SCIAMVS 14 (2013), 149-258

The Tārīkh-i Qitā in the Zīj-i Īlkhānī—The Chinese calendar in Persian—Yoichi ISAHAYAJapan Society for the Promotion of Science / The University of Tokyo
amirsahibqiran@yahoo.co.jp

I.

Introduction

In this article, we provide a translation with commentary and an edition of a Chinese
calendar described in a zīj (astronomical handbook with tables), the Zīj-i Īlkhānī compiledin 1272. Naṣīr al-Dīn Ṭūsī (1201–1274), a polymath in his age, incorporated a chapter ona Chinese calendar—entitled the Qitai calendar (Tārīkh-i Qitā)1—into his zīj, having
obtained the information from “a sage of the Qitai.”2As a result, as far as surviving
sources are concerned, this zīj became the first astronomical handbook in which the Qitai
calendar was described. Later, the Qitai calendar continued to appear in zījes that weremainly written in Persian (although a few are in Arabic), as can be seen in the following
table.3 The parameters of the Qitai calendar, however, were little modified in the laterzījes, almost all of which fundamentally followed the Qitai calendar in the Zīj-i Īlkhānī,
despite the presence of small differences among the zijes in the wording and epoch year
(van Dalen et al. 1997, 112).

1

Hereafter, the Chinese calendar in zījes is cited as the “Qitai calendar.” The word Qitai (Qitā/Khaṭā in

Persian) originally referred to a nomadic people who, by the tenth century, dominated a vast area in northern
China and established the Liao dynasty (916–1125). By the Mongol period, the Turko-Mongols and thepeople from the west of Turkistan used this word to refer to northern China and its inhabitants. Moreover, theRussian word for China, Китай, is derived from Qitai (as is the earlier English word “Cathay”) (cf. Pelliot
1959-73, 1: 216-229).
2

For the sage and situation about the compilation of the calendar, see Isahaya (2009)3

Benno van Dalen sent me this list, which I have slightly revised, in an e-mail dated October 1, 2009.

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Yoichi ISAHAYA

N.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.

AuthorNaṣīr al-Dīn ṬūsīMuḥyī al-Dīn Maghribī
Jamāl al-Dīn b. Maḥfūẓ
al-Baghdādī‘Alā al-Munajjim al-Bukhārī
Sayf al-Munajjim al-BāyzdiwīNāṣir b. Haydar al-Shīrāzī
Shams al-Munajjim al-Wābiknawī
Giyāth al-Dīn Jamshīd al-Kāshī
Ulugh Beg
Rukn al-Dīn b. Sharaf al-Dīnal-Āmulī‘Abd al-Qādir b. Ḥasan al-Rūyānī
Maḥumūd Shāh Kaljī
Farīd Ibrāhīm Dihlawī

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Title
Zīj-i Īlkhānī
Adwār al-Anwār
Unknown

Year
1272
1276
1286

‘Umdat al-Īlkhānīya
Zīj-i Ashrafī
Zīj-i Nāṣirī
Zīj al-Muḥaqqaq al-Sulṭānī
Zīj-i Khāqānī
Zīj-i Sulṭānī
Zīj-i Jāmi‘-i Sa‘īdī

1287/88ca. 1303
ca. 1310
ca. 1320
1413
1440
1457

Zīj-i Mulakhkhaṣ-i Mīrzā’ī
Zīj-i Jāmi‘
Zīj-i Shāh-Jahānī

1490
16 c.
ca. 1630

Given the above circumstances, we can appreciate the high value of the Qitai calendar
in the Zīj-i Īlkhānī, especially from two standpoints: it is the first Chinese calendar
described in zījes, and it is a primary source produced as a result of cross-cultural contact
during the period of the Mongol empire in Iran.1 In the commentary, we analyze thecontents of the Qitai calendar in comparison with Chinese astronomical tradition. To
confirm the importance of this approach, we trace the course of studies on the Qitai
calendar.
The Qitai calendar in zījes has received attention from academics over the last few
centuries. We could consider Ideler to be the forerunner of studies on the Qitai calendar inzījes (Ideler 1832). In his study, Ideler dealt with Ulugh Beg’s Zīj-i Sulṭānī—one of themost influential zījes—that was keenly investigated by early modern scholars in Europe.
Then, Sédillot edited, translated the Persian text of the calendar into French, and wrote acommentary on it on the basis of the Zīj-i Sulṭānī as part of his work to edit and translatethat zīj (Sédillot 1847–1853). In the course of the nineteenth century, therefore, the Qitai
calendar was studied along with an interest in the Zīj-i Sulṭānī, which was regarded as a
1

Regarding astronomical interrelation between China and Iran in this period, while the situation of theeastern side was relatively well documented, the number of these kinds of sources is apparently small in thewest (Allsen 2001, 161-175; van Dalen 2002).

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zīj representative of “Islamic astronomy.” Although these studies were useful enough tocomprehend the general structure of the Qitai calendar, we should point out the inevitableproblem of the text in the Zīj-i Sulṭānī, in which many Chinese technical terms
transcribed in Persian are ignored. They would have found much of interest in thesetechnical terms not only from a historical standpoint, but also from a linguistic one.
From the beginning of the twentieth century, when the history of science establisheditself as a discipline in the academic world, more detailed studies on this subject began toappear; first, we should refer to Kennedy’s study (Kennedy 1964). Kennedy
mathematically scrutinized the contents of the Qitai calendar, mainly by referring toKāshī’s Zīj-i Khāqānī, and provided later scholars with a reliable foundation to study thismaterial. He explained the leading characteristics of the calendar consisting of thefollowing three astronomical periods: (1) the solar year divided into twenty-four equal
divisions, (2) the mean lunation, and (3) the anomalistic month. He also clarified someinteresting facts in it; for example, he stated that a method in the lunar equation of the
Qitai calendar was of Babylonian origin, as we shall discuss in the commentary.
Although we have pioneering works by Imai (1962) in which the Qitai calendar wascontextualized in the Chinese astronomical tradition, the Qitai calendar attracted more
attention in Japan after Kennedy’s article. This interest is connected to the discovery of afragment manuscript of the solar table of a Chinese astronomical system—the Fu-tian li
符天曆1—in Japan in 1963. As we shall see in the discussion of this astronomical system,
it was never adopted as an official system by any Chinese dynasty, but it continued in use
and even influenced several official astronomical systems. In China, there are few known
sources that shed light on its contents. Nakayama, who carried out a close investigation
into the fragment, noted that the specific method concerning the solar equation in theastronomical system can be identified as the same as that in the Qitai calendar (Nakayama
1966, 451-452).
Afterwards there appeared studies that dealt with the original source, the Zīj-i Īlkhānī.
In an article focusing on the Zīj-i Īlkhānī, Mercier mentioned the Qitai calendar and tried
to reconstruct several Chinese technical terms appearing in Persian transcriptions(Mercier 1984, 49-51). As a source for the Qitai calendar, he referred to the Revised

1

For the notion of the Chinese term li 曆, which is better translated as an “astronomical system,” seeMartzloff (2009, 367-372) and Sivin (2009, 38-40).

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Da-ming li 重修大明曆, which was officially adopted at the end of the Jin Dynasty(1182–1234) and initially used by the Mongols (Mercier 1984, 51-52).
From mathematical and astronomical viewpoints, this course of studies on the Qitai
calendar resulted in a collaborative work by van Dalen, Kennedy, and Sayid (van Dalen etal. 1997). The study, which focused on the Qitai calendar, covers almost all the contentsof the calendar. In addition, the authors reconstructed an extensive table for conversion
between the Qitai and Hijri calendars. This table is attached at the end of the chapter on
the Qitai calendar in the Zīj-i Īlkhānī. The study regards the Revised Da-ming li and
Fu-tian li as main sources for the calendar. Therefore, it is clear that the Qitai calendar, infact, does not completely accord with any known Chinese astronomical system but is anamalgam of various elements from several astronomical systems.
After elucidating its mathematical structure, studies followed attempting to embed thecalendar into a historical context. Van Dalen assigned one section to the description of thecalendar in his article concerning the astronomical interaction between Iran and China
under Mongol domination (van Dalen 2002, 333-336). Although this calendar has beentermed the “Chinese-Uighur” calendar, I have published an article in which I argued thatthe involvement of contemporary Uighurs in compiling the calendar is hard to validate(Isahaya 2009). This is why we call this calendar the “Qitai calendar” different from theconventional nomenclature.
In this way, the calendar has been investigated thoroughly from both mathematical andhistorical perspectives; however, we should acknowledge that some issues worth treating
have been left unsolved. Among them, priority should be given to contextualizing theresults achieved by previous studies concerning this calendar in the Chinese astronomical
tradition. Although we have Imai’s pioneering work, which is probably the only work
undertaking this kind of approach, it is based on Sédillot’s edition of Ulugh Beg’s Zīj-iSulṭānī. Now we need to scrutinize the contents of the Qitai calendar on the basis of thetext of the Zīj-i Īlkhānī, critically edited on the basis of various manuscripts, to reassess
all of the contents of the calendar in a comparison with the series of studies on Chinese
astronomy accumulated over the last fifty years. Through continued analysis of this kind,
we can gradually deepen our understanding of astronomical interrelation in Eurasia. For
these purposes, a translation with commentary and an edition of the Qitai calendar shallbe prepared.

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II. Editorial Procedures
For textual criticism, we have Maas’s comprehensive description of the stemmatic
approach to philology (Maas 1958). Then, West’s Textual Criticism and Editorial
Technique (West 1973) can be regarded as a replacement for Maas’s work. Whereas
Maas’s work treated contamination—which also has to be considered in this case—as aregrettable deviation, West reframed it into the “general” textual analysis. In addition, thiswork also deals with editorial method, which is not amply covered by Maas’s work.
Although West’s focus is on Greek and Latin texts, the researchers of Arabic script-based
text are also greatly benefited by his work. As a critical edition of a source written in
Arabic script, Mano’s edition of the Bābur-nāma can be considered to be a modelingwork made by collating various manuscripts and reassessing the previous studies (Mano
1995). In addition, the draft of an edition and the English translation of the Sheng-wu
qin-zheng lu 聖武親征錄 by Atwood has instructed me in the standard of a criticaledition (Atwood forthcoming).
Among the many extant manuscripts of the Zīj-i Īlkhānī, the following nine, copied inrelatively early periods, are collated to edit the text. As shall be explained after the short
introduction of each manuscript, we can broadly classify these manuscripts into three
versions: original, annotated, and embedded.
BoL (Oxford, Bodleian Library, 1513 [Hunt. 143]), was set as the base text for thisedition, because this is the unique manuscript categorized into the embedded version
which incorporates the marginal annotations—probably due to Ṭūsī himself—into themain text. This manuscript, in which author’s revisions are reflected on the main text, canbe considered the “final” version of this work. It was copied by Muḥammad b. Maḥmūd.
b. ‘Abd al-Raḥmān in 679 AH./1280–81. However, the first eleven leaves, including thedescription of the Qitai calendar (2v-10r), “are supplied later by other hands on white
paper in a very bad and awkward hand writing” (Sachau & Ethé 1889, 926). So, the exact
date when the part of the Qitai calendar was copied is unknown. In addition, BoL is a rare
manuscript, in which the Qitai-Uighur calendar (Tārīkh-i Khaṭā wa Uyghūr) is explainedin the sixth chapter (14v-19r), which is assigned to the explanation of the Jewish calendar

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Yoichi ISAHAYASCIAMVS 14

in all other manuscripts we used.1 Regarding the tables, unfortunately, almost all of thesewere illegible or not filled in. The leaf number appearing in the edited text is based on
this manuscript.
BL (London, British Library, Or. 7464) was made at Maragha in 676 AH./1277–78,
only three years after the death of Ṭūsī. This is a rare manuscript including the “longer”
introduction (Boyle 1963). In this manuscript, supplemental annotations appear in themargin. Because of many differences of expression from other manuscripts, thismanuscript seems to be categorized into a different group in terms of the wording.
KM (Tehran, Kitābkhāna, Mūza wa Markaz-i Asnād-i Majlis-i Shūrā-yi Islāmī, 181)
was copied in the thirteenth century according to the introduction of the facsimile version
recently published in Iran (Tusi 2012, 29). With regard to references to the Qitai calendar,
unfortunately, the parts from the second section to the fifth section are missing. The main
text is supplemented by marginal annotations as in BL.
SB (Berlin, Staatsbibliothek zu Berlin, Sprenger 1853)2 was made in 689 AH./1290.
The main text is similar to that of KM, but almost all the marginal notes appearing in BL
and KM are little found in this manuscript.
DK (Cairo, Dār al-Kutub al-Miṣrīya, Dār al-Kutub Mīqāt Fārsī 1) was made at
Maragha in 692 AH./1293 (King 1981, 203). The main text is close to that of SB, and thismanuscript also lacks the marginal annotations appearing in some manuscripts like BL
and KM.
BN (Paris, Bibliothéque nationale de France, Ms. Ancien fonds persan 163)3 wascopied by a son of the author, Aṣīl al-Dīn b. Naṣīr al-Dīn (d. 715 AH./1315), according to
the first pages on the manuscript (Richard 1989, 179). He and his brother were in chargeof the Maragha after the death of their father (Sayılı 1960, 217-218). With regard to thedescription on the Qitai calendar, the main text is well explained in contrast to the simple
sentences appearing in SB and DK. But we do not find explanatory notes similar to themarginal annotations in BL and KM or those in the main text of BoL; therefore, this1

The contents of the Qitai-Uighur calendar, consisting of ten sections in this manuscript, are by and large

parallel with those of the Qitai calendar, but we find quite a few differences in the wording and values. In
addition, many Persian transcriptions of the Chinese technical terms are cut off there.
2

We can read the Berlin manuscript on the website of the Staatsbibliothek zu Berlin:(http://digital.staatsbibliothek-berlin.de/dms/werkansicht/?PPN=PPN635599538).

3This manuscript is available through Gallica, the digital library of the Bibliothèque nationale de France:(http://gallica.bnf.fr/ark:/12148/btv1b8410891x.r=Persan+163.langEN).

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manuscript seems to be classified into an entirely independent group. The copyist was
undoubtedly familiar with astronomical computation—we could conjecture that this is theaforementioned Aṣīl al-Dīn, though this is conjecture, because the end of the manuscript,
from which we can usually take information about the copyist and date of copying, ismissing. The copyist did not only revise the text but also the values in the tables.
NK: (Istanbul, Nuruosmaniye kütüphanesi, No. 2933) is a contaminated manuscript
made by a cross-reference both to an embedded version, such as BoL, and the family of
SB. In the manuscript, the marginal notes of the annotated versions like BL and KM
appear in the main text as well as BoL. In addition, the specific values in the table of theseventh section only appear in this manuscript except for SB.
KDT (Tehran, Kitābkhāna-yi Dānishgāh-i Tihrān, Ḥikmat 165) is also noteworthy,
because it is the only manuscript, besides the BL, which includes a longer introduction(Sawadi & Nik-Fahm 2012, 367). However, the wordings of the main text are a little bit
different from that of BL; it is rather closer to the manuscripts of the other original andannotated versions. According to the catalogue, the manuscript was copied during the 14thand 15th centuries (Danish-Pazhuh, 1960-63, 1: 23). As far as the description of the Qitai
calendar is concerned, the parts from the middle of the seventh section are omitted. This
manuscript is also a contaminated one like NK, but the textual structure is closer to theoriginal and annotated versions, unlike NK, which is closer to the embedded version.
BML (Florence, Biblioteca Medicea Laurenziana, Or. 24) has similar components
with BL, KM and KDT, in which the contents of the main text are supplemented with
marginal annotations. This manuscript is also made around 15th century as a result ofcontamination and the wording is close to the annotated versions. In regard to the values
in the tables and Persian transcriptions of the Chinese technical terms, the copyist of themanuscript improved the values, probably through recomputation, and revised someforeign terms, perhaps through consultation with someone from China. Therefore, interms of the tables and transcriptions, it is the most reliable manuscript among thosewhich are used for this edition.

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Yoichi ISAHAYASCIAMVS 14

KDT (17v): we can see marginal annotations surrounding the main text.

As mentioned above, the aforementioned manuscripts can be classified into three
versions: original, annotated, and embedded. The original versions include SB and DK.
The main text of these manuscripts is sometimes too simple to explain the contents of the
Qitai calendar. For this reason, further explanation would need to be added to the margins,
as we shall discuss concerning the second versions. The second, annotated version
consists of BL and KM, in which the main text of the original versions is supplemented
by marginal annotations. There is little difference between the marginal annotations of thetwo manuscripts, so we can assume the close relationship of the manuscripts in thisversion. The annotations in the margins of the manuscripts appear in the main text of BoL
which is classified into the third, embedded, version.
To consider the relationship among these three versions, we can refer to the case of theTadhkira fī ‘Ilm al-Hay’a also compiled by Ṭūsī. Through an investigation into
manuscripts of the work, Ragep identified two versions: the “original” Maragh and “final”
Baghdad versions (Ragep 1993, 1: 70-75). The original version was revised at various

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times by Ṭūsī himself between 1261 and 1274, and the revision process can be seen in themargins of several manuscripts. “Ṭūsī would approve an original version and then havethe copyist place the revisions he had made up to that point in the margins” (Ragep 1993,
1: 74). The final version refers to the one that incorporates all of the previous revisions
into a new fair copy of the text, although it cannot be ascertained whether this version
occurred before or after Ṭūsī’s death (Ragep 1993, 1: 75).
The process of revision can be applied to the case of the Zīj-i Īlkhānī—at least in thepart of the Qitai calendar—which was compiled around the same time as the Tadhkira.
The original versions were probably revised by Ṭūsī himself. At first, revisions took theform of marginal annotations, and later, these annotations were incorporated into the maintext. As Ragep did when editing the text of the Tadhkira (Ragep 1993, 1: 86), I have also
designated the embedded version (BoL), which provides a consistent explanation of thecontents, as the basic text for this edition.
Among the manuscripts to which we have referred, BN’s position is relatively isolated.
There is little marginal annotation in this manuscript. To clarify the meaning of thesentences, explanation was added in the main text of this manuscript; however, this
explanation is original and it is not found in other manuscripts.
The other three manuscripts—NK, KDT, and BML—were made as a result ofcontamination; however, the characteristics of NK are quite different from the those of
the other two. The text of NK was apparently based on an embedded version, like BoL, so
that marginal notes appearing in the annotated versions are embedded into the main text;
but, NK sometimes takes the description in the text and values in the tables from the otherversions. Regarding the table of the seventh section, the values of a column arecompletely identical to those of SB and are not found in any other manuscript. On theother side, KDT and BML are essentially categorized into the annotated versions, like BL
and KM; however, some passages are apparently also taken from embedded versions. We
interpret this to mean that contamination occurred in these three manuscripts.
Since the first sentences about the lunar argument in the seventh section are quite agood example to show the abovementioned relationship among these nine manuscripts,
we shall list the variations of this part in each version.
First, the text of SB, categorized into an original version, is taken:
For the lunar argument, “the initial value of the lunar argument” at the beginning of a year must be
known, which is called jūnjūn kā in the Qitai language.

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Yoichi ISAHAYASCIAMVS 14‫و اما حصۀ ماه را ابید که اصل حصۀ ماه در مبدأی یک سال معلوم ابشد و به لغت قتا أن‬‫را «جوجنوناک» خوانند‬As we can see, the specific value of the “the initial value of the lunar argument” is not
mentioned in the original version. In the manuscripts of the annotated versions, the value
is supplemented in the form of the marginal annotations as we can see the sentences in
BL:
For the lunar argument, “the initial value of the lunar argument” at the beginning of a year must be
known.
(Marginal annotation) The value is 78 days and 3,948 funks—78d 1, 5, 48f—in the year of the rat
corresponding to the year 633 of the Yazdigird era, and then the value annually increases 7d 0, 5,
38f.
The value is called jūnjūn kā in the Qitai language.

‫و اما حصۀ ماه را ابید که اصل حصۀ ماه در مبدأی یک سال معلوم ابشد‬،‫ عح روز و اهمح فنک بوده است؛ و بعد از أن‬،‫(حاش یه) و أن در سال موش که موافق خلج یزدجردی است‬‫هحل مقدار میابید افزود‬٠‫هر سال را این ز‬‫و به لغت قتا أن را «جوجنوناک» خوانند‬The marginal annotation is incorporated into the main text of the BoL, the embedded
version:For the lunar argument, “the initial value of the lunar argument” at the beginning of a year must be
known, which is 78 days and 3,948 funks—78d 1, 5, 48f—in the first year of the Superior Epochcorresponding to the year 633 (of the Yazdigird era), and which is called jūnjūn kā in the Qitai
language.

