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'''Nasirudin Tusi''' ([[Perzijski jezik|perzijski]]: محمد بن محمد بن حسن طوسی), punog imena '''Muhammad ibn Muhammad ibn al-Hasan al-Tūsī''', bio je [[Perzijanci|perzijski]] [[polihistor]], [[arhitekt]], [[filozof]], [[liječnik]], [[znanstvenik]] i [[teolog]].<ref>{{cite book|last1=Bennison|first1=Amira K.|title=The great caliphs : the golden age of the 'Abbasid Empire |url=https://archive.org/details/greatcaliphsgold00benn|date=2009 |publisher=Yale University Press |location=New Haven |isbn=978-0-300-15227-2 |page=[https://archive.org/details/greatcaliphsgold00benn/page/n214 204] |quote=Hulegu killed the last ‘Abbasid caliph but also patronized the foundation of a new observatory at Maragha in Azerbayjan at the instigation of the Persian Shi‘i polymath Nasir al-Din Tusi.}}</ref><ref>{{cite book|last1=Goldschmidt|first1=Arthur |last2=Boum|first2=Aomar |title=A Concise History of the Middle East|url=https://books.google.com/books?id=hSOdBAAAQBAJ |year=2015 |publisher=Avalon Publishing |isbn=978-0-8133-4963-3 |quote=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 ...}}</ref><ref>{{cite book|author1=Bar Hebraeus |authorlink1=Bar Hebraeus|last2=Joosse|first2=Nanne Pieter George|title=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|url=https://books.google.com/books?id=eYV3AAAAMAAJ|year=2004 |publisher=Brill |isbn=978-90-04-14133-9|page=11|quote=the Persian scholar Naṣīr al-Dīn al-Ṭūsī}}</ref><ref>{{cite book |author=Seyyed Hossein Nasr|title=Islamic Philosophy from Its Origin to the Present: Philosophy in the Land of Prophecy |url=https://books.google.com/books?id=0k5iy4RvAwcC |year=2006 |publisher=State University of New York Press |isbn=978-0-7914-6800-5 |page=167 |quote=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 along 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>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</ref><ref>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><ref>{{cite book|last1=Glick|first1=Thomas F.|authorlink1=Thomas F. Glick|last2=Livesey|first2=Steven John|last3=Wallis|first3=Faith|authorlink3=Faith Wallis|title=Medieval Science, Technology, and Medicine: An Encyclopedia|url=https://books.google.com/books?id=SaJlbWK_-FcC|year=2005|publisher=Psychology Press|isbn=978-0-415-96930-7|quote=drawn by the Persian cosmographer al-Tusi.}}</ref><ref>{{cite book|last=Laet|first=Sigfried J. de |title=History of Humanity: From the seventh to the sixteenth century|url=https://books.google.com/books?id=PvlthkbFU1UC|year=1994|publisher=UNESCO |isbn=978-92-3-102813-7|page=908|quote=the Persian astronomer and philosopher Nasir al-Din Tusi.}}</ref><ref>{{cite book|last=Mirchandani|first=Vinnie|title=The New Polymath: Profiles in Compound-Technology Innovations|url=https://books.google.com/books?id=v7bP_KlooLwC&pg=PA300|year=2010|publisher=John Wiley & Sons|isbn=978-0-470-76845-7|page=300|quote=Nasir. al-Din. al-Tusi: Stay. Humble. Nasir al-Din al-Tusi, the Persian polymath, talked about humility: “Anyone who does not know and does not know that he does not know is stuck forever in double ...}}</ref> Često se smatra tvorcem [[Trigonometrija|trigonometrije]] kao samostalne matematičke discipline.<ref>{{Citiranje weba|url=http://www-history.mcs.st-andrews.ac.uk/Biographies/Al-Tusi_Nasir.html|title=Al-Tusi_Nasir biography|website=www-history.mcs.st-andrews.ac.uk|access-date=5. 8. 2018|quote=One of al-Tusi's most important mathematical contributions was the creation of trigonometry as a mathematical discipline in its own right rather than as just a tool for astronomical applications. In Treatise on the quadrilateral al-Tusi gave the first extant exposition of the whole system of plane and spherical trigonometry. This work is really the first in history on trigonometry as an independent branch of pure mathematics and the first in which all six cases for a right-angled spherical triangle are set forth.}}</ref><ref>{{Citiranje weba|url=https://www.cambridge.org/core/books/the-cambridge-history-of-science/islamic-mathematics/4BF4D143150C0013552902EE270AF9C2|title=the cambridge history of science}}</ref><ref>{{Citiranje weba|url=http://www.iranicaonline.org/articles/tusi-nasir-al-din-bio|title=ṬUSI, NAṢIR-AL-DIN i. Biography – Encyclopaedia Iranica|last=electricpulp.com|website=www.iranicaonline.org|language=en|access-date=5. 8. 2018|quote=His major contribution in mathematics (Nasr, 1996, pp. 208-14) is said to be in trigonometry, which for the first time was compiled by him as a new discipline in its own right. Spherical trigonometry also owes its development to his efforts, and this includes the concept of the six fundamental formulas for the solution of spherical right-angled triangles.}}</ref> Muslimanski učenjak [[Ibn Haldun]] ([[1332.]] – [[1406.]]) smatrao je Tusija najvećim od kasnijih perzijskih učenjaka.<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 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>
