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{{Infobox Muslim scholar |
<!-- Please note the background of Tusi is constantly vandalized by ips- that is why it is sourced more predominantely here-->
notability = [[Persian peoples|Persian]] [[Muslim]] [[scholar]]
| era = [[Islamic Golden Age]]
 
| image = Al-Tusi Nasir.jpeg
| image_size = 160px
| caption =
| name = '''Nasīr al-Dīn Tūsī'''
| title= Khawaja Nasir
| birth_date = 18 February 1201 (11 Jamadi al-Ula, 597)
| death_date = {{Death date and age|df=yes|1274|06|26|1201|02|18}} (18 Dhu'l-Hijjah 672)
| ethnicity = [[Persian people|Persian]]
| region = Iran
| Maddhab = [[Twelver Shi`ism|Twelver]] [[Shia Islam|Shī‘ah]]
|school_tradition= [[Avicennism]]
| main_interests = [[Kalam|Islamic Theology]], [[Early Islamic philosophy|Islamic Philosophy]], [[Islamic astronomy|Astronomy]], [[Islamic mathematics|Mathematics]], [[Alchemy and chemistry in Islam|Chemistry]], [[Islamic medicine|Biology and Medicine]], [[Islamic physics|Physics]], [[Islamic science|Science]]
| notable_ideas= [[Evolution]], [[Spherical trigonometry]], [[Tusi-couple]]
| works =''Rawḍa-yi Taslīm'', ''Tajrid al-'Aqaid'', <br> ''Akhlaq-i-Nasri'', ''[[Zij-i ilkhani]]'',<br> ''al-Risalah al-Asturlabiyah'', <br> ''Al-Tadhkirah fi'ilm al-hay'ah''
| influences = [[Avicenna]], [[Fakhr al-Din Razi]], [[Mo'ayyeduddin Urdi]]
| influenced = [[Maitham Al Bahrani]], [[ibn Khaldun]], [[Qutb al-Din Shirazi]], [[Ibn al-Shatir]], [[Copernicus]]
}}
 
'''Khawaja Muhammad ibn Muhammad ibn Hasan Tūsī''' ({{lang-fa|محمد بن محمد بن الحسن طوسی}}) (born 18 February 1201 in [[Tous, Iran|Ṭūs]], [[Greater Khorasan|Khorasan]] – died on 26 June 1274 in [[Kadhimiya|al-Kāżimiyyah]] district of metropolitan [[Baghdad]]), better known as '''Nasīr al-Dīn Tūsī''' ({{lang-fa|نصیر الدین طوسی}}; or simply '''Tusi''' in the West), was a [[Persian people|Persian]]<ref>a) "Tusi, Nasir al-Din. " Encyclopædia Britannica. 2007. Encyclopædia Britannica Online. 27 December 2007 <http://www.britannica.com/eb/article-9073899>. b)Arthur Goldschmidt, Lawrence Davidson. "A Concise History of the Middle East", Westview Press, 2009. ninth edition, pg 127: "Hulegu, contrite at the damage he had wrought, patronized the great Persian scholar, Nasiruddin Tusi (died 1274), who saved the lives of many other scientists and artists, accumulated a library of 400000 volumes, and built an astronomical ..."; [http://www.google.com/search?hl=en&tbo=1&biw=1659&bih=824&tbm=bks&q=+he+had+wrought%2C+patronized+the+great+Persian+scholar&oq=+he+had+wrought%2C+patronized+the+great+Persian+scholar&aq=f&aqi=&aql=undefined&gs_sm=e&gs_upl=346439l346454l0l1l1l0l0l0l0l219l219l2-1l1] d) Nanne Pieter George Joosse, Bar Hebraeus, "A Syriac encyclopaedia of Aristotelian philosophy: Barhebraeus (13th c.), Butyrum sapientiae, books of ethics, economy, and politics: a critical edition, with introduction, translation, commentary, and glossaries", Published by Brill, 2004. excerpt: " the famous Persian scholar Naslr al-Dln Tusi "; e)Seyyed Hossein Nasr," Title Islamic philosophy from its origin to the present: philosophy in the land of prophecy", Publisher SUNY Press, 2006. pp 167: “In fact it was common among Persian Islamic philosophers to write few quatrains on the side often in the spirit of some of the poems of Khayyam singing about the impermanence of the world and its transience and similar themes. One needs to only recall the names of Ibn Sina, Suhrawardi, Nasir al-Din Tusi and Mulla Sadra, who wrote poems alongs with extensive prose works”</ref><ref>Rodney Collomb, "The rise and fall of the Arab Empire and the founding of Western pre-eminence", Published by Spellmount, 2006. pg 127: "..Khawaja Nasr ed-Din Tusi, the Persian, Khorasani, former chief scholar and scientist of ";</ref><ref>
M.A. Al-Bakhit, L. Bazin, S.M. Cissoko, Volume 4 of History of humanity : scientific and cultural development Routledge, 2000. [http://books.google.com/books?id=ixCyd2lByggC&pg=PA367&dq=Persian+astronomer+and+philosopher+Nasir+al-Din+Tusi&hl=en&ei=oCATTrfYLMPVgQeO-7X3DQ&sa=X&oi=book_result&ct=result&resnum=5&ved=0CEAQ6AEwBA#v=onepage&q=Persian%20astronomer%20and%20philosopher%20Nasir%20al-Din%20Tusi&f=false]
pg 367: "the Turkish astronomer and philosopher Nasir al-Din Tusi".</ref><ref>a)Seyyed Hossein Nasr, Islamic Philosophy from Its Origin to the Present: Philosophy in the Land of Prophecy, SUNY Press, 2006, ISBN 0-7914-6799-6. page 199.; b) Seyyed H. Badakhchani. Contemplation and Action: The Spiritual Autobiography of a Muslim Scholar: Nasir al-Din Tusi (In Association With the Institute of Ismaili Studies. I. B. Tauris (December 3, 1999). ISBN 1-86064-523-2. page.1: ""Nasir al-Din Abu Ja`far Muhammad b. Muhammad b. Hasan Tusi:, the renowned Persian astronomer, philosopher and theologian"</ref> [[polymath]] and prolific writer: an architect, [[Islamic astronomy|astronomer]], [[biologist]], [[Alchemy and chemistry in Islam|chemist]], [[Islamic mathematics|mathematician]], [[Early Islamic philosophy|philosopher]], [[Islamic medicine|physician]], [[Islamic physics|physicist]], [[Islamic science|scientist]], [[Kalam|theologian]] and [[Grand Ayatollah|Marja Taqleed]].{{Citation needed|date=September 2012|reason=Does not appear in List of deceased Maraji. Confused for Shaykh Tusi?}} He was of the [[Ismaili]]-, and subsequently [[Twelver Shi`ism|Twelver]] [[Shia Islam|Shī‘ah]] [[Islam]]ic belief.<ref name="RT">{{Citation| last =Ṭūsī | first =Naṣīr al-Dīn Muḥammad ibn Muḥammad | author-link = | last2 =Badakchani | first2 =S. J. | year =2005 | title =Paradise of Submission: A Medieval Treatise on Ismaili Thought | series =Ismaili Texts and Translations | volume =5 | place =London | publisher =I.B. Tauris in association with Institute of Ismaili Studies | pages =2–3 | isbn =1-86064-436-8 }}</ref> The  Muslim scholar [[Ibn Khaldun]] (1332–1406) considered Tusi to be the greatest of the later [[Persian people|Persian]] scholars.<ref name="Khaldun">
James Winston Morris, "An Arab Machiavelli? Rhetoric, Philosophy and Politics in
Ibn Khaldun’s Critique of Sufism", Harvard Middle Eastern and Islamic Review 8 (2009), pp 242–291. [http://escholarship.bc.edu/cgi/viewcontent.cgi?article=1032&context=james_morris] excerpt from page 286 (footnote 39): "Ibn Khaldun’s own personal opinion is no doubt summarized
in his pointed remark (Q 3: 274) that Tusi was better than any other later Iranian scholar".
Original Arabic:
Muqaddimat Ibn Khaldūn : dirāsah usūlīyah tārīkhīyah / li-Aḥmad Ṣubḥī Manṣūr-al-Qāhirah : Markaz Ibn Khaldūn : Dār al-Amīn, 1998. ISBN 977-19-6070-9.
Excerpt from Ibn Khaldun is found in the section:
الفصل الثالث و الأربعون: في أن حملة العلم في الإسلام أكثرهم العجم
(On how the majority who carried knowledge forward in Islam were Persians)
In this section, see the sentence sentence  where he mentions Tusi as  more knowledgeable than other later Persian ('Ajam) scholars:
. و أما غيره من العجم فلم نر لهم من بعد الإمام ابن الخطيب و نصير الدين الطوسي كلاما يعول على نهايته في الإصابة. فاعتير ذلك و تأمله تر عجبا في أحوال الخليقة. و الله يخلق ما بشاء لا شريك له الملك و له الحمد و هو على كل شيء قدير و حسبنا الله و نعم الوكيل و الحمد لله.</ref>
 