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The Tārīkh-i Qitā in the Zīj-i Īlkhānī159‫و اما حصۀ ماه را ابید که اصل حصۀ ماه در مبدأی یک سال معلوم ابشد؛ و أن در اول‬‫سال شانکون موافق خلج هفتاد و هشت روز و سه هزار وهنصد و چهل و هشت فنک بوده‬‫ ارقام أن عح اهمح و به لغت خطاییان را «جوجنوناک» خوانند‬،‫است‬The marginal passage “and then the value annually increases 7d 0, 5, 38f” in BL is notfound in BoL. But the same explanation follows after the passage “the value is called
jūnjūn kā in the Qitai language,” so that the sentence of BL is repetitive.
Then we see the sentences of BN as below:
For the lunar argument, “the initial value of the lunar argument” at the beginning of a year must be
known. The value is 23 days and 2,836 funks—23d 0, 47, 16f—in the first year of the Superior Epoch.
The value is called jūnjūn kā in the Qitai language.

‫و اما حصۀ ماه را ابید که اصل حصۀ ماه در مبدأی یک سال معلوم ابشد؛ و أن در اول‬‫شانکون بیست و سه روز و دو هزار و هش تصد و یس و شش فنک بوده و ارقامش کج‬‫مزیو؛ و به لغت قتا أن را «جوجنوناک» خوانند‬٠The difference of the “initial value” between 78.3948 and 23.2836 days is caused by
the fact that the latter subtracted the period of an anomalistic month as many times as
possible from the value of the first. Although this difference does not affect the final
result, the following marginal annotation related to this passage is worth noticing forconsideration of the relationship of the manuscript with others:
In the poor exemplar, the junjūn(s) (i.e., anomalistic months) have been added to the “initial value ofthe lunar argument.” It has been set as 78d 1, 5, 48f in the first year of the Superior Epoch.

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Yoichi ISAHAYASCIAMVS 14‫ «جنجون» بر اصل حصۀ ماه افزوده است و در اول شانکون‬،‫در نسخۀ اصل ضعیف‬‫هناده و ارقامش این است عح اهمح‬From this, we know that the copyist of the manuscript revised the original sentence of
the “poor exemplar,” probably an original version.
Now, we refer to the contaminated manuscripts, and, first of all, the sentences of NK
are addressed:
For the lunar argument, “the initial value of the lunar argument” called the “first value to be kept” at the
beginning of a year must be known.
(Marginal annotation 1) The value is 23 days and 2,836 funks—23d 0, 47, 16f—in the first year of
the Superior Epoch corresponding to the year 633 (of the Yazdigird era).
(Marginal annotation 2) The value is 78 days and 3,948 funks—78d 1, 5, 48f—in the first year fromthe cycle of the Superior Epoch.
The value is called jūnjūn kā in the Qitai language.

‫و اما حصۀ ماه را ابید که اصل حصۀ ماه را که حمفوظ اول خوانمی در مبدأی یک سال معلوم‬‫ابشد‬‫مزیو فنک‬۰ ‫(حاش یۀ اول) و أن در اول شانکون موافق خلج کج روز بوده است‬‫(حاش یۀ دوم) و أن در سال اول از دور شانکون هفتاد و هشت روز و سه هزاز و هنصد و چهل و هشت فنک‬‫بوده است که ارقامش این است عح اهمح‬‫و به لغت قتا أن را «جوجنوناک» خوانند‬

There are two marginal annotations in NK; the first denotes the same value as that ofBN, and the second is taken either from the text of an embedded version or from amarginal note of the annotated versions. The manuscript contains two values taken fromdifferent sources.
Next are the sentences of KDT in the same part:SCIAMVS 14

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The Tārīkh-i Qitā in the Zīj-i Īlkhānī

For the lunar argument, “the initial value of the lunar argument”—(marginal annotation) we will call(it) the “first value to be kept”—at the beginning of a year must be known. The value is 23 days and2,836 funks—23d 0, 47, 16f—in the first year of the Superior Epoch.
(Marginal annotation) The value is 78 days and 3,948 funks—78d 1, 5, 48f—in the first year of thecycle of the Superior Epoch.
The value is called jūnjūn kā in the Qitai language.

‫و اما حصۀ ماه را ابید که اصل حصۀ ماه –(حاش یه) که حمفوظ اول خواهمی خواند— در‬‫ و أن در اول سال شانکون بیست و سه روز و دو هزار و‬.‫مبدأی یک سال معلوم ابشد‬‫مزیو‬۰ ‫هش تصد و یس و شش بود ارقامش این است کج‬‫(حاش یه) و أن در اول سال شانکون هفتاد و هشت روز و سه هزار و هنصد و چهل و هشت فنک وده است و‬‫ارقامش این است عح اهمح‬‫و به لغت قتا أن را «جوجنوناک» خوانند‬The main text of KDT is quite similar to that of BN, but the marginal annotation in
NK are also taken.
Finally, we refer to the sentences of BML, which is also a contaminated manuscript:
For the lunar argument, “the initial value of the lunar argument”—(marginal annotation 1) we will call(it) the “first value to be kept”—at the beginning of a year must be known.
(Marginal annotation 2) The value is 78 days and 3,948 funks—78d 1, 5, 48f—in the first year of theSuperior Epoch.
The value is called jūnjūn kā in the Qitai language.

—‫و اما حصۀ ماه را ابید که اصل حصۀ ماه –(حاش یه) که أن را حمفوظ اول خواهمی خواند‬‫در مبدأی یک سال معلوم ابشد‬‫(حاش یه) و أن در اول شانکون هفتاد و هشت روز و سه هزار و هنصد و چهل و هشت فنک وده است و‬‫ارقامش این است عح اهمح‬162

Yoichi ISAHAYASCIAMVS 14‫و به لغت قتا أن را «جوجنوناک» خوانند‬
The text is almost identical to that of the annotated versions, but the first marginal
annotation is the same as that of NK.
We can hardly determine a single archetype, considering the constant revisions madeto the text. This fact makes it clear that no stemma can be decisively constructed. Under
these circumstances, we should be reconciled to see what groupings are apparent among
these nine manuscripts (cf. West 1973, 42). Considering the variations between the
manuscripts, therefore, we can make a table as below. While we have edited the text of
the Qitai calendar on the basis of BoL, all variations between the manuscripts have been
embedded in the footnotes of the edition.
Versions

Manuscripts (the Date of Coying)

Original Versions

SB (1290) and DK (1293)

Annotated Versions

BL (1277/78) and KM (13 c.)

Embedded Version

BoL (after 1280/81)

Revised Version

BN (by 1315)

Contaminated Versions

NK, KDT (14-15 c.) and BML (ca. 14 c.)

The values of all entries in the table have been recomputed through the computer
program SCTR (Sexagesimal Calculator prepared by Benno van Dalen) on the basis of
the constants taken from the text. These “exact” values have been filled in the tables ofthe edited text and translation. However, in some cases, every manuscript put a value
different from the recomputed one in an entry. The variants different from the recomputed
values are recorded in the footnote.
In editing this text, we adopted the modern Persian orthography according to aprocedure followed by Nīk-Fahm and Shahīdī (Nik-Fahm & Shahidi 2009, 59-60). The
edited text is punctuated to facilitate reading, though no markings appear in the original
sentences. The letters “‫پ‬,” “‫چ‬,” and “‫ ”گ‬are represented as “‫ب‬,” “‫ج‬,” and “‫ک‬,” in mostmanuscripts, and we basically revise the forms of the original text to suit modern
orthography.
In addition, we have to mention our principle for transliterating Chinese characters
into the Latin script. In the text, we encounter many Chinese words transcribed into

SCIAMVS 14

The Tārīkh-i Qitā in the Zīj-i Īlkhānī

163

Persian, which undoubtedly have significant value from a linguistic standpoint. As is wellknown, Chinese pronunciation in the thirteenth century differed from that in the present;
hence, we have to consider the then pronunciation—i.e. Yuan-era early Mandarin—inorder to reconstruct the original Chinese characters from the phonetic transcriptions in the
text. We refer to Li and Zhou’s tabular work and Pulleyblank’s lexicon concerning
Yuan-era early Mandarin to deal with the Persian transcription forms in this text
(Pulleyblank 1991; Li & Zhou 1993). On the other hand, in some cases, we find it moreconvenient to provide the present pronunciation; therefore, we parallelize twotransliteration forms along with the Chinese characters. For example, let us take the caseof ke 刻 (khiai). The italicized ke is the present pronunciation according to the Pinyin
system, which is followed by the Chinese character 刻 . Then, the historicalpronunciation “khiai” using the International Phonetic Alphabet is shown withinparentheses.
In any case, the Persian transcriptions seem somewhat inconsistent, when not
obviously incorrect, as in the case of the “History of China” in Jāmi‘ al-Tawārīkh
compiled in Iran under Mongol rule (cf. Wang 2006). In some cases, copyists transcribed
the same Chinese character in different ways in a manuscript. For example, in the table ofthe twenty-four solar divisions (the third section), the term xiao 小 (siau) appears fourtimes: the eighth, eleventh, twentieth, and twenty-third divisions. In the table, there are
two distinctly different transcriptions as siyū and siyāu. We are interested in the obvious
mistakes in the transcriptions. For example, pī for yi 乙 (i), the second of the cycle of theten “heavenly stems.” One would have to assume in the beginning pī was yī. But very
early on, it seems they got corrupted, as can be seen in BoL, SB, and NK. But somemanuscripts seem to have the correct form such as BL and BML. Since we can hardly
find the direct relationship between BL and BML, it is possible that the BML copyist
relied on some informant—probably Chinese—for the Persian transcriptions. I am notfamiliar with linguistics, but hopefully, this material will also have some value for
specialists in that field.1
Before moving to the translation, we review the characteristics of the Zīj-i Īlkhānī
itself, and then consider the significance of the Qitai calendar from the standpoint of its
contents. Although the Zīj-i Īlkhānī is considered to be the major production by the1

For the discussion of this paragraph, I am definitely indebted to comments upon the draft by Christopher

Atwood.

164

Yoichi ISAHAYASCIAMVS 14

scholars of the Maragha observatory, who achieved a series of astronomical innovations
leading to the Copernican heliocentric celestial model, this zīj follows the Ptolemaic
tradition, and the parameters underlying the solar, lunar, and planetary tables were takenfrom the previous zījes, such as ones compiled by Ibn A‘lam, Ibn Yūnus, and Bīrūnī. As
King and Samsó point out, what is new in the Zīj-i Īlkhānī is the calendrical material; thatis, the introduction of the Qitai calendar which covers more than the half of the first book(maqāla)—concerning chronology and calendar conversion—of the zīj (King & Samsó
2001, 46; 2002, 499). We list the table of contents of the chapter on the Qitai calendar in
the Zīj-i Īlkhānī as follows (cf. Mercier 1984, 41-42).
Chapter 1
Description of the Qitai Calendar, on Knowing Its Years and Months.
Section 1
On the explanation of the divisions of a night-day among the people of the Qitai.
Section 2
On the consideration of the cycle of days.
Section 3
On knowing the years of the Qitai and their divisions in each year.
Section 4
On the consideration of the cycles of years among the Qitai and their era.
Section 5
On knowing the beginning of the divisions of the solar years which occur in each year.
Section 6
On knowing the beginning of the first month on mean motion.
Section 7
On knowing the arguments of the sun and the moon in the beginning of each year.
Section 8
On finding the equation of the sun.
Section 9
On finding the equation of the moon.
Section 10
On knowing the beginnings of each required year and determining an intercalarymonth in a year in which it occurs.
Section 11

SCIAMVS 14

The Tārīkh-i Qitā in the Zīj-i Īlkhānī

165

On knowing the fourth cycle.
Section 12
On knowing the Qitai calendar from the Arabic calendar.
Symbols( ): In the case of the Persian text, folio numbers from the BoL manuscript are given
inside parentheses ( ) in the main text. In the case of the English translation, in addition to
the former usage, parentheses ( ) are reserved for adding clarifying information to theoriginal text or words.
[ ]: In the Persian text, passages or words which are missing from the base manuscript
and were restored on the basis of evidence from other manuscripts are enclosed in square
brackets [ ]. Square brackets are also used in cases in which the form found in the basemanuscript was corrected on the basis of forms found in other manuscripts. In both cases,
the source of evidence with other variants is given in footnotes.
« »: In the Persian edition, the Chinese technical terms transcribed into Persian are
given inside double angular brackets « » in the main text. These terms are marked initalics in the English translation.
: The abjad numerals are underlined in the Persian text.

166

Yoichi ISAHAYASCIAMVS 14

III. Translation(2v) Chapter 1
Exposition of the Qitai Calendar, on Knowing Its Years and Months
Consisting of the Twelve Sections
Section 1
On the explanation of the divisions of a night-day among the people of the
Qitai
Scholars in the Qitai and Turkistan establish a cycle of twelve for the divisions of anight-day, days and years, and apply a name to each twelve. The names of the twelve in
two languages (i.e., Chinese and Turkish) are as follows.
Numbers

1

2

3

4

5

6

Names in Chinese

zhih

chīu

yim

māu

chin

ṣiz

Names in Turkish

kuskū

ūṭ

bars

ṭāushqan

lū

yīlān

Numbers

7

8

9

10

11

12

Names in Chinese

wū

wī

shin

yū’u

sū

khā’ī

Names in Turkish

yūnd

qūy

bījīn

dāqūq

īt

ṭūnghūz

They also divide each night-day, in the same manner as our arithmeticians divide it
into twenty-four, into twelve chāghs (i.e., double-hours).1 (3r) They subdivide eachdouble-hour into eight kih2 and also divide the whole night-day into 10,000 funks.1 Thus,
1

This is a Turkish word čāğ, which means “time” (Dihkhuda et al. 1998, 5: 7998). According to Clauson,

this word is not found in Turkish before the Mongol period, when it replaced öd (Clauson 1972, 404). For öd,
see Bazin (1991, 43, 259-260). Here, the čāğ is equivalent to the Chinese shi 時, which is a double-hour; thatis to say, a unit dividing a day into twelve equal intervals (Sivin 2009, 82-83). It is most likely that the wordčāğ became synonymous with the Chinese shi through cultural contact during the Mongol period, and then,holding the meaning of a double-hour, was transmitted further west.
2

Chinese ke 刻 (khiai). In Chinese astronomy, a ke was usually taken as a hundredth of a day, slightly lessthan the value of one ninety-sixth used in this calendar. The reason for adopting this value in this calendar
might be ascribed to making one double-hour (chāgh) equal to an integral number of kes. In fact, sometimes
efforts were made to modify the traditional value of ke in China, in order to make the system commensuratewith the double-hours; in one of these reforms, Emperor Wu of the Liang dynasty in 507 reduced the number

SCIAMVS 14

The Tārīkh-i Qitā in the Zīj-i Īlkhānī

167

each double-hour is 833 funks and one-third, and each kih is 104 funks and one sixth.
They regard the starting point of a night-day as midnight, that is the point when the firsthalf of the double-hour of zhih or rat passes, and the second half remains.2 After that, thedouble-hours continually pass one by one until the midday that falls on the middle of the
double-hour of wū or horse. At the time when the length of a day and night are equal, thebeginning of the day is the middle of the double-hour of māu or hare, and the beginningof the night is the middle of the double-hour of yū’u or cock. Because the length of day
and night increases and decreases, the beginning of a day or night sometimes falls earlier
and at other times later; however, the times of midnight and midday do not move at all.
We have determined parts of double-hours and kihs with funks, and put the results in atable in order to easily determine what time has passed in each double-hour and kih.
According to the custom of our astronomers/astrologers, we have marked funks in the
sexagesimal form, and put (those on the table), and also marked fractional parts in the
sexagesimal form. The whole funks of a night-day are marked in the sexagesimal form, 2,
46, 40f. Then, whenever the number of funks exceeds 10,000 funks, it ought to be
subtracted from that number. In place of the subtracted 10,000 funks, a night-day is added.
If a night-day is required to be represented in funks, one is subtracted from the numbers ofnight-days and this number (i.e., 10,000 funks) is put in place of it (i.e., a night-day) for
the required calculation. The table is as follows.

of ke in a day-night to ninety-six, the same as in this calendar. But this improvement, which made themexactly equivalent to the Chinese modern ke system, lasted only a very short time (Needham et al. 1960,
199).
1

Chinese fen 分 (fuan). In Chinese astronomical systems li 曆, generally, the fractions of a day are denotedby means of specific denominators (called, for example rifa 日法; there are several nomenclatures for thefractions in Chinese astronomical systems, which might cause some confusion); with rifa 5230, for instance,
the lengths of a year and month were represented as 365 1274/5230 and 29 2775/5230, respectively, in the
Revised Da-ming li 重修大明曆, which was adopted as an official astronomical system at the end of the Jin
dynasty (1182–1234) and was also initially used by the Mongols. Instead of a specific denominator, however,the Qitai calendar divided one day into 10,000 funks, which is practically equivalent to adopting a decimal
notation system up to the fourth decimal fraction; for example, as shall be mentioned later, the length of thesolar year in this calendar is represented as 365 days and 2,436 funks = 365.2436d (for fractions in the Chinese
astronomy, see e.g., Sivin 2009, 63).
2

The Chinese double-hours are called 12 shi-chen 時辰 and are represented by the twelve branches

mentioned before. The first unit, the double-hour of zi 子, begins at 11:00 p.m. of the previous day and ends
at 1:00 a.m, so that a day starts in the middle of the double-hour of zi.

168

Yoichi ISAHAYASCIAMVS 14

Table on knowing the beginning of the double-hours and kih s in terms of the funk s of the night-day in sexagesimal form
In Chiense

zhih

chīu

yim

māu

chin

ṣiz

wū

wī

shin

yū’u

sū

khā’ī

In Turkish

kuskū

ūṭ

bārs

ṭāushqan

lū

yīlān

yūnd

qūy

bījīn

dāqūq

īt

ṭūnghūz

1,30,16,40

1,44,10, 0

1,58, 3,20

2,11,56,40

2,25,50, 0

2nd Power, 1st Power, Funk s, Fractions

Number of finks
1 2,39,43,20

0, 6,56,40

0,20,50, 0

0,34,43,20

0,48,36,40

1, 2,30, 0

1,16,23,20

2 2,41,27,30

0, 8,40,50

0,22,34,10 0,36,27,30

0,50,20,50

1, 4,14,10

1,18, 7,30

1,32, 0,50

1,45,54,10 1,59,47,30 2,13,40,50

2,27,34,10

3 2,43,11,40

0,10,25, 0

0,24,18,20 0,38,11,40

0,52, 5, 0

1, 5,58,20

1,19,51,40

1,33,45, 0

1,47,38,20 2, 1,31,40

2,15,25, 0

2,29,18,20

4 2,44,55,50

0,12, 9,10

0,26, 2,30

0,39,55,50

0,53,49,10

1, 7,42,30

1,21,35,50

1,35,29,10

1,49,22,30 2, 3,15,50

2,17, 9,10

2,31, 2,30

5 0, 0, 0, 0

0,13,53,20 0,27,46,40 0,41,40, 0

0,55,33,20

1, 9,26,40

1,23,20, 0

1,37,13,20

1,51, 6,40

2, 5, 0, 0

2,18,53,20

2,32,46,40

6 0, 1,44,10

0,15,37,30 0,29,30,50 0,43,24,10

0,57,17,30

1,11,10,50

1,25, 4,10

1,38,57,30

1,52,50,50 2, 6,44,10

2,20,37,30

2,34,30,50

7 0, 3,28,20

0,17,21,40 0,31,15, 0

0,45, 8,20

0,59, 1,40

1,12,55, 0

1,26,48,20

1,40,41,40

1,54,35, 0

2,22,,21,40

2,36,15, 0

8 0, 5,12,30

0,19, 5,50

0,32,59,10 0,46,52,30

1, 0,45,50

1,14,39,10

1,28,32,30

1,42,25,50

1,56,19,10 2,10,12,30 2,24, 5,50

2,37,59,10

2, 8,28,20

Section 2
On the consideration of the cycles of days
The Qitai have another cycle by which they take days and years into consideration. Thatis a cycle of ten, names of which are as follows: 1. kā, 2. yī, 3. pīn, 4. tīn, 5. wū, 6. kī, 7.
kin, 8. sin, 9. zhim, 10. kūy. By combining this cycle with the cycle of twelve, a cycle ofsixty is obtained. They count years and days with this cycle. This cycle is their substitutefor our week. We call this cycle the “sixty-cycle.” The compound of these two cycles is in
the way that was put in the following table.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

kā-zhihyī-chīu

pīn-yimtīn-māu

wū-chinkī-ṣizkin-wū

sin-wī

zhim-shinkūy-yū’u

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

kā-sū

yī-khā’ī

pīn-zhihtīn-chīu

wū-yimkī-māukin-chinsin-ṣizzhim-wūkūy-wī

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

kā-shinyī-yū’upīn-sū

tīn-khā’ī

wū-zhihkī-chīu

kin-yimsin-māu

zhim-chinkūy-ṣiz

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

kā-wū

yī-wī

pīn-shintīn-yū’u

wū-sū

kī-khā’ī

kin-zhihsin-chīuzhim-yim

kūy-māu

41.

