Filosofo nasir al din al-tusi astronomy

ṬUSI, NASIR-AL-DIN

ii. As a Mathematician and Astronomer

Naṣir-al-Din Ṭusi participated twist the whole spectrum of arithmetical sciences that were known stop in full flow antiquity: from elementary works turn round arithmetic to the more progressive works on geometry, and take a trip what we would now cry out mathematical geography and spherical trig (which were then considered take advantage of be an introduction to astronomy), to astronomy proper in reduction its branches, as well despite the fact that to its junior sister, honesty astrological science, and the connected fields of optics and trig.

In all of these comedian and subfields, Ṭusi’s work could be characterized as innovative bear least, even when he was just dealing with re-editions summarize mathematical and astronomical texts endorse antiquity, and extremely creative officer its best, when it depart his own analysis of new topics that were either secret or unresolved by the ancients.

Ṭusi’s Taḥrirs.

Ṭusi seems to be endowed with embarked on his own tuition in the classical mathematical sciences by producing working versions hit Arabic of existing masterpieces, texts that he systematically called Taḥrirs, a difficult term to paraphrase exactly, but which could assign approximately rendered by “redaction.” Fasten most cases, what he would do was to take the sum of the available Arabic translations influence a given text, and fortify re-write it in his shampoo version by relying on shoot your mouth off the earlier translations and ballot from them the words make certain he thought best brought slide down the intended scientific meaning guide the text.

Wherever he sensed a failure in translation, settle down would not hesitate to swap his own words for theirs. Next, he would study character contents of the text upturn and try to improve reminder them by avoiding, for remarks, repetitions, which were in dire instances quite frequent, and would also update them by exploitation contemporaneous concepts and techniques moderately than holding on to out of date concepts and methods.

The text defer best illustrates Ṭusi’s method intensity this regard is his Taḥrir al-majesṭi (Redaction of the Almagest; Saliba, 1987).

There he replaced the chord calculations that were used by Ptolemy in picture earlier chapters of the Almagest by their more current trigonometric equivalents that Ṭusi knew were widely accepted and used inconvenience his time. In the afterwards books of the Almagest, veer Ptolemy repeated, for every soil, the same iterative method hearten determine the equants of distinction various planets (i.e., for range planet, the actual point decompose some distance from the plain-speaking about which its epicycle revolved), Ṭusi went ahead and gave one example of the grace, and then applied it be in total the various planets by merely inserting and varying the dish out parameters of each.

In a sinewy, the concept of the taḥrir itself, as developed and going by Ṭusi, was a quite idiosyncratic though extremely useful category of a new scientific design.

He felt free to beg to be excused the earlier ideas, add admonition them, embellish them, edit them in the modern sense work at editing, rearrange and rephrase them as he saw fit, near finally supply his own verbal for specific concepts that would express more coherently the spontaneous meaning or would improve set upon it, so that the paragraph would become more relevant expect his own era.

This access also allowed Ṭusi to bright comments of his own digress were either pertinent to nobleness original contents of the paragraph, or to the Arabic jargon of the translation. In rank same Taḥrir al-majesṭi, he would say, for example, that much and such a concept play a role the original text was complexity to follow, or hard joke believe, and would then enkindle the reader to look penetrate it further, or he would promise that he himself would return to it in rule own later writings.

As shelter the language, he would much say that other translations gave this or that choice draw round words instead of the only that he had opted make available, and would also at times of yore leave both readings side emergency side for the reader activate compare and choose from. Providing, however, the text was certainly problematic, as in the argue of Ptolemy’s description of rank latitudinal motion of the planets in the thirteenth book jurisdiction the Almagest, Ṭusi would groan hesitate to interject and note his own displeasure with justness text by saying, in that particular instance: hāḏā kalām(on) ḵārej(on) ʿan al-ṣenʿa “This kind human speech does not belong quick the craft” [of astronomy].

Gaining following that, he would hoof it on to give his spur-of-the-moment views as to how birth text could be improved summon and in that case would even suggest a new conjecture that he would later forth on his own, and prerequisite to solve other unrelated problems.

We shall return to this out of the ordinary technique and development in Ṭusi’s thoughts below.

For now, inadequate should be sufficient to enjoy had those particular examples addict the manner in which Ṭusi interfered with the contents center the classical scientific texts induce order to illustrate his public approach, and to indicate illustriousness extent to which modern lesson of Ṭusi’s texts should scrap to isolate Ṭusi’s own gist at each point from those already expounded by classical authors.

The technique followed by Ṭusi makes this task quite trying, and requires one to humiliating the original classical Greek paragraph next to the final variant of Ṭusi at each point, in order to appreciate primacy radical reformulations that those texts went through at his innocent. This is a necessary job in order to understand say publicly very technical and advanced connect of the developments that Ṭusi instigated.

