Taqi al-Din

Taqi al-Din Muhammad ibn Ma'ruf al-Shami al-Asadi (Arabic: تقي الدين محمد بن معروف الشامي السعدي, Turkish: Takiyuddin) (1526–1585) was a major Ottoman Turkish [cite journal
last = Douglas | first = A. V.
year =1963
title = Tenth International Congress-History of Science
journal = Journal of the Royal Astronomical Society of Canada
volume = 57 | pages = p. 1] or Arabcitation|first=Svat|last=Soucek|title=Piri Reis and Ottoman Discovery of the Great Discoveries|journal=Studia Islamica|volume=79|year=1994|pages=121-142 [123 & 134-6] ] Muslim polymath: a scientist, astronomer and astrologer, engineer and inventor, clockmaker and watchmaker, physicist and mathematician, botanist and zoologist, pharmacist and physician, Islamic judge and Mosque timekeeper, Islamic philosopher and theologian, and Madrasah teacher. He was the author of more than 90 books on a wide variety of subjects, including astronomy, astrology, clocks, engineering, mathematics, mechanics, optics and natural philosophy,cite web|author=Dr. Salim Ayduz|title=Taqi al-Din Ibn Ma’ruf: A Bio-Bibliographical Essay|url=http://muslimheritage.com/topics/default.cfm?ArticleID=949|date=26 June 2008|accessdate=2008-07-04)] citation|first=Hüseyin Gazi|last=Topdemir|title=Takîyüddîn'in Optik Kitabi|publisher=Ministry of Culture Press, Ankara|year=1999 (cf. cite web|author=Dr. Hüseyin Gazi Topdemir|title=Taqi al-Din ibn Ma‘ruf and the Science of Optics: The Nature of Light and the Mechanism of Vision|publisher=FSTC Limited|url=http://muslimheritage.com/topics/default.cfm?ArticleID=951|date=30 June 2008|accessdate=2008-07-04)] though only 24 of those works have survived. He was widely regarded by his contemporaries in the Ottoman Empire as "the greatest scientist on earth". [cite web|title=Astronomical Instruments of Tycho Brahe and Taqi al-Din|publisher=FSTC Limited|url=http://www.muslimheritage.com/topics/default.cfm?ArticleID=504|date=21 April 2005|accessdate=2008-07-04] [cite web|title=The Machines of Al-Jazari and Taqi Al-Din|publisher=FSTC Limited|url=http://www.muslimheritage.com/topics/default.cfm?ArticleID=466|date=30 December 2004|accessdate=2008-07-04]

One of his books, "Al-Turuq al-samiyya fi al-alat al-ruhaniyya" ("Arabic: الطرق السامية في الآلات الروحانية")("The Sublime Methods of Spiritual Machines") (1551), described the workings of a rudimentary steam engine and steam turbine, predating the more famous discovery of steam power by Giovanni Branca in 1629.cite web |url=http://www.history-science-technology.com/Notes/Notes%201.htm |title=Taqi al-Din and the First Steam Turbine |accessdate=2008-03-29|last=Hassan |first=Ahmad Y |authorlink=Ahmad Y Hassan |work=History of Science and Technology in Islam] Taqi al-Din is also known for the invention of a six-cylinder 'Monobloc' pump in 1559, the invention of a variety of accurate clocks (including the first mechanical alarm clock, the first spring-powered astronomical clock, the first watch measured in minutes, and the first clocks measured in minutes and seconds) from 1556 to 1580, the invention of an early telescope some time before 1574, his construction of the Istanbul observatory of al-Din in 1577, and his astronomical activity there until 1580.