42.

43.

44.

45.

46.

47.

48.

49.

50.

kā-chinyī-ṣizpīn-wū

tīn-wī

wū-shinkī-yū’ukin-sū

sin-khā’īzhim-zhih

kūy-chīu

51.

52.

53.

54.

55.

56.

57.

58.

59.

60.

kā-yimyī-māupīn-chintīn-ṣiz

wū-wū

kī-wī

kin-shinsin-yū’uzhim-sūkūy-khā’īSCIAMVS 14

The Tārīkh-i Qitā in the Zīj-i Īlkhānī169(3v) Section 3
On knowing the years of the Qitai and their divisions in each year
The years of the Qitai are solar, that is, they are measured from the time when the sunreaches a certain point on the celestial sphere until the time when the sun returns to thesame place. According to them, this amounts to 365 days and 2,436 funks which in the
sexagesimal form is 365d 0, 40, 36f and which is called suijū in their language.1 As ourastronomers/astrologers divide a year into twelve, they divide the length of a year into
twenty-four equal parts, each of which comprises 15 days and 2,184 5/6 funks—which inthe sexagesimal form is 15d 0, 36, 24f 50. Each part is called one kīja in their language.2
Moreover, each season consists of six kīja and the beginnings of our seasons fall in the
middles of their seasons. Thus, the beginning of spring among them approximately falls
in the middle of the sign Aquarius. The four points of the solstices and equinoxes are in
the middles of their seasons. The names of the divisions of a year in their language andthe numbers of days and funks in the sexagesimal form from the beginning of the year
through to the end are presented in the following table.

1

The term suijū might well be the phonetic transcription of the Chinese sui-zhou 歳周 (sui-tʂiau), the lengthof a solar year, taken as 365.2436d in this case. Although there are various values taken as the length of a solar
year in the Chinese astronomical systems, the value in the Zīj-i Īlkhānī is almost equal to that of the Revised
Da-ming li (365.243594...d) adopted in the later Jin and early Yuan periods (1182–1234 and 1215–1280) (Jinshi, 21: Bu qi-shuo 1; Yabuuti 1990, 388-393). This is one reason why we can regard this astronomical system
as one of sources of the Qitai calendar (other reasons shall be discussed below). This term has also been
ascribed to sui-shi 歳實 (sui-ʂi) (van Dalen et al. 1997, 149), but this term denotes the Year Numerator(3,652,436 funks in this case), not exactly the days of the solar year (Sivin 2009, 615). From the viewpoint of
the Persian transcription, furthermore, it is somewhat difficult to read the term in such a way.
2

The term kīja is probably the Chinese qi-ce 氣策 (khi-tʂhai), the length of the twenty-four equal divisionsof a solar year, each 15.21848333... days long in this case (cf. Sivin 2009, 79-81). This term appears in the
Revised Da-ming li and Shou-shi li 授時曆, the official astronomical systems of the Jin and Yuan dynasties
respectively (Jin shi, 21: Bu qi-shuo 1; Yuan shi, 54: Bu qi-shuo 1; Sivin 2009, 79-81, 604). Although thisterm has been interpreted in other ways such as jie-qi 節氣 (tsiɛ-khi) or zhong-qi 中氣 (tʂiuŋ-khi), both ofthese are far from the Persian transcription form and the latter does not denote each of the twenty-four
divisions of a solar year but only the even-numbered ones (Mercier 1984, 50; van Dalen et al. 1997, 149).

170

Yoichi ISAHAYASCIAMVS 14

Table of the beginnings of each solar division, calculated in days and funks
in sexagesimal form
The Spring Season

The Summer Season
2nd Power, 1st Power,

Funks, Fractions

Days

Names of Divisions

Number of Divisions

2nd Power, 1st Power,

Funks, Fractions

Days

Names of Divisions

Number of Divisions
1

lījun

0

0,0,0,0,

7

līkha

91

0,51,49,0

2

wūshī

15

0,36,24,50

8

siyū-man106

1,28,13,50

3

kin-jih30

1,12,49,40

9

manjun121

2,4,38,40

4

shūn-fūnd

45

1,49,14,30

10

shājir136

2,41,3,30

5shīnk-mīnk

60

2,25,39,20

11

siyāu-shū

152

0,30,48,20

6

kūwū

76

0,15,24,10

12

dāy-shū167

1,7,13,10

The Autumn Season

The Winter Season
2nd Power, 1st Power,lījū’u182

1,43,38,0

19

lītūn

273

2,35,27,0

14

chīu-shū197

2,20,2,50

20

siyāu-shih

289

0,25,11,50

15

baylū

213

0,9,47,40

21

dāy-shih304

1,1,36,40

16

siyū-fan

228

0,46,12,30

22

dūnjin319

1,38,1,30

17khanlū

243

1,22,37,20

23

siyū-khan

334

2,14,26,20

18

shūn-kūn

258

1,59,2,1024

dāy-khan350

0,4,11,10

lījun

365

0,40,36,0

Days

Funks, Fractions

Names of Divisions

Number of Divisions

Funks, Fractions

2nd Power, 1st Power,

Days

Names of Divisions

Number of Divisions
13

Section 4
On the consideration of the cycles of years among the Qitai and their era
The Qitai count years in the sixty-cycle (4r) and unite the cycles to the (following) threenames; the first is called the cycle of the “Superior Epoch,” the middle is the cycle of the

SCIAMVS 14

The Tārīkh-i Qitā in the Zīj-i Īlkhānī

171“Middle Epoch,” and the final is the cycle of the “Inferior Epoch.” The period of the threecycles is 180 years, and years are united to these cycles. If they want to consider a period
exceeding this amount, they derive it from the creation of the world. According to their
computation, 8,863 wans had completely elapsed from the beginning up to the first yearof Genghis Khan’s reign. Each wan is 10,000 years. 9,679 years had passed in the current
wans, and the (9,6)80th year is that of the accession of Genghis Khan that corresponds to
the 60th year of the sixty-cycle—the final year of the cycle of the Middle Epoch.
According to the computation of the Persians, the year 633 of the Yazdigird era is the firstyear of the cycle of the Superior Epoch. But Turks only use a cycle of twelve and count itin their language. The regulation of their calendar is unknown to us.

Section 5
On knowing the beginnings of the divisions of the solar years which occur ineach year
In order to know the beginning of one of the twenty-four solar divisions in a given year,
we must know which day and double-hour within the sixty-cycle falls on the beginning of
the lījun (i.e., first solar division) before or after the year. We call it the “initial value ofthe divisions of a year,” and it is called kījū in the language of the Qitai.1 The initial valueis 11 days and 7,660 funks—11d 2, 7, 40f—in the first year of the cycle of the Superior
Epoch after the accession of Genghis Khan. In order to know the beginning of anotheryear, we ascertain whether the year is before the “epoch year” or after; and how many
years are between the two. We multiply the balance by the excess of a solar year over 360,
i.e. 5 days and 2,436 funks—5d 0, 40, 36f—, which is called suiyū in their language.2
Regarding funks that exceed 10,000—i.e., 2, 46, 40f—, we consider each 10,000 to be one
day and add (it) to the number of days, and then subtract 10,000 (from the funks) in orderto obtain the interval between the epoch year and the required year.

1

Qi-shou 氣首 (khi-ʂiau) denotes the beginning of the first division of any solar year (van Dalen et al. 1997,

149).
2

Sui-yu 歳餘 (sui-iu) indicates the excess of a solar year over 360, namely 5.2436 days (van Dalen et al.
1997, 149). This constant is called tong-yu 通餘 (thuŋ-iu) in the Shou-shi li; the former is used for denoting
the surplus of the days of a solar year in this system, that is, 2,436 funks in this case (Yuan shi, 54: Bu
qi-shuo 1; Sivin 2009, 271-273, 390-391).

172

Yoichi ISAHAYASCIAMVS 14

Then, if a required year is after the epoch year, we add that interval to theaforementioned initial value. (4v) If the funks exceed 10,000—i.e., 2, 46, 40f—, wesubtract this amount (i.e., 10,000 funks) and add one day to the days. If the number ofdays exceeds 60, we subtract 60 from it. If the required year is before the epoch year, we
subtract the interval from the epoch. If the days cannot be subtracted, we add 60 to theepoch and subtract (the days from it). If the funks cannot be subtracted, we subtract one
day and add 10,000—i.e., 2, 46, 40f—to the funks.
What results after the addition or subtraction is the beginning of the lījun in therequired year in the sixty-cycle. We consider the funks to be one day, and each place thatis reached marks the beginning of the required year, and the whole years are attached to
the names (of the sixty-cycle).
For example, if we want to know the beginning of the 10th year of the cycle of theSuperior Epoch that corresponds to the year 642 of the Yazdigird era and is the kūy-yū’u
in the Qitai language—the year of the cock in Turkish—we multiply the interval between
the epoch year and the required year—the value is 9—by the sui-yū (i.e., 5d 2,436f); 45
days and 21,924 funks—45d 6, 5, 24f—is obtained. For 20,000 funks—i.e., 5, 33, 20f—,
we get two days; it becomes 47 days, and 1,924 funks remain—47d 0, 32, 4f—. Then, we
add this amount to the initial value, i.e., 11 days and 7,660 funks—11d 2, 7, 40f—,
because the required year is after the epoch year. The result is 58 days and 9,584
funks—58d 2, 39, 44f—, which is the beginning of the required year. We consider the
funks to be one day and add it to the days, so that the total becomes 59 days. The 59th dayof the sixty-cycle is zhim-sū, that is the day of the dog (īt kūn) in Turkish.1 Since thebeginning of the day, 9,584 funks have elapsed—2, 39, 44f—. If we seek that (value) in
the table for the beginnings of double-hours and kihs, we find (it) between the first andsecond (double-hours). The excess over the beginning of the first double-hour—2, 39, 43f
20—is two-thirds of a funk. Thus, we know that the beginning of the 10th year of the
sixty-cycle corresponding to the year of the cock is (5r) in the first kih among the
double-hour of zhih corresponding to the double-hour of rat in the 59th day of the
sixty-cycle corresponding to the day of the dog; (the others can be known) also by
analogy with this.
When the beginning of a year has been determined, we add the divisions of the year tothe beginning, in order to know the beginning of each required division. For example, if

1Turkish kün, which means “a day.”SCIAMVS 14

The Tārīkh-i Qitā in the Zīj-i Īlkhānī173

we want to know the beginning of the seventh division in this year, in the table of the
beginnings of the divisions of the years, we see that (it is) 91 days and 51, 49f after (thebeginning of the year). We add this to the days and funks of the head of the year; it
becomes 149 days and 3, 31, 33f. Then, we subtract a day—i.e., 2, 46, 40f— from the
funks, which results in 150d 0, 44, 53f. We subtract 60 from the days as many times as
possible, and 30 remain. We know that, in the 31st day of the sixty-cycle—i.e., the day of
kā-wū corresponding to the day of the horse in Turkish—the beginning of the seventh
division is in the sixth kih from the double-hour of māu—hare in Turkish—and 89 funks
have elapsed since the beginning of the kih; (the others can be known) by analogy withthis.
We have made a table consisting of the beginnings of years during 24 years from thecycle of the Superior Epoch, and another table on the beginnings of the divisions of theyear of the cock as an example; these tables are as follows.

174

Yoichi ISAHAYASCIAMVS 14

Table of the beginning of lījun in several years
Name of Beginning of Lījun inName of the Beginning of Lījun

yī-khā’īṭūnghūz

634

yī-chīu

ūṭ

170,1,36sin-ṣizīlān

635

pīn-yimbars

22

0,42,12pīn-sū

īt

636

tīn-māu

ṭāushqan27

1,22,48

sin-māu

ṭāushqan637

wū-chinlū

32

2,3,24pīn-shin

bījīn

638

kī-ṣizyīlān

37

2,44,0sin-chīuūṭ639

kin-wū

yūnd

43

0,37,56

tīn-wī

qūy

640

sin-wī

qūy

48

1,18,32zhim-zhih

kuskū

641

zhim-shin

bījīn

53

1,59,8tīn-ṣizīlān

642

kūy-yū’u

dāqūq

58

2,39,44zhim-sū

īt

643

kā-sū

īt

4

0,33,40

wū-chinlū

644

yī-khā’īṭūnghūz

9

1,14,56

kū’y-yū’u

dāqūq

645

pīn-zhih

kuskū

14

1,54,52

wū-yimbars

646

tīn-chīuūṭ

19

2,35,28

kūy-wī

qūy

647

wū-yimbars

25

0,29,24

kī-chīu

ūṭ

648

kī-māuṭāushqan30

1,10,0

kā-wū

yūnd

649

kin-chinlū

35

1,50,36kī-khā’īṭūnghūz

650

sin-ṣiḍ

yīlān

40

2,31,12kā-chinlū

651zhim-wūyūnd

46

0,25,8kin-sū

īt652

kūy-wī

qūy

51

1,5,44yī-māuṭāushqan653

kā-shinbījīn

56

1,46,20

kin-shin

bījīn

654

yī-yū’udāqūq

12,26,56

yī-chīu

ūṭ655

pīn-sū

īt

70,20,52

sin-wī

qūy

656

tīn-khā’īṭūnghūz

12

1,1,28pīn-zhih

kuskū

657

wū-zhihkuskū

17

1,42,4sin-ṣizyīlān

Turkish

2,7,40in Qitai

Funks

11

2nd Power

Name of the Sixty –Cycle

kuskū

1st Power

Qitai Yearskā-zhihTurkish Years

Yazdigird Years
633

SCIAMVS 14

175

The Tārīkh-i Qitā in the Zīj-i Īlkhānī

Table of the beginnings of divisions of the year of the cockcorresponding to the year 642 of the Yazdigird era
The Times ofDivisions from the

Position of the Sun

Names of the

Beginnings ofDivisions in Qitai

2nd Power

1st Power

Funks

Days of the

Sixty-Cycle

Names of the Divisions
lījun

58

2,39,44zhim-sū (īt)

Mid. Aquarius

wūshī

14

0,29,29

wū-yim (bārs)

Begin. Pisceskin-jih29

1,5,54kūy-ṣiz (īlān)Mid. Piscesshūn-fūnd

44

1,42,19wū-shin (bījīn)Begin. Aries

shīnk-mīnk

59

2,18,43

kūy-khā’ī (ṭūnghūz)Mid. Aries

kūwū

15

0,8,28kī-māu (ṭāushqan)

Begin. Taurus

līkha

30

0,44,53kā-wū (yūnd)Mid. Taurus

siyū-man45

1,21,18

kī-yū’u (dāqūq)Begin. Gemini

manjun0

1,57,43kā-zhih (kuskū)Mid. Gemini

shājir15

2,34,8kī-māu (ṭāushqan)

Begin. Cancersiyāu-shū

31

0,23,52

yī-wī (qūy)

Mid. Cancerdāy-shū46

1,0,17

kin-sū (īt)

Begin. Leolījū’u1

1,36,42yī-chīu (ūṭ)

Mid. Leochīu-shū16

2,13,7

kin-chin (lū)

Begin. Virgo

baylū

32

0,2,52pīn-shin (bījīn)Mid. Virgosiyū-fan47

0,39,17

sin-khā’ī (ṭūnghūz)

Begin. Libra

khanlū

2

1,15,42pīn-yim (bārs)Mid. Libra

shūn-kūn

17

1,52,6sin-ṣiz (īlān)Begin. Scorpio

lītūn

32

2,28,31pīn-shin (bījīn)Mid. Scorpio

siyāu-shih

48

0,18,16zhim-zhih (kuskū)

Begin. Sagittarius

dāy-shih30,54,41

tīn-māu (ṭāushqan)

Mid. Sagittarius

dūnjin18

1,31,6zhim-wū (yūnd)

Begin. Capriconsiyū-khan

33

2,7,30tīn-yū’u (dāqūq)Mid. Capricondāy-khan48

2,43,55

zhim-zhih (kuskū)

Begin. Aquarius

lījun

4

0,33,40

wū-chin (lū)

Mid. Aquarius

176

Yoichi ISAHAYASCIAMVS 14(5v) Section 6
On knowing the beginning of the ārām ay (i.e., the first month) in mean motion
First, the interval in a year between the beginnings of the first month—the head of ayear—and wūshī—the second division from the divisions of a solar year—must be known.
In the first year of the cycle of the Superior Epoch corresponding to the year 633 of theYazdigird era, the value is 14 days and 4,676 funks—14d 1, 17, 56f—, as shall bementioned on a table. It is called shūnjan in the Qitai language,1 and we call it “the initialvalue of the head of years.”Then, we obtain the difference between that year and the required year. We multiply itby the excess of a solar year over a lunar year, i.e., 10 days and 8,764 funks—10d 2, 26,
4f—, which is called suijā in the Qitai language.2 We add the result to “the initial value ofthe head of years,” if the required year is after that year (i.e., the year 633 of the Yazdigirdera). The period of the mean lunar month is 29 days and 5,306 funks—29d 1, 28, 26f—,
which is called shūja in the Qitai language. 3 If (the period of the month) can be
subtracted from the addition of the result of the multiplication to shūnjan, we subtract as
many times as (the remainder) becomes smaller than the period of a month. Each time,
when we subtract (the period of a month), an “intercalary month” (māh-i shūn)4 falls in

1

This term is likely the Chinese run-ying 閏應 (ɽiuan-iaŋ). It represents the interval from the mean firstmonth (ārām ay) to the second solar division (wūshī) for any particular year (van Dalen et al. 1997, 150). In
the case of the Shou-shi li, this term is used for denoting the interval between the winter solstice of the epoch
year and the last new moon (Yuan shi, 54: Shou-shi li jing 1; Sivin 2009, 392, 396).
2

Probably, Chinese sui-chai 歳差 (sui-tʂha). This term denotes the difference between the solar year andtwelve mean lunar months, 10.8764d. This constant is called tong-run 通閏 (thuŋ-ɽiuan) in the Shou-shi li
and resembles sui-run 歳閏 (sui-ɽiuan) mentioned in the Song dynastic history (Song shi, 77: Guan-tian li;
Yuan shi, 54: Bu qi-shuo 1; van Dalen et al. 1997, 150; Sivin 2009, 390-391). Sui-chai 歳差 (sui-tʂha), on
the other hand, means “annual precession” in the official Chinese astronomical systems in the later period.
3

Chinese shuo-ce 朔策 (ʂau-tʂhai), a mean synodic month, 29.5306d. This constant is slightly different

from that of the Revised Da-ming li. It would be appropriate to consider that the value was rounded off frommost Chinese values including that of the Revised Da-ming li (29.53059...d), by means of the ten-thousandfunks method (Jin shi, 21: Bu qi-ce bu gua-hou bu ri-chan bu gui-lou; cf. van Dalen et al. 1997, 123).
Although Mercier reconstructed the Persian phonetic form as shou-shi 朔實 (ʂau-ʂi) which van Dalenfollowed (Mercier 1984, 51; van Dalen et al. 1997, 150), shou-ce 朔策 (ʂau-tʂhai) is more appropriate thanshou-shi 朔實 (ʂau-ʂi) from the standpoint of the meaning and the Persian form as in the case of sui-zhou 歳
周 (sui-tʂiau) discussed before.
4

This is a combination of the Persian term māh with Chinese run 閏 (ɽiuan), which means “intercalary.”

SCIAMVS 14

The Tārīkh-i Qitā in the Zīj-i Īlkhānī

177

the years between the epoch year and the required year, and the year (in which anintercalary month falls) includes thirteen months.
If the required year is before the epoch year, we subtract the result of themultiplication of the year interval by the excess of a solar year over a lunar year from “theinitial value of the head of years.” If it cannot be subtracted, we add several times thelength of a month (i.e., 29d 1, 28, 26f) to “the initial value of the head of years”; then,from that, we subtract the result of the multiplication (of the year interval by the excess ofa solar year over a lunar year) as the remainder becomes smaller than the period of amonth.
What remains smaller than the period of month is the interval between the beginningof the first month and the wūshī in the required year, and that is the initial value of thehead of the year. Then, we find the days of the wūshī in that year, and subtract the interval
between the beginning of the first month and the beginning of the wūshī from that. If it
cannot be subtracted, we add 60 to the day of the wūshī (6r) and subtract from thisamount. What remains is the sixty-cycle of the beginning of the first month in mean
(lunar) motion. Then, we see the sixty-cycle of the beginning of the lījun (i.e., the firstdivision of a solar year) in that year, in order to know which beginning (of the first monthor the lījun) precedes the other and how much difference lies between them, an amountthat is inevitably smaller than the period of a division of a solar year.