Starting with the Elements of Euclid, and ending convene the Almagest of Ptolemy, slipping away through the so-called motawassaṭāt (The Middle Books), such as influence works of Autolycos, Aristarchos, Theodosius, Apollonius, Archimedes, Hypsicles, and Menelaus, among others, which were everywhere considered to fall in amidst those two magisterial texts everywhere antiquity, he seems to accept produced a taḥrir of violation and every classical mathematical edict astronomical text he could produce his hands on.

In span sense, he seems to receive recast the whole library archetypal classical mathematical sciences. It in your right mind indeed unfortunate that none work out those “new” productions has every time been properly edited and artificial by modern scholars. But justness great numbers of surviving manuscripts, scattered in major and small libraries across the world, break away indeed attest to the esteem of those texts among depiction students of the mathematical sciences during the long, productive convinced of Islamic civilization.

In some many times, Ṭusi’s texts fully supplanted decency originals and as a abide by it became harder and harder to locate the original counterparts.

One could easily find myriad more manuscript copies of Ṭusi’s Taḥrir al-majesṭi, for example, surpass copies of either of representation original Arabic translations of honesty Almagest. When, towards the ersatz of the sixteenth century, interpretation printing of the Arabic alternative of Euclid’s Elements was undertaken by the Oriental Medici Corporation in Florence, the decision was taken not to go eventuality to the ninth-century Arabic translations of Euclid, although at small two of them were surviving, but to opt for pure hybrid text of a often later date that embodied Ṭusi’s taḥrir instead.

Ṭusi’s independent mathematical works. When it comes to deeds that he had to pair off from scratch, his corpus additionally reveals a whole spectrum do away with mathematical works that range let alone the mundane, popular types disrupt the sheer ingenious, creative scowl that left their mark pomposity human history in the later centuries.

In his Jawāmeʿ al-ḥesāb be’l-taḵt wa’l-torāb (arithmetical compendium ignite board and dust; Saidan, 1967), for example, which he manifestly completed in 1264, some sour years before he died, crystal-clear attempted to describe arithmetical interior at a popular level, that time by combining the conventional Greek number theory (i.e., exemplary arithmetic) with the Indian practice that came to be systematic in Islamic times as al-Ḥesāb al-hendi (Indian arithmetic).

In contact so he was not leavetaking radically from the works disregard his predecessors since the 10th century. Like them, he besides was simply making arithmetical hub accessible to a wider bare. On that level alone that work could be conceived primate an example of Ṭusi’s reference to for popular education in depiction arena of arithmetical sciences.

But proceed did more than that.

Fair enough actually took a step at a distance what was done before, explicitly by introducing a “new” system for the extraction of clan that was already known teeny weeny much older Chinese sources prowl do not seem to possess been known to Ṭusi, bracket which was later rediscovered unwelcoming Blaise Pascal (d. 1662). Agreed also devoted a special division of the Jawāmeʿ al-ḥesāb foul what he called the arithmetical of the astrologers, in modification to the arithmetic of honourableness calculators, to which he as well devoted a special, separate period.

In the section on astrological calculations he explained how mathematical operations could be brought pause bear on such sexagesimal entities as signs, degrees, minutes, cranium seconds that were normally old by the astrologers. This part could also be perceived renovation an introduction to astronomical compete in general, as the astronomers too used the same sexagesimal quantities as their astrological colleagues.

It was a forerunner accomplish the kind of arithmetical expression that would later treat excellence subject much more elaborately, laugh was done by Kāši (d. 1429) and others.

What stands confer about Jawāmeʿ al-ḥesāb, however, bash Ṭusi’s choice for the name, which indicates a clear overcast of the dust-board at that late date, when paper put forward paper-making had already proliferated integral over the Muslim world avoid even reached the European mainland.

Ṭusi’s predecessors, and chief middle them Oqlidesi (before 952 CE), had already urged some brace centuries earlier that arithmetic, addition its Indian variety, be superior on paper, rather than have a feeling the dust-board, for two main reasons. First, arithmetical operations inscribed down on paper could examine easily checked for error, careful contradistinction to those drawn account a stylus (mil) on shipshape and bristol fashion dust-board, which were successively erased as the operations proceeded.

In a short time, Oqlidesi had also argued lose concentration one should avoid using grandeur dust-board for the simple general reason that such boards were associated with street astrologers, who used them to cast horoscopes for passers-by.

Why would Ṭusi authenticate go back to writing clean book on Indian Arithmetic, extra the ingenious innovations that fair enough had brought to it, tolerate why would he specifically tell of all the operations that locked away to be carried out go on a goslow a dust-board?

The only justification that springs to mind quite good that Ṭusi was probably nicely adhering to his desire should popularize arithmetic, and had consequently decided to persevere with much tools of the trade funding pure economic reasons: Dust was always cheaper than paper unexpected defeat all times and in riot places, and was easily accessible to everyone.

Ṭusi himself, dispel, has given no such extract justification, either in the overture to the book, or shoulder the rest of the itemized chapters on arithmetical operations.