'''Nasirudin Tusi''' ([[Perzijski jezik|perzijski]]: محمد بن محمد بن حسن طوسی), punog imena '''Muhammad ibn Muhammad ibn al-Hasan al-Tūsī''', bio je [[Perzijanci|perzijski]] [[polihistor]], [[arhitekt]], [[filozof]], [[liječnik]], [[znanstvenik]] i [[teolog]].<ref>{{Citiranje knjige|last1=Bennison|first1=Amira K.|title=The great caliphs : the golden age of the 'Abbasid Empire |url=https://archive.org/details/greatcaliphsgold00benn|date=2009 |publisher=Yale University Press |location=New Haven |isbn=978-0-300-15227-2 |page=[https://archive.org/details/greatcaliphsgold00benn/page/n214 204] |quote=Hulegu killed the last ‘Abbasid caliph but also patronized the foundation of a new observatory at Maragha in Azerbayjan at the instigation of the Persian Shi‘i polymath Nasir al-Din Tusi.}}</ref><ref>{{Citiranje knjige|last1=Goldschmidt|first1=Arthur |last2=Boum|first2=Aomar |title=A Concise History of the Middle East|url=https://books.google.com/books?id=hSOdBAAAQBAJ |year=2015 |publisher=Avalon Publishing |isbn=978-0-8133-4963-3 |quote=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 ...}}</ref><ref>{{Citiranje knjige|author1=Bar Hebraeus |authorlink1=Bar Hebraeus|last2=Joosse|first2=Nanne Pieter George|title=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|url=https://books.google.com/books?id=eYV3AAAAMAAJ|year=2004 |publisher=Brill |isbn=978-90-04-14133-9|page=11|quote=the Persian scholar Naṣīr al-Dīn al-Ṭūsī}}</ref><ref>{{Citiranje knjige |author=Seyyed Hossein Nasr|title=Islamic Philosophy from Its Origin to the Present: Philosophy in the Land of Prophecy |url=https://books.google.com/books?id=0k5iy4RvAwcC |year=2006 |publisher=State University of New York Press |isbn=978-0-7914-6800-5 |page=167 |quote=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 along 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>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</ref><ref>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><ref>{{Citiranje knjige|last1=Glick|first1=Thomas F.|authorlink1=Thomas F. Glick|last2=Livesey|first2=Steven John|last3=Wallis|first3=Faith|authorlink3=Faith Wallis|title=Medieval Science, Technology, and Medicine: An Encyclopedia|url=https://books.google.com/books?id=SaJlbWK_-FcC|year=2005|publisher=Psychology Press|isbn=978-0-415-96930-7|quote=drawn by the Persian cosmographer al-Tusi.}}</ref><ref>{{Citiranje knjige|last=Laet|first=Sigfried J. de |title=History of Humanity: From the seventh to the sixteenth century|url=https://books.google.com/books?id=PvlthkbFU1UC|year=1994|publisher=UNESCO |isbn=978-92-3-102813-7|page=908|quote=the Persian astronomer and philosopher Nasir al-Din Tusi.}}</ref><ref>{{Citiranje knjige|last=Mirchandani|first=Vinnie|title=The New Polymath: Profiles in Compound-Technology Innovations|url=https://books.google.com/books?id=v7bP_KlooLwC&pg=PA300|year=2010|publisher=John Wiley & Sons|isbn=978-0-470-76845-7|page=300|quote=Nasir. al-Din. al-Tusi: Stay. Humble. Nasir al-Din al-Tusi, the Persian polymath, talked about humility: “Anyone who does not know and does not know that he does not know is stuck forever in double ...}}</ref> Često se smatra tvorcem [[Trigonometrija|trigonometrije]] kao samostalne matematičke discipline.<ref>{{Citiranje weba|url=http://www-history.mcs.st-andrews.ac.uk/Biographies/Al-Tusi_Nasir.html|title=Al-Tusi_Nasir biography|website=www-history.mcs.st-andrews.ac.uk|access-date=5. 8. 2018|quote=One of al-Tusi's most important mathematical contributions was the creation of trigonometry as a mathematical discipline in its own right rather than as just a tool for astronomical applications. In Treatise on the quadrilateral al-Tusi gave the first extant exposition of the whole system of plane and spherical trigonometry. This work is really the first in history on trigonometry as an independent branch of pure mathematics and the first in which all six cases for a right-angled spherical triangle are set forth.}}</ref><ref>{{Citiranje weba|url=https://www.cambridge.org/core/books/the-cambridge-history-of-science/islamic-mathematics/4BF4D143150C0013552902EE270AF9C2|title=the cambridge history of science}}</ref><ref>{{Citiranje weba|url=http://www.iranicaonline.org/articles/tusi-nasir-al-din-bio|title=ṬUSI, NAṢIR-AL-DIN i. Biography – Encyclopaedia Iranica|last=electricpulp.com|website=www.iranicaonline.org|language=en|access-date=5. 8. 2018|quote=His major contribution in mathematics (Nasr, 1996, pp. 208-14) is said to be in trigonometry, which for the first time was compiled by him as a new discipline in its own right. Spherical trigonometry also owes its development to his efforts, and this includes the concept of the six fundamental formulas for the solution of spherical right-angled triangles.}}</ref> Muslimanski učenjak [[Ibn Haldun]] ([[1332.]] – [[1406.]]) smatrao je Tusija najvećim od kasnijih perzijskih učenjaka.<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 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>


