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Ghazan Khan's astronomical innovations at Maragha observatory.


Everything we know about the observatory in Tabriz founded by Ghazan Khan (r. 12711304), the seventh ruler of the Ilkhanid dynasty of Persia (1295-1304), was published by Aydin Sayili some fifty years ago). (1) Relying on primary historical sources, he presented an adequate description of its astronomical activities and of the many skills of Ghazan Khan in the field of observational instrumentation. (2) Sayi1i also presented a good overview of the Maragha observatory from 1260-1283, (3) but due to a lack of reliable evidence for the period after ca. 1280, he made some statements--especially concerning Ghazan Khan's astronomical innovations--that could not be substantiated. A recently discovered treatise has now revealed the exact type and location of Ghazan Khan's innovations, which we enumerate below. Our treatise begins where Sayili left off and appears to give dependable information that we can use to illuminate the later period at the Maragha observatory, during which very little is known concerning the type and extent of astronomical activity.

We begin by introducing Rashid al-Din Tabib's claim as to Ghazan Khan's astronomical activities and innovations. We then examine the validity of the claim with the help of the newly discovered treatise, as well as verify the reliability of the information in the treatise as to the type, structure, and location of Ghazan Khan's newly made instruments. For this purpose, it was necessary to examine Ghazan Khan's innovations both in the context of the Maragha astronomical tradition (as the dominant tradition of the time) and in the context of medieval observational instrumentation in general. We follow with a general classification of the instruments and argue their possible relation to later Western models; and we conclude by describing the instruments in the order in which they appear in the treatise.


According to his vizier, Rashid al-Din Tabib (d. 718/1318), Ghazan Khan was a prominent artisan, an alchemist, an expert in medicine and botany (he invented a new antitoxin called tiryaq-i ghazani), and a mineralogist, as well as being interested in theology. (4) In his youth he was taught by Mongol Buddhist monks, but he later converted to Islam. (5) Upon his victory over the Mamluk army at the battle of Wadi 1-Khaznadar, Ghazan arrived in Maragha, the site of the renowned observatory built in the thirteenth century under the direction of Nasir al-Din al-Tusi, where he resided from 15 Ramadan until 24 Shawwal 699 (June 4--July 13, 1300). (6) After he arrived,
  On the next day, he went to watch the observations; he looked at all
  the operations (a'mal) and instruments, studied them, and asked about
  their procedures, which he understood in spite of their difficulty.
  He ordered the construction of an observatory next to his tomb in
  Abwab al-Birr tin the district] of al-Sham in Tabriz (7) for several
  operations. He clearly explained how to do those operations so that
  local wise men marveled at his intelligence, because such work
  ('amal) had not been done in any era. Those wise men said that
  constructing it [the observatory] would be extremely difficult. He
  guided them, whereupon they commenced building it and they finished
  it per his instructions. Those wise men and all the engineers agreed
  that nobody had done such a thing before nor had imagined doing it.

  On several occasions he went to Maragha, asked for an explanation of
  the instruments there, examined their configuration (kayfiyya)
  carefully, and studied them. He had a general idea of them. As per
  his nature (tab'), everything having to do with the siting and the
  building of the [Maraghal observatory he commanded to construct. (9)

Rashid al-Din Tabib also reported that he ordered the construction of a hemispherical instrument (gunbad) for solar observations at Tabriz observatory and described it in technical detail for his astronomers. (10)

The Maragha observatory

The Maragha observatory was built in 1259 by Hulegu (d. 1265), the founder of the Ilkhanid dynasty; for the circa fifty-eight years it functioned, it represented the acme of Islamic astronomy. We have divided the astronomical activities in Maragha into two distinct periods: the first from its beginnings to 1283, the second from ca. 682/1283 to 716/1317. (11) Even before the construction of the observatory it appears that observations had been undertaken in Maragha: in his treatise on the astrolabe (Fi kayfiyyat al-tastih al-basit al-kuri), Ibn al-Salah al-Hamadhani (d. 1153) wrote that in MarAgha he found the magnitude of 23;35[degrees] for the obliquity of the ecliptic (mayl al-kulli); (12) there also appeared three important zijes (astronomical handbooks or tables) that later had bearing on work undertaken during the second period: al-Khazini's Zij al-sanjari (510/1116), (13) al-Fahhad's Zij of ca. 1166, (14) and Zij al-shahi of Husam al-Din al-Salar, who was killed by order of Hulegu on 8 Muharram 661/November 22, 1262. (15) The first two were translated into Greek while the third was mentioned in these translated texts. (16)

During the first period of the observatory, two prominent zijes were written: al-Tusi's Zij-i ilkhani in Persian and Muhyi 1-Din al-Maghribi's Adwar al-anwar in Arabic (completed in 1275). (17) Both were reliably quoted in the second period, by works either connected to the observatory, such as al-Wabkanawi's Zij-i muhaqqaq-i sultani (18) and Greek translations made by Gregory Chioniades, (19) or independent of it, such as al-Kamali's Zij-i ashrafi, completed by the end of the Persian year 681 (i.e., March 12, 1303) in Shiraz. (20) The instrument-maker in the first period was Mu'ayyad al-Din al-'Urdi (d. 1266) (see below).

In the second period there were at least five outstanding scientists in the field of mathematical science connected with Ghazal Khan's court:(21)

1. Qutb al-Din al-Shirazi, who apparently spent his time in a solitary manner between 1283 and 1311 in Tabriz. He revised his Zij-i ridwani in 690/1291-2. (22)

2. Shams al-Din Muhammad al-Wabkanawi al-Bukhari, the author of Zij-i muhaqqaq-i sultani. (23) In this work we are confronted with one of the most preeminent Islamic zijes produced from direct observations. He sharply criticized al-Tusi's Zij-i ilkhani for the reason that the calculated positions of the seven planets were never in agreement with actual observations, and because it was only a copy of earlier zijes, especially in the fundamental planetary parameters. He referred to Muhyi 1-Din al-Maghribi's Adwar as being "based on the new Ilkhanid observations" (i.e., Muhyi 1-Din's own observations) for the sake of making a distinction between it and Zij-i ilkhani, which was assumed to be obtained through the "Ilkhanid observations" (i.e., the observational plans supervised by al-Tusi and performed by his colleagues). (24)

Al-Wabkanawi introduced some new topics such as a rule for conjunctions between Jupiter and Saturn, the report of their triple conjunction in 1305-6 and their single one of January 1286, and the exact report of the annular eclipse of January 30, 1283 in detailed numerical values. (25) The period of his observations, as he himself says, extended over forty years. (26)

3. Shams al-Din Muhammad b. Mubarakshah Mirak al-Bukhari al-Hirawi (d. 1340).

4. Nizam al-Din al-Nisaburi, who is wrongly known as the author of Zij al-'ala'i, actually written by al-Fahhad.

5. Shams al-'Ubaydi, a mathematician. (27)

Also during this period Gregory Chioniades (d. ca. 1320) was in Tabriz where he translated al-Khazini's Zij al-sanjari, al-Fahhad's Zij al-'ala'i, and a text on 'dm al-hay'a (28) into Greek. (29) According to Chioniades, he used the oral instructions of a person named [SIGMA][alpha][mu][psi][PI]ov[chi]a[rho][eta][zeta] born at Bukhara on June 11, 1254, (30) who is most likely Shams al-Din Muhammad al-Wabkanawl. al-Bukhari. (31) In his As'ila wa-ajwiba ("Questions and Answers"), Rashid Tabib answered the theological questions of a "Frankish sage" (hakim-i farang), (32) who is probably the same Chioniades. (33)


The anonymous Persian treatise studied in this article is entitled Risalat al-ghazaniyya fi l-alat al-rasadiyya ("Ghazan's Treatise on Observational Instruments") and provides entirely new information about Ghazan's approach to observational instruments and his innovations in this field. We find a full description of twelve instruments allegedly invented by him, which were employed at the observatory at Maragha instead of at his "new" observatory in Tabriz (our author clearly says this, and he also has included tables of oblique ascensions for the latitude of Maragha).

Three copies of this treatise are preserved in libraries in Tehran (34) --in Sipahsalar Library (no. 555D, fols. 15v-49v, henceforth S), in the library of the Parliament (no. 791, pp. 29-97; henceforth P), and--an incomplete one--in Malik National Library (no. 3536, pp. 41-56; henceforth M). (35) The manuscript collections of which S and P are a part are similar in many aspects; they appear to have been copied by a single scribe, with the title ra'is al-kuttab, on Thursday, 23 Jumada 11 1294 (July 5, 1877). (36)

After praising God and introductory words on the necessity of astronomical instrumentation, the treatise begins with the description of the five instruments mentioned in Ptolemy's Almagest: halqa nuhasiyya (two meridian rings, I, 12); lubna (quadrant, I, 12); another halqa nuhasiyya (equinoctial ring, III, 1); dhat al-halaq (armillary sphere, V. 1); and dhat al-shu'batayn (parallactic instrument, V. 12).

The description of no. 3 makes clear that it has been wrongly given the name of no. 1 in the list (in all ms copies); it should be correctly named halqat Although both instruments were mostly made of copper (nuhas), only the instrument known as "two meridian rings" was customarily called halqa nuhasiyya. (37)

The author of the treatise reviews the classical instruments and rejects the adequacy of each. In the case of the equinoctial ring, he repeats (S: fol. 17r--v, M: p. 44) the same difficulty that Ptolemy mentioned in the Alma gest (III, 1), namely, that the very weight of the ring causes it to veer from its true position of angle 90-[empty set]) in respect to the horizon. (38)

In the case of the armillary sphere, used for measuring the longitude of any star, he notes that we must first have the coordinate of a reference star. In the Alma gest (V, 1), Ptolemy described a method by which one considers the position of the sun determined beforehand (from the tables based on the solar theory) as the primary reference, and goes on to measure the unknown coordinate of a given star with the moon's position as an intermediate reference. (39) Thus, says our author, the measurements will be approximate, not certain, or not completely derived from observation. The sun's true position can be obtained by the armillary sphere, but Ptolemy made no mention of this. To do this, the instrument should be set in its correct position (regarding the geographical latitude, the zenith [vertical orientation], and placement of the instrument in the meridian plane). The ecliptic ring of the instrument should be placed in such a position that its upper, sunward limb obscures its lower limb so that the ecliptic ring's inner surface will be in shadow. In this case, the instrumental ecliptic will be in the plane of the true ecliptic. Now the sun's position can be obtained by placing the outer latitudinal ring in line with the sun.