Biography

Taqi al-Din was born in 1521 in Damascus, Syria, and was educated in Cairo, Egypt. He became a Qadi (judge in Islamic law), Islamic theologian, "muwaqqit" (religious timekeeper) at a Mosque and teacher at a Madrasah for some time, while publishing a number of scientific books during this time. In 1571, he moved to Istanbul to become the official astronomer for Sultan Selim II of the Ottoman Empire. When Selim II died, Murad III became the new sultan, and al-Din convinced Murad to fund the building of a new observatory on the basis that it would help in making accurate astrological predictions. The project began in 1575, and was completed in 1577, at nearly the same time as Tycho Brahe's observatory at Uraniborg. This would become known as the Istanbul observatory of al-Din, an observatory built to rival Ulugh Beg's Samarkand observatory. At the new observatory, Taqi al-Din updated the old "Zij" astronomical tables, particularly Ulugh Beg's "Zij-i-Sultani", describing the motions of the planets, sun, moon and stars.cite web|author=İhsan Fazlioǧlu|title=Taqi al-Din Ibn Ma’ruf: Survey on his Works and Scientific Method|url=http://muslimheritage.com/topics/default.cfm?ArticleID=961|publisher=FSTC Limited|date=4 July 2008|accessdate=2008-07-16]

Within months of the observatory's completion, however, al-Din witnessed a comet and, thinking the comet was an omen, predicted an Ottoman military victory. This prediction was incorrect, and because of this, the Sultan saw no other use for the observatory and decided to destroy it in order to reserve his funds for his war efforts. The observatory was razed in 1580.

Mechanical treatises

Taqi al-Din wrote the following treatises on mechanics:

#"The Brightest Stars for the Construction of Mechanical Clocks" ("Al-Kawākib al-durriyya fī wadh' al-bankāmāt al-dawriyya") (1556 or 1559): The first Ottoman book on automatic machines. Taqi al-Din discusses various mechanical clocks from a geometrical–mechanical perspective.
#"On Science of Clepsydras": Treatise on water clocks.
#"The Sublime Methods in Spiritual Devices" ("Al-Turuq al-saniyya fi'1-alat al-ruhaniyya") (1551): Covers six chapters on clepsydra water clocks, devices for lifting weights, devices for raising water, fountains and continually playing flutes and kettle-drums, irrigation devices, and the steam-powered and self-moving spit. Taqi al-Din focuses on the geometrical-mechanical structure of clocks previously examined by the Banū Mūsā brothers and Al-Jazari, and he describes his water-raising six-cylinder pump, some machines for lifting weights, and his early steam turbine as a prime mover for the self-rotating spit.
#"Risāla fī ‘amal al-mīzan al-tabi'ī": A treatise about hydrostatics, weights and measurements, and the specific gravity of substances. It describes the scale of Archimedes and other instruments created by Muslim physicists.

"The Sublime Methods of Spiritual Machines"

;Practical steam turbine and self-rotating spit and smoke jack

In 1551, Taqi al-Din invented an early practical steam turbine as a prime mover for the first steam-powered and self-rotating spit and smoke jack. In his book, "Al-Turuq al-samiyya fi al-alat al-ruhaniyya" ("The Sublime Methods of Spiritual Machines"), completed in 1551 AD (959 AH), Taqi al-Din wrote:

;Six-cylinder 'Monobloc' pump

Taqi al-Din also invented a 'Monobloc' pump with a six cylinder engine, first described in "The Sublime Methods of Spiritual Machines". It was a hydropowered water-raising machine incorporating valves, suction and delivery pipes, piston rods with lead weights, trip levers with pin joints, and cams on the axle of a water-driven scoop-wheel. [cite journal | first = Donald | last = Routledge Hill | authorlink = Donald Routledge Hill | title = Engineering | editor = Roshdi Rashed | journal = Encyclopedia of the History of Arabic Science | volume = 2 | pages = pp. 751–795 | publisher = Routledge | location = London and New York] It also employed a crankshaft-connecting rod mechanism, like that of the twin-cylinder reciprocating suction piston pump earlier invented by Al-Jazari in 1206. Al-Din's Monobloc pump also included a vacuum, which was formed "as the lead weight moves upwards, it pulls the piston with it, creating vacuum which sucks the water through a non return clack valve into the piston cylinder." [cite web|author=Salim Al-Hassani|title=The Machines of Al-Jazari and Taqi Al-Din|url=http://www.muslimheritage.com/topics/default.cfm?ArticleID=466|publisher=22nd Annual Conference on the History of Arabic Sciences|date=23-25 October 2001|accessdate=2008-07-16]