Section 7
On knowing the arguments of the sun and the moon at the beginning of eachyear
For the solar argument, we subtract the interval between the beginnings of the first monthand the wūshī from one sixth of the period of a solar year, i.e., 60 days and 8,740
funks—60d 2, 25, 40f—called kījā by them.1 What remains is the solar argument at the
beginning of the year.
For the lunar argument, “the initial value of the lunar argument” at the beginning of ayear must be known, which is 78 days and 3,948 funks—78d 1, 5, 48f—in the first year of1

The interval between the twenty-second solar division (the winter solstice) and the second solar division(yu-sui 雨水), namely one-sixth of a solar year, is 60.8740 days. The Persian transcription may bereconstructed as qi-chai 氣差 (khi-tʂha).

178

Yoichi ISAHAYASCIAMVS 14

the cycle of the Superior Epoch corresponding to the year 633 (of the Yazdigird era), andwhich is called jūnjūn kā in the Qitai language.1 Then, we obtain the difference between
that year and the required year. We multiply the difference by 7 days and 338 funks—7d 0,
5, 38f—, which is called jūnjā in the Qitai language.2 In my opinion, that is the excess ofa solar year over thirteen anomalistic cycles. If the required year follows the epoch year,
we add the result to the initial value of the lunar argument; otherwise, we subtract (theresult from the initial value of the lunar argument), in the manner described in the sixth
section. We call the result the “first number to be kept.” Thus, we subtract the interval
between the beginnings of the first month and the wūshī from that amount. If it cannot be
subtracted, we add 60 to the days, and then subtract. We call what remains the “second
number to be kept.” Thus, from the second number to be kept, we subtract the period of acycle for the lunar argument—the value of which is 27 days and 5,556 funks—27d 1, 32,
36f—, and called junjūn (i.e., an anomalistic month) by them—as many times as (theremainder) becomes smaller than the cycle.3 What remains is a ninth of the initial valueof the lunar argument. We multiply that by 9 to obtain the lunar argument of the
beginning in the required year. If it exceeds 248 days, we subtract 248 days from thosedays. What remains is the lunar argument of the beginning in the required year.
(6v) We multiply an anomalistic month (i.e., 27.5556 days) by several numbers andput the resulting (values) in a table, so that the (required values) can easily be obtained
from there. In addition, we put all (values) mentioned in the sixth and seventh sections in
the case of two twelve-cycles from the beginning of the cycle of the Superior Epoch intoa table as an example. The table is as follows.

1

Although the transcribed form jūnjūn kā is somewhat obscure, it could be read as the zhuan-zhong ying 轉

終應 (tʂiuɛn-tʂiuŋ iaŋ) from the standpoint of the meaning. The first part jūnjūn undoubtedly denotes
zhuan-zhong 轉終 (tʂiuɛn-tʂiuŋ), a (Lunar) Revolution Terminal Constant, that is to say, an anomalisticmonth (cf. van Dalen et al. 1997, 149; Sivin 2009, 606). The corresponding term in the Shou-shi li is denoted
as zhuan-ying 轉應 (tʂiuɛn-iaŋ), that is, a Revolution Interval Constant between the epochal winter solsticeand the preceding lunar perigee (Yuan shi, 54: Bu yue-li 4; Yabuuti & Nakayama 2006, 21; Sivin 2009, 455).
2This Persian transcribed form can probably be reconstructed as the Chinese zhuan-chai 轉差 (tʂiuɛn-tʂha)which, in this case, means the excess of a solar year over thirteen anomalistic months.
3

The Chinese form of junjūn is zhuan-zhong 轉終 (tʂiuɛn-tʂiuŋ), i.e., an anomalistic month.

SCIAMVS 14179

The Tārīkh-i Qitā in the Zīj-i Īlkhānī

Table of the two aforementioned cycles from the beginning of the "Superior Epoch"
Lunar Argument

One-Ninth of the Initial Value of the
Lunar Argument

Second Number to Be KeptFirst Number to Be Kept

Solar Argument in the Head of theYears

Years in Which the First Month
Precede the Lī jun

Sixty-Cycle of the Beginning of theFirst Month in Mean Motion

Sixty-Cycle of the Beginning of the
Wū shī

Turkish Years

Interval between the Beginnings of theFirst Month and the Wū shī, i.e., theInitial Value of the Head of Years

Qatai Years

Yazdigird Yearsshūn

633 kā-zhih

kuskū

14

1, 17, 56

262, 44, 512

1, 26, 9

46

1, 7, 4478

1, 5, 48

63

2, 34, 32

82, 16, 079634 yī-chīuūṭ25

0, 57, 20

32

0, 38, 1

6

2, 27, 21 muqaddam

35

1, 28, 2085

1, 11, 26

60

0, 14, 6

42, 42, 14

44

2, 6, 46635 pīn-yim

bars

6

1, 54, 58

37

1, 18, 3730

2, 10, 1954

0, 30, 42

92

1, 17, 485

2, 8, 46

3

0, 17, 38

27

2, 38, 42

0, 57, 20636 tīn-māuṭāushqan

17

1, 34, 2242

1, 59, 13

25

0, 24, 51 muqaddam

43

0, 51, 18

99

1, 22, 42

81

2, 35, 0 26

2, 16, 28 241

1, 1, 32shūn

637 wū-chinlū28

1, 13, 46

472, 39, 49

19

1, 26, 3 muqaddam

32

1, 11, 54

106

1, 28, 2078

0, 14, 34 22

2, 42, 42 206

2, 10, 58

638 kī-ṣiz

yīlān

9

2, 11, 24

53

0, 33, 45

43

1, 9, 151

0, 14, 16

113

1, 33, 58

83

2, 9, 140, 18, 6

2, 42, 54

shūn

639 kin-wū

yūnd

20

1, 50, 28

58

1, 14, 2137

2, 10, 33 muqaddam

40

0, 35, 12120

1, 39, 36

99

2, 35, 48 17

0, 44, 40 155

1, 8, 40

640 sin-wīqūy

20, 1, 46

3

1, 54, 57

1

1, 53, 1158

2, 23, 54

127

1, 45, 14 125

1, 43, 28 15

1, 6, 24 138

1, 37, 36

shūn

1

9

641 zhim-shin bījīn

122, 27, 50

82, 35, 33

56

0, 7 4347

2, 44, 30

134

1, 50, 52 121

2, 9, 42 11

1, 32, 38 104

0, 0, 22642 kūy-yū’u

dāqūq

23

2, 7, 14140, 29, 29

50

1, 8, 55 muqaddam

37

0, 18, 26

141

1, 56, 30 117

2, 35, 56

7

1, 58, 52

69

1, 9, 48
1, 41, 44643 kā-sūīt

50, 18, 12

19

1, 10, 5

140, 51, 53

55

2, 7, 28148

2, 2, 8 143

1, 43, 56

52, 20, 5652644 yī-khā’īṭūnghūz

15

2, 44, 16

24

1, 51, 21

81, 53, 45 muqaddam

44

2, 28, 4

155

2, 7, 46 139

2, 10, 10

20, 0, 30

18

0, 4, 30shūn

645 pīn-zhih

kuskū

26

2, 23, 40

29

2, 31, 17

30, 7, 37 muqaddam

34

0, 2, 0162

2, 13, 24 135

2, 36, 24 25

1, 59, 20 231

1, 14, 0646 tīn-chīuūṭ80, 34, 38

35

0, 25, 1326

2, 37, 1552

1, 51, 2169

2, 19, 2 161

1, 44, 24 23

2, 21, 24 214

1, 45, 56

shūn

647 wū-yim

bars

19

0, 14, 240

1, 5, 49

21

0, 51, 47 muqaddam

41

2, 11, 38

176

2, 24, 40 157

2, 10, 38 20

0, 0, 58 180

0, 8, 42648 kī-māuṭāushqan0

1, 11, 40

45

1, 46, 25450, 34, 45

60

1, 14, 0183

2, 30, 18 183

1, 18, 38 18

0, 23, 2 163

0, 40, 38

shūn

shūn

shūn

649 kin-chinlū

110, 51, 4

50

2, 27, 1

39

1, 37, 57

49

1, 34, 36

190

2, 35, 56 189

1, 44, 52 24

0, 49, 16 218

1, 50, 4650 sin-ṣiz

yīlān

22

0, 30, 28

56

0, 20, 57

33

2, 37, 9 muqaddam

38

1, 55, 12

197

2, 41, 34 175

2, 11, 6 10

1, 15, 30

0, 12, 5094651 zhim-wū

yūnd

3

1, 28, 6

1

1, 1, 3357

2, 20, 757

0, 57, 34

205

0, 0, 32 201

1, 19. 6

81, 37, 34

77

0, 44, 46652 kūy-wī

qūy

14

1, 7, 30

6

1, 42, 952

0, 34, 39

46

1, 18, 10

212

0, 6, 10 197

1, 45, 20

42, 3, 48

42

1, 54, 12653 kā-shin

bījīn

25

0, 46, 54

112, 22, 45

46

1, 35, 51 muqaddam

35

1, 38, 46219

0, 11, 48 193

2, 11, 34

02, 30, 2

80, 16, 58654 yī-yū’u

dāqūq

6

1, 44, 32

17

0, 16, 41

10

1, 18, 49

54

0, 41, 8226

0, 17, 26 219

1, 19, 34 26

1, 38, 2 239

0, 48, 58655 pīn-sūīt

17

1, 23, 56

220, 57, 17

42, 20, 1 muqaddam

43

1, 1, 44233

0, 23, 4 215

1, 45, 48 22

2, 4, 16 204

1, 58, 24656 tīn-khā’īṭūnghūz

28

1, 3, 2027

1, 37, 53

59

0, 34, 33

32

1, 22, 20

240

0, 28, 42 211

2, 12, 2 18

2, 30, 30 170

0, 21, 10657 wū-zhih

kuskū

9

2, 0, 58

32

2, 18, 29

230, 17, 31

51

0, 24, 42247

0, 34, 20 237

1, 20, 2 17

0, 5, 54 153

0, 53, 6658 kī-chīuūṭ20

1, 40, 22372, 59, 517

1, 18, 43 muqaddam

40

0, 45, 18

214

0, 39, 58 193

1, 46, 16

2, 4, 442, 2, 3606Section 8
On finding the equation of the sun
We obtain the solar argument at the beginning of a year. To the argument, we add thelength of a lunar month (i.e., synodic month), which is 29 days and 5,305 funks—29d 1,
28, 26f—called shūja in the Qitai language; as a result, the arguments of (the beginningsof the successive) months become known in order. Every time the argument exceeds thelength of a solar year, 365d 0, 40, 36f, we subtract the length from the value. If we want toknow the (solar) argument at (the beginning of) a month in the middle of a year, we
multiply the number of months between the first and the required months by the shūja.
We add the result to the (solar) argument at the beginning of the year to obtain the (solar)
argument at the head of that month. We multiply the result of the multiplication of the
shūja by various numbers, and put (the resulting values) in a table to obtain (the required
values) from there.

180

Yoichi ISAHAYASCIAMVS 14

When the solar argument is known, if the number of days without funks is smaller thanthe half-circle—that is, 182, called bījūtin by them1—we subtract the argument from 182
and also keep the original value. Then, we multiply the result of the subtraction by theoriginal value.2 We double the result, and obtain a ninth of the amount. The result is thesolar equation, which is an additive value, they call the additive nū.3
If the days of the argument exceed 182, we calculate the excess over 182. We subtract
the argument from the double of 182, which is the whole circle, and multiply the excessby the remainder of the subtraction. We double the result, and obtain a ninth of theamount. What is obtained is the solar equation, which is a subtractive value and they callthe subtractive tiyā’ū, meaning “subtractive.”4 They call the solar equation tāyānk zhikī.5
We have made a table of the solar equation. We have put the funks of the equation
corresponding to the arguments in the sexagesimal form in that table, (7r) so that (values)

1This term is the Chinese ban zhou-tian 半周天 (puɜan tʂiau-thiɛn), or the Celestial Half-Circle. The term

appears in the fragment of the Fu-tian li on the solar equation (we shall address this fragment below) as wellas in the Shou-shi li (Momo 1969, 401; Sivin 2009, 410, 614).
2

For the obscure sentence “pas ḥiṣṣa rā dar tamām-i ḥiṣṣa ḍarb kunīm,” there is a marginal note in the

manuscript BN (9v) as follows: “Maqṣūd az ḥiṣṣa-yi awwal ānche hama bāqī mānda az nīma-yi daur-i āftāb,
wa maqṣūd az tamām-i ḥiṣṣa ḥiṣṣa-yi āftāb ast dar sar-i māh-i maṭlūb.” (The meaning of the first “ḥiṣṣa” iswhat remains after subtracting from the half-cycle of the sun, and the meaning of the “tamām-i ḥiṣṣa” is thesolar argument at the head of the required month.)
3

The Chinese nu 朒 is used for the slow phase of the luminaries. Here, it means “additive,” as applied tothe solar and lunar equations (van Dalen et al. 1997, 149).
4The Chinese tiao 朓 is used for the fast phase of the luminaries. Here, it means “subtractive,” as applied tothe solar and lunar equations (van Dalen et al. 1997, 150).
5Regarding the term tāyānk zhikī, some obscurity remains. But at least we are able to affirm that the zhikī,

the latter half of this technical term, is ru-qi 入氣 (ɽi-khi). It is a temporal parameter used for thecomputation of the solar equation (Martzloff 2009, 178, 181-189). With regard to the first half tāyānk, as vanDalen has mentioned, it would be appropriate to consider the word to be tai-yang 太陽 (thai-iaŋ), “the sun”
(van Dalen et al. 1997, 150). So, we would like to suggest the compound tai-yang ru-qi 太陽入氣 (thai-iaŋɽi-khi) as a highly probable form from the standpoints of the Persian transliteration, meaning, and context.
Mercier has argued that this term is comparable to the Turkish tänkäš (Mercier 1984, 50); however, it would
be difficult to make this argument as far as the manuscripts we used are concerned. If it were permissible toread the tāyānk in this way, we would not interpret well the latter half words zhikī.
As I have discussed in a previous article, the contemporary Uighurs were scarcely involved in compilingthe Qitai calendar, but this calendar was directly brought from China into Iran by a Qitai sage—a Taoist
master—accompanying his Mongol ruler (Isahaya 2009). In consideration of the fact that almost all technicalterms are Chinese, there is little justification for regarding the term as Turkish one.

SCIAMVS 14

The Tārīkh-i Qitā in the Zīj-i Īlkhānī

181

corresponding to the (solar) arguments at the heads of months are obtained from thattable.

(7v) Section 9
On finding the equation of the moon
We establish the lunar argument at the beginning of a year, which is called jūnjūn kā in
the Qitai language. For the other months, we add 17 days and 7,754 funks—17d 2, 9,
14f—, which is called junjūn shā by them,1 to the argument at the beginning of theyear—when the argument exceeds 248, 248 is subtracted from it and the remainder is
kept—so that the argument at the head of each month is obtained. We set a tableconsisting of the values of multiplying the junjūn shā by several numbers, so that we add
what corresponds with each different number to the argument of the beginning of a year;
as a result, the argument at the head of the required month is obtained.
If the days of the argument are smaller than 124, which is called banjūshā,2 we
subtract the number of days from 124 and keep the original value. We multiply the daysby the original value. What is obtained is the lunar equation; it is called nū, meaning“additive.” If (the days) exceed 124, we multiply the excess by the original value after
subtracting (the original) from 248. What is obtained is the lunar equation. It is calledtiyā’ū, meaning “subtractive.” They call the lunar equation tāyānk zhichūn.3

1

As Mercier has assumed, we should read this term as zhuan-zhong chai 轉終差 (tʂiuɛn-tʂiuŋ tʂha), whichmeans “nine times the excess of a lunar month over an anomalistic month” (27.5556 days, in this case), i.e.,
17.7754 days (Mercier 1984, 51). As mentioned before, the excess of a lunar month over an anomalisticmonth is represented as zhuan-chai 轉差 (tʂiuɛn-tʂha) in the Shou-shi li.
2This term should be read as ban zhou-xian 半周限 (puɜan tʂiau-hian), the parts of the half-cycle, or 124.

The cycle of an anomalistic month is divided into 248 parts in this calendar, so that the half-cycle consists of
124 parts. The parts of the cycle zhou-xian 周限 (tʂiau-hian) are used in the Shou-shi li; in this case, thecycle is approximately divided into 336 parts (Sivin 2009, 453).
3

In this case, also, we could not offer the definite reconstruction form; however, the latter part, zhichūn,

could probably be interpreted as ru-zhuan 入轉 (ɽi-tʂiuɛn) which is a temporal parameter to use for thecomputation for the lunar equation as well as ru-li 入曆 (ɽi-li) (Martzloff 2009, 189-196). Although we
could consider the first half to be the same form as tai-yang ru-qi 太陽入氣 (thai-iaŋ ɽi-khi), we would liketo suggest that the first half is, rather, tai-yin 太陰 (thai-iam), “the moon.” Therefore, the compound form
could be reconstructed as tai-yin ru-zhuan 太陰入轉 (thai-iam ɽi-tʂiuɛn).

182

Yoichi ISAHAYASCIAMVS 14

We have made a table illustrating the lunar equation, so that (the values)
corresponding with the arguments of the heads of months are obtained from thattable.The tables are as follows.

Table of the solar equation that is called "Tāyānk Zhikī "Positive
Solar Equation
Solar Argument0
182
0, 0, 01
181
0, 0, 402
180
0, 1, 203179
0, 1, 59
4
178
0, 2, 38
5
177
0, 3, 176
176
0, 3, 557
175
0, 4, 328174
0, 5, 99173
0, 5, 46
10
172
0, 6, 2211
171
0, 6, 5812170
0, 7, 3313
169
0, 8, 814
168
0, 8, 43
15
167
0, 9, 1716
166
0, 9, 5017
165
0, 10, 2318
1640, 10, 56
19163
0, 11, 2820
162
0, 12, 021
1610, 12, 3122
1600, 13, 223
159
0, 13, 3324
1580, 14, 325
157
0, 14, 32
26
1560, 15, 127
155
0, 15, 3028
154
0, 15, 5829
153
0, 16, 26

Negative
Positive
Solar Equation
Solar Argument Solar Argument
182
364
30
152
0, 16, 53
183
363
31
151
0, 17, 20
184
362
32
150
0, 17, 47
185
361
33
149
0, 18, 13
186
360
34
148
0, 18, 38
187
359
35
147
0, 19, 3
188
358
36
146
0, 19, 28
189
357
37
145
0, 19, 52
190
356
38
144
0, 20, 16
191
355
39
143
0, 20, 39
192
354
40
142
0, 21, 2
193
353
41
141
0, 21, 25
194
352
42
140
0, 21, 47
195
351
43
139
0, 22, 8
196
350
44
138
0, 22, 29
197
349
45
137
0, 22, 50
198
348
46
136
0, 23, 10
199
347
47
135
0, 23, 30
200
346
48
134
0, 23, 49
201
345
49
133
0, 24, 8
202
344
50
132
0, 24, 27
203
343
51
131
0, 24, 45
204
342
52
130
0, 25, 2
205
341
53
129
0, 25, 19
206
340
54
128 0, 25. 36
207
339
55
127
0, 25, 52
208
338
56
126
0, 26, 8
209
337
57
125
0, 26, 23
210
336
58
124
0, 26, 38
211
335
59
123
0, 26, 53

Negative
Positive
Negative
Solar Equation
Solar Argument
Solar Argument
Solar Argument
212
334
60
122
0, 27, 7
242
304
213
333
61
121
0, 27, 20
243
303
214
332
62
120
0, 27, 33
244
302
215
331
63
119
0, 27, 46
245
301
216
330
64
118
0, 27, 58
246
300
217
329
65
117
0, 28, 10
247
299
218
328
66
116
0, 28, 21
248
298
219
327
67
115
0, 28, 32
249
297
220
326
68
114
0, 28, 43
250
296
221
325
69
113
0, 28, 53
251
295
222
324
70
112
0, 29, 2
252
294
223
323
71
111
0, 29, 11
253
293
224
322
72
110
0, 29, 20
254
292
225
321
73
109
0, 29, 28
255
291
226
320
74
108
0, 29, 36
256
290
227
319
75
107
0, 29, 43
257
289
228
318
76
106
0, 29, 50
258
288
229
317
77
105
0, 29, 57
259
287
230
316
78
104
0, 30, 3
260
286
231
315
79
103
0, 30, 8
261
285
232
314
80
102
0, 30, 13
262
284
233
313
81
101
0, 30, 18
263
283
234
312
82
100
0, 30, 22
264
282
235
311
83
99
0, 30, 26
265
281
236
310
84
98
0, 30, 29
266
280
237
309
85
97
0, 30, 32
267
279
238
308
86
96
0, 30, 35
268
278
239
307
87
95
0, 30, 37
269
277
240
306
88
94
0, 30, 38
270
276
241
305
89
93
0, 30, 39
271
275
90
92
0, 30, 40
272
274
91
91
0, 30, 40
273
273

SCIAMVS 14

Table of the lunar equation that is called "Tāyānk Zhichūn "Positive

Negative

Funks

9
31
54
16
26
48
11
33
43
5
28
50
13
22

14
48
22
56
10
44
18
52
6
40
14
48
22
36

Nos.