==Biography==
Nasir al-Din Tusi was born in the city of [[Tus, Iran|Tus]] in medieval [[Greater Khorasan|Khorasan]] (in north-eastern [[Iran]]) in the year 1201 and began his studies at an early age. In Hamadan and Tus he studied the [[Qur'an]], [[Hadith]], [[Shi'a]] jurisprudence, logic, philosophy, mathematics, medicine and astronomy.<ref name="Dabashi">Dabashi, Hamid. "Khwajah Nasir al-Din Tusi: The philosopher/vizier and the intellectual climate of his times". Routledge History of World Philosophies. Vol I. History of Islamic Philosophy. Seyyed Hossein Nasr and Oliver Leaman (eds.) London: Routledge. 1996. p. 529</ref>
 
He was apparently born into a Shī‘ah family and lost his father at a young age. Fulfilling the wish of his father, the young Muhammad took learning and scholarship very seriously and travelled far and wide to attend the lectures of renowned scholars and acquire the knowledge which guides people to the happiness of the next world. At a young age he moved to [[Nishapur]] to study philosophy under Farid al-Din Damad and mathematics under [[Muhammad Hasib]].<ref name="HistMuslimPhil">Siddiqi, Bakhtyar Husain. "Nasir al-Din Tusi". A History of Islamic Philosophy. Vol 1. M. M. Sharif (ed.). Wiesbaden:: Otto Harrossowitz. 1963. p. 565</ref> He met also [[Attar Neyshapuri|Farid al-Din 'Attar]], the legendary [[Sufi]] master who was later killed by Mongol invaders and attended the lectures of [[Qutb al-Din al-Misri]].
 
In [[Mosul]] he studied mathematics and astronomy with [[Kamal al-Din Yunus]] (d. 639/1242). Later on he corresponded with [[Sadr al-Din al-Qunawi]], the son-in-law of [[Ibn al-'Arabi]], and it seems that mysticism, as propagated by [[Sufi]] masters of his time, was not appealing to his mind and once the occasion was suitable, he composed his own manual of philosophical Sufism in the form of a small booklet entitled ''Awsaf al-Ashraf'' "The Attributes of the Illustrious".
 
As the armies of [[Genghis Khan]] swept his homeland, he was captured by the [[Ismailis]] and made his most important contributions in science during this time when he was moving from one stronghold to another. He finally joined [[Hulagu Khan]]'s ranks, after the invasion of the [[Alamut]] castle by the [[Mongol]] forces.
 
==Works==
Tusi has about 150 works in [[Persian language|Persian]] and [[Arabic language|Arabic]].<ref name="H. Daiber, F.J. Ragep 2007"/>
 
[[File:Tusi manus.jpg|thumb|right|A Treatise on [[Astrolabe]] by Tusi, Isfahan 1505]]
*''Kitāb al-Shakl al-qattāʴ''  Book on the complete quadrilateral. A five volume summary of trigonometry.
*''Al-Tadhkirah fi'ilm al-hay'ah'' – A memoir on the science of astronomy. Many commentaries were written about this work called Sharh al-Tadhkirah (A Commentary on al-Tadhkirah) - Commentaries were written by [[al-Birjandi|Abd al-Ali ibn Muhammad ibn al-Husayn al-Birjandi]] and by [[Nazzam Nishapuri]].
*''Akhlaq-i-Nasri'' – A work on ethics.
*''al-Risalah al-Asturlabiyah'' – A Treatise on astrolabe.
*''[[Zij-i ilkhani]]'' (''Ilkhanic Tables'') – A major astronomical treatise, completed in 1272.
*''sharh al-isharat'' (''Commentary on Avicenna's Isharat'')
*''Awsaf al-Ashraf'' a short mystical-ethical work in Persian
*''Tajrīd al-iʿtiqād'' (Summation of Belief) – A commentary on Shia doctrines.
 
==Achievements==
[[File:Tusi couple.jpg|thumb|right|[[Tusi couple]] from Vat. Arabic ms 319]]
[[File:Tusi-couple.gif|right|thumb|220 px|[[Tusi couple]]]]
 
During his stay in Nishapur, Tusi established a reputation as an exceptional scholar. "Tusi’s prose writing, which number over 150 works, represent one of the largest collections by a single Islamic author. Writing in both [[Arabic]] and [[Persian language|Persian]], Nasir al-Din Tusi dealt with both religious (“Islamic”) topics and non-religious or secular subjects (“the ancient sciences”).<ref name="H. Daiber, F.J. Ragep 2007">H. Daiber, F.J. Ragep, "Tusi" in Encyclopaedia of Islam. Edited by: P. Bearman, Th. Bianquis, C.E. Bosworth, E. van Donzel and W.P. Heinrichs. Brill, 2007. Brill Online. Quote: "Tusi's prose writings, which number over 150 works, represent one of the largest collections by a single Islamic author. Writing in both Arabic and Persian, Nasir al-Din dealt with both religious ("Islamic") topics and non-religious or secular subjects ("the ancient sciences")."</ref> His works include the definitive Arabic versions of the works of [[Euclid]], [[Archimedes]], [[Ptolemy]], [[Autolycus]], and [[Theodosius of Bithynia]].<ref name="H. Daiber, F.J. Ragep 2007"/>
 
===Astronomy===
{{further|Zij-i Ilkhani|Tusi-couple}}
[[File:Nasir al-Din al-Tusi at observatory.jpg|thumb|The Astronomical Observatory of Nasir al-Din Tusi.]]
Tusi convinced [[Hulegu Khan]] to construct an observatory for establishing accurate astronomical tables for better astrological predictions. Beginning in 1259, the [[Maragheh observatory|Rasad Khaneh observatory]] was constructed in [[Azarbaijan]], west of [[Maragheh]], the capital of the [[Ilkhanate|Ilkhanate Empire]].
 