This method has some practical difficulties--as is evident, in this method only an object on the ecliptic can be used as the primary reference. But only the sun is both on the ecliptic and so luminous that it can place the inner surface of the instrumental ecliptic in shadow, thus determining whether or not the ecliptic ring is exactly in its true position. (Accordingly, if we do not use the sun, we need a source giving us the beforehand determined position of such an object.) That the reference star must be an object on the ecliptic (which should be the sun) causes some limitations in utilizing the instrument. This is where the treatise's author criticizes the instrument (S: fol. 18r--v, M: p. 45). In his judgment, that procedure will make the measurements approximate (bi taqrib), not certain (br talmiq). (40)

With regard to the parallactic instrument, the author states:
  With this instrument, the ultimate altitudes of the stars on the
  Meridian circle that are not in excess of 30[degrees] will [only] be
  Known approximately; because this instrument's third rule, by
  which the chord of the [zenith] angle is known, truly does not
  show the chord of [this large] angle. (S: fol. 18v, M: p. 46) (41)

With Ptolemy's parallactic instrument with a chord rule of only 60P, altitudes below 300 could not be measured but only estimated. (42)
  About Ghazan Khan's new approach, the treatise's author says:
  Over the years I have been praying for the imperial government of
  the king of the world, the great Ilkhan, the King of Kings on Earth,
  the patron Ghazgn Khan--may God perpetuate his kingdom and
  spread his shadow over all the inhabitants of the world. I
  sometimes thought about and searched for observational instruments
  by which observations can be produced precisely and certainly without
  suffering and trouble, until in the government of the world's king
  [i.e., Ghazan Khan], twelve kinds of observational instruments
  appeared that had not appeared with any of his antecedents and
  their descendants, and had not been possible [to conceive] for them.
  By them [i.e., these instruments], all observations can be exactly
  and certainly known with the least cost and effort, because these
  instruments consist entirely of rules and straight lines. Although
  they are long, constructing them fully straight and dividing them
  into minutes and seconds is possible and by them those
  [observational] matters can be found exactly, whereas finding
  them by the five classical instruments is not possible, as we will
  describe. (S: fols. 18v--19r; M: pp. 47-48)

The panegyrical introduction in the above quote assures us that the description that follows is of the twelve instruments invented by Ghazan and also that they are in their original forms, because it implies that the treatise was written during Ghazan's lifetime (or between 1300 and 1304).

The author then introduces the two parts (qism) of his treatise (S: fol. 19r; M: p. 48): "To mention observational instruments and to know their applications" and "To determine the stars' positions in ecliptical longitude and latitude." The second part, however, is not found in the extant copies S, P, and M.

On the superiority of construction over the older instruments, the new ones being based on long straight beams and avoiding circular structures, he notes:
  This instrument [no. 2, below] is preferable and superior to all
  [observational] instruments for four reasons. First, each [older]
  instrument, which is well known and in common use, is dedicated
  to an important [application]--as we said earlier--while with this
  [new] instrument the determination of all quantities that can be
  found by those [previous] instruments is possible. Second, the
  expenditure, cost, effort, and occupation of [constructing] this
  instrument are less than for the preceding instruments, as a whole.
  Third, what was observed was not revealed with certainty and
  exactitude by the [previous] instruments, because all those
  instruments are made up of arcs and circles, so that if they are
  small, it is not possible to divide them into minutes and seconds,
  and the results are approximate. If they are large, it is not
  possible to make them completely circular, as they ought to be,
  and then their defect (fasad) and disorder (khalal) are more than
  their benefit, whereas these [new] instruments are made up of
  straight rules (mistara-haty-i mustaqim) and straight lines
  (khututt-i mustaqim), [so that] however long, to construct them
  being straight, without disorder and trouble, is possible. And,
  fourth, in those [old] instruments, the arcs are determined
  [directly], whereas in these [new] instruments, the parts
  [functions of arcs; i.e., sin, tan, etc.] whose corresponding
  arc (hissa-yi qaws) is often smaller are determined; therefore
  the arcs are determined [more] exactly and with certainty.
  (S: fol. 23r--v; M: pp. 54-56)

A comparison with instruments described before this era confirms our author's claims of new instruments. In addition to portable instruments (e.g., astrolabes) of which a variety of models are known and plenty of examples are extant, observational instruments before the founding of the Maragha observatory appear to have been large models of instruments known from classical times, modified to a certain degree, and named after patrons. For example, in the first observational program established by the 'Abbasid caliph al-Ma'man (r. 812-833), under the directorship of Yahyd b. Abi Mansur (fl. ca. 820), an armillary sphere with divisions for each ten arc minutes and a circle "whose nature is unclear43 had been used (see below), while in the second observational program, a mural quadrant (lubna) and a gnomon (shakhis) were used. From the Buwayhid period (932-1062), we find a large version of Ptolemy's "two circles" named halqat al-'adudiyya (after 'Mud al-Dawla, d. 983), which mentioned in his Suwar al-kawakib al-thabita. (44) There was also a sextant built by Abu Mahmud al-Khujandi (d. 1000) for his patron Fakhr al-Dawla (r. 976-997), called suds al-Fakhri, which was an instrument similar to the lubna erected in the meridian plane but consisting instead of one-sixth of a circ1e. (45) From the Ghaznawid period (975-1187), al-Birtini describes a halqat al-yamini (after Yamin al-Dawla Mahmud of Ghaznd, d. 1030), which seems to have been a solstice ring established along the meridian. And al-Khdzini left a few treatises from the period of the Saljuq sultan Malikshah I (r. 1073-1092) in which he describes the classical instruments. (46)

More importantly, in his Risala fi kayfiyyat al-irsad the Damascene astronomer Mu'ayyad al-Din al-'Urdi described the instruments built in Maragha for al-Tusi: (47) (1) a great mural quadrant; (2) an armillary sphere (with some improvements over that of Ptolemy); (3) solstitial and equinoctial armillae; (4) Hipparchan dioptra (with improvements to observe eclipsed diameters of the sun or moon); (5) dhat al-rub'ayn, a double quadrant from copper inside a circular wall, capable of measuring, at the same time, azimuth and altitudes of two objects; (6) an improved version of Ptolemy's parallactic instrument; (7) dhat al-jayb wa-l-samt, an instrument to determine sine (of zenith distance) and azimuth using a wooden bar rotating on an iron axis inside another circular wall, on which one end the alidade can slide, the other end sliding up a vertical central pillar; (8) dhifit al-jayb wa-l-sahm, a similar instrument to determine sine and versine; and (9) alat al-kamila 'perfect instrument', consisting of a rotating parallactic rule inside a circular wall.

The four new instruments al-'Urdi. introduces (5, 7, 8, and 9) appear to be a combination of quadrants or rulers (in different ways in order to employ various trigonometric functions) for determining the star's altitude and, by mounting the complex on an elevated circle, for measuring azimuth. However, azimuth instruments (in the sense of the instruments specifically used in the simultaneous measurements of altitude and azimuth) were apparently not so novel. The author of our treatise ascribes an alat-i samtiyya ('azimuth instrument') to Abu 1-'Abbas al-Lawkari, (48) and we know that Ibn Sing built a model of it in Isfahan between 1024 and 1037. (49) Muhyi 1-Din al-Maghribi traced the use of an azimuth instrument in the Islamic period even further back, ascribing it to Yahya b. Abi Mansur (50) and suggesting that the azimuth ring was used in order to determine the ecliptical coordinates, which, however, is far beyond the usual applications of the known versions of an azimuth instrument (e.g., those of Ibn Sind and al-'Urdi). While the nature of the instrument is as yet unclear, it appears to have been an instrument having the same applications as the armillary sphere. (51)

Therefore, we can consider at most five observational instruments (apparently models of azimuth instruments) to have been innovative in the Islamic period up to Ghazan Khan's time, over a period of five centuries. In this light our author's claim of a new approach taken by Ghazan to observational instruments, and of his new models and their differences from the older ones, is at least not inconsistent with (if not justified by) the historical sources. (52) Ghazan's new instruments appeared within one decade.

Besides the principal difference in the basic approach to observational instrumentation, another explicit distinction between al-'Urdi's instruments and those described in our treatise is that the former are mostly made of teak from India (53) with only circular parts cast from copper, whereas metals play a more important role in the latter. (54)

In all three manuscripts--S, P, and M--the spaces for the names of the new instruments are left blank. We find the names of instruments 1 and 2 in the description of the latter, where they are called, respectively, the "triangle instrument" (alat-i muthallath) and the "perfect instrument" (alat-i kamila). (55) Instrument 12 is introduced with a rather long description. The treatise's author adds that the best observational instrument to date was the "azimuth instrument" (alat-i samtiyya) invented by Abu 1-'Abba's al-Lawkari, which, however, also suffered from the above-mentioned issues.

The Tables in the Treatise

The following tables are only present in manuscript S (and P):

1. Zill-i mustawi (cotangent, or umbra recta; S: fol. 44v).

2. Mayl-i awwal and mayl-i thani (first and second declinations; S; fol. 45r).

3. Zill-i ma'kus (tangent, or umbra versa; S: fol. 45v).

4. Jayb (sine; S: fol. 46r).

5. Sahm-i qaws-i nisf-i dawr (versine for the arcs 0, ..., 180[degrees]; S: fol. 46v).

6. Matali'-i mustaqim va ma'il (right and oblique ascension of the parts of the ecliptic for the latitude of Maragha; S: fol, 47r).

7. Hadha al-jadwal [correct: jadwal al-samt alladhi li-hadhihi 1-'urud li-kull khums rub' [read: daraj rub' da'irat al-ufuq, an unusual table entitled "The table of azimuths of these [geographical] latitudes for each quadrant of the horizon circle per five degrees," whose purpose is obscure.

The author writes that he copied these tables from Zij-i ilkhani, in which we were unable to find table no. 7, however. In the manuscript, tables 6 and 7 are the only complete tables; 1-5 were left empty. From the text it can be deduced that the treatise had also contained other tables for the equation of daylight and the number of daylight hours for the equator and for Maragha, which are also not available in these copies.


Two centuries after the fall of the Buwayhids, Persian scholars again began writing in their native language, such that the very large majority of mathematical and astronomical treatises written after the mid-thirteenth century are in Persian. The language of these treatises is not as pure, however, as that of their tenth-century counterparts; Arabic and Mongolian are used liberally (although the latter is less frequent in astronomical treatises, except in descriptions of the Chinese-Uighur calendar). This has a corrupting influence on phraseology, and since mathematical and astronomical treatises, whether in Arabic or Persian, also usually adopted a simple unitary style, the combination of both makes the definitive distinction of a literary style very difficult.