2
1
0
0
2
1
1
0
2
2
1
0
0
2

Funks

1st Power

17
35
53
71
88
106
124
142
159
177
195
213
231
248

1st Power

26
1
27
1 32
36
12
2
55
0 18
32
38
3
82
1 51
8
24
4 110
0 37
4
50
5 137
2
9
40
36
6 165
0 55
36
2
7 192
2 28
12
48
8 220
1 14
8
14
9 248
0
0
4
0
26
The Value of the Sum of
12 Half-Night and a Day in Each
Month Approx.

Multiples of "Jūnjūn Shā ,"i.e.,
Arg. of Begin. of the Month

1
2
3
4
5
6
7
8
9
10
11
12
13
14

2nd Power

28
10
38
20
48
30
59
40
9
51
19
1

Days

Nos.

1
0
1
0
1
0
1
0
2
0
2
1

Funk s

Funks

29
59
88
118
147
177
206
236
265
295
324
354

1st Power

1
2
3
4
5
6
7
8
9
10
11
12

2nd Power

216
215
214
213
212
211
210
209
208
207
206
205
204
203
202
201
200
199
198
197
196
195
194
193
192
191
190
189
188
187
186

2nd Power

156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186

Days

0, 49, 40, 50, 30, 51, 00, 51, 55
0, 52, 48
0, 53, 39
0, 54, 28
0, 55, 15
0, 56, 00, 56, 43
0, 57, 24
0, 58, 30, 58, 40
0, 59, 15
0, 59, 48
1, 0, 19
1, 0, 48
1, 1, 15
1, 1, 40
1, 2, 3
1, 2, 24
1, 2, 43
1, 3, 01, 3, 15
1, 3, 28
1, 3, 39
1, 3, 48
1, 3, 55
1, 4, 01, 4, 3
1, 4, 4

Days

92
91
90
89
88
87
86
85
84
83
82
81
80
79
78
77
76
75
74
73
72
71
70
69
68
67
66
65
64
63
62

Nos.

32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62

Nos.

248
247
246
245
244
243
242
241
240
239
238
237
236
235
234
233
232
231
230
229
228
227
226
225
224
223
222
221
220
219
218
217

Multiples of "Junjūn ,"i.e., the Anomalistic
Month

Funk sLunar Equation

124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155

Multiples of "Shūja ," i.e.,
The Period of the Lunar
Month

Negative

Lunar Equation

0, 0, 00, 2, 30, 4, 40, 6, 30, 8, 00, 9, 55
0, 11, 48
0, 13, 39
0, 15, 28
0, 17, 15
0, 19, 00, 20, 43
0, 22, 24
0, 24, 30, 25, 40
0, 27, 15
0, 28, 48
0, 30, 19
0, 31, 48
0, 33, 150, 34, 40
0, 36, 30, 37, 24
0, 38, 43
0, 40, 00, 41, 150, 42, 28
0, 43, 39
0, 44, 48
0, 45, 55
0, 47, 00, 48, 3

Positive

Lunar Argument

Lunar Argument

124
123
122
121
120
119
118
117
116
115
114
113
112
111
110
109
108
107
106
105
104
103
102
101
100
99
98
97
96
95
94
93

Lunar Equation

Lunar Argument
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31

183

The Tārīkh-i Qitā in the Zīj-i Īlkhānī

MonthsFunk s11
1, 56, 40
12102, 0, 01
92, 3, 202
8
2, 6, 40
3
7
2, 10, 0
4
6
2,
13, 205Multiples of Funk s of a
Night-Day
2 46
1
40
5 33
2
20
8 20
3
0
11
4
6
40
13 53
5
20
16 40
6
0
19 26
7
40
22 13
8
20
25
9
0
0

Section 10
On knowing the beginnings of each required year,
and determining an intercalary month in a year in which it occurs
From the solar argument at the beginning of a month, we know the (solar) equation, andknow whether (the equation) is additive or subtractive. From the lunar argument at the
beginning of a month, we also know the (lunar) equation, and know whether (theequation) is additive or subtractive. If both of the two equations are additive or
subtractive, we add them together; otherwise, we obtain the excess of one over the other,and we call that the “compound equation.” Then, if both of the equations or the excess are
additive, the compound equation is additive. If both of the equations or the excess are
subtractive, the compound equation is subtractive. Then, we obtain the sixty-cycle of thefirst day of the first month on the mean motion. We add the value of a month, which is 29
days and 5,306 funks—29d 1, 28, 26f—, i.e., shūja, to the first day. Whenever the days

184

Yoichi ISAHAYASCIAMVS 14

exceed 60, we reduce 60; so that, the sixty-cycle of the first day of each month on mean
motion is obtained. Then, if the compound equation is additive on the first day of eachmonth, we add (it) to the first day of that month. If (the equation) is subtractive, we
reduce (it); so that the sixty-cycle of the first day of each month becomes precisely known.
If the funks are smaller than the value of a half-night and one day, we count it as one day,and add it to the days. If (the funks) exceed the value of a half-night and one day, we
count it as two days, and add them to the days. Then, we insert the result into the table ofthe sixty-cycle, so that the cycle of the first day of each month in the cycle becomes
known. From the sixty-cycles of the first days of a month and the month that follows it, it
becomes known whether the former month has 30 days or 29 days. There must not be
more than two consecutive 29-day months, nor more than three consecutive 30-day
months. Then, they take into consideration the sixty-cycles of the first days of thedivisions of a solar year, which fall in each month. If (the year is) an intercalary one inwhich there are 13 months, a month in which only the sixty-cycle of the first day of adivision of a solar year falls is the intercalary month and each month in which thesixty-cycles of the first days of two divisions fall is not an intercalary month.
As an example, we have computed (the values of) months in the 10th year from thecycle of the Superior Epoch, which is the year of kūy-yū—the year of the cock in
Turkish—and the year of 642 of the Yazdigird era according to the calculation of the
Persians. We have detailed the operations in a table, so that (the others can be known)
also by analogy with this. That table is as follows.

Table of the calendar for the 10th year that is "kūy-yū'u " and the year of the cock corresponding to the 642nd year of the Yazdigird era, constructed as an example

MonthsSolar Argument

Solar Equ.

Lunar Argument

Lunar Equ.

Compound Equ.

Beginnings of theMonths in Mean
MotionBeginnings of theTrue Months

Days of Names ofthetheMonths Beginnings

Tthe Values of the Solar Year That
Occur in Each Months

Ārām

37

0, 18, 26 (+) 0, 19, 52

69

1, 9, 48(+) 1, 3, 15(+) 1, 23, 7

50

1, 8, 55

50

2, 32, 229 yī-māu

8 zhim-sū

23 tīn-chīuĪkindi66

1, 46, 52 (+) 0, 28, 21

87

0, 32, 22(+) 0, 53, 59(+) 1, 22, 20

19

2, 37, 21

20

1, 13, 130 kā-shin

10 kūy-ṣiz

25 wū-shin

Ujunj

96

0, 28, 38 (+) 0, 30, 35

104

2, 41, 36(+) 0, 34, 40(+) 1, 5, 15

49

1, 19, 749

2, 24, 2229 kā-yim

10 kūy-khā'y

26 kī-māu

Tūrtūnj

125

1, 57, 4 (+) 0, 26, 23

122

2, 4, 10(+) 0, 4, 4(+) 0, 30, 27

190, 0, 53

19

0, 31, 20

29 kūy-wī

12 kā-wū

27 kī-yū'u

Bīshīnj

155

0, 38, 50 (+) 0, 15, 30

140

1, 26, 44(-) 0, 28, 48(-) 0, 13, 18

48

1, 29, 19

48

1, 16, 1

30 zhim-zhih

13 kā-zhih

28 kī-māu

Altīnj184

2, 7, 16158

0, 49, 18(-) 0, 51, 0(-) 0, 52, 20

18

0, 11, 5

172, 5, 25

29 zhim-wū

14 yī-wī

29 kin-sū

15 yī-chīu(-) 0, 1, 20

Shūn

214

0, 49, 2(-) 0, 17, 47

176

0, 11, 52(-) 1, 2, 24(-) 1, 20, 11

47

1, 39, 31

47

0, 19, 20

29 sin-khā'ī

Yitīnj243

2, 17, 28(-) 0, 27, 20

193

2, 21, 6(-) 1, 3, 15(-) 1, 30, 35

17

0, 21, 17

16

1, 37, 22

30 kin-chin

1 kin-chin

17 pīn-shin

Sikisīnj

273

0, 59, 14(-) 0, 30, 40

211

1, 43, 40(-) 0, 53, 39(-) 1, 24, 19

46

1, 49, 43

460, 25, 24

30 kin-sū

2 sin-khāy

17 pīn-yimṬūqsūnj

302

2, 27, 40(-) 0, 27, 33

229

1, 6, 14(-) 0, 33, 15(-) 1, 0, 48

16

0, 31, 29

15

2, 17, 21

29 kin-chin

2 sin-ṣiz

17 pīn-shin

Unūnj

332

1, 9, 26(-) 0, 17, 47

247

0, 28, 48(-) 0, 2, 3(-) 0, 19, 50

45

1, 59, 55

45

1, 40, 530 kī-yū'u

4 zhim-zhih

19 tīn-māu

Biryikizminj

361

2, 37, 52(-) 0, 1, 59

16

2, 38, 2(+) 0, 28, 48(+) 0, 26, 49

15

0, 41, 41

15

1, 8, 30

30 kī-māu

4 zhim-wū

19 tīn-yū'u

Jaqshābāṭ

26

0, 39, 2(+) 0, 15, 1

34

2, 0, 36(+) 0, 51, 0(+) 1, 6, 1

44

2, 10, 745

0, 29, 28

30 kī-yū'u

4 zhim-zhih

20 wū-chin

Ārām

55

2, 7, 28 (+) 0, 25, 52

52

1, 23, 10(+) 1, 2, 24(+) 1, 28, 16

14

0, 51, 53

14

2, 20, 9kī-māuSCIAMVS 14

The Tārīkh-i Qitā in the Zīj-i Īlkhānī185(8r) Section 11
On knowing the fourth cycle
The people of Qitai have another cycle on which they rely for the “choice of days.” Thisis also a cycle of twelve, and the names of those twelve are as follows: 1. kin 2. chū 3.
man 4. pin 5. tin 6. chih 7. pū 8. wī 9. chin 10. shīu 11. khā’ī 12. pī. Among these, four
numbers are khī, meaning “black”1 and incline toward corruption; those are kin, man, pin,and shīu. Four are khūnk, meaning “yellow,”2 and incline toward beneficence; those arechū, tin, chih, and wī. Two are pah, meaning “white,”3 and are extremely beneficent;those are chin and khā’ī. Two are hūn4 representing extremely corrupt; those are pū andpī. They count the days of the solar divisions in the same order (of this cycle) as
mentioned at the beginning (of this section). When the turn comes to odd-numbereddivisions such as the first, third, and fifth divisions, they count the first day of thatdivision and the preceding day as one; that is to say, what comes about in the preceding
day is repeated at the first day of the division. The remaining days are in order.
We noted what turn comes about at the beginnings of years in the two (twelve-)cycles
from the first year of the cycle of the Superior Epoch, so that the order is counted fromthere. We put what turn comes about on the first day of the lījun in each year. Each year
after that, the turn comes to the sixth (from the order of the cycle on the lījun of thepreceding year). If that year is an intercalary year, the turn comes to the seventh. We haveplaced a “k” next to the intercalary years. (The others) can (be known) by analogy with
this.

1

The term khī, as mentioned here, means “black” hei 黒 (hei).

2

The term khūnk means “yellow” huang 黄 (huaŋ).

3

The term pah means “white” bai 白 (pai).

4

For this color, no manuscript has a translation into Persian except for DK, in which this color is expressedas the aghbar, meaning “dusty (color)” (12 v). In the Zīj-i Khāqānī compiled later, this color is expressed as
the khāk-i ālūd “polluted soil” (van Dalen et al. 1997, 123)

186

Yoichi ISAHAYASCIAMVS 14

bars

pī

chin

648

ṭāushqan tin

636ṭāushqan chū

649

lū

shīu

637

lū

pū

650

yīlān

man

638

yīlān

pī

651

yūnd

chin

639

yūnd

chih

652

qūy

chū

640

qūy

khā'ī

653

bījīn

pū

641

bījīn

pin

654

dāqūq

pī

642

dāqūq

chin

655

īt

chih

643

īt

man

656

ṭūnghūz

khā'ī

644

ṭūnghūz

wī

657

kuskū

pin

645

kuskū

kin

634

ūṭ

635

bars

k

k

Intercalary Years

First Turn of the Cycle of

647

shīu

"Lījun"Yazdigird Years

pin

kuskū

Turkish Years

Intercalary Years

First Turn of the Cycle ofchih"Lījun"ūṭTurkish Years

646

Yazdigird Years

k

633

k

k

k

Section 12
On knowing the Qitai calendar from the Arabic calendar
Since the Hijri calendar is more familiar to our astronomers/astrologers, we have put the
Hijri years and months for a hundred years from the first year of Genghis Khan’s reign ina table. The (Hijri) years are in the right side, the (Hijri) months are at the head of thetable, and the months of the Mongols are in the middle of the table with numerals. The
name of the Turkish year and an intercalary month are inserted. The table includes the
weekday of the first day of the Arabic month on the upper part (of an entry), and also the
sixty-cycle of the first day of the Qitai month, and the number of the days of the (Qitai)
month. The table is on the next page.

SCIAMVS 14

187

The Tārīkh-i Qitā in the Zīj-i Īlkhānī

IV. Commentary
Section 1
In the first section, the units of time in the Qitai calendar are explained. Among them, thefirst is the cycle of the twelve “terrestrial branches” (tu-zhi 地支), which functioned as
basic unit of time in the Chinese chronology.
These were originally abstract notions; however, from early on in China, each branch
was attached to an animal name and this twelve-animal cycle was quite popular in thecivil sphere. The Turks in the northern and western steppes also adapted the Chinese
calendar, replacing this abstract and official cycle of twelve branches with its popular
equivalent, namely, the twelve-animal cycle, which was not used for date-reckoning in
the Chinese official chronology (Bazin 1991). The Turko-Mongols in the Ilkhanid periodalso used this twelve-animal cycle to denote their years: for example, the “year of the rat”
(Melville 1994). The order of the cycle both in Chinese and Turkish is as below:

ChineseTurkishAnimals

ChineseTurkishAnimals

1
zi 子
(tsï)
kuskū
rat

2
chou
丑
(tʂhiau)
ūt
ox

3
yin
(ian)
bars
tiger

7
wu
(u)
yūnd
horse

8
wei
(vui)
qūy
sheep

9
shen
申
(ʂian)
bījīn
monkey

午

未

寅

4
mao
卯
(mau)
ṭāushqan
hare

5
chen
辰
(tʂhian)lūdragon

6
si 巳
(sï)
yīlān
snake

10
you
酉
(iau)
daqūq
cock

11
xu
(ʂiu)
īt
dog

12
hai
亥
(hai)
ṭūnghūz
pig戌

Then, three units for a night-day are explained: the chāgh, kih, and funk. The chāgh(double-hour) is denoted with the twelve branches shown above, such as the double hourof zi, or rat (chāgh-i zi or kuskū). The ratio of each unit is shown in the following table:
1 day

12 chāghs

1 chāgh

8 kihs

1 day

10,000 funks

1 chāgh

833 and 1/3 funks

1 kih

104 and 1/6 funks

188

Yoichi ISAHAYASCIAMVS 14

The funks are also marked with the sexagesimal form in accordance with the usage ofastronomers/astrologers in Iran.
The method dividing a day into 10,000 funks called the “ten-thousand funks method”(wan-fen fa 万分法) was rarely adopted by official Chinese astronomical systems.
Yabuuti has argued that this method was first introduced into China through the Fu-tian li
符天曆 compiled by Cao Shi-wei 曹士蔿 during the late Tang period, the Jian-zhong
建中 era (780–783). In regard to the Fu-tian li, the Xin wu-dai shi 新五代史 offers thefollowing passage:
During the Jian-zhong era, an astrologer, Cao Shi-wei, first changed the old method. He set the fifth
year of the Xian-qing era (i.e., 661 AD) as the start of the epoch and yu-shui as the starting point of theyear. He entitled (the astronomical system) the Fu-tian li. It was used only among the people as an
unofficial astronomical system.
唐建中時，術者曹士蒍始變古法，以顯慶五年為上元，雨水為歲首，號符天曆。然世謂之小曆，
祇行於民間。
(Xin wu-dai shi, 58: Si-tian kao; Yabuuti 1982, 2)

In addition, regarding Cao Shi-wei 曹士蔿, we can find another source, Ma Duan-lin
馬端臨’s Wen-xian tong-kao 文獻通考 compiled in the Yuan period (1271–1368), in
which the author mentions the Ge-yuan wan-fun li 合元万分曆 compiled by this Cao
Shi-wei:
Chao said: Cao Shi-wei compiled (it) in the Tang period. His name is unknown. The epoch was derived
from the fifth year of the Xian-qing era, and it was an unofficial astronomical system that was current
in the civil sphere. The method was based on Indian astronomical system. I heard it from Li Xian-chen.
晁氏曰。唐曹氏撰, 未知其名。曆元起唐高宗顯慶五年庚申, 蓋民間所行小曆也。本天竺曆為法,李獻臣云。
(Wen-xian tong-kao, 219: Jing-ji kao 46; Yabuuti 1982, 3)

Judging from the accordance of the epochs and the same designation as an “unofficial”
astronomical system, without doubt, the Ge-yuan wan-fun li is another name of the
Fu-tian li. Although the contents of this calendar are only partially known, it is most
likely that this system adopted the ten-thousand funks method judging from the nameSCIAMVS 14

189

The Tārīkh-i Qitā in the Zīj-i Īlkhānī

wan-fun li [Ten-Thousand Funks Astronomical System]. Yabuuti has conjectured that thiswas one of new methods of Cao Shi-wei who “changed the old method” (Yabuuti 1982,
5). In fact, this method was unknown in the Chinese astronomical systems before theFu-tian li. It was also adopted by the Shou-shi li 授時曆: 1281–1384, the official
astronomical system of the Yuan dynasty, distributed from 1281 sometime after thecompilation of the Zīj-i Īlkhānī. The system has gained fame as the masterpiece oftraditional Chinese astronomical systems.