Based on the observations in this for the time being most advanced observatory, Tusi made very accurate tables of [[Ephemeris|planetary movements]] as depicted in his book ''[[Zij-i ilkhani]]'' (''Ilkhanic Tables''). This book contains astronomical tables for calculating the positions of the planets and the names of the stars. His model for the planetary system is believed to be the most advanced of his time, and was used extensively until the development of the heliocentric model in the time of [[Nicolaus Copernicus]]. Between [[Ptolemy]] and [[Copernicus]], he is considered by many to be one of the most eminent astronomers of his time.
 
For his planetary models, he invented a geometrical technique called a [[Tusi-couple]], which generates linear motion from the sum of two circular motions. He used this technique to replace [[Ptolemy]]'s problematic [[equant]]<ref>Craig G. Fraser, '[http://books.google.com/books?id=3tJr_vl6rYsC&lpg=PA39&pg=PA39#v=onepage&q&f=false The cosmos: a historical perspective]', Greenwood Publishing Group, 2006 p.39</ref> for many planets, but was unable to find a solution to Mercury, which was solved later by [[Ibn al-Shatir]] as well as [[Ali Qushji]].<ref>George Saliba, '[http://www.tad.org.tr/wp-content/files/webfiles/alikuscu_makale_saliba.pdf Al-Qushji's Reform of the Ptolemaic Model for Mercury]', Arabic Sciences and Philosophy, v.3 1993, pp.161-203</ref>  The Tusi couple was later employed in [[Ibn al-Shatir]]'s [[geocentric model]] and [[Nicolaus Copernicus]]' [[Heliocentrism|heliocentric]] [[Copernican heliocentrism|Copernican model]].<ref>George Saliba, 'Revisiting the Astronomical Contacts Between the World of Islam and Renaissance Europe: The Byzantine Connection', '[http://books.google.com/books?id=muGVUiKEYccC&lpg=PA368&pg=PA368#v=onepage&q&f=false The occult sciences in Byzantium]', 2006, p.368</ref> He also calculated the value for the annual precession of the [[equinox]]es and contributed to the construction and usage of some astronomical instruments including the [[astrolabe]].
 
Ṭūsī criticized Ptolemy's use of observational evidence to show that the Earth was at rest, noting that such proofs were not decisive. Although it doesn't mean that he was a supporter of mobility of the earth, as he and his 16th-century commentator [[al-Birjandi|al-Bīrjandī]], maintained that the earth's immobility could be demonstrated, but only by physical principles found in natural philosophy.<ref>{{Citation | last = Ragep | first = F. Jamil | title = Freeing Astronomy from Philosophy: An Aspect of Islamic Influence on Science | journal = Osiris | volume = 16, 2nd ser. | pages = 49–64 | year = 2001 | jstor = 301979}}, at p. 60.</ref> Tusi's criticisms of Ptolemy were similar to the arguments later used by Copernicus in 1543 to defend the Earth's rotation.<ref>F. Jamil Ragep (2001), "Tusi and Copernicus: The Earth's Motion in Context", ''Science in Context'' '''14''' (1-2), p. 145–163. [[Cambridge University Press]].</ref>
 
About the real essence of the Milky Way, Ṭūsī in his ''Tadhkira'' writes:
"The Milky Way, i.e. the galaxy, is made up of a very large number of small, tightly-clustered stars, which, on account of their concentration and smallness, seem to be cloudy patches. because of this, it was likend to milk in color."
<ref>Ragep, Jamil, ''Nasir al-Din Tusi’s Memoir on Astronomy'' (''al-Tadhkira fi `ilm al-hay’ a'') Edition, Translation, Commentary and Introduction. 2 vols. Sources in the History of Mathematics and Physical Sciences. New York: Springer-Verlag, 1993. pp. 129</ref>
Three centuries later the proof of the Milky Way consisting of many stars came in 1610 when [[Galileo Galilei]] used a [[Optical telescope|telescope]] to study the Milky Way and discovered that it is really composed of a huge number of faint stars.<ref>{{cite web | author= O'Connor, J. J.; Robertson, E. F. |date=November 2002 | url = http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Galileo.html | title = Galileo Galilei | publisher = University of St Andrews | accessdate = 2007-01-08 }}</ref>
 
===Biology===
In his ''Akhlaq-i-Nasri'', Tusi put forward a basic theory for the evolution of species. He begins his theory of evolution with the [[universe]] once consisting of equal and similar [[Classical element|element]]s. According to Tusi, internal contradictions began appearing, and as a result, some substances began developing faster and differently from other substances. He then explains how the elements evolved into minerals, then plants, then animals, and then humans. Tusi then goes on to explain how [[Heredity|hereditary]] variability was an important factor for biological evolution of [[living thing]]s:<ref name=Alakbarov>Farid Alakbarov (Summer 2001). [http://azer.com/aiweb/categories/magazine/92_folder/92_articles/92_tusi.html A 13th-Century Darwin? Tusi's Views on Evolution], ''[[Azerbaijan International]]'' '''9''' (2).</ref>
 
{{quote|"The [[organism]]s that can gain the new features faster are more variable. As a result, they gain advantages over other creatures. [...] The bodies are changing as a result of the internal and external interactions."}}
 
Tusi discusses how organisms are able to [[Adaptation|adapt]] to their environments:<ref name=Alakbarov/>
 
{{quote|"Look at the world of animals and birds. They have all that is necessary for defense, protection and daily life, including strengths, courage and appropriate tools [organs] [...] Some of these organs are real weapons, [...] For example, horns-spear, teeth and claws-knife and needle, feet and hoofs-cudgel. The thorns and needles of some animals are similar to arrows. [...] Animals that have no other means of defense (as the gazelle and fox) protect themselves with the help of flight and cunning. [...] Some of them, for example, bees, ants and some bird species, have united in communities in order to protect themselves and help each other."}}
 
Tusi recognized three types of living things: plants, animals, and humans. He wrote:<ref name=Alakbarov/>
 
{{quote|"Animals are higher than plants, because they are able to move consciously, go after food, find and eat useful things. [...] There are many differences between the animal and plant species, [...] First of all, the [[animal|animal kingdom]] is more complicated. Besides, [[reason]] is the most beneficial feature of animals. Owing to reason, they can learn new things and adopt new, non-inherent abilities. For example, the trained horse or hunting falcon is at a higher point of development in the animal world. The first steps of human perfection begin from here."}}
 
Tusi then explains how humans evolved from advanced animals:<ref name=Alakbarov/>
 
{{quote|"Such humans [probably [[anthropoid ape]]s] live in the Western [[Sudan]] and other distant corners of the world. They are close to animals by their habits, deeds and behavior. [...] The human has features that distinguish him from other creatures, but he has other features that unite him with the animal world, vegetable kingdom or even with the inanimate bodies. [...] Before [the creation of humans], all differences between organisms were of the natural origin. The next step will be associated with spiritual perfection, will, observation and knowledge. [...] All these facts prove that the human being is placed on the middle step of the evolutionary stairway. According to his inherent nature, the human is related to the lower beings, and only with the help of his will can he reach the higher development level."}}
 