It is clear that our author is a professional astronomer with ample knowledge of observational astronomy and instrumentation and capable of sound comparative discussion and critical conclusions about them. We can therefore propose al-Wabkanawi, with high probability, and al-Nisaburi, with less, as our most probable candidates for authorship. In some aspects--particularly the type and order of explanation, the frequency of technical terminology, the sentence structure, and the remarkably sparse descriptive material--our treatise is so similar to al-Wabkanawi's Zij that the authorial voice seems to be identical; in equal measure it is less like al-Nisaharr s treatises, in which, for example, there is an excess of explanation. In our treatise we also find the same description of instrument 12, accompanied by some additional notes, as in al-Wabkanawi's ZU (IV, 15, $), (56) where he describes the instrument as one of the marvels of observational work. In addition, the style of both treatises seems to be identical. All this, along with the fact that al-Wabkanawi was Ghazan's astronomer-royal and had his royal order, yarligh, to complete a zy in that period, leaves little room for doubt in the identification of our author as al-Wa-bkanawi.


We can classify the twelve new instruments into seven types as shown in Table 1. In types A, D, and E, we see that the latter instrument of each type is an improved and more sophisticated version of the first one of the respective type. Nos. 9 and 4 in type F can be compared in a similar way. In other words, the treatise follows an approximately evolutionary model for describing the instruments. The instruments of type C form a related couple, where one instrument is better for higher elevations than the other.
Table 1 The Types of the Twelve Instruments

Type                              Involved functions      Nos.

A (triangle-type instruments)  Special function            1, 2
                               described in the

B                              Chord arm on circle            3

C (wire instruments)           Sine, chord, and tangent    5, 6

D (square-type instruments)    Tangent                     7, 8

E                              Sine and versine          10, 11

F (improved Ptolemy's          Chord                       9, 4
parallactic instrument)

G                              Pinhole device                12

Some of the instruments allegedly designed by Ghazan Khan show a great similarity with instruments constructed in Europe in the following centuries. The most remarkable similarity is between nos. 7 and 8 and Georg von Peuerbach's geometrical square (described in Canones Gnomonis, MS Vienna no. 5292, fols. 86v--93r, printed in Nuremberg, 1516). Instrument no. 12 is a pinhole image device, and the factors taken into consideration and applied in its construction are similar to those described at least two decades later by Levi ben Gerson (1288-1344). As we will see below, instrument no. 12 is the link between the dioptra and the instruments that were later used as a camera obscura. Although there is no concrete evidence of how such knowledge was transferred, there were widespread politico-cultural relations between Iran and Europe at that time, which might account for easy access. (57)

Five circular traces have been discovered to the south, southeast, and north of the central building of the observatory in Maragha. Al-'Urdi described only three big circular instruments at Maragha. More importantly, with an average rainfall of 300-1000 mm during the spring and long periods of freezing weather (over one hundred days), the wooden instruments noted three decades earlier by al-'Urdi and especially their fine gradations required for observations had probably been destroyed by Ghazan Khan's time. Al-'Urdi died eight years before al-Tusi; thus he clearly could not reconstruct his own instruments. Therefore it now seems quite likely that these five locations had been given over to the "new" instruments.

Except for three instruments--nos. 1, 2, and 12--the instruments are described in the treatise without being named, so we will refer to them by their sequence number. Below we provide a short description of each, following the treatise, and a virtual reconstruction, remarking on difficulties with the translation and practical considerations. Instrument no. 12 will be presented in more detail with a full translation.

The treatise gives numerous dimensions of the instruments and their parts. The dhira' used in the reconstruction is the royal cubit (dhira' al-malik or al-dhira' al-hashimi) of 665 mm, as used in al-'Urdi's treatise and shown in Table 2. Frequently, however, not all dimensions are given, and for the reconstruction we had to estimate useful dimensions ourselves. In addition, some numbers are clearly copying errors and do not make sense. We note such errors in our remarks.
Table 2. Units of Measurement Used in the Treatise

Symbol      Unit     Arabic  Persian  Relation         Length (mm)
cb      cubit        Dhira'  gaz                24 fg          665
sh      handspan     Shibr   wajab      1/3 cb   8 fg       221.67
hd      handbreadtb  qabda   --         1/6 cb   4 fg       110.83
fg      finger       asba'   Angusht   1/24 cb   1 fg        27.71

Several instruments are based on the concept of rigid right isosceles triangles, or moving triangle legs with a chord rule for measuring the chord of the angle, crd[alpha] = 2sin([alpha]/2). As was common, lengths and angles are defined so that the base length of the triangle legs is divided into sixty parts, which are each divided into sixty "minutes," and the hypotenuse/chord of the triangle shows a gradation in the same units, so we will write Crd[alpha] = 60crd[alpha], and similarly, Sina = 60 sina, etc. The hypotenuse of the right triangle will then be of length Crd90[degrees] = [check][2.60.sup.P] = [84.sup.P]51'10". Most instrument descriptions with chord rules mention chord rules with regular gradations up to [85.sup.p], obviously for practical purposes.

Instrument 1


The applications of this instrument are altitude and zenith distance of a [culminating] star, determination of the obliquity of the ecliptic, and finding local latitude. The instrument consists of a right isosceles triangle with horizontal basis, fixed in the meridian. A centrally mounted alidade carries two sights. Its fiducial edge is formed by omitting one half of its outermost one-third of length. The triangle legs are graduated regularly in units of one-sixtieth the triangle's height from the top and both lower ends towards the center points of the legs, where the scales meet at 42;[25.sup.P]. The scales are split into three parallel bands showing parts, minutes, and seconds. (58) The description omits absolute sizes for the instrument, but adds a detailed description to compute the altitude or zenith angles, respectively, from the values read on the scale. Effectively, it replaces a mural quadrant with its circular scale.

Instrument 2


The second instrument adds the capability of measuring altitude in any azimuth to instrument 1. On a base cross of 15 cb teak wood or copper bars, aligned with the meridian and supported with cross beams, a vertical triangle of copper bars with base length 7.5 cb is erected. The triangle is mounted on a central iron shaft 3 fg in diameter. Alternatively, the triangle can be put on a 2 fg iron shaft mounted on a wooden cylinder of 0.5 cb diameter. The copper alidade's fiducial edge is again formed by removing half of it outward of two-thirds of its length from its axis. The triangle can be moved in azimuth, and the altitude measured on the scale as on instrument 1.

Our author gives definite sizes and dimensions for many of the rules, and directions as to which material to use for construction. If made from copper, the 4 fg x 2.5 fg x 8 cb base bar would weigh about 364 kg. The perpendicular rule (no thickness given explicitly) of (assumed) 2 fg x 2 fg x 7.5 cb adds 137 kg, and the chord rule of 2 fg x 2 fg x 7.5[check]2 cb another 193 kg. An alidade of only (assumed) 1 fg x 1 fg x 7.5 cb would weigh another impressive 28 kg, but should be even heavier if the dimensions of the rules are larger. In total, this gives a moving mass of more than 700 kg. It seems clear that this instrument could only have been used to measure the altitude of a celestial object in a preselected azimuth, held by several strong assistants. For high altitudes, a ladder was obviously required to read the scale value.

Instrument 3


Contradicting the straight-rule concept, this instrument uses a graduated ring for reading azimuths. (59) It is 3 fg wide and 2 fg thick and of "large" diameter, to be installed 0.5 cb [sic] above ground. A central wooden cylinder topped by an iron plate supports an iron shaft on which rotates a wooden azimuth bar, which protrudes over the ring and carries a nail indicating the azimuth on the ring's graduated scale. An alidade is mounted in an excavated hole close to the axis and carries a chord rule jointed to its other end. The graduated chord rule slides through a dovetail slit on the outer end of the azimuth rule.

The length of the downward-pointing chord rule dictates that the ring must have a certain height. Therefore we must assume that nim (0.5) for the height of the ring is a copyist's error for du va nim (2.5). As shown in the reconstruction, the moderate size with a ring of 3 cb diameter in 2.5 cb corrected height provides a comfortable instrument for a single user, aided by an assistant standing outside the ring and reading the values from the scales. Made from copper, however, the alidade mass for 3 fg x 3 fg x (2 cb--1 hd) would be more than 75 kg, requiring again at least another strong assistant, but for teak wood we can estimate about one-tenth of this weight.

Instrument 4


This is a rotating parallactic rule: a base cross of 4 fg square rules is aligned in the meridian and east--west lines. Two brass or copper rules of 2 fg square and equal length are hinged on their upper ends. One is attached vertically with several rings on a central iron shaft of 3 fg diameter. On the lower end of the vertical rule, the chord rule is attached. The other rule is the alidade with sights and a slit on its lower end for the chord rule. On the east and west ends of the base cross, azimuth rules are attached. After measuring altitude, the chord rule is laid horizontally on the ground. On its [60.sup.P] mark, a nail protrudes downward. One azimuth rule is rotated towards this nail, and from the length read on the nail the azimuth can be derived.

Although rule lengths are not given, we estimate 3 cb length for the vertical and alidade rules in order for the instrument to be functional. It is interesting to note that al-'Urdi's "perfect instrument" likewise used a parallactic rule, but inside a circle, so the azimuth was read by putting the chord rule onto the azimuth ring. (60)

Instrument 5


Although not explicitly mentioned, instruments 5 and 6 form a pair, usable for different altitude ranges. Contrary to what was recommended by al-Urdi, (61) here and with instrument 6, a catgut rope or copper wire (khayt) is used for measuring parts.

Instrument 5 includes a central high round or rectangular pillar (height P) of sun-dried bricks, topped by a conical copper or iron roof of 1 sh height. On its peak, a kawkabah-shaped shaft (62) supports a ring that holds the first khayt. An Indian circle encloses the pillar. (63) On the base of the pillar placed underground, there is a hidden thickness (thikhan-i nahani) of firm wood or iron. (64) Around the base of the pillar, there is a circular excavation of 0.5 fg (depth and width) in which an iron circle can freely move around the pillar. (65)

A second khayt, called shadow khayt (or tangent khayt, khayt-i zill), is connected with the top ring (66) and leads through the base ring, and a third khayt is placed on the meridian line, close to the base of the pillar and secured with a nail and a ring, representing the meridian line. An alidade of 0.25 cb length is mounted on the first khayt and has a ring on its outer end, through which a conical plummet on a fourth khayt can be dropped to the ground. A long graduated rule of wood is used for measurements, and steps of stones for lower altitudes if needed.