Section 2
This section explains what is called the cycle of the ten “heavenly stems” (tian-gan 天
干). The order is as below:
1

2

3

4

5

6

7

8

9

10

jia 甲

yi 乙

bing 丙ding 丁wu 戊

ji 己geng 庚

xin 辛

ren 壬

gui 癸

(kia)

(i)

(piaŋ)(tiaŋ)(vu)(ki)(kiaŋ)(sian)(ɽiam)(kui)

In China, traditionally, the sexagenary cycle called gan-zhi 干支 was used forreckoning days and years. It is constituted by combining the ten-stem cycle with thetwelve-branch cycle mentioned in the previous section. The combination of each element
is as below (Sivin 2009, 69):
1. jia-zi 甲子

2. yi-chou 乙丑

3. bing-yin 丙寅

4. ding-mao 丁卯

5. wu-chen 戊辰

6. ji-si 己巳

7. geng-wu 庚午

8. xin-wei 辛未

9. ren-shen 壬申10. gui-you 癸酉

11. jia-xu 甲戌

12. yi-hai 乙亥

13. bing-zi 丙子

14. ding-chou 丁丑

15. wu-yin 戊寅

16. ji-mao 己卯

17. geng-chen 庚辰

18. xin-si 辛巳

19. ren-wu 壬午

20. gui-wei 癸未

21. jia-shen 甲申

22. yi-you 乙酉

23. bing-xu 丙戌

24. ding-hai 丁亥

25. wu-zi 戊子

26. ji-chou 己丑

27. geng-yin 庚寅

28. xin-mao 辛卯

29. ren-chen 壬辰

30. gui-si 癸巳

31. jia-wu 甲午

32. yi-wei 乙未

33. bing-shen 丙申34. ding-you 丁酉

35. wu-xu 戊戌

36. ji-hai 己亥

37. geng-zi 庚子

38. xin-chou 辛丑

39. ren-yin 壬寅

40. gui-mao 癸卯

41. jia-chen 甲辰

42. yi-si 乙巳

43. bing-wu 丙午

44. ding-wei 丁未

45. wu-shen 戊申46. ji-you 己酉

47. geng-xu 庚戌

48. xin-hai 辛亥

49. ren-zi 壬子

50. gui-chou 癸丑

51. jia-yin 甲寅

52. yi-mao 乙卯

53. bing-chen 丙辰

54. ding-si 丁巳

55. wu-wu 戊午

56. ji-wei 己未

57. geng-shen 庚申

58. xin-you 辛酉

59. ren-xu 壬戌

60. gui-hai 癸亥190Yoichi ISAHAYASCIAMVS 14

Section 3
The third section is assigned for the explanation of the year of the Qitai and thetwenty-four divisions of a year. For the Qitai, the length of a year is the period when thesun returns to the same position on the celestial sphere, which was counted as 365.2436 d
and called suijū in their language. They also divide the length of a year into twenty-four
equal parts called kīja; that is 15.21848333...d. The name of each division is as follows:
1. li-chun 立春

2. yu-sui 雨水

3. jing-zhe 驚蟄

4. chun-fun 春分(li-tʂhiuan)(iu-ʂui)(kiŋ-tʂi)(tʂhiuan-fuan)

5. qing-ming 清明

6. gu-yu 穀雨

7. li-xia 立夏

8. xiao-man 小滿(tshiaŋ-miaŋ)(ku-iu)(li-hia)(siau-muan)

9. mang-zhong 芒種

10. xia-zhi 夏至

11. xiao-shu 小暑

12. da-shu 大暑(muaŋ-tʂiuŋ)(hia-tʂɪ)(siau-ʂiu)(tai-ʂiu)

13. li-qiu 立秋

14. chu-shu 處暑

15. bai-lu 白露

16. qiu-fun 秋分(li-tshiau)(tʂhiu-ʂiu)(pai-lu)(tshiau-fuan)

17. han-lu 寒露

18. shuang-jiang 霜降

19. li-dong 立冬

20. xiao-xue 小雪(han-lu)(ʂaŋ-kiaŋ)(li-tuŋ)(siau-siuɛ)

21. da-xue 大雪

22. dong-zhi 冬至

23. xiao-han 小寒

24. da-han 大寒(tai-siuɛ)(tuŋ-tʂɪ)(siau-han)(tai-han)The end of the section addresses the difference between China’s and Iran’s notions of
seasons. Turkic people, composing the main body of the “Mongol” troop, had a seasonal
notion more similar to that of Iran than that of China, at least concerning spring. Since
ancient times, the Turko-Mongols had appreciated solar motion not directly byastronomical observations or calculations, but indirectly, through its effect on vegetation,
in a way suitable to their pastoral economy (Bazin 1991, 119). In the official Chinese
history of the sixth-century dynasty, it is stated that “(Turks) do not know the successionof years, and only count it based on the grass turning green” (Zhou shu, 50: Yi-yu chuan
2; Bazin 1991, 118). In steppes across northern and western China, this timing falls
around the spring equinox, which is considered the starting point of spring in Iran. On theother hand, the starting point of the Chinese notional spring usually falls during theseverity of winter in the steppes. In the course of unifying Mongolia, the Turko-Mongols
seem to have adopted the Chinese calendar through contacts with the Jin dynasty (1115–1234) around 1201 (Bazin 1991, 402). As a rule, the adoption of the Chinese calendar by
the neighboring steppe people was a measure of Chinese success in imposing its authority

SCIAMVS 14

The Tārīkh-i Qitā in the Zīj-i Īlkhānī

191

and the benefits of its civilization upon the so-called “barbarians.” Despite thedisharmony between the astronomically determined beginning of the Chinese year andthe Turkic nomadic tradition, according to which the year starts at the beginning of spring,
the Turko-Mongols accepted the Chinese calendar. At about the same time, from the
beginning of their conquest of northern China in 1215, the Mongols acquired an official
Chinese calendar, in conformity with their status as a Chinese imperial power (Melville
1994, 84).
Outside China proper, where the root of living was based on its own time, theTurko-Mongols used the Chinese calendar as well as in China proper. Xu Ting 徐霆,
who was the Sung ambassador to the Mongol court in 1237, reported that he encountered
the Chinese calendar on the way to Mongolia. Upon his inquiry, the calendar was
identified as the one made by Yelü Chucai 耶律楚材, a sinicized Qitan 契丹 who
accompanied Genghis Khan on several campaigns, and was famous as the chief “Chinese”
adviser of the early Mongol rulers (Allsen 2001, 165-166).
We might be tempted to conjecture that the Qitai calendar is exactly the one compiled
by Yelü Chucai and used in the Mongol court in a period close to that of the compilationof the Zīj-i Īlkhānī. But, according to the Yuan shi 元史, the Xi zheng geng-wu yuan li 西征庚午元曆 he compiled is identical to the Revised Da-ming li with the exception of asmall correction due to the difference in geographical longitude (Yuan shi, 56-57:
Geng-wu yuan li 1-2; Yabuuti 1997, 11-12). As shall be discussed in detail, we cannot
identify the Qitai calendar as the Revised Da-ming li, despite the fact that the latter canundoubtedly be regarded as one of main sources of the former. Therefore, Yelü Chucai’s
astronomical system also differs from the Qitai calendar.

Section 4
The way of reckoning years is explained in this section. The sixty-cycle is attached to thethree epochs by the following order: first, the cycle of the Superior Epoch (shānk wan),then the cycle of the Middle Epoch (jūnk wan), and the final is the cycle of the Inferior
Epoch (khā wan):

192

Yoichi ISAHAYASCIAMVS 14

PersianEnglish Translation

Piyin

Characters

Yuan-Era Early Mandarin

Lengthshānk wanSuperior Epochshang-yuan

上元ʐĭaŋ-iuɛn

60 yearsjūnk wan

Middle Epochzhong-yuan

中元tʂiuŋ-iuɛn

60 yearskhā wanInferior Epochxia-yuan

下元hia-iuɛn

60 years

These epochs, called san-yuan jia-zi 三元甲子, appear from the Tang period onwards.
Furthermore, we can find them in annotated calendars among Uighurs and Tibetans fromthe Tang period, in collaboration with nine-color palaces (jiu-fang se 九方色). Bazin has
found Indian influence in this collaboration, in connection with nine luminaries (jiu-yao九曜), including Mars, Mercury, Jupiter, Venus, and Saturn, the Sun, the Moon, as well as
positions in the sky: Rāhu (ascending lunar node) and Ketu (descending lunar node).
Interestingly, this epoch starts from 784. Bazin ascribed this to the 1260 years grand cycle
consisting of the three epochs: sexagenary cycle, nine-color palaces, and 28 “nakshatra”(Bazin 1991, 265-273). However, Arrault, who investigated several series of documents
and fragments excavated at Dunhuang, has connected the era with the beginning of thecycle of tai-yi 太一 in the Sui period in 604 (784–180) (Arrault & Marzloff 2003, 109 n.
100).
To count years over this 180-year epoch, the accumulated years from the creation aretaken into consideration. According to the computation of the Qitai calendar, 8,863
wans—Chinese wan 万 (van) means 10,000 years—and 9,679 years had elapsed fromthe creation to the year of the accession of Genghis Khan. As described in the longer
introduction in the Zīj-i Īlkhānī, the “year of the accession” is the year of the legendary“Baljuna covenant” in 1203 (Boyle 1963, 250-251).
The Chinese astronomical systems set up a starting point for a great cosmic cycle,
from which all celestial phenomena start. Each system has a different origin, mainly inthe distant past (Sivin 2009, 73). The era of the Qitai calendar completely correspondswith that of the Revised Da-ming li, which regards 88,639,656 years as the elapsed years
from the starting point to A.D. 1180 (Jin shi, 21: Bu qi-ce bu gua-hou bu ri-chan bu
gui-lou). This accordance is strong evidence that the astronomical system is one of thesources of the Qitai calendar.
The beginning year of the Superior Epoch after the accession of Genghis Khan is inaccordance with the year 633 of the Yazdigird era (A.D. 1264)—which is named after thelast Sassanid king—commencing with A.D. 632. The era fixing the annual length as 365
days without a fractional remainder survived after the collapse of the dynasty and is often

SCIAMVS 14

The Tārīkh-i Qitā in the Zīj-i Īlkhānī

193

referred to in Islamic and Byzantine astronomical treatises because of its convenience incalculation (Neugebauer 1957, 81; van Dalen 2000, 267).
The final sentences of this section are also of interest: “Turks only use a cycle oftwelve and count it in their language. The regulation of their calendar is unknown to us.”
As mentioned in the first section, the Turks in the northern and western steppes employed
only the twelve branches in the form of the twelve-animal cycle, not the ten stems. Even
after the Mongol court adopted the “proper” Chinese calendar, probably a large numberof the Turko-Mongols continued to recognize time passing from their pastoral
circumstances and not from observation or astronomical computation; this obscurity
might well be reflected in the above-quoted passage.

Section 5
This section is assigned for explaining the way to compute the beginning of the firstdivision of a solar year, the lījun (li-chun 立春). All official astronomical systems in the
Chinese dynasties adopted the beginning of the twenty-second division dong-zhi 冬至—the winter solstice—as the standard of astronomical computation. But, as one of thegestures to signal a change of heavenly mandate, early dynasties shifted the first month ofthe civil year. The final shift in 103 B.C. situated the civil new year at the beginning of
the second lunar month after the winter solstice. Therefore, the new year falls around at
the beginning of the lījun. Although the official Chinese astronomical systems used theirown “astronomical year,” which differed from the civil year in that its Astronomical First
Month (tian-zheng 天正) contained the winter solstice, the civil new year is taken into
consideration in the Qitai calendar (Sivin 2009, 75-76); therefore, the beginning of thelījun is computed as “the initial value of the divisions of a year” in this calendar.
As found in the passage, the initial value is set as 11.7660 in the epoch era of the Qitai
calendar (A.D. 1264). 360 is multiples of 60. By a year, therefore, the initial value slides
by 5.2436 days, which is equal to the excess of a solar year over 360, also called suiyū.
Then, if the required year falls after the epoch year, the initial value (11.7660) is added tothe product of the suiyū and the interval between the epoch and required years. Finally,
the result is diminished by 60 as many times as possible. As a result, we can obtain aformula to compute “the initial value of the divisions of a year” as follows:
11.7660 + 5.2436 T – [60]r (I)194

Yoichi ISAHAYASCIAMVS 14

T = the interval between the epoch and required years.
[x]r = subtracting x as many times as possible (i.e., taking the remainder of the divisionby x) (cf. Imai 1962, 32).
We shall compare the above formula with the formula in the Revised Da-ming li. We
quote the following passage which computes the beginning of the twenty-second division
dong-zhi 冬至—the winter solstice—in the epoch year (A.D. 1180):
To compute the Winter Solstice in the Astronomical First Month
Set up the Accumulated Years from the First Year of the Superior Epoch, and multiply it by the Year
Numerator to yield the Accumulated Funks. Cast out the full Sexagenary-Days Cycles from that.
Simplify (i.e., divide) the remainder by the Day Divisor to yield the days. The remainder is expressedas the fractions. Do not count the First Year. The result is the desired days and fractions on the WinterSolstice (from the beginning of the month).
求天正冬至
置上元甲子以來積年，歲實乘之，為通積分。滿旬周去之，不盡以日法約之為日，不盈為餘。命甲子算外，即所求天正冬至日大小餘。
（Jin shi, 21: Bu qi-shuo 1）

That is to say, as mentioned in the commentary of the fourth section, 88,639,656 years
are accumulated years from the first days of the Superior Epoch to A.D. 1180 inaccordance with the computation of the Revised Da-ming li. It is multiplied by the Years
Numerator that is the funks of a year (1,910,224 funks), and the result is
169,321,598,242,944 funks. From the value, we subtract the Sexagenary-Days Cycle,
which is the value obtained by the multiplication of the Day Divisor (the funks of a day:
5,230 funks) by 60, as many times as possible. As a result, we obtain 5.6489... days as
falling on the winter solstice from the beginning of the eleventh month in the epoch year
(A.D. 1180). On the basis of this initial value in the epoch year, we devise the following
formula to compute the winter solstice in another year (Imai 32):5.6489 + 5.2435946 T – [60]rIf we convert it into a formula for A.D. 1264, the era of the Qitai calendar, by adding
84 (1264–1180) times 5.2435946 and canceling multiples of 60, the following is
obtained:
26.1108 + 5.2435946 T – [60]r

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195

Furthermore, by adding the time between the winter solstice and the beginning of thelījun (the interval of the three solar divisions or one eighth of a solar year, 45.65545 days),
we convert it again into a formula on the basis of the lījun, as in the Zīj-i Īlkhānī:11.7662 + 5.2435946 T – [60]r (II)As we can see, the initial values in formulas (I): 11.7660 and (II): 11.7662 are almost
identical. The small difference in the fourth decimal position may be ascribed to the factthat the former calendar adopts the ten-thousand funks method explained in thecommentary of the first section, in which the fifth and further decimal places are
disregarded. From this fact, we can point out the great possibility that the Qitai calendar
borrowed constants from the Revised Da-ming li to compute the beginning of the lījun.
In the latter half of this section, the beginning of the lījun in the 10th year of theSuperior Epoch is computed as an example. To obtain the value, we substitute 9—theinterval from the epoch year—into the formula (I). So, first 9 is multiplied by 5 days and2,436 funks and we obtain 45 days and 21,924 funks. As explained in the first section,
20,000 funks equal 2 days; therefore, the result is converted into 47 days and 1,924 funks.
Then, 11 days and 7,660 funks—“the initial value”—is added to the former result, and we
obtain 58 days and 9,584 funks. Since the remaining funks are counted as a day, we obtain
59, making the 59th day beginning of the lījun in the 10th year of the Superior Epoch. The
59th day is the zhim sū in the sixty-cycle. More precisely, the beginning of the lījun in thisyear is considered the point at which 9,584 funks have elapsed since the beginning of theday. From the last table of the first section, we know that 9,584 funks—2, 39, 44— fall in
the first double-hour; specifically, it is the time at which the two-thirds of a funk elapsed
since the first double hour began.
Once we have determined the beginning of the lījun, we can obtain the beginning ofother solar divisions in the year. As an example, the beginning of the seventh division iscomputed. From the table in the third section, we know that the seventh division starts 91
days and 3,109 funks—0, 51, 49—later than the beginning of the lījun. We add the value
to the beginning of the lījun (58 days and 9,584 funks). We obtain 149 days and 12,693
funks—3, 31, 33—, convert 10,000 funks into one day, and yield a total of 150 days and2,693 funks—0, 44, 53. To obtain the beginning of the seventh division, we need tosubtract 60 from the days as many times as possible; as a result, 30 days and 2,693 funks
remain. Therefore, we know that the 31st day—the day of kā-wū—is the beginning day ofthe seventh division in the year. Regarding the remaining 2,693 funks—0, 44, 53—, weknow that the beginning falls in the fourth double-hour; more precisely, it is the time at

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which 89 funks have elapsed since the beginning of the sixth kih of the fourth
double-hour.

Section 6
This section demonstrates the computation of the beginning of the first month, the ārāmay. Since we discussed how to compute the beginning of the lījun in the previous section,
we can also find the beginning of the wūshī (the second solar division). This section
explains how to compute the interval between the beginnings of the first month andwūshī.
The names of the months in the Chinese calendar as found in Persian sources of theMongol period are Turkish ordinal numbers followed by the Turkish term ay that means“month,” except for the first and twelfth months. The first month appears in the form of
ārām. According to Bazin, we can find the influence of Buddhism in the use of this term.
The term quite likely comes from the Persian rām, meaning “joyous.” The name of thetwelfth month, čaqšapat, was borrowed from the Soghdian language, whose original is
the Sanskrit śikṣāpada, which means “prescriptions” (Bazin 1991, 294; van Dalen et al.
1997, 124). The Soghdian language belongs to the Iranian language group. In the Mongol
period, these names were used by Turko-Mongols in Iran and Central Asia, and theaforementioned names of the two months were probably borrowed from Soghdians who
were quite flourishing in these regions from the period before the Mongols. The names ofthe months are as follows (van Dalen et al. 1997, 124):
1. aram ay

2. ikindi ay

3. üčünč ay

4. törtünč ay

5. bešinč ay

6. altïnč ay

7. yetinč ay

8. sekizinč ay

9. toquzïnč ay

10. onunč ay

11. biryegirminč ay

12. čaqšapat ay

In Chinese astronomical systems in the later period, each lunar month must include thebeginning of an even-numbered division of a solar year—called zhong-qi 中 氣(tʂiuŋ-khi)—corresponding to odd-numbered divisions called jie-qi 節氣 (tsiɛ-khi). The
correspondence relation between even-numbered solar divisions and lunar months is asfollows:

SCIAMVS 14

Month
NumberSolar
Division
Month
NumberSolar
Division

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1

2

3

yu-sui雨水
7

chun-fun gu-yu
春分
穀雨
8
9

chu-shu處暑

qiu-fun
秋分

4

5

6

xiao-man
小滿
10

xia-zhi
夏至
11

da-shu大暑
12shuang-jiang xiao-xue
霜降
小雪

dong-zhi da-han
冬至
大寒

The interval between two even-numbered divisions (30.4375d) is a little bit longer thanthe period of a lunar month (in this case, 29.5306d). In several years, therefore, a monththat does not contain the beginning of an even-numbered division will occur. This monthis regarded as an intercalary month, which is named according to the ordinal number ofthe preceding month prefixed by the word run 閏 (ɽiuan), meaning “intercalary,” forexample “the intercalary twelfth month 閏十二月” (Yabuuti 1990, 275-276). In Chinese
astronomical systems, the position of an intercalary month is not fixed, and can fall in any
month.
The winter solstice (the beginning of the twenty-second solar division), whose
position was determined through a series of observations, was the standard ofcomputation in Chinese official astronomical systems. As explained in the commentary of
the previous section, however, the civil year gets under way from the second new moonafter the winter solstice, in which the beginning of the second division wūshī must be
included. Therefore, the interval between the beginnings of the first month (ārām ay) andthe wūshī is taken into consideration in this section.
According to the passage in this section, the interval between the beginnings of thefirst month and the wūshī is 14.4676 days in the epoch year. Since the month moves inaccordance with lunation and the wūshī is based on the solar motion, the interval of bothannually increases 10.8764 days—which is the difference between the solar year andtwelve mean lunar months called suijā. If the year is after the epoch year, we compute theinterval between the beginnings of the first month and the wūshī in a year as follows:
after computing the interval between the epoch and the required years, the result is
multiplied by the suijā and added to 14.4676 days which is the initial value of the epoch
year. However, the beginning of wūshī should fall in the first month, so that the interval
should be shorter than the length of a mean lunar month (29.5306 days). That is the

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reason why the value of the length must be subtracted as many times as possible from theresult. The formula is set up as below:
14.4676 + 10.8764 T – [29.5306]r (III)
Here, as in the previous section, we shall compare the formula with that of the Revised
Da-ming li for A.D. 1180 on the basis of the winter solstice (dong-zhi 冬至). The passage
on how to compute it is as follows:
To compute the beginning of the Astronomical First Month
Cast out the full Lunation Numerators from the Accumulated Funks (from the First Year of the Superior
Epoch) to yield the Intercalary Surplus. Subtract it from the Accumulated Funks to yield the
Accumulated Funks until the Beginning (of the Astronomical First Month). Cast out the fullSexagenary-Days Cycles from that. Simplify the remainder by the Day Divisor to yield the days. The
remainder is expressed as the fractions. The result is the desired days and fractions on the beginning of
the Astronomical First Month.
求天正經朔
以朔實去通積分，不盡為閏餘，以減通積分為朔積分。滿旬周去之，不盡如日法而 一為日，不盈為餘，即所求天正經朔大小餘也。
(Jin shi, 21: Bu qi-shuo 1)

That is to say, the Lunation Numerator (the funks of a mean lunar month, totaling
154,445 funks) is subtracted as many times as possible from the Accumulated Funks fromthe first year of the Superior Epoch—that is, 169,321,598,242,944 funks, as computed in
the previous section. By this computation, we obtain the Intercalary Surplus 75,749 funks,
which represents the interval between the winter solstice and the beginning of the monthprior to the winter solstice. By division of the value by the Day Divisor (5,230 funks), we
obtain 14.48355... days as the interval between the winter solstice and the beginning of
the month prior to the winter solstice in the epoch year (A.D. 1180). Therefore, theformula to compute the interval between the winter solstice and the beginning of themonth prior to the winter solstice can be devised as follows:
14.4836 + 10.8764818 T – [29.5305927]r
By adding 84 times 10.8764818 and canceling multiples of 29.5305927, we canconvert the above formula into one for A.D. 1264, the epoch of the Qitai calendar, and thefollowing formula is obtained:
12.6597 + 10.8764818 T – [29.5305927]r

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Furthermore, we convert it again into the formula on the wūshī as in the Zīj-i Īlkhānī,by adding the time between the winter solstice (the twenty-second solar division) and the
beginning of the wūshī, one-sixth of a solar year, i.e., 60.8739 days, being 1.8127 days
more than two whole lunar months:
14.4724 + 10.8764818 T – [29.5305927]r (IV)As with the formula to compute the beginning of the lījun, we find a close similarity inthe constants of the both formulas (III): 14.4676 and (IV): 14.4724 between the Qitai
calendar and the Revised Da-ming li; the slight difference is caused by the adoption of the
ten-thousand funks method in the former calendar. Therefore, it is clear that thiscomputation is also based on that of the Revised Da-ming li (cf. Imai 1962, 32-33).