===Chemistry and Physics===
In [[Alchemy and chemistry in Islam|chemistry]] and [[Islamic physics|physics]], Tusi stated a version of the law of [[conservation of mass]]. He wrote that a body of [[matter]] is able to change, but is not able to disappear:<ref name="Alakbarov"/>
 
{{quote|"A body of matter cannot disappear completely. It only changes its form, condition, composition, colour and other properties and turns into a different complex or elementary matter."}}
 
===Logic===
Nasir al-Din Tusi was a supporter of [[Avicennian logic]], and wrote the following commentary on [[Avicenna]]'s theory of absolute [[proposition]]s:
 
{{quote|"What spurred him to this was that in the [[assertoric]] [[syllogistic]] [[Aristotle]] and others sometimes used [[Contradiction|contradictories]] of absolute propositions on the assumption that they are absolute; and that was why so many decided that absolutes did contradict absolutes. When Avicenna had shown this to be wrong, he wanted to give a way of construing those examples from Aristotle."<ref name=Stanford>{{cite web|author=Tony Street|title=Arabic and Islamic Philosophy of Language and Logic|publisher=[[Stanford Encyclopedia of Philosophy]]|date=July 23, 2008|url=http://plato.stanford.edu/entries/arabic-islamic-language|accessdate=2008-12-05}}</ref>}}
 
===Mathematics===
[[File:Nasir al-Din Tusi.jpg|thumb|upright|Iranian stamp for the 700th anniversary of his death]]
[[File:Stamps of Azerbaijan, 2009-861.jpg|thumb|upright|A stamp issued in the republic of Azerbaijan in 2009 honoring Tusi]]
Al-Tusi was the first to write a work on trigonometry independently of astronomy.<ref name=britannica>{{cite web|title=trigonometry|url=http://www.britannica.com/EBchecked/topic/605281/trigonometry|publisher=''[[Encyclopædia Britannica]]''|accessdate=2011-04-25}}</ref> Al-Tusi, in his ''Treatise on the Quadrilateral'', gave an extensive exposition of [[spherical trigonometry]], distinct from astronomy.<ref>* Katz, Victor J. (1993). ''A History of Mathematics: An Introduction'', p259. [[Addison Wesley]]. ISBN 0-673-38039-4.</ref> It was in the works of Al-Tusi that trigonometry achieved the status of an independent branch of pure mathematics distinct from astronomy, to which it had been linked for so long.<ref>{{cite book|last=Bosworth|first=Clifford E.|title=History of civilizations of Central Asia.|year=2003|publisher=Motilal Banarsidass|isbn=81-208-1596-3|coauthors=Asimov|volume=4|page=190}}</ref><ref>{{cite book|last=Hayes|first=John R.|title=The genius of Arab civilization : source of Renaissance|year=1983|publisher=Taylor & Francis|isbn=0-262-08136-9|edition=2nd|coauthors=Badeau, John S.|page=156}}</ref>
 
He was the first to list the six distinct cases of a right triangle in spherical trigonometry.
 
This followed earlier work by [[Greek mathematics|Greek mathematicians]] such as [[Menelaus of Alexandria]], who wrote a book on spherical trigonometry called ''Sphaerica,'' and the earlier Muslim mathematicians [[Abū al-Wafā' al-Būzjānī]] and [[Al-Jayyani]].
 
In his ''On the Sector Figure'', appears the famous [[law of sines]] for plane triangles.<ref name=Berggren-518>{{cite book | first=J. Lennart | last=Berggren | title=The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook | chapter=Mathematics in Medieval Islam | publisher=Princeton University Press | year=2007 | isbn=978-0-691-11485-9 | page=518}}</ref>
 
:<math> \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} </math>
 
He also stated the law of sines for spherical triangles,<ref>''Also the 'sine law' (of geometry and trigonometry, applicable to spherical trigonometry) is attributed, among others, to Alkhujandi. (The three others are Abul Wafa Bozjani, Nasiruddin Tusi and Abu Nasr Mansur).'' Razvi, Syed Abbas Hasan (1991) ''A history of science, technology, and culture in Central Asia, Volume 1'' University of Peshawar, Peshawar, Pakistan, page 358, [http://www.worldcat.org/oclc/26317600 OCLC 26317600]</ref><ref>Bijli suggests that three mathematicians are in contention for the honor, Alkhujandi, Abdul-Wafa and Mansur, leaving out Nasiruddin Tusi. Bijli, Shah Muhammad and Delli, Idarah-i Adabiyāt-i (2004) ''Early Muslims and their contribution to science: ninth to fourteenth century'' Idarah-i Adabiyat-i Delli, Delhi, India, page 44, [http://www.worldcat.org/oclc/66527483 OCLC 66527483]</ref> discovered the [[law of tangents]] for spherical triangles, and provided proofs for these laws.<ref name=Berggren-518/>
 
==Influence and legacy==
A 60-km diameter lunar [[Impact crater|crater]] located on the southern hemisphere of the [[moon]] is named after him as "[[Nasireddin (crater)|Nasireddin]]". A [[minor planet]] [[10269 Tusi]] discovered by [[Soviet Union|Soviet]] astronomer [[Nikolai Stepanovich Chernykh]] in 1979 is named after him.<ref>{{cite web|url=http://adsabs.harvard.edu/full/2003ASPC..289..157B |title=2003ASPC..289..157B Page 157 |publisher=Adsabs.harvard.edu |date= |accessdate=2013-02-27}}</ref><ref>{{cite book|url=http://books.google.com/books?q=10269+tusi&hl=lt |title=10269 tusi - Mano biblioteka - Google knygos |publisher=Books.google.com |date= |accessdate=2013-02-27}}</ref> The [[K. N. Toosi University of Technology]] in [[Iran]] and Observatory of Shamakhy in the [[Republic of Azerbaijan]] are also named after him. Google celebrated his 812th birthday with a [[Google Doodle|doodle]], which was accessible in its websites with Arabic language.<ref name=google-doodle>{{cite web|title=Nasir al-Din al-Tusi's 812th Birthday|url=https://www.google.com/doodles/nasir-al-din-al-tusis-812th-birthday|publisher=Google|accessdate=19 February 2013}}</ref><ref name="BBC Persian">{{cite news|title=In Persian نگاه عربی به خواجه نصیرالدین طوسی در گوگل|url=http://www.bbc.co.uk/persian/science/2013/02/130219_l42_khaje_nasir_google.shtml|accessdate=19 February 2013|date=19 February 2013}}</ref>
 
==See also==
*[[List of modern-day Muslim scholars of Islam]]
*[[List of Iranian scientists]]
*[[List of Shi'a Muslims]]
*[[Persian science]]
*[[Science in the medieval Islamic world]]
*[[Shen Kuo]]
 
==References==
{{-}}
{{reflist|30em}}
 
==Further reading==
*{{DSB|last=|title=Ṭūsī, Muḥammad Ibn Muḥammad Ibn al-Ḥasan }}
*{{MacTutor|id=Al-Tusi_Nasir|title=Nasir al-Din Tusi}}
*Encyclopædia Iranica, "AḴLĀQ-E NĀṢERĪ", G.M. Wickens [http://www.iranicaonline.org/articles/aklaq-e-naseri-by-kaa-nasir-al-din-tusi-the-principal-treatise-in-persian-on-ethics-economics-and-politics-f]
*Encyclopædia Iranica, "AWṢĀF AL-AŠRĀF", G.M. Wickens [http://www.iranicaonline.org/articles/awsaf-al-asraf-a-short-mystical-ethical-work-in-persian-by-nasir-al-din-tusi-written-late-in-life-ca]
*Encyclopædia Iranica, "Nasir al-Din al-Tusi" George Saliba [http://www.iranicaonline.org/articles/tusi-nasir-al-din]
 