To measure altitude, the first khayt is stretched, and the plummet dropped when the star is seen through the alidade. The distance from the pillar's foot is the cotangent of the altitude and can be measured along the shadow khayt. (67) To measure the co-azimuth, (68) we stretch the meridian khayt parallel to the meridian and measure its perpendicular distance from the plummet mark. (69)

The description of this instrument is very confusing and leaves many details out; constructing an instrument that fits the description and still provides correct and usable measurement results was not easy. We propose the following which only contradicts the description in one detail: the attachment point of the meridian khayt.

Our pillar shown here is 10 cb high with a diameter of 1 cb, both dimensions not explicitly given. The key purpose of this instrument as we interpret it--although not described in the treatise as such and even contradicting the original sketch--appears to be that the fiducial triangle does not use the central axis of the pillar but a vertical line that is formed by the point where the first khayt bends around the corner of the flat conic roof on top of the pillar and the small ring (zirih) on the base ring, where the shadow khayt, and quite likely also the meridian khayt, are attached. The only dimensional instruction found in the treatise is a roof height of 1 sh, which would form the low angle shown with our (assumed) pillar diameter of 1 cb. This flat cone appears to be a required component, its angle defining the minimum altitude of observation, and its diameter must be identical to the base ring's diameter to form the vertical fiducial line.

The meridian khayt is described in the text as being attached to a fixed point on the pillar's base on the meridian line. In this event it would be pointless to have another movable khayt, because the meridian line permanently drawn on the ground would fulfill the same purpose. Also, the measurements and calculation of the azimuth would have to take the radius of the pillar (or, for a rectangular pillar, the radius of the base ring) into account. To be functional as described, it would seem that this khayt was likewise attached to the base ring at the same place as the shadow khayt, so that a "local coordinate system" was cleverly carried around the pillar.

Instrument 6


A small central shaft inside an Indian circle with meridian and east--west lines harbors a khayt with an ahdade on its end. From this, a plummet on a second khayt can be dropped to the ground and its impact point measured by a long ruler. For high altitudes, an observing platform can be used.

It seems that this instrument complements no. 5 for objects in low altitudes. Clearly, however, all instruments involving rope lengths suffer from their flexibility and slack.

Instrument 7





A square is made up of four graduated rules and fixed in the meridian plane. In its top corners an alidade can be mounted, depending on northern or southern targets. The scales provide the tangent or cotangent of the meridian altitude. In effect, it also replaces a mural quadrant, but with a graduation different from no. 1.

This instrument is practically identical to the quadratum geometricum or geometrical square of Georg von Peuerbach (1423-1461). We do not know whether Peuerbach knew about this instrument or invented it independently. It might also have not been completely new to both authors: Dieter Lelgernann describes a reconstruction of a skiotherikos gnomon (shadow frame) as precursor of the geometric square, for use as a (terrestrial) trigonometric survey instrument. (70) The eleventh-century polymath al-Biruni used a similar instrument for terrestrial surveys. (71)

Instrument 8


This instrument extends no. 7 by mounting it on an iron shaft of 3 fg diameter and surrounding it with a "large" cardinally aligned copper square with gradations up to 60P (and parallel smaller gradations) from each side's center point to its corners. The inner square, on which the alidade is mounted in the lower corner, rotates on top of the outer to read tangent of azimuth. Using viable dimensions, this smaller instrument allows better handling than instrument no. 2. We estimate the upper frame to have 2 cb x 2 fg x 2 fg bars, giving still about 160 kg of moving mass for the frame with alidade.

Our author sets great store by this instrument:
  This instrument provides the altitude and the azimuth of a
  given star with complete accuracy and certainty. By means of
  this instrument, all observations that were known through the
  observational instruments, as well as several other matters,
  are known and witnessed. This instrument is preferable to
  other observational instruments for the reasons mentioned
  earlier [see quote on p. 402, above]. (S: fol. 70v)

Instrument 9


A double pillar of teak wood is set up in the meridian with a gap of 4 fg. A slightly shorter alidade of <4 fg x 2 fg with two sights is joined to the pillar by a nail to leave 0.5 cb (72) space to the ground. A graduated chord rule of 2 fg x 1 fg thickness and 85/60 the alidade's length is mounted by a nail in a split on the alidade's lower end, where also the scale begins. The chord rule's free end is fed through the double pillar where the alidade ends when hanging vertical. A rope of catgut (khayti az rudkish) runs from the alidade's end over a pulley wheel (bakra) mounted on another pillar of equal height, standing in the meridian outside the ali-dade's swing area.

This instrument is used for determining the maximum altitude of a given star. We pull the rope (lifting the alidade) until a given star is seen through both sights of the alidade. The distance between the halving split end of the alidade and the other end of the chord rule (73) is the chord of the zenith distance (co-altitude) of that star.

This is obviously another variant of Ptolemy's parallax instrument (Almagest V, 12). The interesting differences are the full-length chord rule and the pulley (both already described by al-[.sup.c]Urdi, (74) who mounted the latter onto an arm extending from a wall) and the mounting of the chord rule on the alidade. The latter, however, makes it necessary to raise the point where the free end of the chord intersects the double pillar: for a chord rule of length [check]2 of the base length, the chord will point one-quarter of the base length below this contact point at zenith distance z [approximately equal to] 41.41[degrees], and may collide with the ground if it is not high enough. (75) We chose 5 cb as base length, this size being identical to the similar instrument described by al-[.sup.c]Urdi, which, however, has the chord attached to the base of the double pillar. This length provides us with 55 mm per part on the chord rule, or just short of 1 mm per minute. The text says literally, "the lower end of the alidade is 0.5 cb above ground," which would allow for no more than 2 cb base length. Assuming another scribal error for 1.5 cb true elevation solves the problem; otherwise a trench of almost 1 cb depth for the chord rule just south of the double pillar must be assumed, of which there is, however, no mention in the text. Thus the double pillar may have been as tall as 7 cb, with a base length of 5 cb, and a chord contact point at 1.5 cb height.

Instrument 10


This instrument consists of two copper rules of equal length, where the thicker and wider, vertical sine rule has a hole and on which is attached the smaller, horizontal versine rule (or sahm, lit. arrow). A rope of catgut (zih) connecting the top of the sine rule to the end of the sahm prevents it from being detached. An alidade of size equal to the sahm is connected to its outer end. The sine rule is graduated from the hole to the top, the sahm from the end opposing the alidade joint. This instrument is installed in the meridian plane so that the sine rule is perpendicular on the horizon and the versine rule is parallel to it.

We move the alidade until a given star is seen through both of its sights, then the sine rule is moved to touch the alidade on the point that gives the sine of the star's altitude. The length of the sahm protruding from the hole shows the versine of altitude.

Dimensions of the rules are not presented in the text. From the description of instrument no. .1.1 we estimate for this instrument also a length for the rule of 3 cb, so that the "minute" divisions are about 0.55 mm apart. Based on this length and dimensions for the rules found earlier in this text, an alidade and versine rules of 1 fg x 1 fg x 3 cb is about 14 kg each; the sine rule, with estimated 1.5 fg x 1.5 fg x 3 cb, would be about 31 kg.

The author does not state how the instrument is to be installed, just directing it to be placed in the meridian. It would be reasonable to assume that the instrument was installed higher than the horizon, e.g., on a wall. About 1.5 cb seems to be a practical height. Given the sliding sine rule and the purpose of the catgut to prevent the sine rule from falling off the versine rule, the only fixed point can be the end of the versine rule where also the alidade is attached. Such a solution would suffer problems from flexure, however, so a support for the other end would be required.

In all likelihood this description was only included as a prelude to the next instrument, and instrument no. 10 was never built. The same principle was described and used by al-[.sup.c]Urdi in his "instrument with sine and versine." (76)

Instrument 11


This instrument again is built on a base cross of teak wood or copper rules aligned on the meridian and east--west lines and further strengthened by supportive rules of 1 cb length. In its intersection an iron shaft of 2 fg diameter is mounted firmly on the ground. The versine rule, an extremely round copper rule of 2.5 fg diameter, is mounted with one end on the central shaft. Its outer end should coincide with the ends of the base cross rules. A rectangular sine rule of equal length, 2 fg x 0.5 fg, is mounted on a short pipe (anbuba) of 3 fg length, which slides along the versine rule. Another copper rule of equal length is mounted as an alidade on the outer end of the versine rule, bearing two sights.

The versine and sine rules are again graduated in three bands, one of 60 parts, the others into finer fractions. To measure altitude, the sine rule is held in a vertical position and slid along the versine rule until it touches the targeting alidade (instr. 11a). To gain azimuth, we keep the versine rule in place and rotate the sine rule into the horizontal plane. Then the sine rule is moved until its graduated edge aligns with the outer end of the east--west rule (instr. 11b).

At this point,

[bar.VW] = SinA sine of azimuth of observed object, jayb-i samt-i [irtifa.sup.c]

[bar.OV] = Sin(90-A) co-sine of azimuth of observed object, jayb-i samt-i tamam-i [irtifa.sup.c]

The original, very confusing figure in the treatise shows catgut between the sine and ver-sine rules, which is, however, not mentioned in the text and appears unnecessary. Objects close to the horizon (h<15[degrees]) and zenith cannot be measured due to collisions between the pipe and the ends of the versine rule.

The original drawing shows three concentric circles labeled as having semi-diameters of 1.6 cb, 2 cb, and 3 cb, and with the largest being of equal radius to the rule lengths, from which we assume this base length of 3 cb for the versine, sine, and alidade rules. A copper alidade of 1 fg x 1 fg x 3 cb weighs about 14 kg, which seems reasonable.

The purpose of these circles is not documented. The circle of 1.6 cb radius would indicate an altitude angle of 62[degrees] 11', or a culminating declination of [delta] = 9[degrees] 31', while the circle with 2 cb radius indicates h = 70[degrees] 31', or a culminating declination of [delta] = 17[degrees] 52', equivalent to ecliptic longitudes of [gamma]24[degrees] or 1520[degrees], respectively; the purpose of these data is, however, unclear.