"The Brightest Stars for the Construction of Mechanical Clocks"

;Mechanical alarm clock

The first mechanical alarm clock was invented by Taqi al-Din. He described the alarm clock in his book, "The Brightest Stars for the Construction of Mechanical Clocks" ("Al-Kawākib al-durriyya fī wadh' al-bankāmat al-dawriyya"), published in 1556 or 1559. His alarm clock was capable of sounding at a specified time, which was achieved by means of placing a peg on the dial wheel to when one wants the alarm heard and by producing an automated ringing device at the specified time.cite web|author=Salim Al-Hassani|title=The Astronomical Clock of Taqi Al-Din: Virtual Reconstruction|publisher=FSTC Limited|url=http://muslimheritage.com/topics/default.cfm?ArticleID=947|date=19 June 2008|accessdate=2008-07-02]

;Spring-powered astronomical clock

In "The Brightest Stars for the Construction of Mechanical Clocks", Taqi al-Din invented the first astronomical clock to be powered by springs. This was also one of the first spring-powered mechanical clocks, created around the same time as Peter Henlein in 1556.

;Spring-powered pocket watch

Taqi al-Din also created one of the first spring-powered pocket watches,cite web|author=Donald Routledge Hill and Ahmad Y Hassan|title=Engineering in Arabic-Islamic Civilization|url=http://www.history-science-technology.com/Articles/articles%2011.htm|work=History of Science and Technology in Islam|accessdate=2008-07-03] shortly after the first such watch was created by Peter Henlein in 1524. Taqi al-Din's watch, however, was the first to measure time in minutes, by having three dials for the hours, degrees and minutes.

Observational clock

His mechanical astronomical clock, which he called the "observational clock" in "The Brightest Stars for the Construction of Mechanical Clocks", was the first to measure time in minutes. He made use of his mathematical knowledge to design three dials which showed the hours, degrees and minutes.

He later improved the design of his observational clock to measure time in seconds in his "In the Nabik Tree of the Extremity of Thoughts", written at his Istanbul observatory of al-Din. He described his observational clock as "a mechanical clock with three dials which show the hours, the minutes, and the seconds." This is considered one of the most important innovations in 16th century practical astronomy, as previous clocks were not accurate enough to be used for astronomical purposes.

He further improved the observational clock, as described in his "Sidrat al-muntaha", using only one dial to represent the hours, minutes and seconds. He describes this observational clock as "a mechanical clock with a dial showing the hours, minutes and seconds and we divided every minute into five seconds." His invention is described as follows in "The Astronomical Instruments for the Emperor's Table":citation|first=Aydin|last=Sayili|authorlink=Aydin Sayili|title=The Observatory in Islam|year=1991|pages=289-305 (cf. cite web|author=Dr. Salim Ayduz|title=Taqi al-Din Ibn Ma’ruf: A Bio-Bibliographical Essay|url=http://muslimheritage.com/topics/default.cfm?ArticleID=949|date=26 June 2008|accessdate=2008-07-04)]

"Book of the Light of the Pupil of Vision and the Light of the Truth of the Sights"

Around 1574, Taqi al-Din wrote the "Book of the Light of the Pupil of Vision and the Light of the Truth of the Sights" ("Kitab Nūr hadaqat al-ibsār wa-nūr haqīqat al-anzār"), a book on optics containing experimental investigations in three volumes on vision, the light's reflection, and the light's refraction. The book deals with the structure of light, its diffusion and global refraction, and the relation between light and colour. Like his predecessors in optics, Ibn al-Haytham (Alhazen, 965-1039) and Kamāl al-Dīn al-Fārisī (1267-1320), Taqi al-Din relied heavily on the scientific method for his investigations. The contents of the "Book of the Light of the Pupil of Vision and the Light of the Truth of the Sights" are described by al-Din as follows:

Book I: Direct Vision
#Inquiry into the Properties of Direct Vision
#Inquiry into the Properties of Lights and into the Manner of Radiation of Lights
#The Effect of Light upon Sight
#The Structure of the Eye
#The Formation and the Nature of Vision
#The Causes of Errors of Sight