Section 7
The explanation for the solar and lunar equations commences in this section. This section
explains the way to determine the arguments of the sun and moon at the beginning of a
year.
In a Babylonian tradition that has survived into modern astronomy, a celestial circle isdivided into 360 degrees. Chinese instead defined their basic unit du 度 (or Chinese“degree”) to record celestial positions as one day’s mean solar travel among the stars(Sivin 2009, 89); so that, in the case of the Qitai calendar in which a solar year is definedas 365.2436 days, the cycle of the annual solar motion is rendered 365.2436 Chinese
degrees.
Due to variation in the distance between the sun and the earth as the latter moves on
its elliptical orbit, the observed velocity of the sun undergoes a change. In the Chinese
astronomical system, it was established that the inequality of the sun was zero at thesolstices and symmetrical about them. Chinese astronomers considered the winter solstice
to be the standard of computation for the solar equation. The equation of center is positive
during the period when the sun moves from the winter to the summer solstices; during theother half-year, on the other hand, the equation of center is negative (Sivin 2009,408-412).
To obtain the solar argument at the beginning of a year, therefore, it is necessary toknow the time elapsed since the winter solstice (Imai 1962, 33). To compute the intervalfrom the winter solstice to the beginning of the first month, the interval between the

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Yoichi ISAHAYASCIAMVS 14

beginnings of the first month and the wūshī in a year is subtracted from one-sixth of asolar year (60.8740 days), corresponding with the interval between the twenty-second
solar division (the winter solstice) and the wūshī.
To compute the inequality of the lunar motion, in turn, the anomalistic month is taken
into consideration. That is the period of the moon’s travel from perigee back to perigee.
Since there was no explicit concept of perigee or apogee in their astronomical vocabulary,
Chinese saw the anomalistic month as the revolution for which the Revolution Terminal
Constant (zhuan-zhong 轉終) is named and transcribed it as junjūn in Persian. In the
Chinese astronomical system, the standard point is the perigee in the moon’s orbit when it
is closest to the earth, and its apparent speed is fastest (Sivin 2009, 101-102). In thissection, therefore, “the initial value of the lunar argument” that means the interval
between the beginnings of wūshī and the anomalistic month preceding the former in theepoch year is obtained as 23.2836 days called junjūnkā (van Dalen et al. 1997, 149). The
value of the interval annually slides by 7.0338 days called jūnjā, which means the excess
of a solar year over thirteen anomalistic months.
In consideration of this computation, we obtain the value of an anomalistic month by
the following formula:(365.2436 – 7.0338)/13 = 27.5546 days
This value is almost the same as the values used in various Chinese astronomicalsystems, including the Revised Da-ming li (van Dalen et al. 1997, 126).
To compute the value of the interval between the beginnings of the wūshī and theanomalistic month preceding the former in another year, therefore, the initial value isadded to the value of the multiplication of the interval between the epoch and required
years by the jūnjā when the required year falls after the epoch year. The value of theinterval between the beginnings of the wūshī and the anomalistic month preceding theformer is called the “first number to be kept.” Then, the interval between the beginningsof the first month and wūshī computed in the previous section is subtracted from the firstnumber to yield the interval between the beginnings of the first month and the anomalisticmonth preceding the former, which is called the “second number to be kept.” If thesubtraction is not possible, the value of the sixty-cycle is added prior to the subtraction.
From the second number, the length of an anomalistic month whose value is 27.5556 days,
is subtracted as many times as possible. That is because the interval between the
beginnings of the first month and the anomalistic month preceding the former must be
shorter than the length of an anomalistic month.

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201

However, it is somewhat odd to denote the value as 27.5556 days here, given its
difference from the value of 27.5546 days computed in terms of jūnjā, the excess of asolar year over thirteen anomalistic months as shown below. In comparison with thisvalue, which is common in Chinese astronomical systems, the value 27.5556 is quite
inaccurate, and we never find this value in any Chinese historical record since description
on the Qian-xiang li (乾象曆: 206–237), in which an anomalistic month was first used
(Imai 1962, 33). But adopting this value here is not unreasonable, because it is only used
to calculate the age of an anomalistic month within a year, and nine of these anomalisticmonths are equal to an integer value 248 (248/9 = 27.5555..., rounded to 27.5556), whichis convenient for the calculation of the lunar equation (Imai 1962, 33-34). By means of
this period relation, the “second number to be kept” is multiplied by 9 to yield the lunar
argument at the beginning of a year. If the value exceeds 248 days, 248 is subtracted fromthe value.
Between the Qitai calendar and Revised Da-ming li, we can compare the computation
to obtain the interval between the beginnings of the certain solar division and theanomalistic month preceding the former. In the case of the Qitai calendar, the following
formula is devised to compute the interval between the beginnings of the wūshī andanomalistic month preceding the former in a required year:
23.2836 + 7.0338 T – [27.5556]r (V)We compare this formula with that of the Revised Da-ming li; in this case, the formulacomputes the interval of the beginnings of the winter solstice (the twenty-second solar
division) and the anomalistic month preceding the winter solstice. In this astronomicalsystem, an anomalistic month is defined as 144,110.6066 funks (Jin shi, 22: Bu yue-li 5).
From the Accumulated Funks from the first year of the Superior Epoch, the value of ananomalistic month is subtracted as many times as possible. The result is divided by the
Day Divisor to yield the days of the interval between the beginnings of the winter solsticeand the preceding anomalistic month in the epoch year (A.D. 1180); the value is 19.0981
days. Since the value of the excess of a solar year over thirteen anomalistic months is7.03367384… days and an anomalistic month is 27.55460929… days, we devise theformula to compute the interval as follows:
19.0981 + 7.0336738 T – [27.5546093]r
The converted formula for A.D. 1264, the epoch year of the Qitai calendar, is asfollows:
3.7253 + 7.0336738 T – [27.5546093]r202

Yoichi ISAHAYASCIAMVS 14

From this, we may derive a formula for the interval between the beginnings of the
wūshī and the preceding anomalistic month, by adding the time between the wintersolstice and the wūshī, one-sixth of a solar year, i.e., 60.8739 days. After canceling two
anomalistic months, 5.7647 days are left, and the value is added to 3.7253 to yield theinitial value:
9.4900 + 7.0336738 T – [27.5546093]r (VI)
As we can see, there is a significant difference between the constants of the two
formulas (V): 23.2836 and (VI): 9.4900. However, recomputing the lunar mean anomaly
for the time of the beginning of the wūshī from the planetary tables in the Zīj-i Īlkhānī, wefind it to be 301; 22° at noon on the first day of the wūshī (February 13, 1264),
corresponding to 83.7% of its cycle, i.e., 23.1 days. That is very close to the epoch valueof 23.2836; therefore, there is little problem as far as the computation in the Zīj-i Īlkhānī
is concerned, although we have had no way thus far to judge whether or not this value
was intentionally adjusted according to parameters in planetary tables in the Zīj-i Īlkhānī.1

Section 8
The computation of the solar equation is the subject of this section. Since the solar
argument at the beginning of a year was obtained in the previous section, we can computethe arguments at the beginnings of months in the year in such a way that the argument at
the beginning of the year is added to the result of the multiplication of a synodic month(29.5305 days) by the interval between the first and required months.
If the argument is smaller than 182 (called bīnjūtin), the value is subtracted from 182
and the result is multiplied by the original value. Then, the result is doubled and a ninth of
the amount is obtained; what is obtained is the solar equation. The value, called nū, ispositive. If the argument is larger than 182, the excess over 182 is obtained. Then, theargument is subtracted from 364 (182 doubled). The excess is multiplied by the result of
the subtraction; finally, the result is doubled and a ninth of the amount is obtained; what is
obtained is the solar equation. The value, called tiyā’ū, is negative.
In this calendar, the celestial cycle (zhou-tian 周天), which accords with the length ofa solar year in Chinese official astronomical systems as explained in the commentary of

1

Regarding the computation of this paragraph, I received great assistance from Benno van Dalen.

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203

the previous section, was shortened to 364 degrees, which is a crude approximation to thesolar year, but is the best approximation for making a quarter of the cycle an integer(Kennedy 1964, 440); therefore, the half-cycle bīnjūtin becomes 182 degrees. The sun’s
path has been halved symmetrically at the two solstices. As also explained in the previous
section, the equation of center is positive during the period when the sun moves from thewinter to the summer solstices; so that, the equation of center from 0 degree (the wintersolstice) to 182 degrees (the summer solstice) becomes positive. During the otherhalf-year, on the other hand, the equation of center is negative.
In consideration of the passage of this section, a quadratic interpolation scheme is used
for the computation of the solar equation. The formula can be devised as follows:int [(2⁄9) ∙ 𝑛(182 − 𝑛)] 𝑓𝑜𝑟 0 ≤ 𝑛 < 182−int [(2⁄9) ∙ (𝑛 − 182)(364 − 𝑛)] 𝑓𝑜𝑟 182 ≤ 𝑛 ≤ 364 (VII)n = the integral part of the solar argument (van Dalen et al. 1997, 129)As Imai pointed out, the maximum of the solar equation in this formula is ±1,840
funks, different from ±1,797 funks in the case of the Revised Da-ming li; after all, thelatter’s equation is not computed by any quadric function (Jin shi, 21: Er-shi si qi zhong-ji
ji tiao-nu; Imai 1962, 34). Therefore, we do not find the similarity between the Qitai
calendar and the Revised Da-ming li that we have observed in previous cases.
From these formulas, however, we can detect a certain relation of the calendar with the
Fu-tian li, which we have regarded as one of the sources of the Qitai calendar due toseveral similarities between them. The contents of the Fu-tian li had been unknown for along time until a small fragment entitled “Futenreki nitten sa rissei” 符天曆日躔差立成[the table of the solar equation in the Fu-tian li] was found at Tenri Library, Japan, in
March 1963. From this, it has been proven that this astronomical system uses thefollowing formula for the solar equation (Nakayama 1966, 451; van Dalen et al. 1997,
129):
1⁄3300 ∙ 𝑛(182 − 𝑛) (XIII)
The difference between the formulas (VII) and (XIII) is derived mainly from the factthat the former regards the equation in the funks of lunar elongation instead of solar
motion (van Dalen et al. 1997, 129). The maximum is 2.47 degrees in the Fu-tian li and2.24 degrees in the Qitai calendar from the modern point of view, so we can find thedifferences in terms of the values.
However, we identify these formulas in terms of the algebraic method. This kind of
method was not popular among the Chinese astronomical systems and was not used

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Yoichi ISAHAYASCIAMVS 14

before the Fu-tian li, since traditionally Chinese astronomical systems relied on adifferent, empirical method on the basis of the observations of the midday
gnomon-shadow lengths over a period of ten days (Nakayama 1992, 877). Afterward, thealgebraic method was succeeded by several official astronomical systems in the Songdynasty such as Yi-tian li 儀天曆 (1001–1023), Ming-tian li 明天曆 (1065–1076), andGuan-tian li 觀天曆 (1094–1102). Finally, this tradition developed into the method of
the Shou-shi li, in which two third-order formulas are used (Chen 1986; Sivin 2009, 415).
In addition to the adoption of the ten-thousand funks method, therefore, we also find asimilarity between the Qitai calendar and the Fu-tian li in the method for the computationof the solar equation. Especially, the way of dividing the celestial cycle into 364 parts isdifferent from any other astronomical system except for these two. From this fact, we cantrace a certain line between the two systems. We know that, although the Fu-tian li wasconsidered “unofficial” and was never adopted as an official astronomical system, it wasquite influential in the Tang and Five Dynasties’ periods in the civil sphere and evenofficials in the Bureau of Astronomy used it for astrological purposes. Then, the Fu-tian li
is known to have kept its status as one of the important texts on astrology in the Song
period (Yabuuti 1982, 6-7). In addition, the Fu-tian li was adopted as a text for theexaminations of the Bureau of Astronomy in the Jin and Yuan dynasties (Yamada 1980,
119-125). Until the period when the Zīj-i Īlkhānī was compiled, therefore, the Fu-tian li
continued to be used in China, and its use was not confined to civil sphere, butbureaucrats also made use of this text for matters of astrology.

Section 9
This section is for the computation of the lunar equation. As in the case of the solar
equation, the lunar argument at the beginning of a year has been obtained in the seventh
section; therefore, we can compute the arguments at the beginnings of months by thefollowing way where the argument at the beginning of the year is added to the result ofmultiplication of the interval between the first and required months by the junjūn shā(17.7754 days). This term means nine times the excess of a synodic month over ananomalistic month. Month by month, the starting-point of an anomalistic month shifts by
the excess of a synodic month over an anomalistic month. We should also consider the

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period relation equalizing 9 anomalistic months with 248 days to compute the lunar
argument at the beginning of a month.
If the argument is smaller than 124 (called banjūshā), the value is subtracted from 124
and the result is multiplied by the original value to yield the lunar equation. The value,called nū, is positive. If the argument is larger than 124, the excess over 124 is obtainedon the one hand; on the other hand, the argument is subtracted from 248 (124 doubled).
Then, the excess is multiplied by the result of the subtraction to yield the lunar equation.
The value, called tiyā’ū, is negative. The 248 divisions of an anomalistic month areyielded in consideration of the period relation equalizing nine anomalistic months with
248 days.
In consideration of the passage of this section, a quadratic interpolation scheme is also
used for the computation of the lunar equation. The formula can be devised as follows:int [𝑛 (124 − 𝑛)] 𝑓𝑜𝑟 0 ≤ 𝑛 < 124−int [(𝑛 − 124)(248 − 𝑛)] 𝑓𝑜𝑟 124 ≤ 𝑛 < 248 (IX)
The maximum of these formulas is ±3,844 funks, which is different from that of the
Revised Da-ming li, whose maximum is ±4,144 funks (Jin shi, 22: Zhuan ding fen ji ji-dutiao-nu shuai; Imai 1962, 34). As with the case of the solar equation, we find hardly any
similarity between the Qitai calendar and the Revised Da-ming li in terms of the lunar
equation.
There are several interesting points with regard to the period relation equalizing nine
anomalistic months with 248 days. This kind of period relation is of ancient Babylonian
origin and subsequently appears in Sanskrit treatises on mathematical astronomy, such as
the sixth century Pañcasiddhāntikā of Varāhamihira, probably through the mediation of
the Greek tradition (Kennedy 1964, 441; Jones 1983/84, 11-). Some elements of those
Sanskrit texts are known to have appeared in a Chinese astronomical system based on
Indian methods, the Jiu-zhi li 九執曆 compiled in 718, although this 248-day scheme is
not found in the system itself (Jones 1983/84, 34). In China, we know that this scheme
was at least used in the Qin-tian li 欽天曆 (956–963) of the late Zhou Dynasty (Xinwu-dai shi, 58: Si-tian kao; Yabuuti 1963, 95; van Dalen et al. 1997, 128). The Qin-tian li
is derived from the eighth-century Fu-tian li (Yabuuti 1990, 105), whose “method wasbased on Indian astronomical system,” as we have mentioned in the commentary of thefirst section. Therefore, we can conjecture a connection between the Fu-tian li and Qitai
calendar here as well (Isahaya 2009, 33). In addition, we know that there is a tradition ofusing “two” anomalistic months depending on the purpose in Babylonia; one of which is

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Yoichi ISAHAYASCIAMVS 14

the value extracted by the aforementioned period relation 248/9 ≈ 27.5556 days
(Neugebauer 1957, 161-162).

Section 10
This section is assigned to the explanation for determining the madkhal of a month on thetrue motions of the two luminaries. In the zījes, the madkhal—which literally means“entrance”—is used as a term to denote the weekday of the first day of a year or month orof a particular date (van Dalen 2000, 270). As in the following passage from the second
section, the sixty-cycle is considered a substitute for a weekly cycle in the Qitai calendar:
By combining this cycle with the cycle of twelve, a cycle of sixty is obtained. They count years anddays with this cycle. This cycle is their substitute for our week. We call this cycle the “sixty-cycle.”

Therefore, we can regard the madkhal as the sixty-cycle of the first day of a year ormonth in this calendar.
Until the previous section, we can obtain the values of the solar and lunar equations at
the beginning of a month in a year. In addition, we can compute the beginning of the firstmonth in a year on mean motion. By adding the value to a synodic month as many times
as required, we can obtain the beginning of a required month on mean motion. If thevalue of the equations is additive, it is added to the beginning; and if the value issubtractive, it is subtracted from the beginning.
In terms of the funks, if the value is shorter than that of a day and the half of a night(namely, shorter than 7,500 funks), it is considered to be a day; larger than that value, thefunks are considered to be two days. This method is called jin-shou 進朔 in the Chinese
astronomical system. If the total days exceed 60, 60 is subtracted from the total to yield
the first day of a month.
By computing the first days of the successive two months, we can know the length of
the former month. In the Chinese astronomical system, there are two months: the longmonth containing 30 days and short month containing 29 days. In regard to the pattern ofmonth lengths, there were various ways in each Chinese astronomical system, as
discussed by Martzloff (2009, 72-75). In the Qitai calendar, it is stipulated that more than
two consecutive 29-day months is not permissible, and more than three consecutive
months is not permissible in the case of the 30-day months.

SCIAMVS 14

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207

According to the text, the intercalary month is that which contains only the beginningof one solar division; however, as explained in the commentary of the sixth section, thefollowing expression is more precise; that is to say, a month which does not contain the
beginning of an even-numbered division is regarded as an intercalary month.

Section 11
In this section, the “fourth cycle,” which functioned as the standard for the “choice ofdays” (ikhtiyār-i rūz-hā) is explained. In the Islamicate world, the term ikhtiyārāt (theplural form of ikhtiyār) means the literature or method concerning astrological choices,the discernment of auspicious and inauspicious days. Of course, the literature on
ikhtiyārāt were well established in the world long before the introduction of the Chinesesystem (Fahd 1995, 107-108); especially in Iran, this kind of astrology flourished inconnection with the worship of Imams (Ja‘fariyan 2011).
This cycle, called jian-chu 建除 or shi-er zhi 十二直—twelve-presage cycle—, iswritten down on annotated calendars to determine auspicious and inauspicious days foreach specific action (e.g., war, moving, marriage, etc.). These names are as follows.