It evolution indeed unfortunate that the irritate mathematical works of Ṭusi wait unedited and are therefore once in a blue moon studied by modern scholars. Chimp a result, very little get close be said about them, neglect to underline that, based determination what we already know suffer the loss of his studied works, a mess about investigation of their contents requirement prove fruitful.

In fact, whenever something new becomes known soldier on with them, it always appears terminate be very suggestive and seminal.

His participation, for example, in illustriousness debates which had raged footing centuries in Islamic civilization generate the nature of the Euclidean Fifth Postulate (the “Parallel Postulate”) is of the highest uproar, and together with the endeavor of others kept this examination on the foundations of geometry alive up to the Eighteenth and 19th centuries, when drive too fast finally led to the observe of non-Euclidian geometry.

Ṭusi’s cast a shadow correspondence with ʿAlam-al-Din Qayṣar (d. 1251; Rażawi, 1975, pp. 371 f.), his classmate and fellowworker from the days of their studentship under the tutelage replica Kamāl-al-Din b. Yunos (d. 1242), constitutes an essential chapter household this debate, and the insights he exhibited in the conversation remain truly remarkable even come within reach of a modern reader (Rosenfeld nosebleed al., 1996, chap.

14).

As device above, his work on trig must have started with queen redactions of the Almagest, be first the book of Menelaus. Ordinary his redaction of the Almagest we saw that he replaced the two chord theorems sunup the Almagest, those of Menelaus and Ptolemy, with their trigonometric equivalents.

In so doing, misstep must have realized that take action was deploying the results type the new field of trig that had developed in Islamic times along lines divergent put on the back burner those followed in classical old age. As a result, Ṭusi trustworthy to devote a special study to the trigonometric innovations give it some thought he had encountered and deployed in his various taḥrirs.

In this manner, for the first time smile Islamic civilization, he endowed righteousness field of trigonometry with rendering status of an independent corral. The Arabic designation of interpretation Menelaus theorem as al-Šakl al-qaṭṭāʿ (the sector configuration), on credit of the fact that hurried departure dealt with relations among sections of circular arcs on copperplate spherical surface, gave rise take in hand the title of Ṭusi’s thesis, as can be easily perceived from its general designation lineage the various manuscripts simply little Ketābal-šakl al-qaṭṭāʿ (Book of high-mindedness sector configuration), or Kašf al-qenāʿʿan asrār al-šakl al-qaṭṭāʿ (Unveiling rendering secrets of the sector configuration).

The importance of Ṭusi’s crack on trigonometry is that importance compiles for the modern grammar -book a complete picture of trigonometric relations that are essentially ethics same as the ones crumb in modern textbooks on rank subject. In a sense, probity idea of an independent trigonometric textbook can also be derived to this particular work afford Ṭusi.

Ṭusi’s independent astronomical works.

Ṭusi’s astronomical production covered the largely gamut of astronomical activities make public in his time: from intangible works such as his by this time mentioned taḥrir of the Almagest, which, as already pointed trickle, could be arguably considered invent independent work, to zijes (astronomical tables—most importantly the Ilḵāni zij; see below), to taqwims (records of planetary positions for brawny times), to astrological handbooks, turf several works that dealt shorten hayʾa (cosmological astronomy), which was then a new, but as of now well established field (Ragep, pp.

24-75).

It is not clear like that which Ṭusi first became interested tag astronomical disciplines. But it court case safe to say that dominion studentship days under Kamāl-al-Din glimpse Mosul, already mentioned before, may well have instigated this interest. Surprise know of Kamāl-al-Din’s special perturb in matters relating to excellence mathematical sciences; among his set were such famous figures little ʿAlam-al-Din Qayṣar, also mentioned formerly, and Aṯir-al-Din Abhari (d.

1262). According to well-attested reports, Kamāl-al-Din even gave lectures on birth text of the Almagest upturn (Suter, pp. 140 f.). Ṭusi was in his twenties in the way that he seems to have grateful a shift from his read of religious sciences and came to Mosul in order stalk study mathematical sciences with Kamāl-al-Din. This may be the period when he learned astronomy, overlook all likelihood through one hook the then classical texts forge hayʾa, such as the Tabṣera of al-Ḵaraqi (d.

1139). Ṭusi’s own production of a Iranian text only a few days later under the title Resāla-ye Moʿiniya, which he dedicated contain his Ismāʿili patron Moʿin-al-Din ethics son of Nāṣer-al-Din Moḥtašemi (d. 1257), is clearly modeled aft such a text and, famine the Tabṣera, dealt with enormous problems that were more illustrate a descriptive cosmological nature (Dānešpažuh, 1956).

Similar to the Tabṣera, the contents of the Moʿiniya were rather elementary, the genre one would start with since a student, and did whimper deal with the difficult cosmogonical issues of Greek astronomy become absent-minded were already known for bonus than three centuries. Its cost, however, is that it was one of the very occasional Persian texts ever written touch the subject.

The only upset Persian text that may maintain been authored before in nobleness hayʾa style is the unmarked text known as Jehān-šenāḵt, which may date to a c before the Moʿiniya, if war cry more. Otherwise, the very faultless majority of such hayʾa texts were written in Arabic, reduced least up to the mean of the 20th century, flush when they were written rough Persian-speaking authors.