Book II: Catoptrics
#Inquiry into the Properties of Reflected Lights
#Inquiry into the Properties of Reflection
#Inquiry into the Properties of Reflective Objects
#On the Formation of Images by Reflection
#On the Properties of Images by Reflection
#On the Causes of Errors of Images by Reflection

Book III: Dioptrics
#Inquiry into the Properties of Refracted Lights
#Inquiry into the Properties of Refraction
#On the Formation of Images by Refraction
#On the Causes of Errors of Images by Refraction
#On the Properties of Images by Refraction
#On the Ratio of Refracted Angels

Book I: Direct Vision

In the first volume, Direct Vision, he discusses "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". He also provides the first satisfactory explanation for the formation of colour, clearly stating that colour is formed as a result of reflection and refraction of light, two centuries before Isaac Newton arrived at the same conclusion. Like his predecessors Ibn al-Haytham and al-Farisi, Taqi al-Din also supported the intromission model of vision, where light is reflected from objects into the eyes. Whereas his predecessors constructed instruments such as the camera obscura and pinhole camera to demonstrate this, al-Din instead used a simpler example from astrophysics to demonstrate it. He stated that if the ray of light had come from the eye, it would take too long to see the stars, which are millions of kilometres away from the Earth. He then states that since the speed of light is constant, "it would take too long 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."

Book II: Catoptrics

In the second volume, Catoptrics, al-Din provides "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."

Book III: Dioptrics

The third volume, Dioptrics, analyzes "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." He also came very close to formulating Snell's law of sines, though he did not find the exact constant ratio between the sine of incidences and refraction angles. Nevertheless, he was instead able to make another more important discovery: the invention of an early rudimentary telescope, [citation|title=Topkapi’s Turkish Timepieces|first=Paul|last=Horton|year=1977|journal=Saudi Aramco World, July-August 1977|pages=10-13|url=http://www.saudiaramcoworld.com/issue/197704/topkapi.s.turkish.timepieces.htm|accessdate=2008-07-12] which he describes as an instrument that makes objects located far away appear closer to the observer, and he claims to have been inspired by legends regarding the Tower of Alexandria. He states:

Al-Din further states that the instrument helps to see distant objects in detail by bringing them very close. He also states that he wrote another earlier treatise explaining the way this instrument is made and used, suggesting that he invented it some time before 1574. However, it is unknown whether or not he employed the instrument for his later astronomical observations at the Istanbul observatory of al-Din from 1577.

Astronomy

Istanbul observatory of Taqi al-Din

In 1577, Taqi al-Din built an observatory, which consisted of two large structures perched on a hill overlooking the European section of Istanbul and offering a wide view of the night sky. Much like a modern institution, the main building was reserved for the library and the living quarters of the staff, while the smaller building housed a collection of astronomical instruments built by Taqi al-Din. These included a giant armillary sphere and an astronomical clock for measuring the position and speed of the planets. With these instruments, Taqi al-Din had hoped to update the old Zij astronomical tables describing the motion of the planets, sun, and moon.

;Instruments

Taqi al-Din wrote an important treatise on astronomical instruments entitled the "Observational Instruments of the Emperor's Catalogue", which describes the astronomical instruments used in the Istanbul observatory of al-Din. These included ancient instruments such as the armillary sphere, paralactic ruler and astrolabe; medieval Muslim instruments such as the universal astrolabe, azimuthal and mural quadrants, and sextants; and several instruments he invented himself, including the "mushabbaha bi'l manattiq", a framed sextant with cords for the determination of the equinoxes similar to what Tycho Brahe later used, and a wooden quadrant for measuring azimuths and elevations. His most important astronomical instrument, however, is the "observational clock", which in his "In the Nabik Tree of the Extremity of Thoughts", he describes as "a mechanical clock with three dials which show the hours, the minutes, and the seconds." He used this for astronomical purposes, specifically for measuring the right ascension of the stars. This is considered one of the most important innovations in 16th century practical astronomy, as previous clocks were not accurate enough to be used for astronomical purposes.cite encyclopedia | first = Sevim | last = Tekeli | title = Taqi al-Din | year = 1997 | encyclopedia = Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures | publisher = Kluwer Academic Publishers | ISBN = 0792340663 | url = http://www.springer.com/philosophy/philosophy+of+sciences/book/978-1-4020-4425-0 ]