Instrument 12


The description of this instrument in our manuscript appears as an appendix to the treatise, after the date of copy (S, fol. 49r-v). However, a figure apparently intended to illustrate the description has been drawn five folios earlier (S, fol. 44r) among the sketches of instrument no. 11, although the figure actually appears to depict al-[c.sup.c]Urdi's dioptra for eclipse observation. (77) Nevertheless, the number of instruments will only match twelve, as given by the author, if we include this instrument. As an example of an instrument description with instructions for its use, we provide a close translation in this case.
  The rule with which by the image of the ray ('aks-i shu'a') the
  radial magnitude of the eclipsed sun is found. (78) From a straight
  and rigid wood, we make a rule like the astrolabe's alidade. Two
  pinnulae (lubna) are on both of its two ends. The width of one of
  them is 4 fg, and the other is wider than the first by 2 fg [total:
  6 fg]. On the center of the greater pinnula, there is a perfectly
  round hole (thuqba). Around the center of the smaller sight, which
  is aligned with the center of the greater sight, we draw a circle
  whose radius is equal to the apparent radius of the sun. To draw
  this circle, two days before the eclipse we place this instrument
  facing the sun so that the size of [the circle of] the sunlight
  coming through the hole of the great pinnula and shining on the
  lesser pinnula is known. Then the circle around the center of the
  lesser sight is drawn with the dimensions of the illuminated circle.
  Then we divide this circle's diameter into twelve equal parts, by
  which the digits of the diameter [of the eclipsed sun] (asabi'-i
  qutr-) are revealed. Then the circle's circumference is divided
  into twelve parts, by which the digits of the area [of the eclipsed
  sun] (asabic-i firm) are revealed. We draw semi-diameter lines from
  the center of the circle onto the parts of the circle's circumference
  parts. (79) We draw circles on the digits of the diameter, by which
  the digits of the area [of eclipsed sun] are made clear. If we need
  high accuracy, we will divide the digits of the diameter and those
  of the circumference into minutes.

  On the day of the eclipse, we place the sights facing the sun and wait
  for the appearance of a slight shadow, like a fly's wing. This is the
  beginning of the eclipse. By means of an astrolabe or clepsydra
  (shisha-i sa'at, lit, hourglass), (80) we determine the time of the
  start and end
  of the eclipse. We wait while the shadow increases in size, until
  it no longer grows and starts to decrease in size. By the darkness
  of the circle of the diameter of the sun, the digits of the
  diameter and of the area are revealed. By the times given by the
  clepsydra or determined by the altitude of the sun, the begin and
  end times of the eclipse are found. When darkness vanishes from the
  circle of light, this is the time of complete luminosity [end of
  the eclipse].

This instrument is apparently intended to replace the dioptra of antiquity. An early dioptra seems to have already been described by Archimedes (third century B.C.) in The Sand Reckoner. (81) Ptolemy used a dioptra originally described by Hipparchus with four cubits of length. (82) This dioptra has a fixed (lower) pinnula, on which there is a hole for sighting, and a movable one (outer pinnula), which is placed in front of the sun. The solar/lunar angular diameter is calculated based on the movable pinnula's width and the distance between the two pinnulae.

The classical dioptra was employed to determine the apparent angular diameter of the sun and the moon. Like other medieval scholars, our author noted that Ptolemy said nothing about its construction, but his predecessors did. For instance, in his commentary on Book V of Ptolemy's Almagest, Pappus of Alexandria gave a description of this instrument. Proclus described it slightly differently. (83) Moreover Heron of Alexandria promoted the dioptra and constructed two types (vertical and horizontal). (84) None added details concerning use of this instrument for determining the eclipsed diameter or area of the sun or the moon by drawing a circle on the lower pinnula (as our treatise did) or using a circular plate on the lower pinnula (as al-'Urdi did). This number is usually gained by calculations (Alma gest VI, 7). During antiquity and the early Islamic period, astronomers estimated it without an instrument of any kind, and used their own estimate to check the results of their calculations. (85)

In his treatise al-'Urdi presented an improvement on the classical dioptra for determining the eclipsed diameter of the sun or the moon. (86) Similar to the ancient dioptra, he uses both a movable pinnula and a fixed one, but there is a conical hole on each of them. The angular diameter of sun and moon is calculated based on the width of the hole on the outer pinnula and the distance between the pinnulae. For al-'Urdi, however, the most important application of the instrument is the measurement of the eclipsed diameter of the sun and the moon. For this, he uses two circular brass plates (mir'at, 'mirrors'), one for each type of eclipse. Before the eclipse, the upper pinnula is shifted until the luminary of interest exactly fills its visible diameter. A scale allows one to read the value of its visible diameter. During the eclipse, the respective brass aperture is brought in front of the entrance of the upper pinnula to cover the bright part of the luminary. (87) In any event, the instrument requires looking directly through the pinnulae, which is known to be dangerous in the event of solar observations. Also, use of a device with two conical holes, a movable pinnula with graduated scale, and additional apertures appears to be overly complicated.

Our author presents a new instrument that basically fulfills the same purpose, i.e., measuring solar eclipses, but is significantly easier to produce and does not harm the eyes. The upper pinnula is described as 2 fg larger than the lower, most likely so as to provide good shading for the lower projection screen.

Our author attributed the instrument under discussion to al-Tusi (d. 1274), but we have not found any mention of this in his works. Only in his Exposition of Almagest does al-Tusi note concerning the dioptra described in the Almagest that "it is possible that errors will occur [in the calculation of the apparent diameter] if the length of the rule is much longer than the width of the sight." (88)

Al-Wabkanawi described this same instrument in his Zij, calling it "one of the marvels of the observational works" (min jumli ghara'ib-i a'mal-i ratsadi). (89) The details he gives are the same as in our treatise. Since he worked in the same period as the most important royal astronomer in Ghazan's court, we can infer that the astronomers of that era were aware of this instrument and that it was a new device. In his Zij al-Wabkanawi usually called his own innovations a "marvel."

The prevalent information regarding the basic principle of the construction and early use of the pinhole device is derived from Kitab al-Manazir of Ibn al-Haytham (Alhazen, d. ca. 1038). (90) His work was translated into Latin in 1272 by Vitellio, but the application of pinhole images in astronomical observations, especially for the eclipsed diameter/surface of the luminaries, was known in the West from at least ca. 1187 by Roger of Hereford. He was followed by such figures as William of Saint-Cloud (d. ca. 1292), Levi ben Gerson (Gersonides, d. 344), (91) Henry of Hesse (d. 1397), Leonardo da Vinci, Tycho Brahe, and Johannes Kepler. Nevertheless, Levi ben Gerson is known as the first person to have constructed a dedicated instrument in the form of a pinhole device for astronomical purposes. However, it is evident that al-Wabkanawi--or the writer of our treatise--preceded Levi ben Gerson in this field by about two decades, although there is no evidence about any connection. It should also be noted that the pinhole effect was used in the same period to achieve sharp shadows for solar altitude observations at the Gaocheng observatory in China. (92)

In Almagest VI, 7, Ptolemy describes the relation between eclipse size given in twelfths of solar diameters and size given in twelfths of the visible disk area, sizes our author also refers to. However, a simple regular partition of the circumference does not seem to help to determine fractions of eclipsed area.


In this article we have presented an anonymous Persian treatise about the instruments of the second period of the Maragha observatory, built under the supervision of Ghazan Khan. We think it is possible to identify al-Wabkanawi as the author of this treatise.

The treatise substantiates a hitherto unproven historical claim by Rashid al-Din Tabib that Ghazan Khan was the inventor of several "new" astronomical instruments, which, as we discussed above, were installed during what we have termed the second period of the Maragha observatory. Ghazan utilized a new approach in his instruments, insisting that they were to be made mostly from straight rules instead of circular components.

Following the treatise as closely as possible we created virtual reconstructions of the instruments, but we found several inconsistencies that must be the result of copying errors in the three copies of the treatise available to us. With minor corrections the instruments could be shown to work. However, if made from copper, the weight of some instruments might have rendered them hard to use if the large size recommended to achieve the required accuracy was taken into account. One instrument, no. 12, seems to be the first pinhole device specifically described for solar eclipse observations. On the other hand, the author breaks with the recommendations of his precursor, al-'Urdi, not to use ropes for measuring lengths.

In addition, there appears to be continuity or succession for a few instruments after the second period of the Maragha observatory, notably the geometrical square which appeared in Europe in the mid-fifteenth century. However, despite known contacts between Ghazan Khan's court and European rulers we cannot at this time provide evidence that this manuscript might have been brought to Europe.


1. (p. 401, above) M: p. 46, 11. 5-8; P: p. 35, 11. 3-6; S: fol. 18v, 11. 3-6

2. (p. 401, above) M: pp. 47, 1. 9-48, 1. 4; P: pp. 35, L 17-36, 1. 13; S: fols. 18v, 1. 17-19r, 1. 12

3. (p. 402, above) M: pp. 54-56, 1. 18-56, 1. 3; P: pp. 44. 1. 5-46, 1. 2; S: fols. 23r, 1. 4-25r, 1. 2

4. (p. 414, above) P: pp. 73, 1. 3-74, 1. 2; S: fols. 37v, 1. 3-38r, 1. 2

5. (p. 419-21, above) P: pp. 96, 1. 9-97; S: fol. 49v, 1. 9-49v

Authors' note: Earlier versions of this study have been presented at the symposia "Twenty-third International Congress of History of Science and Technology," held July 28--August 2, 2009 in Budapest, and "Astronomy and Its Instruments, Before and After Galileo," held September 28--October 3, 2009 in Venice. A longer version is forthcoming in Suhayl (2013). This study has been supported financially by the Iran National Science Foundation (INSF) (No. 87071/18) and by the Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Iran (No. 1/1858). We are grateful to Hadi Alimzadeh and Ali Adjabshirizadeh for their support. We thank as well the Journal's anonymous reviewers for their helpful comments.

(1.) A. Sayih, The Observatory in Islam (Ankara: Turk Tarih Kurumu Basimevi, 1960), 224-32.

(2.) The primary sources include (1) Rashid al-Din Tabib, Fadl Allah al-Hamadhani, Jami' al-tawarikh, ed. Muhammad Rawshan and Mustafa. Masawi, 4 vols. (Tehran: Alborz, 1994), 2: 1205ff.; Eng. tr. W. M. Thackston (Cambridge, Mass.: Harvard Univ., Dept. of Near Eastern Languages and Civilizations, 1999); (2) Fakhr al-Din Aba Sulayman Dawad b. Taj al-Din Aba 1-Fad! Mubammad b. Dawud al-Banakiti, Tarikh-i banakiti, ed. Ja'far Shur (Tehran: Society for the Appreciation of Cultural Works and Dignitaries, 1969 [rept 20001); and (3) 'Abd Allah Wassaf al-Hadra al-Nisaburi, Tarikh-i Wassaf, * ed. A. Ayati (Tehran: Iranian Culture Foundation, 1967). For other important sources, see Muhammad Mirkhvand, Tarikh-i rawza al-safa, ed. J. Kiyanfar (Tehran: Asatir, 2002); Khvandamir, habib al-siyar (Tehran, 1954).