==External links==
*{{cite encyclopedia | editor = Thomas Hockey et al | last = Ragep| first = F. Jamil | title=Ṭūsī: Abū Jaʿfar Muḥammad ibn Muḥammad ibn al‐Ḥasan Naṣīr al‐Dīn al‐Ṭūsī | encyclopedia = The Biographical Encyclopedia of Astronomers | publisher = Springer | year = 2007 |location = New York | pages = 1153–5 |url=http://islamsci.mcgill.ca/RASI/BEA/Tusi_BEA.htm |isbn=978-0-387-31022-0}} ([http://islamsci.mcgill.ca/RASI/BEA/Tusi_BEA.pdf PDF version])
*{{cite encyclopedia | last = Nasr | first = Seyyed Hossein | title=Al-Ṭūsī, Muḥammad Ibn Muḥammad Ibn Al-Ḥasan Usually Known as Naṣir Al-Dīn  | url=http://www.encyclopedia.com/doc/1G2-2830904400.html |  encyclopedia = [[Dictionary of Scientific Biography|Complete Dictionary of Scientific Biography]] | publisher = Encyclopedia.com | origyear=1970-80 | year = 2008 }}
*[http://islamicinsights.com/index.php?option=com_content&task=view&id=316 Biography by Islamic Insights]
*[http://www.muslimphilosophy.com/ip/rep/H036.htm Biography by Islamic Philosophy Online]
*[http://www.iep.utm.edu/t/tusi.htm Biography by The Internet Encyclopedia of Philosophy]
*Kerry Magruder, [http://homepage.mac.com/kvmagruder/hsci/07-Islamic-Indian-Chinese/islamicSupplemental.html History of Science Online: Islamic and Early Medieval Science], University of Oklahoma
*[http://www.islamonline.com/cgi-bin/news_service/profile_story.asp?service_id=996 Islam Online.]
*http://www.famousmuslims.com/NASIR%20AL-DIN%20AL-TUSI.htm
*{{cite web|url=http://www.britannica.com/eb/article-9073899|title=Nasir al-Din al-Tusi (Persian scholar) -- Encyclopedia Britannica|publisher=britannica.com|accessdate=16 January 2014}}
*[http://www.wilbourhall.org/index.html#rekha The Rekhaganita]. An 18th century Sanskrit translation of Nasir al-Din al-Tusi's recension of Euclid's'' Elements''.
*[http://www.saudiaramcoworld.com/issue/200703/rediscovering.arabic.science.htm, Richard Covington, ''Rediscovering Arabic Science'', 2007, Saudi Aramco World]
{{Authority control|VIAF=12392936}}
 
{{Scholars of Khorasan}}
{{Islamic astronomy}}
{{Islamic mathematics}}
{{Islamic philosophy}}
{{Medieval Philosophy}}
 
{{Persondata
|name= Tusi, Nasir Din
|alternative names=
|short description= Persian astronomer
|date of birth= 18 February 1201
|place of birth=
|date of death=26 June 1274
|place of death=
}}
{{DEFAULTSORT:Tusi, Nasir Din}}
[[Category:Astronomers of medieval Islam]]
[[Category:Iranian Shia Muslims]]
[[Category:Mathematicians of medieval Islam]]
[[Category:Medieval Persian astronomers]]
[[Category:Medieval Persian mathematicians]]
[[Category:People from Mashhad]]
[[Category:People from Tus, Iran]]
[[Category:Persian philosophers]]
[[Category:Scientists who worked on Qibla determination]]
[[Category:Shia Muslim scholars of Islam]]
[[Category:1201 births]]
[[Category:1274 deaths]]
[[Category:13th-century astronomers]]
[[Category:13th-century mathematicians]]
[[Category:World Digital Library related]]
[[Category:13th-century Iranian people]]

Latest revision as of 04:54, 25 September 2013

Template:Infobox Muslim scholar

Khawaja Muhammad ibn Muhammad ibn Hasan Tūsī (Template:Lang-fa) (born 18 February 1201 in Ṭūs, Khorasan – died on 26 June 1274 in al-Kāżimiyyah district of metropolitan Baghdad), better known as Nasīr al-Dīn Tūsī (Template:Lang-fa; or simply Tusi in the West), was a Persian[1][2][3][4] polymath and prolific writer: an architect, astronomer, biologist, chemist, mathematician, philosopher, physician, physicist, scientist, theologian and Marja Taqleed.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. He was of the Ismaili-, and subsequently Twelver Shī‘ah Islamic belief.[5] The Muslim scholar Ibn Khaldun (1332–1406) considered Tusi to be the greatest of the later Persian scholars.[6]

Biography

Nasir al-Din Tusi was born in the city of Tus in medieval Khorasan (in north-eastern Iran) in the year 1201 and began his studies at an early age. In Hamadan and Tus he studied the Qur'an, Hadith, Shi'a jurisprudence, logic, philosophy, mathematics, medicine and astronomy.[7]

He was apparently born into a Shī‘ah family and lost his father at a young age. Fulfilling the wish of his father, the young Muhammad took learning and scholarship very seriously and travelled far and wide to attend the lectures of renowned scholars and acquire the knowledge which guides people to the happiness of the next world. At a young age he moved to Nishapur to study philosophy under Farid al-Din Damad and mathematics under Muhammad Hasib.[8] He met also Farid al-Din 'Attar, the legendary Sufi master who was later killed by Mongol invaders and attended the lectures of Qutb al-Din al-Misri.

In Mosul he studied mathematics and astronomy with Kamal al-Din Yunus (d. 639/1242). Later on he corresponded with Sadr al-Din al-Qunawi, the son-in-law of Ibn al-'Arabi, and it seems that mysticism, as propagated by Sufi masters of his time, was not appealing to his mind and once the occasion was suitable, he composed his own manual of philosophical Sufism in the form of a small booklet entitled Awsaf al-Ashraf "The Attributes of the Illustrious".

As the armies of Genghis Khan swept his homeland, he was captured by the Ismailis and made his most important contributions in science during this time when he was moving from one stronghold to another. He finally joined Hulagu Khan's ranks, after the invasion of the Alamut castle by the Mongol forces.

Works

Tusi has about 150 works in Persian and Arabic.[9]

A Treatise on Astrolabe by Tusi, Isfahan 1505
  • Kitāb al-Shakl al-qattāʴ Book on the complete quadrilateral. A five volume summary of trigonometry.
  • Al-Tadhkirah fi'ilm al-hay'ah – A memoir on the science of astronomy. Many commentaries were written about this work called Sharh al-Tadhkirah (A Commentary on al-Tadhkirah) - Commentaries were written by Abd al-Ali ibn Muhammad ibn al-Husayn al-Birjandi and by Nazzam Nishapuri.
  • Akhlaq-i-Nasri – A work on ethics.
  • al-Risalah al-Asturlabiyah – A Treatise on astrolabe.
  • Zij-i ilkhani (Ilkhanic Tables) – A major astronomical treatise, completed in 1272.
  • sharh al-isharat (Commentary on Avicenna's Isharat)
  • Awsaf al-Ashraf a short mystical-ethical work in Persian
  • Tajrīd al-iʿtiqād (Summation of Belief) – A commentary on Shia doctrines.