== Životopis ==
== Životopis ==
Redak 82: Redak 82:
Ovaj rad nastavak je ranijih radova grčkih matematičara, poput [[Menelaj Aleksandrijski|Menelaja iz Aleksandrije]], koji je napisao knjigu o sfernoj trigonometriji pod nazivom ''Sphaerica'' kao i ranijih muslimanskih matematičari [[Abu al-Wafa' Buzjani|Abu al-Wafe]] i [[Ibn Muaz Džajani]]ja.
Ovaj rad nastavak je ranijih radova grčkih matematičara, poput [[Menelaj Aleksandrijski|Menelaja iz Aleksandrije]], koji je napisao knjigu o sfernoj trigonometriji pod nazivom ''Sphaerica'' kao i ranijih muslimanskih matematičari [[Abu al-Wafa' Buzjani|Abu al-Wafe]] i [[Ibn Muaz Džajani]]ja.


U svom djelu ''Na sektorskoj slici'' pojavljuje se poznata [[sinusni poučak]] kojom se uspostavljaju određene relacije unutar trokuta.<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 | date=2007 | isbn=978-0-691-11485-9 | page=518}}</ref>
U svom djelu ''Na sektorskoj slici'' pojavljuje se poznata [[sinusni poučak]] kojom se uspostavljaju određene relacije unutar trokuta.<ref name=Berggren-518>{{Citiranje knjige | 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 | date=2007 | isbn=978-0-691-11485-9 | page=518}}</ref>


:<math> \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} </math>
:<math> \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} </math>
Redak 105: Redak 105:


