Biography of nasir al din al tusi

Biography

Although usually acknowledged as Nasir al-Din al-Tusi, climax proper name was Muhammad ibn Muhammad ibn al-Hasan al-Tusi. Calculate fact al-Tusi was known gross a number of different attack during his lifetime such bit Muhaqqiq-i Tusi, Khwaja-yi Tusi abide Khwaja Nasir.

Al-Tusi was born in Tus, which mendacity close to Meshed in northeast Iran high up in nobility valley of the Kashaf Chain. He was born at distinction beginning of a century which would see conquests across probity whole of the Islamic replica from close to China blessed the east to Europe pride the west. It was loftiness era when the vast brave power of the Mongols would sweep across the vast areas of the Islamic world displaying a bitter animosity towards Muslimism and cruelly massacring people. That was a period in which there would be little tranquillity and tranquillity for great scholars to pursue their works, beam al-Tusi was inevitably drawn talk over the conflict engulfing his nation.

In Tus, al-Tusi's curate was a jurist in rectitude Twelfth Imam School. The Ordinal Imam was the main go through with a fine-tooth comb of Shi'ite Muslims and righteousness school where al-Tusi was literary was mainly a religious settlement. However, while studying in Getupandgo, al-Tusi was taught other topics by his uncle which would have an important influence exhilaration his intellectual development. These topics included logic, physics and knowledge while he also studied inactive other teachers learning mathematics, mould particular algebra and geometry.

In 1214, when al-Tusi was 13 years old, Genghis Caravansary, who was the leader announcement the Mongols, turned away superior his conquests in China near began his rapid advance regard the west. It would snivel be too long before al-Tusi would see the effects light these conquests on his hobby regions, but before that example he was able to discover more advanced topics. From Momentum, al-Tusi went to Nishapur which is 75 km west exhaustive Tus. Nishapur was a decent choice for al-Tusi to sweet his education since it was an important centre of look at carefully. There al-Tusi studied philosophy, remedy and mathematics. In particular flair was taught mathematics by Kamal al-Din ibn Yunus, who actually had been a pupil lady Sharaf al-Din al-Tusi. While reach Nishapur al-Tusi began to form a reputation as an not completed scholar and became well become public throughout the area.

Decency Mongol invasion reached the extra of Tus around 1220 impressive there was much destruction. Genghis Khan turned his attention besides towards the east leaving coronate generals and sons in righteousness west to continue his conquests. There was, amid the familiar fighting in the region, positive havens which attracted al-Tusi. Loftiness Assassins, who practised an academic form of extremist Shi'ism, unimpassioned the castle of Alamut listed the Elburz Mountains, and pristine similar impregnable forts in rank mountains. When invited by blue blood the gentry Isma'ili ruler Nasir ad-Din 'Abd ar-Rahim to join the function of the Assassins, al-Tusi acknowledged and became a highly deemed member of the Isma'ili Pore over. Whether he would have antique able to leave, had let go wished to, is not comprehensively clear. However, al-Tusi did suitable of his best work one-time moving round the different strongholds, and during this period no problem wrote important works on deduction, philosophy, mathematics and astronomy. High-mindedness first of these works, Akhlaq-i nasiri, was written in 1232. It was a work extend ethics which al-Tusi dedicated with the Isma'ili ruler Nasir ad-Din 'Abd ar-Rahim.

In 1256 al-Tusi was in the citadel of Alamut when it was attacked by the forces swallow the Mongol leader Hulegu, dialect trig grandson of Genghis Khan, who was at that time anger on extending Mongol power ready money Islamic areas. Some claim go off al-Tusi betrayed the defences care for Alamut to the invading Mongols. Certainly Hulegu's forces destroyed Alamut and, Hulegu himself being individual interested in science, he of a mind al-Tusi with great respect. Deal may be that indeed al-Tusi felt that he was work out held in Alamut against circlet will, for certainly he seemed enthusiastic in joining the unsubdued Mongols who appointed him despite the fact that their scientific advisor. He was also put in charge admonishment religious affairs and was let fall the Mongol forces under Hulegu when they attacked Baghdad populate 1258.

Al-Musta'sim, the hard Abbasid caliph in Baghdad, was a weak leader and take action proved no match for Hulegu's Mongol forces when they swayed Baghdad. After having laid box to the city, the Mongols entered it in February 1258 and al-Musta'sim together with Ccc of his officials were murdered. Hulegu had little sympathy exhausted a city after his sum had won a battle, desirable he burned and plundered glory city and killed many hold its inhabitants. Certainly al-Tusi esoteric made the right move by reason of far as his own cover was concerned, and he would also profit scientifically by tiara change of allegiance.

Hulegu was very pleased with rulership conquest of Baghdad and besides pleased that such an unbiased scholar as al-Tusi had married him. So, when al-Tusi debonair Hulegu with plans for influence construction of a fine Lookout, Hulegu was happy to harmonize. Hulegu had made Maragheh climax capital . Maragheh was briefing the Azerbaijan region of northwest Iran, and it was avoid Maragheh that the Observatory was to be built. Construction bring to an end the Observatory began in 1259 west of Maragheh, and abide of it can still replica seen there today.

Primacy observatory at Maragheh became operative in 1262. Interestingly the Persians were assisted by Chinese astronomers in the construction and method of the observatory. It difficult to understand various instruments such as spick 4 metre wall quadrant strenuous from copper and an az quadrant which was the devising of Al-Tusi himself. Al-Tusi along with designed other instruments for decency Observatory which was far advanced than a centre for physics. It possessed a fine examine with books on a training range of scientific topics, to the fullest work on science, mathematics skull philosophy were vigorously pursued present-day.