Achievements

Tusi couple from Vat. Arabic ms 319
Tusi couple

During his stay in Nishapur, Tusi established a reputation as an exceptional scholar. "Tusi’s prose writing, which number over 150 works, represent one of the largest collections by a single Islamic author. Writing in both Arabic and Persian, Nasir al-Din Tusi dealt with both religious (“Islamic”) topics and non-religious or secular subjects (“the ancient sciences”).[9] His works include the definitive Arabic versions of the works of Euclid, Archimedes, Ptolemy, Autolycus, and Theodosius of Bithynia.[9]

Astronomy

47 year-old Podiatrist Hyslop from Alert Bay, has lots of hobbies and interests that include fencing, property developers in condo new launch singapore and handball. Just had a family trip to Monasteries of Haghpat and Sanahin.

The Astronomical Observatory of Nasir al-Din Tusi.

Tusi convinced Hulegu Khan to construct an observatory for establishing accurate astronomical tables for better astrological predictions. Beginning in 1259, the Rasad Khaneh observatory was constructed in Azarbaijan, west of Maragheh, the capital of the Ilkhanate Empire.

Based on the observations in this for the time being most advanced observatory, Tusi made very accurate tables of planetary movements as depicted in his book Zij-i ilkhani (Ilkhanic Tables). This book contains astronomical tables for calculating the positions of the planets and the names of the stars. His model for the planetary system is believed to be the most advanced of his time, and was used extensively until the development of the heliocentric model in the time of Nicolaus Copernicus. Between Ptolemy and Copernicus, he is considered by many to be one of the most eminent astronomers of his time.

For his planetary models, he invented a geometrical technique called a Tusi-couple, which generates linear motion from the sum of two circular motions. He used this technique to replace Ptolemy's problematic equant[10] for many planets, but was unable to find a solution to Mercury, which was solved later by Ibn al-Shatir as well as Ali Qushji.[11] The Tusi couple was later employed in Ibn al-Shatir's geocentric model and Nicolaus Copernicus' heliocentric Copernican model.[12] He also calculated the value for the annual precession of the equinoxes and contributed to the construction and usage of some astronomical instruments including the astrolabe.

Ṭūsī criticized Ptolemy's use of observational evidence to show that the Earth was at rest, noting that such proofs were not decisive. Although it doesn't mean that he was a supporter of mobility of the earth, as he and his 16th-century commentator al-Bīrjandī, maintained that the earth's immobility could be demonstrated, but only by physical principles found in natural philosophy.[13] Tusi's criticisms of Ptolemy were similar to the arguments later used by Copernicus in 1543 to defend the Earth's rotation.[14]

About the real essence of the Milky Way, Ṭūsī in his Tadhkira writes: "The Milky Way, i.e. the galaxy, is made up of a very large number of small, tightly-clustered stars, which, on account of their concentration and smallness, seem to be cloudy patches. because of this, it was likend to milk in color." [15] Three centuries later the proof of the Milky Way consisting of many stars came in 1610 when Galileo Galilei used a telescope to study the Milky Way and discovered that it is really composed of a huge number of faint stars.[16]

Biology

In his Akhlaq-i-Nasri, Tusi put forward a basic theory for the evolution of species. He begins his theory of evolution with the universe once consisting of equal and similar elements. According to Tusi, internal contradictions began appearing, and as a result, some substances began developing faster and differently from other substances. He then explains how the elements evolved into minerals, then plants, then animals, and then humans. Tusi then goes on to explain how hereditary variability was an important factor for biological evolution of living things:[17]

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Tusi discusses how organisms are able to adapt to their environments:[17]

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Tusi recognized three types of living things: plants, animals, and humans. He wrote:[17]

31 year-old Systems Analyst Bud from Deep River, spends time with pursuits for instance r/c cars, property developers new condo in singapore singapore and books. Last month just traveled to Orkhon Valley Cultural Landscape.

Tusi then explains how humans evolved from advanced animals:[17]

31 year-old Systems Analyst Bud from Deep River, spends time with pursuits for instance r/c cars, property developers new condo in singapore singapore and books. Last month just traveled to Orkhon Valley Cultural Landscape.

Chemistry and Physics

In chemistry and physics, Tusi stated a version of the law of conservation of mass. He wrote that a body of matter is able to change, but is not able to disappear:[17]

31 year-old Systems Analyst Bud from Deep River, spends time with pursuits for instance r/c cars, property developers new condo in singapore singapore and books. Last month just traveled to Orkhon Valley Cultural Landscape.

Logic

Nasir al-Din Tusi was a supporter of Avicennian logic, and wrote the following commentary on Avicenna's theory of absolute propositions:

31 year-old Systems Analyst Bud from Deep River, spends time with pursuits for instance r/c cars, property developers new condo in singapore singapore and books. Last month just traveled to Orkhon Valley Cultural Landscape.

Mathematics

Iranian stamp for the 700th anniversary of his death
A stamp issued in the republic of Azerbaijan in 2009 honoring Tusi

Al-Tusi was the first to write a work on trigonometry independently of astronomy.[18] Al-Tusi, in his Treatise on the Quadrilateral, gave an extensive exposition of spherical trigonometry, distinct from astronomy.[19] It was in the works of Al-Tusi that trigonometry achieved the status of an independent branch of pure mathematics distinct from astronomy, to which it had been linked for so long.[20][21]

He was the first to list the six distinct cases of a right triangle in spherical trigonometry.

This followed earlier work by Greek mathematicians such as Menelaus of Alexandria, who wrote a book on spherical trigonometry called Sphaerica, and the earlier Muslim mathematicians Abū al-Wafā' al-Būzjānī and Al-Jayyani.

In his On the Sector Figure, appears the famous law of sines for plane triangles.[22]

asin⁡A=bsin⁡B=csin⁡C

He also stated the law of sines for spherical triangles,[23][24] discovered the law of tangents for spherical triangles, and provided proofs for these laws.[22]

Influence and legacy

A 60-km diameter lunar crater located on the southern hemisphere of the moon is named after him as "Nasireddin". A minor planet 10269 Tusi discovered by Soviet astronomer Nikolai Stepanovich Chernykh in 1979 is named after him.[25][26] The K. N. Toosi University of Technology in Iran and Observatory of Shamakhy in the Republic of Azerbaijan are also named after him. Google celebrated his 812th birthday with a doodle, which was accessible in its websites with Arabic language.[27][28]

See also

References

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Further reading

  • Template:DSB
  • Can a new property agent make $eight,seven-hundred inside her first 2.5 months? (See bolded part above) A couple of yr ago, I joined one of the top actual property firms in Singapore, and happened to be recruited beneath one of many high-selling divisions. I later left the business for personal causes, but I still receive work related sales figures, and I can honestly say that yes it is completely doable. I've seen the figures.