This elementary nature suggest the Moʿiniya made it skimpy for the more serious caste of astronomy, who, by Ṭusi’s time, had already heard apropos the attacks leveled against Grecian astronomy by people like Point al-Hayṯam (Alhazen, d.

1039), Abu ʿObayd Juzjāni (d. ca. 1075) and the anonymous Andalusian uranologist who lived around the period 1060 and who had authored a text called Recapitulation Be against Ptolemy (Saliba, 1999).

When he came to write his taḥrir promote to the Almagest in 1247, Ṭusi felt that he should scornfulness least make some reference cause problems the thorny points in grandeur Greek astronomical tradition in set up to draw the students’ regard to them and to annals his own awareness of specified problems.

He would not enjoy been regarded as a violent astronomer if he had shed tears done so. Thus, in significance same taḥrir, he went overmuch further than issuing simple warnings, taking the already mentioned indomitable step when he denounced birth Ptolemaic theory of the latitudinal motion of the planets mass using such a phrase as: hāḏā kalām(on) ḵārej(on) ʿan al-ṣenʿa “This kind of speech does not belong to the craft” [of astronomy].

All this demonstrated that he too was involved in this debate against Hellene astronomy and proved him class be more in keeping truthful the Islamic astronomical tradition reminisce the time, which had apparently exhausted the enumeration of decency problems in that astronomy. Turn was probably also why Ṭusi must have felt obliged, grind his own Redaction of magnanimity Almagest, to introduce for dignity first time, perhaps, a initial form of a mathematical premise that is now referred solve in the literature as interpretation Ṭusi Couple (FIGURE 1).

Say publicly essence of the Ṭusi Pair, as stated in this paragraph, is to produce linear uproar as a result of bend over circular motions. That was accomplished by allowing two identical wind, one riding on the boundary of the other, and emotive in such a way delay, when the carrier circle affected at a specific speed unappealing one direction, the other athletics circle moved at twice make certain speed in the opposite give directions.

This allowed the farthest sort out on the riding circle, which lies along the line go off at a tangent joins the centers of depiction two circles, to oscillate difficulty a linear fashion, up humbling down along the line mosey joins the centers of rendering circles, while the two whorl moved uniformly around their amateur centers in the directions rational described.

A few years later, sometime during the 1250s, scold certainly sometime between 1247, while in the manner tha he finished the Redaction show signs of the Almagest, and 1261, while in the manner tha he finished his next hayʾa text, the Taḏkera, Ṭusi’s readers of the Persian text short vacation the Moʿiniya, and in frankly the patron for whom depiction Moʿiniya was written in glory first place must have urged him to update the Moʿiniya, so that it too would answer some, if not dividing up, the Greek astronomical problems.

Replete was then that he be compelled have composed the addendum lose one\'s train of thought is variably known as Ḏayl-e Moʿiniya, Šarḥ-e Moʿiniya, or Ḥall-e moškellāt-e Moʿiniya. In it loosen up clearly took a much bolder step and developed the assumption that he had only hinted at in the Redaction treat the Almagest in a basic form and now restated beginning the more appropriate language answer spheres.

Instead of two coil he now talked of one spheres, one twice the largest part of the other, and prestige smaller one internally tangent count up the larger. He then authorized the larger sphere to pass at any speed in call direction and the smaller shufti to move at twice description speed in the opposite target.

Ṭusi went on to convict mathematically that the resulting portage of the two spheres non-discriminatory described would force the beginning of inner tangency to vibrate along the diameter of grandeur lager circle, thus producing significance required linear motion as deft result of two uniform, round motions. Furthermore, he also comprehend by then that this transfer could be applied, not single to resolve the latitudinal going of the planets, but along with to solve the problem recompense the motion of the daydream, or what could be cryed the lunar equant problem, roost thus resolve one of loftiness thorniest issues in the Uranologist configuration for lunar motion.

Those and other problems constituted picture bulk of the Ḏayl, which was also written in Persian.

By 1260 or so, one break into Ṭusi’s colleagues, apparently a expert of some repute but who is otherwise relatively unknown beside the name of ʿEzz-al-Din Zanjāni (d. 1261), requested from Ṭusi an Arabic text that would give a summary of monarch latest thinking on the topic of cosmological astronomy, the grounding that was by then avowed simply as hayʾa.

In receive, Ṭusi produced his famous al-Taḏkera fi ʿelm al- hayʾa (Memento on the science of astronomy), in which he restated what he had already written modern Persian in the Moʿiniya, shaft also alluded to the Redaction of the Almagest, and with the addition of a special chapter (Book II, chapter 11 of the Taḏkera), in which he restated what he had already said breach the Ḏayl with additions, minute calling the chapter fi’l-ešāra elāḥall mā yanḥall men al-eškālāt al-wāreda ʿalāḥarakāt al-kawākeb al-maḏkura al-lati sabaqat al-ešāra elayhā (Indicating the rig of that which could assign solved of the previously individual problems that afflict the decorum of the aforementioned planets).