Another instrument he constructed at the observatory was a "remarkably modern-looking" terrestrial globe of the Earth, which was one of the earliest of its kind. He also invented a rudimentary telescope during his earlier work on optics, although it is unknown if he employed it for astronomical purposes at his observatory.

;Observations

Taqi al-Din made use of his new "observational clock" to produce a zij (named "Unbored Pearl") and astronomical catalogue more accurate than those of his contemporaries, Tycho Brahe and Nicolaus Copernicus. Taqi al-Din was also the first astronomer to employ a decimal point notation in his observations rather than the sexagesimal fractions used by his contemporaries and predecessors. He also made use of Abū Rayhān al-Bīrūnī's method of "three points observation". In "The Nabk Tree", Taqi al-Din described the three points as "two of them being in opposition in the ecliptic and the third in any desired place." He used this method to calculate the eccentricity of the Sun's orbit and the annual motion of the apogee, and so did Tycho Brahe and Copernicus shortly afterwards, though Taqi al-Din's values were more accurate, due to his his observational clock and other more accurate instruments.

Astronomical treatises

Taqi al-Din wrote the following treatises on Islamic astronomy:

#"Fragrance of Spirit on Drawing of Horary [Lines] on Plane Surfaces" ("Rayhānat al-rūh fī rasm al-sā'āt ‘alā mustawā al-sutūh") (1567): A book dealing with sundials drawn on marble surfaces and their features, with one prologue and three chapters. This book was commented upon by his student Sirāj al-Dīn ‘Umar ibn Muhammad al-Fāriskūrī (d. 1610).
#"Non-perforated Pearls and Roll of Reflections" ("Jarīdat al-durar wa kharīdat al-fikar") (1581-1582): An astronomical table for Cairo containing sine and tangent tables in decimal fractions. He was the first to use decimal fractions in trigonometric functions, and he also prepared tangent and cotangent tables. Jamshīd al-Kāshī (1390-1450) attempted to solve this problem but failed, thus Taqi al-Din was the first to succeed in this area.
#"Book of Ripe Fruits from Clusters of Universal Instrument" ("Kitab al-thimār al-yāni'a ‘an qutāf al-āla al-jāmi'a"): A commentary on Ibn al-Shatir's "Rays of light on operations with the universal instrument" ("al-Ashi'a al-lāmi'a fī 'l-'amal bi-'l-āla al jāmi'a"), describing an astronomical instrument invented by Ibn al-Shātir. It contains a prologue, thirty chapters, and an epilogue.
#"Poem on Sine [Quadrant] " ("Manzūmat al-mujayyab"): A book dealing with the calculations and observations made by the instrument "Rub' al-dastūr". Taqi al-Din later wrote a commentary on this work, followed by another commentary by an unknown author.
#"Culmination of Thoughts in the Kingdom of Rotating Spheres" ("Sidrat muntahā al-afkār fī malakūt al-falak al-dawwār", or "al-Zij al- Shāhinshāhī"): A work prepared according to the results of the observations carried out in Egypt and Istanbul in order to correct and complete Ulugh Beg's "Zij-i-Sultani". The first 40 pages of the work deal with trigonometric calculations, followed by discussions of astronomical clocks, heavenly circles, and information about three eclipses which he observed at Cairo and Istanbul.
#"Book on Knowledge of Position of Horary [lines] " ("Kitab fi ma'rifat wad' al-sa'at"): Treatise composed of 10 chapters.
#"Commentary on His Poem on Conversion of Dates in Different Calendars" ("Al-Abyāt al-tis'a fī istihrāj al-tawārikh al-mashhūra wa-sharhuhā"): A book containing information on the conversion of calendars between the Islamic calendar and other calendars.