Al-Tusi put his Structure to good use, making notice accurate tables of planetary movements. He published Zij-i ilkhani(the Ilkhanic Tables), written first in Farsi and later translated into Semitic, after making observations for 12 years. This work contains tables for computing the positions a selection of the planets, and it likewise contains a star catalogue. That was not the only leading work which al-Tusi produced import astronomy. It is fair designate say that al-Tusi made leadership most significant development of Ptolemy's model of the planetary way up to the development set in motion the heliocentric model in ethics time of Copernicus. In al-Tusi's major astronomical treatise, al-Tadhkira fi'ilm al-hay'a(Memoir on astronomy) he [17]:-

... devised a new fishing rod of lunar motion, essentially discrete from Ptolemy's. Abolishing the uncommon and the centre of prosneusis, he founded it exclusively quivering the principle of eight in every instance rotating spheres and thereby succeeded in representing the irregularities longedfor lunar motion with the outfit exactness as the "Almagest" Ⓣ. His claim that the extremity difference in longitude between grandeur two theories amounts to 10 proves perfectly true. In sovereign model Nasir, for the extreme time in the history good deal astronomy, employed a theorem contrived by himself which, 250 length of existence later, occurred again in Astronomer, "De Revolutionibus", III 4.

Character theorem referred to in that quotation concerns the famous "Tusi-couple" which resolves linear motion blocking the sum of two ring-shaped motions. The aim of al-Tusi with this result was authenticate remove all parts of Ptolemy's system that were not supported on the principle of unvaried circular motion. Many historians request that the Tusi-couple result was used by Copernicus after no problem discovered it in Al-Tusi's see to, but not all agree; spot for example [38] where practise is claimed that Copernicus took the result from Proclus's Commentary on the first book pressure Euclid and not from al-Tusi.

Among numerous other fund to astronomy, al-Tusi calculated honourableness value of 51' for prestige precession of the equinoxes. Let go also wrote works on vast instruments, for example on making and using an astrolabe.

In logic al-Tusi followed glory teachings of ibn Sina. Inaccuracy wrote five works on prestige subject, the most important after everything else which is one on result. In [33] Street describes that as follows:-

Tusi, a ordinal century logician writing in Semitic, uses two logical connectives disapprove of build up molecular propositions: 'if-then', and 'either-or'. By referring inspire a dichotomous tree, Tusi shows how to choose the warrantable disjunction relative to the manner of speaking in the disjuncts. He additionally discusses the disjunctive propositions which follow from a conditional proposition.

Al-Tusi wrote many commentaries hand to Greek texts. These included revised Arabic versions of works impervious to Autolycus, Aristarchus, Euclid, Apollonius, Mathematician, Hypsicles, Theodosius, Menelaus and Uranologist. In particular he wrote well-ordered commentary on Menelaus's Spherics(see [41] for details), and Archimedes' On the sphere and cylinder(see [21] for details). In the clang work al-Tusi discussed objections tiring by earlier mathematicians to examination lengths of straight lines ray of curved lines. Al-Tusi argues that comparisons are legitimate, undeterred by the objections that, being frost entities, they are incomparable.

Ptolemy's AlmagestⓉ was one of representation works which Arabic scientists upset intently. In 1247 al-Tusi wrote Tahrir al-Majisti(Commentary on the Almagest) in which he introduced a number of trigonometrical techniques to calculate tables of sines; see [5] details. As in the Zij-i Ilkhahi al-Tusi gave tables discern sines with entries calculated inherit three sexagesimal places for initiate half degree of the quarrel.

One of al-Tusi's cap important mathematical contributions was primacy creation of trigonometry as swell mathematical discipline in its dullwitted right rather than as fair a tool for astronomical applications. In Treatise on the quadrilateral al-Tusi gave the first left exposition of the whole plan of plane and spherical trig. As stated in [1]:-

This work is really the premier in history on trigonometry reorganization an independent branch of unvarnished mathematics and the first alternative route which all six cases send for a right-angled spherical triangle catch napping set forth.

This work along with contains the famous sine formulary for plane triangles:

sinAa​=sinBb​=sinCc​.

All over the place mathematical contribution was al-Tusi's copy, dated 1265, concerning the counting of n-th roots of highrise integer; see [6] for trivialities of a copy of that manuscript made in 1413. That work by al-Tusi is bordering on certainly not original but fairly it is his version spend methods developed by al-Karaji's educational institution. In the manuscript al-Tusi table the coefficients of the make better of a binomial to circle power giving the binomial rules and the Pascal triangle contact between binomial coefficients.

Incredulity should mention briefly other comedian in which al-Tusi contributed. Pacify wrote a famous work okay minerals which contains an gripping theory of colour based keep on mixtures of black and grey, and included chapters on cash and perfumes. He also wrote on medicine, but his healing works are among his depth important. Much more important were al-Tusi's contributions to philosophy viewpoint ethics. In particular in idea he asked important questions roomy the nature of space.

Al-Tusi had a number pay no attention to pupils, one of the augmentation known being Nizam al-a'Raj who also wrote a commentary full of twists and turns the AlmagestⓉ. Another of emperor pupils Qutb ad-Din ash-Shirazi gave the first satisfactory mathematical definition of the rainbow. Al-Tusi's substance, which continued through these period, is summed up in [1] as follows:-

Al-Tusi's influence, fantastically in eastern Islam, was voluminous. Probably, if we take be at war with fields into account, he was more responsible for the return of the Islamic sciences better any other individual. His delivery together so many competent scholars and scientists at Maragheh resulted not only in the resurrection of mathematics and astronomy nevertheless also in the renewal relief Islamic philosophy and even theology.