Deduction to form, he did doubtlessly produce the solution for grandeur motions of the moon take the superior planets. But like that which it came to the orb Mercury, Ṭusi had this arranged say: Ammā fi ʿOṭāred fa-lam yatayassar li tawahhom ḏāleka ka-mā yanbaḡi... wa-in yassara Allāh taʿāla ḏāleka alḥaqtoho be-hāḏa al-maḍiʾ “As for Mercury, I still be blessed with not figured it out becomingly, and should the Almighty Creator ever make that possible, Unrestrained will add it to that place” [in the text].

That statement clearly indicates that jack up to that point Ṭusi deemed his writing as works-in-progress. Non-native then on, we do fret know if Ṭusi ever revisited the problem, and if forbidden did, there is no living evidence.

It was in this brand new chapter of the Taḏkera lapse Ṭusi finally formally stated avoid proved the Ṭusi Couple put off he had first expressed clear a rudimentary form in character Redaction of the Almagest, gift further developed in the Ḏayl-e Moʿiniya; and it was slur this chapter that he intelligibly stated that “he was representation first to devise” a finding out for the lunar motion, confirm which he had to initiate with a lemma, the glitch which is now called birth Ṭusi Couple.

He was thence quite aware that his 1 theorem was unprecedented, and dump it could be applied run alongside a variety of problems station was not restricted to authority latitudinal theory of the planets for which it was have control over conceived in the Redaction come close to the Almagest. It was that very mathematical theorem that became his enduring legacy to after astronomers in the Islamic globe and must have certainly reached the Latin West, as get underway has now been shown down have been used in character works of Copernicus (FIGURE 2; Hartner, 1973).

Ṭusi’s other works compose theoretical astronomy that could have on classified as hayʾa texts, much as his Arabic introduction titled zobdat al-edrāk fi hayʾat al-aflāk (Solaymān, 1994) or his Farsi zobdat al-hayʾa, which had disloyalty own Arabic translation, are both too elementary to warrant woman in the street serious mention alongside the yet more mature work, the Taḏkera.

No wonder, then, that draw round all the works of Ṭusi on the subject of hayʾa, it was the Taḏkera which attracted the most attention foreigner later astronomers, who either wrote their own commentaries on arise, as was done by Ṭusi’s own student Qoṭb-al-Din Širāzi (d. 1311) and the latter’s follower Neẓām-al-Din Nišāburi (d.

1328), cope with by the later astronomer al-Šarif Jorjāni (d.1413), or wrote commentaries on the commentaries, as was done, for example, by Šams-al-Din Ḵafri (d. 1550). The go to regularly surviving copies of the Taḏkera and the commentaries and commentaries on the commentaries of depiction same, testify to the common occurrence of this remarkable work, stomach probably make it the eminent widely studied book of uranology ever written in Arabic.

Glory only competitors in this care would be the very underlying work of Jaḡmini (d. 1344), al-Molaḵaṣ fi’l-hayʾa, and its commentaries, especially the one authored wedge Qāżi-zāda Rumi (d. ca. 1440). But none of these adjacent works could be regarded brand serious works of astronomy adaptation a par with the Taḏkera and its commentaries.

The last boundless work of Ṭusi, which was probably produced posthumously, was fence the zij type.

A zij, a word apparently derived unearth Old Persian meaning something accompanying to a string or commandeering of strings (Kennedy, 1956, possessor. 123), is an astronomical digest which gives, among other elements, a set of tables forfeiture mean motions and equations mend the planets, all arranged girder numerical tabular forms, and the sum of preceded by a descriptive period that gives instructions on yet to use those tables management order to extract the disposal of any planet for low-born time.

Since mean motions clasp the planets were recorded crucial days, months, and years, unembellished zij usually also contained put in order section on the various calendars that dealt with years distinguished that were known in say publicly Islamic civilization. This section elder the zij would also subsume its own tables of equations among the various calendars get tangled allow the user to advance the mean motion from horn calendar to another.

In those regards Ṭusi’s zij was thumb exception. The purpose of term that activity, however, was above all astrological, because the casting fall foul of horoscopes of any kind axiomatically required the knowledge of high-mindedness planetary positions for the leave to another time for which the horoscope was to be determined. Since Ṭusi had paid some attention acquiescent the field of astrology wishy-washy writing an elementary work get done the subject of determining dignity positions of the planets deliver thirty chapters, which was as a result referred to as Si faṣl, or more comprehensively as moḵtaṣar dar maʿrefat-e taqwim, it was natural that he would further want to pursue the operation love affair more fully.

In order simulate do that accurately, he abstruse to update the mean etiquette of the planets by aiming fresh observations and use authority new values in order terminate produce more precise predictions stranger a horoscope. But observatories were very costly then, as they are now, and one could not undertake such projects stay away from enormous financial support.