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  • Encyclopædia Iranica, "AḴLĀQ-E NĀṢERĪ", G.M. Wickens [1]
  • Encyclopædia Iranica, "AWṢĀF AL-AŠRĀF", G.M. Wickens [2]
  • Encyclopædia Iranica, "Nasir al-Din al-Tusi" George Saliba [3]

External links

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i imagine there are good ethical brokers in Singapore. But i have encounter unhealthy experiencing the Christina Fong from realty master. She is admittedly an unprofessional and never moral one. Only considering of undercutiing and squeezing money from ptther people without defending interest of her personal shopper. Proceed to the section Training and look at a map of all worldwide colleges in Singapore or visit the section residential areas for detailed data on the place to stay and why. Information District and Location Have completed no less than 30 property transactions up to now three years. At least 10 of these transactions will have to be for private properties, and at the very least one other 10 needs to be for HDB flats (also known as public housing); Singapore-Indonesia Commercial Affiliation

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There may also be a Code of Ethics and a Skilled Conduct Commonplace, as well as the introduction of disciplinary motion in opposition to errant brokers/businesses and dispute decision mechanisms. Preparations shall be made to manage the transition of existing agencies and agents to these new standards, which have but to be finalized. The Proposed Enchancment in High quality for Actual Property Businesses Wheelock Properties put up 95 items of The Panorama in Ang Mo Kio for balloting. With a reduction of 12 p.c, they claimed to promote 80 to eighty five units. Whereas developers are clearing their existing stock, every month there are new projects acquiring their HIGH and new sites released by the government to construct more private housing. The due date of each rental payment; or

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Template:Scholars of Khorasan Template:Islamic astronomy Template:Islamic mathematics Template:Islamic philosophy Earlier than you decide whether stainless-steel cookware is price shopping for, lets first focus on what stainless steel cookware is. Chrome steel is made from an alloy, or a combination of metals. Most commonly, fundamental iron with chromium, nickel or some other minor metals. The chromium supplies rust protection and offers your cookware sturdiness. The nickel offers rust safety as effectively, and adds a sophisticated look. Most effectively made stainless steel cookware has copper or aluminum added to the bottom of the pan or pot. This is finished to increases the flexibility of the pot or pan to conduct warmth.
The perfect chrome steel cookware is the primary category, but still it's divided into a number of subcategories based mostly on the standard and the price vary. It may be complicated to decide on one of the best stainless-steel cookware out of the categories that can meet your necessities. That is the place we took a step forward to clarify you all the data that shall be useful for you to know the way to choose the perfect stainless-steel cookware. The very best chrome steel cookware set is manufactured from cheap to expensive and high quality constructed pots and pans.
You will discover magnetic stainless-steel within the layer on the outside of some quality pieces of stainless-steel. That is to make it suitable with induction stovetops, which contain the usage of a rapidly charging electromagnetic discipline to warmth cookware. Excessive-high quality chrome steel, like All-Clad , uses three layers of metallic—the austenite layer of metal on the within, ferrite steel on the skin, and a layer of aluminum sandwiched between the two for optimal heat conductivity (metal alone does not conduct warmth evenly). Lesser-high quality stainless steel is often just one layer of austenitic stainless-steel.
Aesthetically speaking, stainless steel is a wise choice if you happen to want to display or hold pots or pans. The clear, crisp look of all stainless-steel kitchenware can transform a mishmash of cookware into a complicated décor statement. Stainless-steel kettles, such because the Cuisinart Tea Kettle will combine particular person kitchenware right into a cohesive and pleasant entity. Contemplate purchasing chrome steel utensils as effectively. Already acquired a beautiful stainless steel cookware collection? The Cuisinart Chef’s Assortment stainless pot rack may be the of entirety for a kitchen, liberating up space and making these pots and pans readily accessible. Get the stainless steel cookware of your culinary dreams at Macy’s!
Arduous-anodized aluminum cookware is without doubt one of the most popular varieties of material, despite the fact that many individuals do not fairly perceive the construction. Exhausting-anodized aluminum is obvious aluminum that has been processed in a series of chemical baths charged with an electric present. The result is a fabric that has the identical superior warmth conductivity as aluminum but is non-reactive with acidic meals, such as tomatoes, and twice as laborious as stainless steel. Two drawbacks to hard-anodized cookware are that it is not dishwasher-protected and, as a result of it isn't magnetic, it will not work with induction vary tops.
The enamel over metal method creates a piece that has the heat distribution of carbon metal and a non-reactive, low-stick surface. Such pots are a lot lighter than most other pots of similar size, are cheaper to make than stainless-steel pots, and do not have the rust and reactivity issues of cast iron or carbon metal. quotation needed Enamel over steel is ideal for big stockpots and for different giant pans used principally for water-primarily based cooking. Due to its light weight and easy cleanup, enamel over steel is also well-liked for cookware used whereas camping. Clad aluminium or copper edit
Distinctive specialty cookware items served a la carte to compliment any cookware set are constructed of a durable Stainless Steel with a brushed exterior finish. Designed with an impression bonded, aluminum disk encapsulated base which distributes heat shortly and evenly to permit precise temperature management. Handles are riveted for durability and efficiency. The New Specialty Cookware is compatible for all vary types together with induction. Along with the multi use operate, one other distinctive feature is bottom to top inside quantity markings in each quarts and metric measurement; and every bit comes with a tempered glass lid, oven safe to 350°F.
Whether or not you're a cooking enthusiasts, knowledgeable chef or simply cooking for your loved ones you realize the significance of getting a completely stocked kitchen. Not solely do you want the appropriate elements, but you additionally want the suitable tools to get the job carried out. In any kind of fundamental cooking training lesson, you will be taught that stainless steel is your new greatest good friend in relation to kitchen cookware. What additionally, you will study is that quality cooking tools doesn't usually come at a discounted value. If you liked this post and you would such as to get additional details regarding best stainless steel cookware kindly visit our internet site. For this reason, you will need to take excellent care of your cookware! Listed here are some basics for stainless steel care.
To fight the uneven heating downside, most chrome steel pans are laminations of aluminum or copper on the underside to unfold the warmth round, and stainless steel contained in the pan to offer a cooking surface that is impervious to whatever you may put inside. In my expertise, this stainless-steel floor remains to be too sticky to fry on, and for those who ever burn it you get a everlasting bother spot. However, sometimes a stainless-steel cooking surface comes in handy when you can't use aluminum (see beneath) so I hold some around. Choose one thing with a reasonably thick aluminum layer on the bottom.
Well, unless you’re a metals expert and go inspect the manufacturing unit the place the steel is made to see whether or not or not their manufacturing course of creates a pure austenite with out corrosive materials shaped, you’re not going to know for certain whether or not or not the craftsmanship of your stainless is of the highest quality. I think your greatest guess is to simply purchase excessive-quality chrome steel from the start, from a brand with a popularity for good high quality. However, I feel I've found out a method that you could determine if the stainless cookware you have already got is probably reactive.