== Utjecaj i ostavština ==
== Utjecaj i ostavština ==
Krater ''[[Nasirudin (krater)|Nasirudin]]'' promjera 60 km koji se nalazi na južnoj polutci [[Mjesec]]a nazvan je po njemu. [[Mali planet]] 10269 Tusi kojeg je [[SSSR|sovjetski]] astronom [[Nikolaj Stepanovič Černih]] otkrio 1979. godine nazvana je po ovom učenjaku.<ref>{{Citiranje weba|url=http://adsabs.harvard.edu/full/2003ASPC..289..157B |title=2003ASPC..289..157B Page 157 |publisher=Adsabs.harvard.edu |accessdate=27 February 2013}}</ref><ref>{{cite book|url=https://books.google.com/books?q=10269+tusi&hl=lt |title=10269 tusi - Mano biblioteka - Google knygos |publisher=Books.google.com |accessdate=27 February 2013}}</ref> Po njemu su nazvani i [[tehnološko sveučilište K. N. Tusi]], najstarije tehnološko sveučilište u Iranu i zvjezdarnica u [[Šemah]]u, [[Azerbajdžan]]. U veljači [[2013.]] gidube, [[Google (tražilica)|Google]] je 812. godišnjicu od Tusijevog rođenja obilježio s [[Google Doodle|doodleom]], pri čemu je na početnim stranicama ovog pretraživača Tusi nazvan ''al-farsi'' (perzijanac).<ref name=google-doodle>{{Citiranje weba|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>
Krater ''[[Nasirudin (krater)|Nasirudin]]'' promjera 60 km koji se nalazi na južnoj polutci [[Mjesec]]a nazvan je po njemu. [[Mali planet]] 10269 Tusi kojeg je [[SSSR|sovjetski]] astronom [[Nikolaj Stepanovič Černih]] otkrio 1979. godine nazvana je po ovom učenjaku.<ref>{{Citiranje weba|url=http://adsabs.harvard.edu/full/2003ASPC..289..157B |title=2003ASPC..289..157B Page 157 |publisher=Adsabs.harvard.edu |accessdate=27 February 2013}}</ref><ref>{{Citiranje knjige|url=https://books.google.com/books?q=10269+tusi&hl=lt |title=10269 tusi - Mano biblioteka - Google knygos |publisher=Books.google.com |accessdate=27 February 2013}}</ref> Po njemu su nazvani i [[tehnološko sveučilište K. N. Tusi]], najstarije tehnološko sveučilište u Iranu i zvjezdarnica u [[Šemah]]u, [[Azerbajdžan]]. U veljači [[2013.]] gidube, [[Google (tražilica)|Google]] je 812. godišnjicu od Tusijevog rođenja obilježio s [[Google Doodle|doodleom]], pri čemu je na početnim stranicama ovog pretraživača Tusi nazvan ''al-farsi'' (perzijanac).<ref name=google-doodle>{{Citiranje weba|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>


== Izvori ==
== Izvori ==

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Nasirudin Tusi
Nasir al-Din Tusi.jpg
Iranska markica izdata povodom 700 godina od smrti Nasirudina Tusija
Rođenje 18. veljače, 1201.
Tus, Horasan, Iran
Smrt 26. lipnja 1274.
Kazimejn, Irak
Etnicitet Perzijanac
Polje matematika
filozofija
astronomija
fizika
medicina
opća znanost
Poznat po Zij-i Ilkhani

Nasirudin Tusi (perzijski: محمد بن محمد بن حسن طوسی), punog imena Muhammad ibn Muhammad ibn al-Hasan al-Tūsī, bio je perzijski polihistor, arhitekt, filozof, liječnik, znanstvenik i teolog.[1][2][3][4][5][6][7][8][9][10] Često se smatra tvorcem trigonometrije kao samostalne matematičke discipline.[11][12][13] Muslimanski učenjak Ibn Haldun (1332. – 1406.) smatrao je Tusija najvećim od kasnijih perzijskih učenjaka.[14]

Životopis

Tusijev traktat o astrolabu, Isfahan 1505.

Nasirudin Tusi rođen je 18. veljače 1201. godine u gradu Tusu, u srednjovjekovnom Horasanu, današnjem sjeveroistočnom dijelu Irana. Obrazovanje je započeo u ranoj mladosti. U Hamadanu i Tusu proučavao je Kuran, hadis, džaferijsku pravnu filozofiju, logiku, filozofiju, matematiku, medicinu i astronomiju.[15]

Rođen je u šijitskoj obitelji, a u mladosti je izgubio oca. Ispunivši želju svog oca, mladi je Muhamed ozbiljno shvatio učenje i stipendiju i putovao nadaleko, kako bi pohađao predavanja poznatih učenjaka i stekao znanje. U mladosti se preselio u Nišapur, grad koji je u to vrijeme bio znanstveni centar, a nalazio se oko 75 km zapadno od Tusa. Tu je proučavao filozofiju kod učenjaka Feridudina Damada Nišaburija i matematiku kod Muhameda Hasiba.[16] U tom razdoblju u Nišapuru je upoznao i Feriduddina Attara, poznatog sufiju kojeg su kasnije ubili Mongoli, a pohađao je predavanja Kutbudina Misrija.

U Mosulu je studirao matematiku i astronomiju s Kemal el-Din Junusom, učenikom Šarafudina Tusije.[17]

Dok su vojske Džingis-kana harale njegovom domovinom, Tusi je bio u službi nizarske ismailijske države i dao značajan doprinos znanosti u to vrijeme kada je država bila pred slomom pred nadolazećim snagama Mongolskog Carstva.[18] Zarobljen je nakon što su Mongoli izvršili invaziju alamutske regije.[19]

Radovi

Tusi je napisao oko 150 djela, od kojih je 25 na perzijskom, a preostala na arapskom jeziku, a postoji i jedan traktat na perzijskom, arapskom i turskom jeziku.

