in 1556. The two pump engine, which was first described by al-Jazarī, was also the basis of the steam engine. Important works Astronomy Sidrat muntahā al-afkār fī malakūt al-falak al-dawwār (al-Zīj al-Shāhinshāhī): this is said to be one of Taqī al-Dīn's most important works in astronomy. He completed this book on the basis of his observations in both Egypt and Istanbul. The purpose of this work was to improve, correct, and ultimately complete Zīj-i Ulugh Beg, which was a project devised in Samarkand and furthered in the Constantinople Observatory. The first 40 pages of his writing focus on trigonometric calculations, with emphasis on trigonometric functions such sine, cosine, tangent, and cotangent. Jarīdat al-durar wa kharīdat al-fikar is a zīj that is said to be Taqī al-Dīn's second most important work in astronomy. This zīj contains the first recorded use of decimal fractions and trigonometric functions in astronomical tables. He also gives the parts of degree of curves and angles in decimal fractions with precise calculations. Dustūr al-tarjīḥ li-qawā ҁ id al-tasṭīḥ is another important work by Taqī al-Dīn, which focuses on the projection of a sphere into a plane, among other geometric topics. Taqī al-Din is also accredited as the author of Rayḥānat al-rūḥ fī rasm al-sā ҁ āt ҁ alā mustawī al-suṭūḥ, which discusses sundials and their characteristics drawn on a marble surface. Clocks and mechanics al-Kawākib al-durriyya fī waḍ ҁ al-bankāmāt al-dawriyya was written by Taqī al-Dīn in 1559 and addressed mechanical-automatic clocks. This work is considered the first written work on mechanical-automatic clocks in the Islamic and Ottoman world. In this book, he accredits Alī Pasha as a contributor for allowing him to use and study his private library and collection of European mechanical clocks.al-Ṭuruq al-saniyya fī al-ālāt al-rūḥāniyya is a second book on mechanics by Taqī al-Dīn that emphasizes the geometrical-mechanical structure of clocks, which was a topic previously observed and studied by Banū Mūsā and Ismail al-Jazari (Abū al-ҁIzz al-Jazarī). Physics and optics Nawr ḥadīqat al-abṣar wa-nūr ḥaqīqat al-Anẓar was a work of Taqī al-Dīn that discussed physics and optics. This book discussed the structure of light, the relationship between light and color, as well as diffusion and global refraction. See also Inventions in the Muslim world Islamic astronomy Islamic science Notes Further reading Ben-Zaken, Avner. "The Revolving Planets and the Revolving Clocks: Circulating Mechanical Objects in the Mediterranean", History of Science, xlix (2010), pp.