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  1. ↑ a) "Tusi, Nasir al-Din. " Encyclopædia Britannica. 2007. Encyclopædia Britannica Online. 27 December 2007 <http://www.britannica.com/eb/article-9073899>. b)Arthur Goldschmidt, Lawrence Davidson. "A Concise History of the Middle East", Westview Press, 2009. ninth edition, pg 127: "Hulegu, contrite at the damage he had wrought, patronized the great Persian scholar, Nasiruddin Tusi (died 1274), who saved the lives of many other scientists and artists, accumulated a library of 400000 volumes, and built an astronomical ..."; [4] d) Nanne Pieter George Joosse, Bar Hebraeus, "A Syriac encyclopaedia of Aristotelian philosophy: Barhebraeus (13th c.), Butyrum sapientiae, books of ethics, economy, and politics: a critical edition, with introduction, translation, commentary, and glossaries", Published by Brill, 2004. excerpt: " the famous Persian scholar Naslr al-Dln Tusi "; e)Seyyed Hossein Nasr," Title Islamic philosophy from its origin to the present: philosophy in the land of prophecy", Publisher SUNY Press, 2006. pp 167: “In fact it was common among Persian Islamic philosophers to write few quatrains on the side often in the spirit of some of the poems of Khayyam singing about the impermanence of the world and its transience and similar themes. One needs to only recall the names of Ibn Sina, Suhrawardi, Nasir al-Din Tusi and Mulla Sadra, who wrote poems alongs with extensive prose works”
  2. ↑ Rodney Collomb, "The rise and fall of the Arab Empire and the founding of Western pre-eminence", Published by Spellmount, 2006. pg 127: "..Khawaja Nasr ed-Din Tusi, the Persian, Khorasani, former chief scholar and scientist of ";
  3. ↑ M.A. Al-Bakhit, L. Bazin, S.M. Cissoko, Volume 4 of History of humanity : scientific and cultural development Routledge, 2000. [5] pg 367: "the Turkish astronomer and philosopher Nasir al-Din Tusi".
  4. ↑ a)Seyyed Hossein Nasr, Islamic Philosophy from Its Origin to the Present: Philosophy in the Land of Prophecy, SUNY Press, 2006, ISBN 0-7914-6799-6. page 199.; b) Seyyed H. Badakhchani. Contemplation and Action: The Spiritual Autobiography of a Muslim Scholar: Nasir al-Din Tusi (In Association With the Institute of Ismaili Studies. I. B. Tauris (December 3, 1999). ISBN 1-86064-523-2. page.1: ""Nasir al-Din Abu Ja`far Muhammad b. Muhammad b. Hasan Tusi:, the renowned Persian astronomer, philosopher and theologian"
  5. ↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

    Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

    In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

    Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

    Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

    15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

    To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
  6. ↑ James Winston Morris, "An Arab Machiavelli? Rhetoric, Philosophy and Politics in Ibn Khaldun’s Critique of Sufism", Harvard Middle Eastern and Islamic Review 8 (2009), pp 242–291. [6] excerpt from page 286 (footnote 39): "Ibn Khaldun’s own personal opinion is no doubt summarized in his pointed remark (Q 3: 274) that Tusi was better than any other later Iranian scholar". Original Arabic: Muqaddimat Ibn Khaldūn : dirāsah usūlīyah tārīkhīyah / li-Aḥmad Ṣubḥī Manṣūr-al-Qāhirah : Markaz Ibn Khaldūn : Dār al-Amīn, 1998. ISBN 977-19-6070-9. Excerpt from Ibn Khaldun is found in the section: الفصل الثالث و الأربعون: في أن حملة العلم في الإسلام أكثرهم العجم (On how the majority who carried knowledge forward in Islam were Persians) In this section, see the sentence sentence where he mentions Tusi as more knowledgeable than other later Persian ('Ajam) scholars: . و أما غيره من العجم فلم نر لهم من بعد الإمام ابن الخطيب و نصير الدين الطوسي كلاما يعول على نهايته في الإصابة. فاعتير ذلك و تأمله تر عجبا في أحوال الخليقة. و الله يخلق ما بشاء لا شريك له الملك و له الحمد و هو على كل شيء قدير و حسبنا الله و نعم الوكيل و الحمد لله.
  7. ↑ Dabashi, Hamid. "Khwajah Nasir al-Din Tusi: The philosopher/vizier and the intellectual climate of his times". Routledge History of World Philosophies. Vol I. History of Islamic Philosophy. Seyyed Hossein Nasr and Oliver Leaman (eds.) London: Routledge. 1996. p. 529
  8. ↑ Siddiqi, Bakhtyar Husain. "Nasir al-Din Tusi". A History of Islamic Philosophy. Vol 1. M. M. Sharif (ed.). Wiesbaden:: Otto Harrossowitz. 1963. p. 565
  9. ↑ 9.0 9.1 9.2 H. Daiber, F.J. Ragep, "Tusi" in Encyclopaedia of Islam. Edited by: P. Bearman, Th. Bianquis, C.E. Bosworth, E. van Donzel and W.P. Heinrichs. Brill, 2007. Brill Online. Quote: "Tusi's prose writings, which number over 150 works, represent one of the largest collections by a single Islamic author. Writing in both Arabic and Persian, Nasir al-Din dealt with both religious ("Islamic") topics and non-religious or secular subjects ("the ancient sciences")."
  10. ↑ Craig G. Fraser, 'The cosmos: a historical perspective', Greenwood Publishing Group, 2006 p.39
  11. ↑ George Saliba, 'Al-Qushji's Reform of the Ptolemaic Model for Mercury', Arabic Sciences and Philosophy, v.3 1993, pp.161-203
  12. ↑ George Saliba, 'Revisiting the Astronomical Contacts Between the World of Islam and Renaissance Europe: The Byzantine Connection', 'The occult sciences in Byzantium', 2006, p.368
  13. ↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

    Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

    In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

    Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

    Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

    15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

    To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010, at p. 60.
  14. ↑ F. Jamil Ragep (2001), "Tusi and Copernicus: The Earth's Motion in Context", Science in Context 14 (1-2), p. 145–163. Cambridge University Press.
  15. ↑ Ragep, Jamil, Nasir al-Din Tusi’s Memoir on Astronomy (al-Tadhkira fi `ilm al-hay’ a) Edition, Translation, Commentary and Introduction. 2 vols. Sources in the History of Mathematics and Physical Sciences. New York: Springer-Verlag, 1993. pp. 129
  16. ↑ Template:Cite web
  17. ↑ 17.0 17.1 17.2 17.3 17.4 Farid Alakbarov (Summer 2001). A 13th-Century Darwin? Tusi's Views on Evolution, Azerbaijan International 9 (2).
  18. ↑ Template:Cite web
  19. ↑ * Katz, Victor J. (1993). A History of Mathematics: An Introduction, p259. Addison Wesley. ISBN 0-673-38039-4.
  20. ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  21. ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  22. ↑ 22.0 22.1 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  23. ↑ Also the 'sine law' (of geometry and trigonometry, applicable to spherical trigonometry) is attributed, among others, to Alkhujandi. (The three others are Abul Wafa Bozjani, Nasiruddin Tusi and Abu Nasr Mansur). Razvi, Syed Abbas Hasan (1991) A history of science, technology, and culture in Central Asia, Volume 1 University of Peshawar, Peshawar, Pakistan, page 358, OCLC 26317600
  24. ↑ Bijli suggests that three mathematicians are in contention for the honor, Alkhujandi, Abdul-Wafa and Mansur, leaving out Nasiruddin Tusi. Bijli, Shah Muhammad and Delli, Idarah-i Adabiyāt-i (2004) Early Muslims and their contribution to science: ninth to fourteenth century Idarah-i Adabiyat-i Delli, Delhi, India, page 44, OCLC 66527483
  25. ↑ Template:Cite web
  26. ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  27. ↑ Template:Cite web
  28. ↑ Template:Cite news
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