Neki od njegovih najvažnijih radova su:

  • Kitāb al-Shakl al-qattāʴ – knjiga o kompletnom četveroukutu. Peti svezak je sažetak trigonometrije,
  • Al-Tadhkirah fi'ilm al-hay'ah – memoar o astronomiji. Mnogo komentara bilo je napisano o ovom djelu nazvanom Sharh al-Tadhkirah (Komentar al-Tadhkirah) – komentare su napisali El-Bircendi i Nazam Nišapuri,
  • Akhlaq-i Nasiri – djelo o etici,
  • al-Risalah al-Asturlabiyah – traktat o astrolabiji,
  • Zij-i Ilkhani (ilhanidske tablice) – glavni astronomski traktat, završen 1272. godine.
  • Sharh al-Isharat – komentar Ibn Sininog El-Išareta,
  • Awsaf al-Ashraf – kratak mistično-etički rad na perzijskom jeziku,
  • Tajrīd al-Iʿtiqād – sažetak vjerovanja, komentar šiitskih nauka,
  • Talkhis al-Muhassal – sažetak sažetaka,

Postignuća

Tusi je tijekom boravka u Nišapuru stekao reputaciju izuzetnog učenjaka. Tusijevo prozno pisanje, koje broji preko 150 djela, predstavlja jednu od najvećih zbirki jednog islamskog autora. Osim pisanje na arapskom i perzijskom jeziku Nasirudin Tusi bavio se i vjerskim (islamskim) temama i nereligijskim ili svjetovnim temama (drevne znanosti). Njegovi radovi uključuju i konačne verzije arapskog prijevoda djela Euklida, Arhimeda, Ptolemeja, Autolika i Teodozija iz Bitinije.

Astronomija

Vista-xmag.pngPodrobniji članci o temama: Zij-i Ilkhani i Tusijev par

Tusi je uvjerio Hulagu-kana da izgradi zvjezdarnicu za uspostavljanje točnih astronomskih tablica za bolja astrološka predviđanja. Od 1259. godine, izgrađen je zvjezdarnica u Maragi u Azerbajdžanu, južno od rijeke Araks i zapadno od Marage, prijestolnice Ilhanidskog Carstva.

Na osnovu zapažanja u ovom, tada najnaprednijoj zvjezdarnici, Tusi je sastavio vrlo precizne tablice kretanja planeta kao što je prikazano u njegovoj knjizi Zij-i Ilkhani (Ilhanidske tablice). Ova knjiga sadrži astronomske tablice za računanje položaja planeta i imena zvijezda. Smatra se da je njegov model za planetarni sustav bio najnapredniji u to doba, pa se naširoko koristio sve do razvoja heliocentričnog modela u doba Nikole Kopernika. Tijekom razdoblja od Ptolemeja do Kopernika, neki ga smatraju jednim od najistaknutijih astronoma tog vremena.

Za svoje planetarne modele izumio je geometrijsku tehniku ​​pod nazivom Tusijev par, koji generira linearno kretanje kao zbroj dva kružna pokreta. On je koristio ovu tehniku ​​da zamijeni problematični ekvivalent Ptolemeja za mnoge planete, ali nije uspio pronaći rješenje za Merkur, što je kasnije riješio Ibn eš Šatir kao i Ali Kušći. Tusijev par kasnije je upotrebljen u geocentričnom modelu Ibn eš-Šatira i heliocentričnom modelu Nikole Kopernika. Također je izračunao vrijednost za godišnju precesiju ravnodnevnice i pridonio izgradnji i upotrebi nekih astronomskih instrumenata, uključujući astrolabe.

Tusi je kritizirao Ptolomejevu upotrebu opservacijskih dokaza kako bi pokazao da je Zemlja u stanju mirovanja, napominjući da takvi dokazi nisu presudni. Iako to ne znači da je bio zagovornik mobilnosti zemlje, kao što je bio zagovornik i njegov komentator iz 16. stoljeća El-Bircendi, Tusi je tvrdio da se nepokretnost Zemlje može dokazati, samo fizičkim principima koji su pronađeni u prirodnoj filozofiji. Tusijeve kritike Ptolemeja bile su slične argumentima koje je Kopernik kasnije (1543. godine) koristio za obranu teze rotacije Zemlje.

O stvarnoj biti Mliječne staze, Ṭusi u svojem Tadhkirahu piše: „Mliječna staza, tj. Galaksija, sastoji se od vrlo velikog broja malih zvijezda čvrsto povezanih u skup, koje zbog svoje koncentracije i male veličine izgledaju kao zamućene mrlje. Zbog toga sliče mlijeku koje se nalazi u boji. Tri stoljeća kasnije dokazano je da se Mliječna staza sastoji od mnoštva zvijezda kada je 1610. godine Galileo Galilei koristio teleskop za proučavanje Mliječne staze i otkrio da se zaista sastoji od ogromnog broja slabašnih zvijezda.