#"Knowledge on Reckoning of Lunar Stations" ("Fī ma'rifat hisāb manāzil al-qamar"): Treatise on the calculation of lunar mansions.
#"Revision of the Almagest": A revision of Ptolemy's "Almagest".
#"Revision of the Zīj of Ulugh Beg": A revision of Ulugh Beg's "Zij-i-Sultani".
#"Treatise on the Azimuth of the Qibla" ("Risālat samt al-Qibla"): Treatise about finding the direction of the Qibla, with a prologue, one main chapter called "maqsad", and fifteen sections.
#"Pearl of the Ordered Simplification of the Calendar" ("Al-Durr (al-‘iqd) al-nazīm fī tashīl al-taqwīm"): An astronomical table on the way to extract the annual calendars through Ulugh Beg's "Zij-i-Sultani".
#"Uses on Determining the Equator of the Globe and Knowledge of the Sine" ("Fawā'id fī istikhrāj mintaqat al-kura wa ma'rifat af-jayb"): Treatise on determining the Earth's equator.
#"Simplification of the Shahinshah Zīj" ("Tashīl zīj al-a'shāriyya al-shāhinshāhiyya"): Treatise which gives the parts of degree of curves and angles in decimal fractions and carries out calculations accordingly. Besides the table of fixed stars, all the astronomical tables in this Zij were prepared using decimal fractions.
#"Daqa'iq Ikhtilaf al-Ufuqayn": Treatise about the difference between real and false horizons.
#"The Brightest Stars for the Construction of Mechanical Clocks" ("Al-Kawākib al-durriyya fi wadh' al-bankāmat al-dawriyya") (1556 or 1559): Deals with the construction of mechanical clocks and their uses.
#"Al-Mizwala al-Shimāliyya bi-fadli dā'iri ufuqi al-Qustantīniyya": A book determining the latitude of Istanbul's horizon with a round gnomon, containing a prologue, three chapters and an epilogue.
#"Risāla fī ‘amal āla tursamu bihā al-kawākib ‘alā sathin mustawī": Treatise on the method of drawing a map of the sky.
#"Risāla fī al-‘amal bi al-rub' al-Shakāzī: It is uncertain whether this treatise was written by Taqī al-Dīn.
#"Risāla fī 'l-ikhtilāf bayna al-muwaqqitān bi-mahrusat al-Qāhira fi dabt qawsay al-nahār wa-'l-layl wa-dā'irat al-fajr wa-'1-shafaq"
#"Risāla fī ma'rifat al-'ufuq al-hādith: A notice about the finding of seven horizons.
#"Risāla fī sabab ta'akhkhur ghurūb al-Shams"
#"Risāla fi awqāt al-‘ibādāt": A treatise the use of astrolabes in order to determine the time.
#"Tafsīr ba'dh al-ālāt al-rasadiyya": A Turkish text describing eight astronomical instruments used by Taqi al-Din in his observatory, along with illustrations.
#"Urjūza li-'1-jayb wa-'1-dharb wa'1-qisma": A poem on the rules of the "Rub' dā'ira" (quadrant).
#"Preferred Rule in Foundations of Projecting on a Plane" ("Dastūr al-tarjīh fi qawā'id al-tastīh") (1576): A treatise about the projection of a sphere onto a plane and other topics in geometry, and about sundials made on the surfaces.
#"Treatise on the Effect of Refraction at the Horizon and of Differences of Opinions of Cairo Timekeepers Thereon"
#"Treatise on the Difference between True and Visible Horizons"
#"Ālāt al-rasadiya li-zīj al-shāhinshāhiyya": Lists the astronomical instruments used by Taqi al-Din at the Istanbul observatory.
#"Jawāb Su'āl ‘an muthallath min al-'izam gayri qā'im al-zāwiya wa-laysa fī azlā'ihi mā yablugh al-rub' wa-azlā'uhu bi-asrihā, hal yumkinu ma'rifat zawāyāhu"
#"Fawā'id fī istihrāj mintaqat al-kura wa-ma'rifat al-jayb"
#"Risālat taqwīm al-sana 990 [H] ": Treatise on the calendar for the year 990 AH in the Islamic calendar.
#"Sifat ālāt rasadiya bi-naw'in ākhar"