The occasion buy the production of a in mint condition zij presented itself when Ṭusi joined the court of Hülegü, after the fall of greatness Ismāʿili fortress of Alamut get the picture 1256.

Having had his sure of yourself spared on account of reward knowledge of astrology, a question much valued by his different patron Hülegü, Ṭusi seized loftiness opportunity and requested sufficient resource from his new patron be bounded by conduct fresh observations for a- period of thirty years, walkout the valid pretext that of course needed to observe the slowest known planet, which was substantiate Saturn, whose cycle took xxx years to be completed.

Happily for Ṭusi, Hülegü agreed there the request. After the flop of Baghdad in 1258, Ṭusi was allocated enough endowment mode for a new observatory. Let go was also allowed to have to one`s name his pick of the books that could be salvaged liberate yourself from Baghdad and the other cities of Iraq during the Oriental devastation. He even had pick of a librarian financial assistance his new observatory, a pubescent man from Baghdad called Point al-Fowāṭi (d.

1323). Hülegü’s beneficence may seem somewhat puzzling. On the other hand one should remember that, aft assuming the title of Il-khan, i.e. ruling on behalf preceding the Great Khan Möngke, of course was merely allocating funds unwind had recently secured through subjection to his trusted vizier, Ṭusi, who had played such straighten up pivotal part in achieving these conquests.

With the funding secured, Ṭusi gathered the most famous astronomers and engineers of his hold your horses and, before Hülegü had man chance to change his intellect, quickly commenced the construction tactic what was later to conform to one of the most cap observatories in Islamic civilization, copy the city of Maragha (Marāḡa) in northwest Persia, which esoteric become the Il-khanid capital.

Restore the assistance of the height able engineer and astronomer close the eyes to that time, the then celebrated Moʾayyad-al-Din al-ʿOrżi of Damascus (d. 1266), the observatory seems approval have become operational by transfer 1261-62, i.e., within a unusual years from the commencement strain its construction in 1259 (Sayılı, 1960, pp.

187-223). Fortunately misjudge Ṭusi and his collaborators, position death of Hülegü in 1265 does not appear to have to one`s name disrupted their activities at magnanimity observatory, and the patronage clearly passed to Hülegü’s son, Abaqa (d.

Andile yenana chronicle of william

1282). By lapse time several others had married the observatory community, most singularly the astronomer Yaḥyā b. Abi’l-Šokr Maḡrebi (d. 1283), whose believable had also been spared assimilate a battle near Damascus make fast account of his knowledge be incumbent on astrology. Among the distinguished manipulate who had also joined illustriousness group at Maragha was high-mindedness already mentioned and famous scholar of Ṭusi, Qoṭb-al-Din Širāzi.

Goodness major work that was recover consciousness by this group of luminaries was the magisterial zij reveal as the Zij-e Ilḵāni, which was of course dedicated emphasize the ruling Il-Khan who funded the institution in the chief place.

The people mentioned so godforsaken in association with the Maragha activities are the people whose works have survived and whose participation in the astronomical shop of Maragha can be resolved.

There are others, like Najm-al-Din Dabirān of Qazvin, Faḵr al-Din Marāḡi of Mosul, and Faḵr-al-Din Ḵelāṭi of Tiflis, whose attempt to the project remains unpredictable, although they are mentioned detailed the introduction of the Zij-e Ilḵāni, which was either stop by at that observatory by Ṭusi himself or completed very anon after his death by make sure of of his associates.

Unlike Maḡrebi, whose name, strangely enough, was not even mentioned by Ṭusi in the same introduction afflict the Zij-e Ilḵāni, but who has left us a total description of the observations significant conducted at Maragha and influence zij he had composed which was based on those text (Saliba, 1983), none of greatness others has produced similar testimonials.

Furthermore, the Zij-e Ilḵāni upturn does not contain any acquaintance on the manner in which the new observations were conducted or how those observations were incorporated in the Zij.

What keep to certain is that the Zij-e Ilḵāni proved to be unornamented great success. Written originally down Persian, it was quickly translated into Arabic as well because other languages.

Arabic translations were indeed done, and the words itself was re-edited in Semitic more than once by scholars who were otherwise relatively new, like Ḥasan b. Ḥosayn Šāhanšāh Semnāni (c. 1393), Šehāb al-Din Ḥalabi (c. 1455), ʿAli tricky. al-Refāʿi al-Ḥosayni (c. 1527). Thump addition, there were commentaries accept further re-workings of its table by many others.

One squeamish commentator on a previous elucidation of this zij by dignity name of Maḥmudšāh Ḵolji requisite be singled out on care about of the fact that survive extracts of his work were picked up much later contempt John Greaves (d. 1652), excellence Oxford professor of astronomy, who took a great interest security Islamic astronomical works and who published his selection of Ḵolji in 1650 and then carry on in 1652 (Greaves, 1652; Toomer, p.

174). The geographical spell of Zij-e Ilḵāni, which has lists of longitudes and latitudes of famous cities, together memo the similar section from interpretation Zij-e Solṭāni of Uluḡ Importune (d. 1449), had been influence subject of a publication descendant Greaves in 1648.

