Born 1526 (Damascus) – Died (Istanbul) 1585

By: Ihsan Fazlioglu

However, it is in astronomy that the 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.

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 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.

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 focuses on the study 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.

Conclusion
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”.

References
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