Logika

Nasirudin Tusi bio je zastupnik Ibn Sinine logike i napisao je sljedeći komentar njegove teorije apsolutnih propozicije:

„Ono što ga je potaknulo na to je da je u asortorističkom silogističkom Aristotelu i drugima ponekad korištena kontradiktornost apsolutnih prijedloga pod pretpostavkom da su apsolutni; i zato su mnogi odlučili da apsolutnost proturječi apsolutnom. Kad je Ibn Sina pokazao da to nije u redu želio je razviti metodu konstrukcije tih Aristotelovih primjera.”


Matematika

Poštanska markica izdata u Azerbejdžanu 2009. godine u čast Tusija

Tusi je bio prvi koji je napisao djelo o trigonometriji nezavisno od astronomije.[20] U svom Traktatu o četverokutu Tusi je dao opsežno izlaganje sferne trigonometrije, nezavisno od astronomije.[21] Upravo je u djelima Tusija trigonometrija postigla status nezavisne grane matematike koja se razlikovala od astronomije, a s kojom je toliko dugo bila povezana. Bio je prvi koji je nabrojao šest različitih slučajeva pravog trokuta u sfernoj trigonometriji.[22]

Ovaj rad nastavak je ranijih radova grčkih matematičara, poput Menelaja iz Aleksandrije, koji je napisao knjigu o sfernoj trigonometriji pod nazivom Sphaerica kao i ranijih muslimanskih matematičari Abu al-Wafe i Ibn Muaz Džajanija.

U svom djelu Na sektorskoj slici pojavljuje se poznata sinusni poučak kojom se uspostavljaju određene relacije unutar trokuta.[23]

[math]\displaystyle{ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} }[/math]

Također je formulirao i sinusni poučak u sfernoj trigonometriji,[24][25] definirao tangensni poučak za sferne trokute i pružio dokaze za te zakone.[23]

Biologija

U svom djelu Akhlaq-i Nasiri, Tusi je pisao o nekoliko bioloških tema. Branio je verziju Aristotelove scale naturae, u koju je čovjeka stavio iznad životinja, biljaka, minerala i elemenata. Opisao je trave koje rastu bez sjetve ili uzgoja jednostavnim stapanjem elemenata kao najbliže mineralima. Među biljkama datulju je smatrao najrazvijenijom, jer njoj edostaje samo jedna stvar kojom bi mogla dostići stadij životinje, a to je da se otkine iz zemlje i krene u potragu za hranjivim tvarima.

Najnižu razinu među životinjama, koje su bliske području biljaka, prema Tusiju su one životinje koje se šire poput trave, a nesposobne su za parenje, npr. gliste i određene vrste insekata. Životinje koje dostignu fazu savršenstva odlikuju se potpuno razvijenim oružjem, poput rogova, zuba i kandži. Tusi je te organe opisao kao prilagodbe životnom stilu svake vrste, na način koji predviđa prirodnu teologiju. Također je napisao i sljedeće:

„Najplemenitija vrsta je ona vrsta čija je razdražljivost i percepcija takva da prihvaća disciplinu i pouku: time joj pripisuje savršenost koja u njoj nije prvobitno bila stvorena. Takvi su školovani konj i istrenirani sokol. Kako ovaj stupanj znanja više raste u njemu, to više nadilazi svoj rang, sve dok ne dođe do točke u kojoj je samo puko promatranje akcije dovoljno za uputu, na taj način, kad nešto vide, oni to slično izvode mimikrijom, bez prethodne obuke. Ovo je najviši stupanj životinje i prvi stupanj u rangu do čovjeka s kojim je u neposrednoj blizini.”


Tusi je u ovom odlomku opisao različite vrste učenja, prepoznavajući promatračko učenje kao najnapredniji oblik i ispravno ga pripisujući određenim životinjama.

Čini se da je Tusi čovjekovu pripadnost, u svijetu živih bića, shvatio kao pripadnost životinjama, budući da je izjavio da je životinjska duša [koja sadrži sposobnosti percepcije i kretanja ...] ograničena na jedinke životinjske vrste, i to tako što posjeduje ljudsku dušu, [...] čovječanstvo se razlikuje i partikularizira među ostalim životinjama.[26]

Neki učenjaci tumače Tusijeve biološke zapise kao sugestije da se držao neke evolucijske teorije.[27][28] Međutim, Tusi nikad nije izričito izjavio da vjeruje da će se vrste mijenjati s vremenom.