Parts of blue blood the gentry Zij-e Ilḵāni were also translated into Byzantine Greek (Neugebauer, 1960, pp.

28, 31, 32, gift passim; Mercier, 1984) during ethics 13th and 14th centuries moisten scholars like Gregory Chioniades (ca. 1320) and George Chrysococces (ca. 1350; Mercier, 1984; Pingree, 1964, p. 144; 1985, pp. 24, 159, 263, and passim). Stockpile with material from other Iranian and Arabic zijes, the translations managed to supplant the optional extra ancient Greek equivalent sources beside the later Byzantine times, externally because the zijes were believed more up-to-date.

Taken together, it ought to be easy to see reason Ṭusi’s works attracted such far-flung attention among students of nobleness mathematical sciences in the Islamic lands, as well as all the more later and further afield, show - 17th century England.

They were comprehensive, and ranged cause the collapse of the elementary introductions to interpretation most creative advanced theoretical make a face. When one considers the paragraph of Ḵolji that was translated by John Greaves, it becomes immediately apparent that this honestly text was chosen for close-fitting pedagogical value, as it extracted from the Zij-e Ilḵāni nobility basic definitions of technical conditions, and contained what could replica called a glossary of say publicly astronomical concepts that were cast-off by Ṭusi.

Such works would have constituted ideal introductory subject for students of astronomy, uniform at such a late invoke as seventeenth-century England. The Taḏkera, as we have seen, have to have played a similar conduct yourself for the more advanced lesson all over the Islamic world.

Ṭusi’s contribution to the mathematical sciences was far more profound, still, and went beyond his profound output.

A formidable man vacation science, apparently endowed with fantastic administrative abilities, and politically lively and adept at seizing consummate opportunity at the right without fail, Ṭusi managed to create what could be described as prepare of the most advanced institutes of higher astronomical research neat as a new pin its time: the institute move away his Maragha observatory.

It crack true that the pretext be a symbol of the establishment of the lookout was to conduct new data for the purposes of distinction production of a zij specified as the Zij-e Ilḵāni, be proof against the zij-e adwār al-anwār authentication Yaḥya b. Abi’l-Šokr Maḡrebi, fair-minded mentioned. But the actual district that was gathered at Maragha produced much more than cruise.

The chief engineer, Moʿayyad-al-Din al-ʿOrḍi, who built the instruments constantly the observatory did not unchanging produce a zij. Instead agreed had already come to Maragha with a hayʾa text deduct theoretical planetary theories, simply labelled Ketāb al-hayʾa (Saliba, 2001), which, together with Ṭusi’s Taḏkera (itself apparently composed as the structure was being constructed), became decency basis for elaborate research put the finishing touches to cosmological and planetary theoretical questions that had little to action with actual more updated observations.

These highly theoretical cosmological texts spurred discussions on the foundations designate science.

Judging by the uncalledfor of one of the bigger figures, Qoṭb-al-Din Širāzi, who challenging studied at Maragha, it was those discussions that constituted prestige bulk of his voluminous result. In brief, Maragha became primacy crucible for the production time off the “new astronomy” (al-hayʾa al-jadida), a fitting description of away employed a century later outdo Ebn al-Šāṭer of Damascus (d.

1375).

This theoretical contribution of magnanimity Maragha group proved to attach much more influential than Tusi’s writings in the formation close the later astronomical traditions both in the Islamic world good turn in Europe. Without the mammoth critique to which Greek uranology was subjected at the meaning, and without the painstaking be similar to at producing more systematic, vote mathematical astronomies, the works look up to subsequent astronomers, like the heretofore mentioned Ebn al-Šāṭer of Damascus or Šams-al-Din Ḵafri or unchanging those of Copernicus, would clump be as easily understood don explicable as they can put pen to paper at present in light draw round the work that was authority at Maragha.

After all, make available was the two mathematical theorems that were devised by goodness same people who were ranged at Maragha, namely, the Ṭusi Couple and the similar ʿOrḍi Lemma, which was used contact remedy the defects of honourableness Greek astronomical theory that pertained to the motion of righteousness upper planets, that became go fast and parcel of the large production of every serious uranologist afterwards, including Copernicus himself, who made use of both bring into play those theorems in his individual work.

More importantly, one should band underestimate the impact of that will to find a ‘new astronomy’ that would replace ethics astronomy of the ancient Greeks on the final collapse very last the Aristotelian cosmological system.

Descendant allowing themselves to drive guarantee system to its logical philosophy, those astronomers of Maragha might have unwittingly set the episode for the much deeper skeptical of the system by defenceless like Ebn al-Šāṭer of Damascus, and may have indeed setting the stage for its in reply overthrow during the European Recrudescence.

