Taqī al‐Dīn, Muḥammad al‐Rāṣid ibn Ma˓rūf, was a mathematician and astronomer. He was born in Damascus in 1521 and died in about 1585. He wrote several books on mathematics, astronomy, optics, and theology.
The most important of his books are: Jabr wa'l‐Muqābala (Algebra), Bughyat al‐Ṭullāb min ˓ilm al‐Ḥisāb (The Desire of Students for Arithmetic), Sidrat al‐Muntahā fī al‐Afkār (The Nabk Tree of the Extremity of Thoughts), and Ālāt‐i Raṣdīya li Zīj‐i Shāhinshāhīya (Observational Instruments of the Emperor's Catalogue), Al‐Kawākib al‐Durrīya fī Bengamāt al‐Dawrīya (The Brightest Stars for the Construction of Mechanical Clocks).
From the point of view of the history of Ottoman science, the most important event of the sixteenth century was the foundation of the Istanbul Observatory, which Taqī founded under the sponsorship of Murād III (1574–1595). This observatory was an elaborate building which contained dwelling places, a library, and offices for the astronomers. It was conceived as one of the largest of the observatories of Islam and was comparable to Tycho Brahe's (1546–1601) Uranienborg Observatory built in 1576, equipped with the best instruments of his time in Europe. There is a striking similarity between the instruments of Tycho Brahe and those of Taqī al‐Dīn.
The instruments of the observatory included the following. First there were those originally constructed by Ptolemy: the armillary sphere, the parallactic ruler, and the astrolabe. Then there were those invented by Muslim astronomers, such as the azimuthal and mural quadrants. Taqī al‐Dīn invented the mushabbaha bi'l manāṭiq (sextant, an instrument with cords for the determination of the equinoxes), which was also an important invention of Tycho Brahe. In addition, he built a wooden quadrant for the measurement of azimuths and elevations, and clocks for the measurement of right ascensions of the stars. The latter was one of the most important discoveries in the field of practical astronomy in the sixteenth century, because in the beginning clocks were not accurate enough to be used for astronomical purposes.
In The Astronomical Instruments of the Emperor's Catalogue the author says, “The ninth instrument is an observational clock.” The following statement is taken from Ptolemy: “I could have freedom of action if I were able to measure the time accurately. Now our master Taqī al‐Dīn, with the help of God, upon the instructions of the Sultan, planned the observational clocks.” In The Nabk Tree of the Extremity of Thoughts Taqī al‐Dīn says, “We constructed a mechanical clock with three dials which show the hours, the minutes, and the seconds. We divided each minute into five seconds.” On the basis of his observations, Taqī al‐Dīn prepared astronomical catalogues and books.
Hipparchos (second century BCE) used the intervals of seasons for the calculation of the solar parameters. But the variation of the declinations around the tropics in 1 day rendered difficult the correct determination of the beginning of the seasons. In spite of this difficulty, the method was used for a long time. After him, al‐Bīrūnī (d. ca. 1048), Copernicus (1473–1543), and Tycho Brahe were interested in this subject, and used a new method called “three points observation.” Taqī al‐Dīn, a contemporary of Tycho Brahe, says the following in The Nabk Tree: “The moderns follow the method of three points observation, two of them being in opposition in the ecliptic and the third in any desired place.” This method was an important contribution to astronomy. By using this method, Copernicus, Tycho Brahe, and Taqī al‐Dīn calculated the eccentricity of the orbit of the Sun, and yearly mean motion of the apogee. According to Copernicus the eccentricity is 1p 56′; according to Tycho Brahe it is 2p 9′, and according to Taqī al‐Dīn it is 2p 0′ 34″ 6′″ 53″″ 41′″″ 8″″″. As compared to modern calculation, Taqī al‐Dīn's is the most accurate value. According to Copernicus the annual motion of the apogee is 24″; to Tycho Brahe it is 45″, and to Taqī al‐Dīn it is 63″. Its real value is 61″. As far as world astronomy is concerned, Taqī al‐Dīn's results can be said to be the most precise in the calculation of solar parameters.
The next important contribution of Taqī al‐Dīn concerns the use of decimal fractions, the system of numerals formed from initial letters, used in the Hellenic world. This system hindered the development of algebra.
Al‐Khwārizmī (d. 801) presented the decimal system which was inspired by Indians to the Islamic world. The application of this to fractions started with Abū'l‐Ḥasan Aḥmad ibn Ibrāhīm al‐Uqlīdīsī and continued with al‐Kāshī (d. 1437). But its application to astronomic and trigonometric tables was realized by Taqī al‐Dīn. Thus the tables of his zīj named Kharīdat al‐Durar (unbored pearl) and a zīj were prepared using the decimal system and decimal fractions.
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