Kemija

Tusi je doprino kemiji formulacijom ranog zakona o očuvanju mase.[29]

Utjecaj i ostavština

Krater Nasirudin promjera 60 km koji se nalazi na južnoj polutci Mjeseca nazvan je po njemu. Mali planet 10269 Tusi kojeg je sovjetski astronom Nikolaj Stepanovič Černih otkrio 1979. godine nazvana je po ovom učenjaku.[30][31] Po njemu su nazvani i tehnološko sveučilište K. N. Tusi, najstarije tehnološko sveučilište u Iranu i zvjezdarnica u Šemahu, Azerbajdžan. U veljači 2013. gidube, Google je 812. godišnjicu od Tusijevog rođenja obilježio s doodleom, pri čemu je na početnim stranicama ovog pretraživača Tusi nazvan al-farsi (perzijanac).[32][33]

Izvori

  1. PREUSMJERI Predložak:Izvori

Daljnje čitanje

Vanjske poveznice

  1. ↑ Bennison, Amira K. (2009). The great caliphs : the golden age of the 'Abbasid Empire. New Haven: Yale University Press. str. 204. ISBN 978-0-300-15227-2. https://archive.org/details/greatcaliphsgold00benn. "Hulegu killed the last ‘Abbasid caliph but also patronized the foundation of a new observatory at Maragha in Azerbayjan at the instigation of the Persian Shi‘i polymath Nasir al-Din Tusi." 
  2. ↑ Goldschmidt, Arthur; Boum, Aomar (2015). A Concise History of the Middle East. Avalon Publishing. ISBN 978-0-8133-4963-3. https://books.google.com/books?id=hSOdBAAAQBAJ. "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 ..." 
  3. ↑ Bar Hebraeus; Joosse, Nanne Pieter George (2004). 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. Brill. str. 11. ISBN 978-90-04-14133-9. https://books.google.com/books?id=eYV3AAAAMAAJ. "the Persian scholar Naṣīr al-Dīn al-Ṭūsī" 
  4. ↑ Seyyed Hossein Nasr (2006). Islamic Philosophy from Its Origin to the Present: Philosophy in the Land of Prophecy. State University of New York Press. str. 167. ISBN 978-0-7914-6800-5. https://books.google.com/books?id=0k5iy4RvAwcC. "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 along with extensive prose works." 
  5. ↑ 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"
  6. ↑ 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
  7. ↑ 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"
  8. ↑ Glick, Thomas F.; Livesey, Steven John; Wallis, Faith (2005). Medieval Science, Technology, and Medicine: An Encyclopedia. Psychology Press. ISBN 978-0-415-96930-7. https://books.google.com/books?id=SaJlbWK_-FcC. "drawn by the Persian cosmographer al-Tusi." 
  9. ↑ Laet, Sigfried J. de (1994). History of Humanity: From the seventh to the sixteenth century. UNESCO. str. 908. ISBN 978-92-3-102813-7. https://books.google.com/books?id=PvlthkbFU1UC. "the Persian astronomer and philosopher Nasir al-Din Tusi." 
  10. ↑ Mirchandani, Vinnie (2010). The New Polymath: Profiles in Compound-Technology Innovations. John Wiley & Sons. str. 300. ISBN 978-0-470-76845-7. https://books.google.com/books?id=v7bP_KlooLwC&pg=PA300. "Nasir. al-Din. al-Tusi: Stay. Humble. Nasir al-Din al-Tusi, the Persian polymath, talked about humility: “Anyone who does not know and does not know that he does not know is stuck forever in double ..." 
  11. ↑ "Al-Tusi_Nasir biography". http://www-history.mcs.st-andrews.ac.uk/Biographies/Al-Tusi_Nasir.html Pristupljeno 5. 8. 2018. "One of al-Tusi's most important mathematical contributions was the creation of trigonometry as a mathematical discipline in its own right rather than as just a tool for astronomical applications. In Treatise on the quadrilateral al-Tusi gave the first extant exposition of the whole system of plane and spherical trigonometry. This work is really the first in history on trigonometry as an independent branch of pure mathematics and the first in which all six cases for a right-angled spherical triangle are set forth." 
  12. ↑ "the cambridge history of science". https://www.cambridge.org/core/books/the-cambridge-history-of-science/islamic-mathematics/4BF4D143150C0013552902EE270AF9C2 
  13. ↑ electricpulp.com. "ṬUSI, NAṢIR-AL-DIN i. Biography – Encyclopaedia Iranica" (engl.). http://www.iranicaonline.org/articles/tusi-nasir-al-din-bio Pristupljeno 5. 8. 2018. "His major contribution in mathematics (Nasr, 1996, pp. 208-14) is said to be in trigonometry, which for the first time was compiled by him as a new discipline in its own right. Spherical trigonometry also owes its development to his efforts, and this includes the concept of the six fundamental formulas for the solution of spherical right-angled triangles." 
