullah collection, MS 1454). In the ninth part of the second article of this work, following al-Kashī, he developed the arithmetic of decimal fractions both in theoretic and practical frameworks. Furthermore Taqī al-Dīn took up again the famous Delos problem (doubling of a cube) that was dealt with by Abdurrahmān Bistāmī and Molla Lütfi in Ottoman times, and he focused on three ways to solve this problem (OMALT, I, 84-87).

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Figure 4: The colophon of Kitāb Nūr hadaqat al-ibsār wa-nūr haqīqat al-anzār. Süleymaniye Library, Collection Laleli, MS 2558, folio, 3b-4a.

However, it is in astronomy that he heritage of Taqi al-Din is the most outstanding and original. Actually, his most significant achievement in the history of Islamic and Ottoman astronomy is his foundation of the Istanbul Observatory and his activities there. Beside old instruments, he invented new instruments by himself and used a mechanical clock in astronomical observations. These are only a few among many other original features that deserve to be noticed. On the other hand, his application of decimal fractions developed previously by al-Uklidisī, Samaw’al, al-Kāshī and himself to trigonometry and astronomy and his preparation of sinus and tangent tables and zījs suitable to this application are among his most important contributions to astronomy and mathematics.

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Figure 5: The colophon of Sidrat muntahā al-afkār fī malakūt al-falak al-dawwār. Nuruosmaniye Library, MS 2930, cover folio, 1a.

Taqī al-Dīn’s most important work on astronomy is Sidrat muntahā al-afkār fī malakūt al-falak al-dawwār (= al-Zīj al- Shāhinshāhī). This work was prepared according to the results of the observations in Egypt and Istanbul in order to correct and complete Zīj-i Ulugh Beg. The first forty pages of the work are devoted to trigonometric calculations. Then astronomical clocks, heavenly circles etc. are dealt with. The following parts are occupied with the definitions of observational instruments and methods, the observations of lunar and solar motions, and the examination of sinus and trigonometric functions calculated according to sexagesimal notation. Due to the absence of a conclusion part (khātima), it can be said that the extant version of the book is incomplete (Kandilli Observatory, MS 208). Following the Islamic astronomical tradition, Taqī al-Dīn used in this book trigonometric functions such as sinus cosine, tangent, cotangent rather than beams in measuring angles. On the other hand, being inspired by Ulugh Beg, he developed a new method to find the value of Sinus 1°, that Camshid al-Kashī put into the form of an equation of the third degree, and he tried to find this value exactly. Additionally, he employed the method of “three observation points” that was a new one in the calculation of solar parameters and of which Copernicus and Tycho Brahe were aware. In the calculation of the longitudes and latitudes of the fixed stars, he left the use of the Moon as a medium and developed a different method of calculation via the use of Venus, Aldaberan (the alpha or brightest star in the constellation Taurus) and Spica Virginis which are located near the ecliptic. As a result of his calculations, he found 2° 0′ for the eccentricity of the Sun and 63″ for the annual motion of its apogee. When compared with today’s values, those of Taqī al-Dīn are more precise than Copernicus and Brahe’s values. This gives a clear idea about the accuracy of his methods of observation and calculation.

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Figure 6: The colophon of Sidrat muntahā al-afkār fī malakūt al-falak al-dawwār. Nuruosmaniye Library, MS 2930, cover folio, 5b-6a.

Taqī al-Dīn’s second important work on astronomy is a zīj entitled Jarīdat al-durar wa kharīdat al-fikar (Kandilli Observatory, MS 183). He applied in this work decimal fractions to trigonometry and trigonometric functions for the first time, and prepared tangent-cotangent tables. Moreover, in this zīj as in his other zīj entitled Tashīl zīj al-a’shāriyya al-shāhinshāhiyya (Public Library of Patna, MS 2466), he stated the parts of degree of curves and angles in decimal fractions and carried out the calculations in compliance with this. Moreover, excluding the table of fixed stars, he prepared all the astronomical tables in decimal fractions in this zīj.

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Figure 7: The colophon of Jarīdat al-durar wa kharīdat al-fikar. Suleymaniye, Esad Efendi, MS 1976, folio 27b-28a.