(3.) Sayih, Observatory in Islam, 187ff.

(4.) Rashid al-Din Tabib, Jami' al-tawarikh, 2: 1331-41,1348-49; see also Sayih, Observatory in Islam, 227.

(5.) On GhTizan, see P. M. Sykes, A History of Persia (London: Routledge, 2003), 110ff.; A. K. S. Lambton, Continuity and Change in Medieval Persia (New York: Bibliotheca Persica, 1988), esp. 324ff.; H. Halm, Shi'ism, tr. Janet Watson and Marian Hill (Edinburgh: Edinburgh Univ. Press, 2004), esp. 62ff.; on his conversion to Islam, see D. Morgan, The Mongols (London: Blackwell, 2007), esp. 185,196.

(6.) Rashid al-Din Tabib, Jami' al-tawarikh, 2: 1296. Khvandamir (Habib al-siyar, 3: 154) has Ghazan staying in Maragha until Dhu 1-Hijja 699 (September 1300), but, according to Rashid al-Din Tabib, Ghazan left Maragha for Ujan on Tuesday, 24 Shawwal (July 13).

(7.) A rural area south of Tabriz where Ghazal founded from 696 to 702 (1297 to 1302-3) a gigantic dodecahedral tomb around which were built twelve charitable and scholarly buildings (including the observatory). See Rashid al-Din Tabib, Jami' al-tawarikh, 2: 1377-84; al-Nisaburi, Tarikh, 229-31; Sayili, Observatory in Islam, 226. Ghazan himself drew the plans for this complex (Rashid al-Din Tabib, Jami' al-tawarikh, 2: 1376).

(8.) Rashid al-Din Tabib, Jami' al-tawarikh, 2: 1296; al-Banakiti (Tarikh, 463) records nothing about his order to construct the Tabriz observatory.

(9.) Rashid al-Din Tabib, Jami' al-tawarikh, 2: 1340; Sayili, Observatory in Islam, 228.

(10.) Rashid al-Din Tabib, Jami' al-tawarikh, 2: 1340.

(11.) The selection of the initial date of the second period was made on the basis of the death of Muhyi 1-Din al-Maghribi, the last prominent scholar of the first scientific circle at Maragha, who worked independently of Nair al-Din al-Tusi's circle, in Rabi' I 682/June 1283. For the final date, there is no evidence of observations being made in the observatory between 1317 and 1339, when the observatory lay in ruins (Sayih, Observatory in Islam, 212f.).

(12.) See R. Lorch, "Ibn al-Salah's Treatise on Projection: A Preliminary Survey," in Sic itur ad astra: Studien zur Geschichte der Mathematik und Naturwissenschaften, ed. Menso Folkerts and Richard Lorch (Wiesbaden: Harrassowitz, 2000), 401. MS Tehran, Majlis Library, no. 6412, fol. 62r: wa-huwa 'ala ma wajadnahu bi-l-rasad bi-l-Maragha 23 juz' wa-35 daqiqa.

(13.) See E. S. Kennedy, A Survey of Islamic Astronomical Tables (Philadelphia: American Philosophical Society, 1956), 7, no. 27; D. King and J. Samso, "Astronomical Handbooks and Tables from the Islamic World," Suhayl 2 (2001): 45 (the date given as 1150 is wrong). Recently, this Greek translation was edited by J. G. Leichter, "The Zij as-Sanjari of Gregory Chioniades: Text, Translation and Greek to Arabic Glossary," Ph.D. diss., Brown Univ., 2004, under supervision of ID. Pingree.

(14.) Al-Fahhad al-Din Abri 1-Hasan 'Ali b. 'Abd al-Karim al-Fahhad of Shirwan. See Kennedy, Tables, 14, no. 84; King and Samso, "Handbooks," 45; D. Pingree, ed., Astronomical Works of Gregory Chioniades, vol. 1: Zij al-'ala'i (Amsterdam: Gieben, 1985), 7-8.

(15.) Rashid al-Din Tabib, Jami' al-tawarikh, 2: 1045; Kennedy, Tables, 8, no. 32.

(16.) Pingree, Zij al-'ala'i, 53. Both al-Wabkanawi (Zij, A: fol. 3r., B: fols. 4r-5v) and al-Kamali (Muhammad b. Abi 'Abd Allah Sanjar, Zij-i ashrafi, MS Paris, Bibliotheque Nationale, Suppl. Pers. no. 1488/1, fol. 117r) referred to them.

(17.) King and Samso, "Handbooks," 45.

(18.) An entry can be found in 13. van Dalen, "Wabkanawi," in The Biographical Encyclopedia of Astronomers, ed. Thomas Hockey et al. (London: Springer, 2007), 1187-88. See also Kennedy, Tables, 8, no. 35; King and Samso, "Handbooks," 46.

(19.) Pingree, Zij al-'ala'i, 52-53.

(20.) Kennedy, Tables, 2, no. 4; King and Samso, "Handbooks," 44.

(21.) For some of these facts, see Sayih, Observatory in Islam, 211ff. We only add some new results in what follows. For further information on the astronomers mentioned, see B. A. Rosenfeld and E. Ihsanoglu, Mathematicians, Astronomers, and Other Scholars of Islamic Civilization and Their Works (Istanbul: IRCICA, 2003) with corrections given in B. Rosenfeld, "A Supplement to ...," Suhayl 4 (2004): 87-158; Thomas Hockey et al., eds., Biographical Encyclopedia of Astronomers.

(22.) Kennedy, Tables, 4, no. 13.

(23.) (A) MS Istanbul, Aya Sofya, no. 2694, (B) MS Library of Yazd, Iran (without number, its microfilm is available in Tehran Univ. Central Library, no. 2546; henceforth we refer to this copy). Two further partial copies of it are: (C) MS Tehran Univ., no. 2452/3, pp. 122-28 (selected fragment for determination of hours) and (D) MS Tehran Univ., Theology Faculty, no. 190/6d, fols. 163v-175v (King and Samso, "Handbooks," 46, only referred to the first; see n. 18, above).

(24.) For example, al-Wabkanawi, Zij, book 3, section 3, chapter 1: A: fol. 53r, B: fol. 96r; book 3, section 9, chapter 5: A: fol. 60r. B: fol. 108v; book 3, section 13, chapter 6: A: fol. 67r, B: 120v; and many other places. Since al-Wabkanawi rightfully contends that Zij-i ilkhani is based on the earlier astronomical tables rather than obtained from independent observations, he sometimes goes further, stating that only Muhyi 1-Din's Adwar are the "Ilkhanid Observations" (al-Wabkanawi, Zij, prologue: A: fol. 3r; B: 4v). This difference between the two zijes became a standard and was repeated in later periods (e.g., see Sayyid Muhammad, the Astrologer [fl. ca. 1400], Lata'if al-kalam fi ahkam al-a'wam, MS Tehran, Majlis Library, no. 6347, pp. 322-24).

(25.) S. M. Mozaffari, "Wabkanawi and the First Scientific Observation of an Annular Eclipse," The Observatory 129 (2009): 144-46.

(26.) The earliest observation mentioned in his zij is that of the moon on December 3, 1272 (IV, 14: A: fols. 89v-90r; B: fol. 155r). His latest observation is that of the triple conjunctions of Jupiter and Saturn in 1305-6 (V, 1, 4: A: 125r; B: 235r). He states that he made his monumental work by order of Ghazan Khan and dedicated it to Sultan An Saqd Bahadur (the ninth If khanid ruler, r. 1316-1335). He also praised Sultan Oljeytu (the eighth ruler of that dynasty, r. 1304-1316), to whom the author had dedicated a compendium of the Zij before completing its final edition. He acknowledged Qutlugh b. Zangi (Cotelesse in European sources) and Amir Chupan for their support during his career, too. From this we can conclude that Abu Sack) and Amir Chupan were alive at the time of the dedication of the Zij--hence we can confidently define the period from the mid-1280s to the mid-1320s as the period of his observations.

(27.) He wrote three works: Sharh-i matali', Matn-i Uqlidus, and Risalat al-hisab. Hamd Allah al-Mustawfi, Tarikh-i guzida, ed. 'Abd al-Husayn Nawa'i (Tehran: Amir Kabir, 1960), written ca. 730/1329-30; Khvandamir, Habib al-siyar, 3: 191.

(28.) See E. A. Paschos and Panagiotis Sotiroudis, The Schemata of the Stars: Byzantine Astronomy from A.D. 1300 (Singapore and River Edge, NJ: World Scientific, 1998).

(29.) We know for certain that he spent several years between 1295-97 and 1310-14 in Tabriz. See L. Westerink, "La Profession de foi de Gregoire Chioniades," Revue des Etudes Byzantines 38 (1980), 233-45. Since Pingree (Zij al-'ala'i, 22) noted that he was in Constantinople in 1302, and Ghazan Khan received envoys from Emperor Andronicus II in September 1302, Chioniades was probably among them.

(30.) Pingree, Zij al-'ala'i, 16-17.

(31.) According to Pingree (Zij al-'ala'i, 15), this name should be read as Shams al-Bukhari, but he distinguished him from both al-Wabkanawi (each now has a separate entry in the recently published Biographical Encyclopedia of Astronomers) and Shams al-Din Mirak al-Bukhari, who died in 1340. On the other hand, Kennedy and Kunitzsch believe that some tables existing in Greek manuscripts and attributed to Shams al-Bukhari (see Pingree, zy al-calei, 23-29) are fragments of al-Wabkanawi's Zij (Kennedy, Tables, 8, no. 35; P. Kunitzsch, "Das Fixstern-verzeichnis in der Persischen Syntaxis' des Georgios Chrysokokkes,"Byzantinische Zeitschrift 57 [1964]: 382-409 [repr. P. Kunitzsch, The Arabs and the Stars, Northampton: Variorum, 1989]). A comparison of Chioniades's Greek Revised Canons and al-Wabkanawi's Zij shows that several fragments of these Greek translations are direct and faithful translations of the statements of al-Wabkanawi in his own Zij. For an example, see Pingree, Zij al-'ala'i 307, 311 and al-WAbkanawi's Zij, B: fol. 130r. According to Chioniades, Shams wrote a treatise about the astrolabe dedicated to Emperor Andronicus II, although no manuscript of this treatise in Arabic or Persian has survived. It now appears likely, however, that this treatise is the one attributed to al-Wabkanawi (MS Turkey, Topkapi Saray, no. 3327/4). An exact comparison between the Persian (al-Wabkanawr s Zij and his treatise on the astrolabe) and the Greek manuscripts could clarify this identification.