Mathematics

Trigonometry

In Islamic mathematics, Taqi al-Din contributed to trigonometry in his "Sidrat al-Muntaha", in which he was the first mathematician to extract the precise value of Sin 1°. He discusses the values given by his predecessors, explaining how Ptolemy (ca. 150) used an approximate method to obtain his value of Sin 1° and how Abū al-Wafā' al-Būzjānī (959-998), Ibn Yunus (ca. 1000), Al-Kashi (1393-1449), Qāḍī Zāda al-Rūmī (1337-1412), Ulugh Beg (1394-1449) and Mirim Chelebi improved on the value. Taqi al-Din then solves the problem to obtain the precise value of Sin 1°: [cite web|title=Taqi al Din Ibn Ma’ruf's Work on Extracting the Cord 2° and Sin 1°|publisher=FSTC Limited|url=http://muslimheritage.com/topics/default.cfm?ArticleID=941|date=30 May 2008|accessdate=2008-07-04]

$sin\; 1^circ\; =\; 1^P\; 2\text{'}\; 49"\; 43$ 11' 14" 4416""

Mathematical treatises

Taqi al-Din wrote the following treatises on Islamic mathematics:

#"Book on coinciding ratios in algebra" ("Kitāb al-nisab al-mutashākkala fī 'l-jabr wa-'l-muqābala"): Treatise on algebra, with a prologue, three chapters, and an epilogue.
#"Aim of Pupils in the Science of Arithmetic" ("Bughyat al-tullāb fī ‘ilm al-hisāb"): Its codex contains three chapters on arithmetic with decimal numbers, arithmetic with sexagesimal numbers, and algebra.
#"Book on Projecting Spheres onto a Plane" ("Kitāb tastīh al-ukar"): Treatise on stereographic projection containing two chapters.
#"Commentary on "Treatise on Classification in Arithmetic" ("Sharh risālat al-Tajnīs fī '1-hisāb"): Commentary on the treatise "Book on Reduction of the Common Denominator in Arithmetic" ("Kitāb al-Tajnīs fī '1-hisāb") by al-Sakhāwandī.
#"Risāla fī tahqīqi mā qālahu 'l-'ālim Giyāthuddin Jamsid fī bayāni 'l-nisba bayna 'l-muhīt wa-'l-qutr": a discussion on the ideas of Jamshīd al-Kāshī's "al-Risalat al-muhitiyya".
#"Exposition of "Book on Spheres" of Theodosius": Commentary on Theodosius of Bithynia's "Book on Spheres".

Other treatises

Taqi al-Din wrote treatises on several other subjects, including:

*"Al-Masābih al-muzhira fī ‘ilm al-bazdara": Treatise about zoology.
*"Tarjumān al-atibbā' wa-lisān al-alibbā" ("The Interpreter of Physicians and the Language of the Wise concerning Simple Medicaments"): An alphabetical pharmaco-botanical dictionary.

ee also

*Islamic science
*Islamic astronomy
*Inventions in the Muslim world

Notes

References

*
*
*
*
*

External links

* [http://www.salaam.co.uk/themeofthemonth/october01_index.php?l=3 Discoveries of Muslim scholars]
* [http://www.history-science-technology.com/ History of Science and Technology in Islam]
* [http://www.theottomans.org/english/art_culture/science.asp Science and Technology in the Ottomans]

Persondata
NAME=Din, Taqi al-
ALTERNATIVE NAMES=تقي الدين محمد بن معروف الشامي السعدي (Arabic); Din, Taqi Muhammad ibn Ma'ruf al-Shami al-Asadi al- (full name)
SHORT DESCRIPTION=astronomer and inventor
DATE OF BIRTH=c. 1526
PLACE OF BIRTH=either Syria or Egypt
DATE OF DEATH=1585
PLACE OF DEATH=