Besides the above-mentioned three important works, Taqī al-Dīn has some other works of second degree importance about various subjects of astronomy (OALT, I, 202-216). One of them is al-Dustūr al-rajīh li qawā‘id al-tastīh, a text about the levelling of spheres and about geometry (Kandilli Observatory, MS 208/3). Rayhānat al-rūh fī rasm al-sā‘āt ‘alā mustawā al-sutūh is the title of another book in which he focusses on the stidy of sundials drawn on marble surfaces and their features (Süleymaniye Library, Esad Efendi, MS 2033). This book was commented upon by his student Siraj al-Dīn Ömer b. Muhammad al-Fariskuri (d. 1610) in a text entitled Nafh al-fuyūh bi-sharh rayhānat al-rūh; this commentary was translated into Turkish by an unknown writer in the beginning of the 17th century.


In short, Taqī al-Dīn unified his works the scientific traditions of Maragha, Cairo, Damascus and Samarqand in the fields of mathematics and astronomy and tried to complete the parts that Samarqand astronomy school left incomplete. Following the attitude established in Ottoman scientific mentality by Ali Kushju, Taqī al-Dīn, leaving Aristotelian principles of physics and metaphysics, followed a pure mathematical method in his academic studies, especially in mathematics and astronomy. Therefore, he underlined mathematical and especially arithmetical calculation as the tool in scientific enquiry; this, in turn, directed him to develop the calculation of decimal fractions and to apply them to astronomical calculations. Additionally, Taqī al-Dīn improved mathematics as well as producing instruments that would enhance the accuracy, which was achieved in the mathematical sciences before him, especially in astronomy. His research can be summarised with two basic concepts; strong “aesthesis” and “mathematical accuracy”.


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  • Demir, Remzi, Takiyüddin’de Matematik ve Astronomi, Ankara: 2000.
  • Menali, Haldun I.; Unver, Ahmed Suheyl, “The Comet of 1577 and a Turkish-Ottoman Astronomer”, International Comet Quarterly, vol. 26, p. 3-7.
  • Mordmann, “Das Observatorium des Taqi ed-Din zu Pera”, Der Islam, XIII, 1913, 82-96.
  • Ramazan Şeşen – Cevat İzgi – Cemil Akpinar – İhsan Fazlioǧlu (edit. Ekmeleddin İhsanoǧlu), Osmanli Astronomi Literatürü Tarihi (OALT), İstanbul: 1997, I, 199-217 (no. 96).
  • Ramazan Şeşen – Cevat İzgi (edit. Ekmeleddin İhsanoǧlu), Osmanli Matematik Literatürü Tarihi (OMALT), İstanbul: 1999, I, 83-87 (no. 47).
  • Tekeli, Sevim (edit.), Alat el-Rasadiyye li Zic-i Şehinşahiyye, İTED, III/1-2, 1960, pp. 1-30.
  • Tekeli, Sevim, 16’inci Asirda Osmanlilar’da Saat ve Takiyüddin’in “Mekanik Saat Konstrüksiyonuna Dair En Parlak Yildizlar” Adli Eseri (Turkish-English-Arabic text), Ankara 1966.
  • Tekeli, Sevim, “Nasiruddin, Takiyüddin ve Tycho Brahe’nin Rasad Aletlerinin Mukayesesi”, Ankara Üniversitesi, Dil ve Tarih-Coǧrafya Fakültesi Dergisi, vol. XVI/3-4, Ankara 1958, pp. 301-353
  • Tekeli, Sevim, ‘Onaltinci Yüzyil Trigonometri Çalişmalari Üzerine Bir Araştirma: Copernicus ve Takiyuddin”, Erdem, vol. II/4, Ankara 1986, pp. 219-272.
  • Topdemir, Hüseyin Gazi, Takiyüddin’in Optik Kitabi, Ankara: 1999.

*PhD., The University of Istanbul (Turkey). Professor İhsan Fazlioǧlu provided kindly high resolution photographs of Taqī al-Dīn’s manuscripts to illustrate the article (Chief Editor).

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