  14. ↑ 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. [4] 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 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.
  15. ↑ 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
  16. ↑ Siddiqi, Bakhtyar Husain. "Nasir al-Din Tusi". A History of Islamic Philosophy. Vol 1. M. M. Sharif (ed.). Wiesbaden:: Otto Harrossowitz. 1963. p. 565
  17. ↑ Sharaf al-Din al-Muzaffar al-Tusi biography - MacTutor History of Mathematics
  18. ↑ Peter Willey, The Eagle's Nest: Ismaili Castles in Iran and Syria, (I.B. Tauris, 2005), 172.
  19. ↑ Michael Axworthy, A History of Iran: Empire of the Mind, (Basic Books, 2008), 104.
  20. ↑ Script error: No such module "citation/CS1".
  21. ↑ * Katz, Victor J. (1993). A History of Mathematics: An Introduction, p259. Addison Wesley. ISBN 0-673-38039-4.
  22. ↑ http://www-history.mcs.st-andrews.ac.uk/Biographies/Al-Tusi_Nasir.html,"One of al-Tusi's most important mathematical contributions was the creation of trigonometry as a mathematical discipline in its own right rather than as just a tool for astronomical applications. In Treatise on the quadrilateral al-Tusi gave the first extant exposition of the whole system of plane and spherical trigonometry. This work is really the first in history on trigonometry as an independent branch of pure mathematics and the first in which all six cases for a right-angled spherical triangle are set forth"/
  23. ↑ 23,0 23,1 Berggren, J. Lennart (2007). "Mathematics in Medieval Islam". The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook. Princeton University Press. str. 518. ISBN 978-0-691-11485-9 
  24. ↑ 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, <templatestyles src="Module:Citation/CS1/styles.css" />Script error: No such module "Catalog lookup link".
  25. ↑ 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, <templatestyles src="Module:Citation/CS1/styles.css" />Script error: No such module "Catalog lookup link".
  26. ↑ Nasir ad-Din Tusi (1964) The Nasirean Ethics (translator: G.M. Wickens). London: Allen & Unwin, p. 42 (emphasis added).
  27. ↑ Alakbarli, Farid (Summer 2001). "A 13th-Century Darwin? Tusi's Views on Evolution". Azerbaijan International 9 (2): 48–49. http://azer.com/aiweb/categories/magazine/92_folder/92_articles/92_tusi.html 
  28. ↑ Shoja, M.M.; Tubbs, R.S. (2007). "The history of anatomy in Persia". Journal of Anatomy 210: 359–378. doi:10.1111/j.1469-7580.2007.00711.x. PMC 2100290. PMID 17428200. //www.ncbi.nlm.nih.gov/pmc/articles/PMC2100290/ 
  29. ↑ Alakbarli, Farid (2001). "A 13th-Century Darwin? Tusi's Views ojn Evolution". Azerbaijan International 9 (2 (Summer 2001)): 48–49. https://azer.com/aiweb/categories/magazine/92_folder/92_articles/92_tusi.html Pristupljeno 27. siječnja 2018.. "While this reasoning may seem backward to today's Western mind, some of Tusi's theories did have merit. For instance, Tusi believed that a body of matter is able to change, but is not able to entirely disappear. He wrote: 'A body of matter cannot disappear completely. It only changes its form, condition, composition, color and other properties and turns into a different complex or elementary matter'." 
  30. ↑ "2003ASPC..289..157B Page 157". Adsabs.harvard.edu. http://adsabs.harvard.edu/full/2003ASPC..289..157B Pristupljeno 27. veljače 2013. 
  31. ↑ 10269 tusi - Mano biblioteka - Google knygos. Books.google.com. https://books.google.com/books?q=10269+tusi&hl=lt Pristupljeno 27. veljače 2013. 
  32. ↑ "Nasir al-Din al-Tusi's 812th Birthday". Google. https://www.google.com/doodles/nasir-al-din-al-tusis-812th-birthday Pristupljeno 19. veljače 2013. 
  33. ↑ "In Persian نگاه عربی به خواجه نصیرالدین طوسی در گوگل". 19. veljače 2013.. http://www.bbc.co.uk/persian/science/2013/02/130219_l42_khaje_nasir_google.shtml Pristupljeno 19. veljače 2013. 
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