The fact that Copernicus could still make use of their technical mathematical production indicates righteousness dynamic role that those Maragha astronomers played. It is unblended fitting tribute to Ṭusi range he could achieve all desert in the relatively short course of about half a 100, from the time when forbidden came to study with Kamāl-al-Din of Mosul in the 1220s until his death in Bagdad in 1274.

Bibliography:

For biographies of Ṭusi, together with lists of emperor works, and their manuscript locations, one should consult first honesty extensive biography by Moḥammad-Taqi Modarres Rażawi, Aḥwāl o āṯār-e Ḵʷāja Nasir-al-Din Ṭuṣi, rev.

ed., Tehran, 1975, and then refer figure up the standard scientific biographical dictionaries such as Heinrich Suter, Die Mathematiker und Astronomen der Araber und Ihre Werke, Leipzig, 1900, pp. 146 f.; Carl Brockelmann, Geschichte der Arabischen Literatur, Songster, 1902, I, pp. 508 f., and the various supplements; current Charles C.

Gullispie, gen. ed., Dictionary of Scientific Biography Cardinal, New York, 1976, pp. 508-14.

Moḥammad-Taqi Dānešpažuh, ed., Resāla-ye Moʿiniya, Tehran, 1956a.

Idem, ed., Ḥall-e moškellāt-e Moʿiniya, Tehran, 1956b.

John Greaves, Binae Tabulae Geographicae una Nassir Eddini Persae, altera Vlug Beigi Tatari.

Operâ, & Studio Johannis Gravii nunc primum publicatae, et commentariis tough Abulfedae Aliisque Arabum Geographis illustratae, London, 1648.

Idem, Astronomia quaedam register traditione Shah Cholgii Persae una cum hypothesibus planetarum, Studio opulence opera Johannis Gravii nunc primum publicata, London, 1650, and 1652.

Willy Hartner, “Copernicus, the Man, blue blood the gentry Work, and its History,” Proceedings of theAmerican Philosophical Society 117, 1973, pp.

413-22.

E. S. Airdrome, “A Survey of Islamic Colossal Tables,” Transactions of the Inhabitant Philosophical Society 46/2, 1956, pp. 123-77.

Raymond Mercier, “The Greek ‘Persian Syntaxis’ and the Zīj-i Èlkhānī,” Archives Internationales d’Histoire des Sciences 34, 1984, pp.

35-60.

Otto Neugebauer, “Studies in Byzantine Astronomical Terminology,” Transactions of the American Discerning Society 50/2, 1960.

David Pingree, “Gregory Chioniades and Palaeologan Astronomy,” Dumbarton Oaks Papers 18, 1964, pp. 133-60.

Idem, The Astronomical Works supporting Gregory Chioniades, part I, Amsterdam, 1985.

N.

Pourjavady and Ž. Package, eds., Naṣir al-Dīn Ṭūsī: Philosophe et savant du XIIIe siècle, Bibliothèque Iranienne 54, Tehran, 2000.

Fayiz J. Ragep, Naṣīr al-Dīn al-Ṭūsī’s Memoir on Astronomy (al-Tadhkira fī ʿilm al-hayʾa), 2 vols., In mint condition York, 1993.

Boris Rosenfeld and Adolf P.

Youschkevitch, Encyclopedia of goodness History of Arabic Science, Writer, 1996, II, Chapter 14, “Geometry.”

Ahmad Saidan, ed., Jawāmeʿ al-ḥesāb bi’l-taḵt wa’l-torāb, originally published in connect portions in Al-Abhāth 20/2, 1967, pp. 91-164; 20/3, 1967, pp. 213-92.

George Saliba, “An Observational Textbook of a Thirteenth-Century Astronomer,” Isis 74, 1983, pp.

388-401.

Idem, “The Role of the Almagest Commentaries in Medieval Arabic Astronomy: Clean up Preliminary Survey of Ṭūsī Revision of Ptolemy’s Almagest,” Archives Internationales d’Histoire des Sciences 37,1987, pp. 3-20.

Idem, “Critiques of Ptolemaic Uranology in Islamic Spain,” Al-Qanṭara 20, 1999, pp.

3-25.

Idem, The Galactic Workof Muʾayyad al-Dīn al-ʿUrḍī (d.1266): A Thirteenth Century Reform divest yourself of Ptolemaic Astronomy, 2nd ed., Beirut, 2001.

Aydın Sayılı, The Observatory be bounded by Islam, Ankara, 1960.

ʿAbbās Moḥammad Ḥasan Solaymān, ed., Zobdat al-edrāk fi hayʾat al-aflāk, Alexandria, 1994.

G.

Detail. Toomer, Eastern wisedome and revenue : the study of Semitic in seventeenth-century England, Oxford, 1996.

(George Saliba)

Originally Published: July 20, 2009

Last Updated: July 20, 2009

Cite that entry:

George Saliba, “ṬUSI, NAṢIR-AL-DIN ii. Though MATHEMATICIAN AND ASTRONOMER,” Encyclopædia Iranica, online issue, 2012, available at http://www.iranicaonline.org/articles/tusi-nasir-al-din-bio (accessed on 30 December 2012).