(32.) Rashid al-Din Tabib, As'ila wa-ajwiba, ed. Reza Sha'bani (Lahore: Centre for Persian Research, 1993), 1:28-50; 2: 52-94.

(33.) This assumption--along with the dedication of a treatise to Andronicus II (see above, n. 31)--clearly shows a variety of cultural relations existing between these dynasties, more prevalent than the scientific relations between Ilkhanid and European rulers during the first period of Maragha activities. For a study of international scientific relations of the first period, see M. Comes, "The Possible Scientific Exchange between the Courts of Maga and Alfonso X," in Sciences, techniques et instruments dans le monde iranien, ed. N. Pourjavady and Z. Vesel (Tehran: Institut Francais de Recherche en Iran, 2004), 29-50.

(34.) Two other copies--unseen--are in the Sharqi Asafiya Library, Hyderabad, and in the Egyptian National Library, Cairo; cf. C. A. Storey, Persian Literature (London: Luzac, 1958), 2: part 1, 64, no. 96; D. A. King, A Survey of the Scientific Manuscripts in the Egyptian National Library (Winona Lake, Ind.: Eisenbrauns, 1986), 166. Our thanks to the JAOS reviewer who brought these to our attention.

(35.) In M, the prologue of the treatise is wrongly attributed to Ghiyath al-Din Jamshid al-Kashi (d. 1436), probably due to its similarity with al-Kashi's Sharh-i alat-i rasad ("Description of Observational Instruments"), completed in Dhu-Qa'da 818/January 1416. Al-Kashi's two treatises are found in S and M before Risala ft istikhraj jayb daraja wahida ("Treatise on Calculating the Sine of One Degree"; S: fols. 1v-8v) and Sharh-i rasad ("Description of the Observational Instruments"; S: fols. 9v--14v; M: pp. 31-39; ed. E. S. Kennedy, "Al-Kashi's Treatise on Astronomical Observational Instruments," Journal of Near Eastern Studies 20 [19611: 98-108 [repr. in Kennedy, Studies in the Islamic Exact Sciences, Beirut, 1983,394-404]). For al-Kashi's Zij, see Kennedy, Tables, no. 12.

(36.) Both S and P include four treatises: the two above-mentioned works by al-Kashi, the treatise presented here, and an anonymous treatise on mechanics. In both S and P the handwriting, the figures, the scribal errors, and the repetitions are identical. The folios have been paginated in an appreciably similar fashion. The only difference is that the last two tables in S (nos. 6 and 7 in The Tables, below) are filled in, while the others, as well as all the tables in P, are blank. Although the date of copy appears as Thursday, 23 Jumada 11 194 (S: fol. 49r; P: p. 96), on the opening page of P (p. 1) the scribe has explicitly mentioned his name and the date of copy as 1294, and set his own seal below it. Since the two manuscripts are identical, when we refer herein to S, P can be read as well.

(37.) In his treatise al-Kashi designated halqat al-i'tidal as halqat iskandariyya ('Alexandrian circle'), which is connected with Ptolemy's famous observation (Almagest III, 1) which our author relates: "... as happened to the author of the Almagest [i.e., Ptolemy] in Alexandria's 'Gymnasium' or 'Palaestra' ([pi][alpha][lambda][alpha]i[sigma][tau][rho][alpha], al-riwaq al-mal'ab al-iskandariyya), the [Sun's] light appeared in the [equinoctial] circle twice in one equinox" (S: fol. 17r--v; M: p. 44). (It should be noted that "Palaestra" was not a stoa, riwaq, as our author claims.) Some lines earlier, our author speaks of al-riwaq al-murabba' which is identical to "square, [tau][epsilon][tau][rho][alpha][gamma]wv, stoa" in Almagest; see G. J. Toomer, tr.. Ptolemy's Almagest [Princeton: Princeton Univ. Press, 19981, 133, esp. n. 7, and 134). As stated in Almagest III, 1, Ptolemy had "one" equinoctial circle in the square stoa and some in the Palaestra. The terminology of our treatise is adopted from the Arabic translation of Almagest (Arabic Almagest, tr. Hunayn b. Ishaq and Thabit b. Qurra, MS Tehran, Sipahsalar Library, no. 594, copied in 480/1087-8, fol. 28r--v).

(38.) This problem was also noted by the thirteenth-century astronomer Mu'ayyad al-Din (d. 1266), who introduced a solution for preventing this insufficiency by placing the ring into a larger ring erected in the plane of the meridian for supporting the ring. See H. J. Seemann, "Die Instrumente der Sternwarte zu Maragha nach den Mitteilungen von al-'Urdi," in Sitzungsberichte der physikalisch-medizinischen Sozietat zu Erlangen 60 (1928): 57ff., instrument IV.

(39.) Toomer, Ptolemy's Almagest, 219.

(40.) See also J. Wlodarczyk, "Observing with the Armillary Sphere," Journal for the History of Astronomy 18 (1987): 177, 182. It is worth mentioning that in his Talkhis al-majisti Muhyi 1-Din al-Maghribi gave a rather complicated method for determining the ecliptical coordinates of fixed stars and planets, instead of using the armillary sphere. He measured the time interval between the meridian transit of the sun (or another reference star with known longitude) and that of the celestial object whose coordinates were desired, and the meridian altitude of the object. Then, first, the longitude of the culminating ecliptic degree (midheaven, medium coeli) was determined by time and reference to the star's longitude, and, second, the ecliptical coordinates of the object were determined by altitude and midheaven. (For an example of Saturn, see Muhyi 1-Din, Talkhis al-majisti, MS Leiden, Or. 110, fol. 123r--v.) For an introduction to this work, see G. Saliba, "The Observational Notebook of a Thirteenth-Century Astronomer," ISIS 74 (1983): 398-99 [repr. in Saliba, A History of Arabic Astronomy: Planetary Theories During the Golden Age of Islam, New York: New York Univ. Press, 1994].

(41.) For the original Persian text of this citation and others, see the Appendix.

(42.) Seemann, "Die Instrumente ...," 107. Our author's critique is similar to al-'Urdi's opinion of Ptolemy's parallactic rule given at the end of his own treatise. For the configuration of Ptolemy's parallactic instrument, cf. Toomer, Ptolemy's Almagest, 244-47.

(43.) F. Charette, "The Locales of Islamic Astronomical Instrumentation," Journal for the History of Science 44 (2006): 125.

(44.) (Abd al-Rahman al-Sufi, Sumar al-kawakib al-thabita (Hyderabad: Da'irat al-Ma'arif al-'Uthmaniyya, 1954), 302.

(45.) For the applications of the meridian instruments, see nos. 1 and 7 in the list of Ghazal's instruments, below.

(46.) For al-Khazini and his treatises, see R. Lorch, Arabic Mathematical Sciences (Aldershot: Variorum, 1995), nos. XI, XIV; A. Sayih, "Al-Khazini's Treatise on Astronomical Instruments," Ankara Universitesi Dil ye Tarih Cografya Fakultesi Dergisi 14.1-2 (1956): 15-19.

(47.) This treatise has been thoroughly described by Seetnann, "Die Instrumente. ..." Our numbering of the instruments diverges from that of Seemann.

(48.) Abu 1-'Abbas al-Lawkari (d. 464/1071-2), a well-known figure of Islamic philosophy, was a contemporary of the Persian astronomer and poet Umar Khayyam (d. 515/1121). He is one of a famous chain of Islamic peripatetic philosophers: Ibn Sina--Bahmanyar--Abu 1-'Abbas al-Lawkari--[...]--Nair al-Din al-Tusi. Older sources provide little information about him. See Zahir al-Din al-Bayhaqi, Tatimmat al-Siwan al-hikma, ed. Rafiq al-'Ajam (Beirut: Dar al-Fikr, 1994), 110-11; Shams al-Din Muhammad al-Shahrazuri, Nuzhat al-arwah wa-rawdat al-afrah ft tarikh al-hukama' wa-l-falasifa (Hyderabad: Da3irat al-Macarif al-'Uthmaniyya, 1976), 2: 54. There is no evidence of his appearance in the scientific circle around Malikshah I headed by Khayyam, to which all historical matters about the scientific/astronomical activities of that period are connected. Thus we know nothing about al-Lawkari's astronomical activities. He is not mentioned by Ibn al-Athir as one of Khayyam's collaborators in the task of reforming the Iranian solar calendar which Malikshah ordered to commence in 467/1074 and which was inaugurated at the spring equinox of 1079. See Ibn al Athir, al-Kamil fi l-Tarikh (Beirut: Dar Sadir, 1966), 98, and E. S. Kennedy, "The Exact Sciences in Iran under the Saljuqs and Mongols," in The Cambridge History of Iran, ed. J. A. Boyle (Cambridge: Cambridge Univ. Press, 1968), 5: 671-72. We do know, however, that he wrote an encyclopedia entitled Bayan al-haqq ft diman allidq, which included an epitome of Ptolemy's Almagest and to which Qutb al-Din al-Shirafi referred in the prologue on the astronomical part of his own encyclopedia dated 24 Rabic I 674 (September 17, 1275): Durrat al-taj li-ghurrat al-dubaj (Tehran: The Iran Ministry of Culture, 1944), 2: 1.

(49.) E. Wiedemann and Th. W. Juynboll, "Avicennas Schrift iiber em n von ihm ersonnenes Beobachtungsinstru-ment," Acta Orientalia 11(1926): 105ff.

(50.) "Yahya b. Abi Mansur observed the sun around the time of the autumnal equinox on Sunday, 25 Murdhakth 198 of the Yazdgirdi era (September 19, 829); he then found it by the azimuth circle, da'irat al-samtiyya, to be on Virgo 29;43." Al-Maghribi, Talkhis, fol. 58r.

(51.) Al-Maghribi calculates the instant of autumnal equinox from Yahya's observational data to be fifty-four minutes after the sun transits Baghdad's meridian on the given day. At this time, the sun was positioned on Libra 0;17 (or, true longitude = 180;17[degrees]), namely, an error of around 17 arc minutes in Yahya's measurement of the solar longitude, or an error of around 6;54h in his determination of the time of autumnal equinox. Based upon al-Maghribi's further explanations, one can also determine an error of around 10 arc minutes in the solar longitude--or a corresponding error of around 4;14h--in Yabya's data for vernal equinox of the year 198 of the Yazdgirdi era (March 16/17, 830). This gives the impression that the accuracy of Yahya's azimuth circle was that of a typical armillary sphere, like the very model used by him.

(52.) It is curious that our treatise does not refer to al-'Urdi and his instrument descriptions, but since both appear to be of the same tradition and to belong to the same observatory, we will note parallels between the two where appropriate.

(53.) Seemann, "Die Instrumente ...," 29.

(54.) Iron and pure tin (arziz) were brought from Minor Asia (al-Nisaburi, Tarikh, 229). We also find in a seventeenth-century treatise on the construction of the astrolabe that brass was brought from Hashtarkhan (today's Astrakhan) in the north of Azerbaijan. Muhammad Husayn b. Muhammad Baqir al-Yazdi, Mizan al-sana'i', MS Tehran Univ. Central Library, no. 2084, fol. 13v (written in 1072/1661-2).

(55.) Note that al-'Urdi also called one of his instruments, a rotating parallactic rule usable for azimuth and altitude measurements, "the perfect instrument" (Seernann, "Die Instrumente ...," 96-104). He built this instrument for Malik Mansur, the ruler of Hims (the antique Emesa, now Homs), in 650/1252-3, in the presence of Mansur's vizier, Najm al-Din al-Lubudi. Clearly, these "perfect instruments" are not the same.

(56.) A: fol. 92r--v, B: fol. 159r--v.

(57.) On a possible connection of Peuerbach and Maragha astronomy, albeit not concerning instruments, see J. Dobrzycki and R. L. Kremer, "Peurbach [sic] and Maragha Astronomy? The Ephemerides of Johannes Angelus and Their Implications," Journal for the History of Astronomy 27 (1996): 187-237.

(58.) We must assume simply "smaller parts," as this gradation seems pointless.

(59.) Such circular walls with graduated rings had already been used by al-'Urdi in three instruments. Maybe this instrument served as replacement in an existing ring.

(60.) Seemann, "Die Instrumente ...," 96.

(61.) Seemann, "Die Instrumente ...," 107.

(62.) The Arab term kawkab means star, but here apparently the Persian kawkabah is meant, which is a staff with an incurved head, used to prevent the top ring from falling off.

(63.) An Indian circle is a circle drawn on the ground, of an arbitrary radius, at the center of which a gnomon is installed. The sun's shadow crosses the circle at two points in the morning and afternoon. The line connecting those points represents a true east--west line (at least at the solstices, when the sun's declination does not change during the few hours between the events).

(64.) Its purpose is not given, but it is likely to increase the stability of the instrument.

(65.) It is not completely clear whether the circle is attached to the pillar as shown, or it is attached in some undocumented way to the ground (maybe to the "hidden thickness" just mentioned), where it could also encircle a non-circular pillar. The instrument's purpose would not change if this circle was fixed to the ground, but its size must always match the base diameter of the conical roof.

(66.) This connection seems unnecessary, but it may permit the verification of the vertical alignment of the first and second khayt.

(67.) Actually, it is cot h (P-[l.sub.4]) for altitude h and length [l.sub.4] of the plummet khayt.

(68.) We find azimuth a from measured length l=[l.sub.2] sin a, where [l.sub.2] is the distance from the base ring to the plummet mark. This is described as a co-azimuth in the treatise, which counts azimuths from the east--west line.

(69.) In our reconstruction we have understood this instruction to create a true meridian line for the current azimuth setting, i.e., attaching the meridian khayt from the same small ring (zirih) on the base ring where the shadow khayt is attached outward, parallel to the meridian line drawn on the ground in the instrument's center line. The literal text, which has the meridian khayt directly attached to the pillar, suffers from obvious problems.

(70.) D. Lelgemann et al., "Zum antiken astro-geodatischen Messinstrument Skiotherikos Gnomon," Zeitschrift far Vermessungswesen 130.4 (2005): 238-47.

(71.) Al-Biruni, Kitab Tahdid nihayat al-amakin li-tashih al-masafat al-masakin, ed. Muhammad al-Tanji (Ankara: Dogus Ltd., 1962), 210-12.

(72.) Again, this is probably a scribal error or omission for 1.5 (?); see below.

(73.) This description is inexact: we should draw a mark on the two parallel rules where the lower end of the alidade swings through. At the moment of observation, we move the chord rule right below this mark, and then the distance between the head of the alidade and this mark will be the chord of the zenith distance of the star.

(74.) Seemann, "Die Instrumente ...," 86.

(75.) In an instrument of base length 1, the chord rule of length [check]2 extends below the contact point by y = sin 7. ([check]2-crd z). The maximum extent is where d/dz sin z/2. ([check]2-2sin = 0, thus z = 2arcsin [square root of (2)]/4, = 41.41[degrees] where this 4 amount is y = 1/4.

(76.) Seemann, "Die Instrumente ...," 92.

(77.) Seemann, "Die Instrumente ...," 61.

(78.) Instead of a specific term such as dioptra, this long qualitative description may be due to the fact that the term [??] had apparently not been translated or had not entered into Arabic. For Ptolemy's statement, "We too constructed the kind of dioptra which Hipparchus described, which uses a four-cubit rod" (Almagest V, 14; cf. Toomer, Almagest, 251-52; J. L. Heiberg, ed., Syntaxis Mathematica, ... Exstant Omnia [Leipzig: Teubner, 18981, 1: 417), the Arabic translation by Hunayn--Thabit reads: "We, too, constructed the miqyas that Hipparchus made, with a four-cubit rod/rule, mistara" (Arabic Almagest, fol. 74r). In Arabic and Persian, miqyas ('scale', 'measuring tool') is a general term not specifying specialized usage, and in Ghazan's treatise it would have been applied to different things. (In instrument no. 4, miqyas is used for both the central iron shaft and the chord rule's nail pointer.) Therefore, it appears that the Islamic astronomers, following the linguistic style of the Arabic Almagest, appealed to the qualitative practical descriptions such as "the rule by which" for naming the dioptra-shaped instruments.

(79.) The text does not say whether this partition should be regular.

(80.) Al-Wabkanawi uses the term pangon in the otherwise similar paragraph in his own Zij, which is originally a simple Iranian clepsydra (Arabicized as bankam) in the shape of a floating bowl (as), having a hole in its apex and two graduated scales (usually drawn with the aid of an astrolabe) for both equal and unequal hours on its peripheral surface. The bowl was placed in a vessel of water, and the level of water flowing into it determined the time. The first description of it in the Islamic period seems to appear in al-'Amal bi-l-asturlab of al-Sufi (d. 376/986) (Morocco: ISESCO, 1995), 299-302, chaps. 354-57. On the one hand, this instrument was apparently very commonly used for timekeeping when one did not need to know the positions of the celestial objects, a process called "science of bankamat." On the other hand, it seems that it was modified in Maragha in such a manner that it was able to determine even the minutes of an hour, since Muhyi 1-Din al-Maghribi used it for his exact observations (see G. Saliba, "The Determination of New Planetary Parameters at the Maragha Observatory," Centaurus 29 [19861: 24971 [repr. in his History of Arabic Astronomy]. Saliba misread its name as minkam). The origin of this instrument dates back to both Babylonian and Indian texts of the first millennium B.C. (D. Pingree, "The Mesopotamian Origin of Early Indian Mathematical Astronomy," Journal for the History of Astronomy 4 [1973]: 3-4). Archaeological excavations have unearthed early models in India, apparently belonging to the same period (N. K. Rao, "Aspects of Prehistoric Astronomy in India," Bulletin of the Astronomical Society of India 30.4 [2005]: 505-6).

(81.) T. L. Heath, ed., The Works of Archimedes (Cambridge: Cambridge Univ. Press, 1897), 221-32; see also A. E. Shapiro, "Archimedes's Measurement of the Sun's Apparent Diameter," Journal for the History of Astronomy 6 (1975): 75-83.

(82.) 4 cb = 185.28 cm in his case: 1 Greek fg = 19.3 mm; thus 1 cb = 46.32 cm. Almagest V. 14; Toomer, Alma gest., 56.

(83.) B. Goldstein, "Remarks on Gemma Frisius's De Radio Astronomico et Geometrico," in From Ancient Omens to Statistical Mechanics: Essays on the Exact Sciences Presented to Asger Aaboe, ed. J. L. Berggren and B. R. Goldstein (Copenhagen: Copenhagen Univ. Library, 1987), 174-75.

(84.) M. J. T. Lewis, Surveying Instruments of Greece and Rome (Cambridge: Cambridge Univ. Press, 2001), 41-42, 51f.

(85.) See E R. Stephenson and S. S. Said, "Precision of Medieval Islamic Eclipse Measurements," Journal for the History of Astronomy 22 (1991): 195-207; S. S. Said and F. R. Stephenson, "Accuracy of Eclipse Observations Recorded in Medieval Arabic Chronicles," Journal for the History of Astronomy 22 (1991): 297-310.

(86.) Seemann, "Die Instrumente ...," 61-71.

(87.) Seemann ("Die Instrumente ...," 66f.) notes that this description is not completely clear since a mechanism for measuring the amount of the aperture's shift is not described explicitly.

(88.) Al-Tusi, Tahrir al-majisti, MS Iran, Mashhad, no. 453 (copied 1092/1681-2), fol. 37v.

(89.) Al-Wabkanawi, Zij, book IV, sec. 15, ch. 8, fol. 159r-v.

(90.) A. I. Sabra, The Optics of 1bn al-Haytham (London: Warburg Institute and Univ. of London, 1989), 90-91.

(91.) See B. R. Goldstein, The Astronomy of Levi ben Gerson (1288-1344) (New York: Springer, 1985), 146; J. L. Mancha, "Astronomical Use of Pinhole Images in William of Saint-Cloud's Almanach Planetarum (1292)," Archive for History of Exact Sciences 43 (1992): 293.

(92.) Helmer Aslaksen, "Calendars, Interpolation, Gnomons and Armillary Spheres in the Work of Guo Shoujing (1231-1314)," Department of Mathematics, National Univ. of Singapore, 2001, 23-25. Available at (retrieved October 24, 2010).

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Author:Mozaffari, Mohammad S; Zotti, Georg
Publication:The Journal of the American Oriental Society
Article Type:Essay
Geographic Code:7IRAN
Date:Jul 1, 2012
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