N.
1
2
3
4
5
6
7
8
9
10
11
12

Chinesejian 建 (kiɛn)chu 除 (tʂhiu)
man 滿 (muɜn)ping 平 (phiaŋ)ding 定 (tiaŋ)zhi 執 (tʂi)
po 破 (phuɜ)wei 危 (ui)cheng 成 (tʂiaŋ)shou 收 (ʂiau)
kai 開 (khai)bi 閉 (pi)

Text
kin
chū
man
pin
tin
chih
pū
wī
chin
shīu
khā’ī
pī

In the Uighur text Meaningkin
instauration(chuu)
evictionmanplenitudepii
equilibrium(ti)
fixitychip
maintenancepa
destruction
küü
danger(chi)
maturity
shiu
receptionkay
opening(pi)
closing(Bazin 1991, 287; Arrault & Marzloff 2003, 103–104)

208

Yoichi ISAHAYASCIAMVS 14

This twelve-presage cycle frequently appears in Sino-Uighur calendars, but thephonetic transcription forms in the Zīj-i Īlkhānī are somewhat different from thetranscription into Uighur script of the same cycle in a document from 1202, which wehave also incorporated into the above table (Bazin 1991, 286-288). Also, the dates of a
Uighur text written in Brahmi script from 1277 agree with those of the official Chinesesystem (Bazin 1991, 306-308). In consideration of these facts, we conclude that the Qitai
calendar cannot be identified as the contemporary calendar used by Uighurs (Isahaya
2009, 34-35).
The cycle pertains to the twenty-four solar divisions. If the cycle is about torecommence at the beginning of an odd numbered division, the element of the cycle forthe preceding day is repeated, whereupon the cycle begins one day later (van Dalen et al.
1997, 123).

Section 12
The final section explains the conversion table between the Qitai and Hijri calendars.
Since the extensive table for converting from Hijri dates to Chinese dates has been so
intensively investigated by van Dalen et al. (1997, 135-148), we have little to add to theirstudy here. The basic structure of the table is as follows:
Hijri month(the name of the Turkish year )safar(Example 1)
the initial
week day of
the Hijri
month (1-7)

the number ofthe number ofthe Qitaidays inthe
The initial days
month in the
Qitai monthof the Qitai
current Qitai(29 or 30
month (1-7)
year (1-12, ordays)
shūn )

Sha'ban(Example 2)

Horse

6

Hijri year

5

602
29

shūn

5

606
30

1

4

The location of intercalary months on this table is one of the interesting points that
their study made clear. According to their investigation, all positions of intercalarymonths except two agree with the contemporary, official astronomical systems of the Jin
and Yuan dynasties. As they have stated, it seems possibly that intercalary months in thecalendar were adjusted to the computation of the official astronomical systems in China;rather than by the method of calculation in the Zīj-i Īlkhānī (van Dalen et al. 1997, 138).
From this fact, we can assume that the Qitai calendar or the original Chinese source of
this calendar was, from the very beginning, not expected to provide exact computation.

SCIAMVS 14

The Tārīkh-i Qitā in the Zīj-i Īlkhānī

209

For example, determining the positions of intercalary months requires a more
complicated mathematical procedure; rather, this calendar might well have its role in“following” the results of the contemporary official astronomical system concerning, forexample, determination of either the beginning of a year or a solar division during someperiod, in order to make use of it for the purposes of astrological choices as we have seenin the preceding section.

V.

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‫‪SCIAMVS 14‬‬‫‪214‬‬‫‪Yoichi ISAHAYA‬‬‫‪VI. Edition‬‬‫(‪ 2‬اب) ابب اول‬‫در رشح اترخی [قتا]‪ 1‬و معرفت سالها و ماههای أن‪ ،‬و أن مش متل بود بر دوازده فصل‬‫‪2‬‬‫فصل اول‬‫در رشح اقسام ش بانروز نزدیک اهل [قتا]‬‫‪3‬‬‫حکامی [قتا]‪ 4‬و ترکس تان‪ 5‬اقسام ش بانروز و روزها و سالها را دوری هناده اند که بر دوازده میگردد‪.‬‬‫و هر یکی را از أن دوازده انمی هناده اند‪ 6.‬و [انمهای دوازدهگانه به هر دو لغت این است]‪.‬‬‫‪7‬‬‫‪.‬خطاییان ‪; BoL:‬قتا ‪BL, KM, SB, DK, BN, NK, KDT and BML:‬‬‫‪1‬‬‫‪.‬مش متل بر دوازده فصل ‪; KM:‬مش متل بر دوازده فصل است ‪; BL, BN, KDT and BML:‬مش متل بود بر دوازده فصل ‪BoL, SB, DK and NK:‬‬‫‪2‬‬‫‪.‬ختا ‪; BoL:‬خطا ‪; BL and KM:‬قتا ‪SB, DK, BN, NK, KDT and BML:‬‬‫‪3‬‬‫‪.‬خطا ‪; BoL, BL and KM:‬قتا ‪SB, BN, NK, KDT and BML:‬‬‫‪4‬‬‫‪.‬ترکس تاین ‪; SB:‬ترکس تان ‪BoL, BL, KM, SB, DK, BN, NK, KDT and BML:‬‬‫‪5‬‬‫‪.‬هناده ‪; BL, KM, DK and BN:‬هناده اند ‪BoL, SB, NK, KDT and BML:‬‬‫‪6‬‬‫انمهای دوازدهگانه به هر دو لغت این است که در این ‪; BN:‬انمهای دوازده هر دو گفته این است ‪; BoL:‬انمهای دوازدهگانه به هر دو لغت این است ‪BL, KM, DK, SB, NK and BML:‬‬‫‪7‬‬‫‪.‬جدول است‬

‫‪215‬‬‫‪SCIAMVS 14‬‬‫‪The Tārīkh-i Qitā in the Zīj-i Īlkhānī‬‬‫اعداد‬

‫ا‬

‫ب‬
‫‪2‬‬

‫انمها به قتایی‬

‫ژه‬

‫‪1‬‬

‫چیو‬

‫انمها به تریک‬‫کسکو‬

‫اوط‬

‫ج‬

‫د‬

‫ه‬

‫‪3‬‬

‫ماو‬

‫‪4‬‬

‫چن‬

‫ابرس‬‫طاوشقن‬

‫لو‬

‫ی‬

‫و‬
‫‪5‬‬

‫ح‬

‫ز‬

‫ط‬

‫‪6‬‬

‫وو‬

‫‪7‬‬

‫وی‬

‫ییالن‬‫یوند‬

‫قوی‬

‫ص‬

‫ی‬

‫یب‬

‫ای‬
‫‪11‬‬

‫‪8‬‬

‫شن‬

‫‪9‬‬

‫یوو‬

‫‪10‬‬‫سو‬‫‪12‬‬‫بیجنی‬‫داقوق‬‫ایت‬‫خایی‬‫طونغوز‬‫‪13‬‬‫و هر ش بانروزی مهچنانکه حماس بان ما به بیست و چهار ساعت قسمت کرده اند‪ ،‬ایشان به‬‫دوازده «چاغ»‪ 14‬قسمت کرده اند‪ .‬و هر یک (‪ 3‬الف) چاغ به هشت «که» و متامیت ش بانروز را نزی‬‫‪15‬‬‫به ده هزار «فنک» قسمت کرده اند‪ 16.‬پس هر یک چاغ هش تصد و یس و سه فنک ابشد و ثلیث‪ .‬و‬‫هر یک که صد و چهار فنک ابشد و سدیس‪ .‬و أغاز ش بانروز از نمیۀ شب کنند‪ .‬و أن وقت از چاغ‬‫ژه و کسکو یک نمیه گذش ته ابشد و یک نمیه مانده‪ .‬و بعد از أن [یک یک چاغ میگذرد]‬‫‪17‬‬‫پیوس ته‪ 18‬ات نمیۀ روز نمیۀ چاغ وو و یوند ابشد‪ .‬و اول روز در‪ 19‬وقت تساوی شب و روز در نمیۀ‬‫‪.‬زه ‪; BL:‬زه ‪; KM:‬ژه ‪; BoL, DK and BN:‬ژه ‪SB, NK, KDT and BML:‬‬‫‪1‬‬‫‪.‬جیو ‪; BML:‬جیو ‪َ ; NK:‬چیو ‪; BN:‬جیو ‪; DK:‬جیو ‪; SB:‬چیو ‪; KM:‬چیو ‪; BoL:‬جیو ‪; BL:‬چیو ‪KDT:‬‬‫‪2‬‬‫‪.‬ی ‪; KDT:‬ـم ‪;َ DK:‬ی ;‪; BN‬ی ‪; BoL and KM:‬ی ‪BL, SB, NK and BML:‬‬‫‪3‬‬‫‪َ .‬ماوو ‪َ ; BN and BMT:‬ماو ‪; SB, NK and KDT:‬ماو ‪; BoL and DK:‬ماو ‪BL and KM:‬‬‫‪4‬‬‫‪.‬خن ‪; DK:‬چن ‪; BoL and SB:‬جن ‪; KM:‬جن ‪; BL:‬چن ‪BN, NK, KDT and BML:‬‬‫‪5‬‬‫َ‪.‬ض ‪; BN:‬رص ‪; DK:‬ص ‪; KM:‬رص ‪; BoL:‬ص ‪BL, SB, NK, KDT and BML:‬‬‫‪6‬‬‫;وو ‪; SB‬وو ‪; BoL and DK:‬وو ‪BL, KM, NK, KDT and BML:‬‬‫َ‪.‬وو ‪َ BN:‬‬‫‪7‬‬‫‪.‬وی‪; BN‬وی ‪; DK:‬روی ‪; BoL:‬وی ‪BL, KM, SB, NK, KDT and BML:‬‬‫‪8‬‬‫‪.‬سن ‪; SB:‬شن ‪; BoL, KM and DK:‬شن ‪BL, BN, NK, KDT and BML:‬‬‫‪9‬‬‫‪.‬یوو ‪; KDT and BML:‬پوو ‪; BN:‬یوو ‪; BoL, KM and DK:‬یوو ‪BL, SB and NK:‬‬‫‪10‬‬‫‪.‬س پو ‪; BN:‬سـو ‪; DK:‬سو ‪; KM:‬ش یو ‪; BoL:‬سو ‪BL, DK, NK, KDT and BML:‬‬‫‪11‬‬‫‪.‬قوین ‪; BN and BML:‬قوی ‪BoL, BL, KM, SB, DK, NK and KDT:‬‬‫‪12‬‬‫‪.‬طونقوز ‪; SB:‬طونغوز ‪BoL, BL, KM, DK, BN, NK, KDT and BML:‬‬‫‪13‬‬‫‪.‬جاغ ‪; BL, KM, SB, DK, BN and KDT:‬چاغ ‪BoL, NK and BML:‬‬‫‪14‬‬‫‪Not in SB.‬‬‫‪15‬‬‫‪; Not in NK.‬قسمت کرده اند‬‫‪16‬‬‫‪.‬یک چاغ چاغ میگذرد ‪; BoL:‬یک یک چاغ میگذرد ‪BL, KM, SB, DK, BN, NK, KDT and BML:‬‬‫‪17‬‬‫‪.‬پیوس ته به نوبت ‪BL:‬‬‫‪18‬‬‫‪.‬ات ‪NK:‬‬‫‪19‬‬

‫‪Yoichi ISAHAYA‬‬‫‪SCIAMVS 14‬‬‫‪216‬‬‫چاغ ماو و طاوشقن ابشد‪ .‬و اول شب در نمیۀ چاغ یوو و داقوق‪ .‬و به سبب درازی و کواتهی شب‬‫و روز‪ 1،‬اول روز و اول شب پیش از أن ای پس از أن میافتد‪ .‬اما نمیۀ شب و نمیۀ روز از أن هرگز‬‫بنگردد‪ .‬ما حصۀ چاغها و کههای ش بانروز از [فنکها]‪ 2‬معنی کردی‪ .‬و در جدویل هنادی ات به أساین‬‫معلوم کنند که از هر چاغی و هر کهیی چند گذش ته ابشد‪ .‬و فنکها بر عادت منجامن ما از شصت‬‫شصت مرفوع کرده‪ ،‬بهنادی‪ .‬و کسور فنکها مه‪ 3‬از کسور شصت‪ .‬و مجلۀ فنکهای یک ش بانروز‬‫مرفوع کرده‪ ،‬بر این شلک ابشد‪ :‬بموم‪ .‬پس عدد فنکها هرچه از این زایدت شود‪ ،‬این قدر از أن‬‫‪4‬‬‫نقصان ابید کرد و به جای أن نشان یک ش بانروز هناد‪ 5.‬و چون خواهند که‪ 6‬ش بانروزی اب‪ 7‬فنکها‬‫کنند‪ ،‬یکی از عدد ش بانروزها نقصان ابید کرد و این عدد به جای [أن]‪ 8‬هناد‪ ،‬چنانکه مقتضای‬‫حساب ابشد‪ .‬و جدول این است‪.‬‬‫‪9‬‬‫‪10‬‬‫‪.‬روز و شب ‪; BL:‬شب و روز ‪BoL, KM, SB, DK, BN, NK, KDT and BML:‬‬‫‪1‬‬‫‪.‬از چاغها ‪; BoL:‬از فنکها ‪BL, KM, SB, DK, BN, NK, KDT and BML:‬‬‫‪2‬‬‫‪Not in SB.‬‬‫‪3‬‬‫‪.‬او ‪; BL:‬أن ‪BoL, KM, SB, DK, BN, NK, KDT and BML:‬‬‫‪4‬‬‫‪; not in NK.‬به جای ایشان یک ش بانروز هناد ‪; BL:‬به جای أن نشان یک ش بانروز هناد ‪BoL, KM, SB, DK, BN, KDT and BML:‬‬‫‪5‬‬‫‪Not in SB.‬‬‫‪6‬‬‫‪Not in DK.‬‬‫‪7‬‬‫‪.‬او ‪; BoL:‬أن ‪BL, KM, SB, DK, BN, NK, KDT and BML:‬‬‫‪8‬‬‫‪Not in BL.‬‬‫‪9‬‬‫‪ ; not in BN.‬و جدول این است‬‫‪10‬‬

‫‪217‬‬‫‪SCIAMVS 14‬‬‫‪The Tārīkh-i Qitā in the Zīj-i Īlkhānī‬‬‫به قتایی‬

‫ژه‬

‫چیو‬

‫ی‬

‫ماو‬

‫چن‬

‫ص‬

‫وو‬

‫وی‬

‫شن‬

‫یوو‬

‫سو‬

‫خایی‬‫به تریک‬‫کسکو‬‫اوط‬‫ابرس‬‫طاوشقن‬‫لو‬‫ییالن‬‫یوند‬‫قوی‬‫بیجنی‬‫داقوق‬‫ایت‬‫طونغوز‬‫عدد کهها‬‫مرفوع دوابر‬‫مرفوع یک ابر‬‫فنکها‬‫کسور‬‫جدول معرفت مبادی جاغها و کهها از فنکهای ش بانروز مرفوع به شصت شصت‬‫ا‬‫بلطمجک‬‫‪٠‬ونوم‬‫‪٠‬کن‪٠‬‬‫‪٠‬دلمجک‬‫‪٠‬محلوم‬‫ابل‪٠‬‬‫ایوکجک‬‫الیوم‬‫امدی‪٠‬‬‫احنجک‬‫بایهوم‬‫بکجن‪٠‬‬‫ب‬‫بماکزل‬‫‪٠‬حمن‬‫‪٠‬کبدلی‬‫‪٠‬لوکزل‬‫‪٠‬نکن‬‫ادیدی‬‫احیزل‬‫الب‪٠‬ن‬‫امهندی‬‫انطمزل‬‫بجیمن‬‫بکزدلی‬‫ج‬‫بمجایم‬‫‪٠‬یکه‪٠‬‬‫‪٠‬کدحیک‬‫‪٠‬حلایم‬‫‪٠‬نبه‪٠‬‬‫اهحنک‬‫ایطانم‬‫اجلنه‪٠‬‬‫امزحلک‬‫باالم‬‫بیهکه‪٠‬‬‫بکطحیک‬‫د‬‫بمدنهن‬‫‪٠‬یبطی‬‫‪٠‬کوبل‬‫‪٠‬لطنهن‬‫‪٠‬جنمطی‬‫ازمبل‬‫ااکهلن‬‫اهلکطی‬‫امطکبل‬‫بجیهن‬‫بیزطی‬‫بالبل‬‫ه‬‫‪٠٠٠٠‬‬‫‪٠‬جیجنک‬‫‪٠‬کزموم‬‫‪٠‬مام‪٠‬‬‫‪٠‬نهجلک‬‫اطکوم‬‫اکجک‪٠‬‬‫الزجیک‬‫اانوم‬‫به‪٠٠‬‬‫بحیجنک‬‫بلبموم‬‫و‬‫‪٠‬امدب‬‫‪٠‬یهلزل‬‫‪٠‬کطلن‬‫‪٠‬مجکدی‬‫‪٠‬نزیزل‬‫اایین‬‫اکهدی‬‫احلنزل‬‫انبنن‬‫بومدی‬‫بکلزل‬‫بدللن‬‫ز‬‫‪٠‬جکحک‬‫‪٠‬یزاکم‬‫‪٠‬الیه‪٠‬‬‫‪٠‬مهحک‬‫‪٠‬نطام‬‫ایبنه‪٠‬‬‫اکومحک‬‫اممام‬‫اندهل‪٠‬‬‫بحکحک‬‫بکباکم‬‫بلویه‪٠‬‬‫ح‬‫‪٠‬هیبل‬‫‪٠‬یطهن‬‫‪٠‬لبنطی‬‫‪٠‬مونبل‬‫ا‪٠‬مهن‬‫ایدلطی‬‫اکحلبل‬‫امبکهن‬‫انویطی‬‫بییبل‬‫بکدهن‬‫بلزنطی‬‫(‪ 4‬اب) فصل دوم‬‫در اعتبار دور در روزها‬‫[قتاییان]‪ 1‬را دوری دیگر است که در روزها و سالها اعتبار میکنند‪ .‬و أن‪ 2‬دور بر ده می گردد و‬‫انمهای أن‪ 3‬ده این است‪ .‬ا اک‪ 4،‬ب [یی]‪ 5،‬ج پنی‪ ،‬د تنی‪ ،‬ه وو‪ ،‬و یک‪ ،‬ز کن‪ 6،‬ح سن‪ ،7‬ط ژم ی‬‫‪.‬خطاییان ‪; BoL, BL, SB, BN, NK, KDT and BML:‬قتاییان ‪DK:‬‬‫‪1‬‬‫‪.‬این ‪; BL:‬أن ‪BoL, SB, DK, BN, NK, KDT and BML:‬‬‫‪2‬‬‫‪.‬این ‪; BL:‬أن ‪BoL, SB, DK, BN, NK, KDT and BML:‬‬‫‪3‬‬‫‪.‬ناک ‪; BL:‬اک ‪BoL, SB, DK, BN, NK, KDT and BML:‬‬‫‪4‬‬‫‪.‬یب ‪; KDT:‬ـی ‪; DK and BN:‬پیی ‪; BoL, SB and NK:‬یی ‪BL and BML:‬‬‫‪5‬‬‫‪.‬کق ‪; BL:‬کن ‪BoL, SB, DK, BN, NK, KDT and BML:‬‬‫‪6‬‬‫‪.‬شن ‪; SB, DK, BN and NK:‬سن ‪BoL, BL, KDT and BML:‬‬‫‪7‬‬

‫‪SCIAMVS 14‬‬‫‪218‬‬‫‪Yoichi ISAHAYA‬‬‫کوی‪ .‬و چون [این]‪ 1‬دور اب دور دوازدهگانه ترکیب کنند‪ ،‬دوری حاصل أید که بر شصت گردد‪ .‬و‬‫سالها و روزها به أن دور میشامرند‪ .‬و أن دور ایشان را در روزها به جای اایم هفته است ما را‪ .‬و ما‬‫این دور را «دور س تیین» میخوانمی‪ .‬و ترکیب این دو دور بر این گونه ابشد [که در این جدول هناده‬‫شد]‪.‬‬‫‪2‬‬‫ا اک ژه‬‫ب یی چیو‬‫ج پنی ی‬‫د تنی ماو‬‫ه وو چن‬‫و یک ص‬‫ز کن وو‬‫ح سن وی‬‫ط ژم شن‬‫ی کوی یوو‬‫ای اک سو‬‫یب یی خایی‬‫جی پنی ژه‬‫ید تنی چیو‬‫یه وو ی‬‫یو یک ماو‬‫یز کن چن‬‫حی سن ص‬‫یط ژم وو‬‫ک کوی وی‬‫اک اک شن‬‫کب یی یوو‬‫کج پنی سو‬‫کد تنی خایی‬‫که وو ژه‬‫کو یک چیو‬‫کز کن ی‬‫کح سن ماو‬‫کط ژم چن‬‫ل کوی ص‬‫ال اک وو‬‫لب یی وی‬‫جل پنی شن‬‫دل تنی یوو‬‫هل وو سو‬‫لو یک خایی‬‫لز کن ژه‬‫حل سن چیو‬‫لط ژم ی‬‫م کوی ماو‬‫ما اک چن‬‫مب یی ص‬‫مج پنی وو‬‫مد تنی وی‬‫مه وو شن‬‫مو یک یوو‬‫مز کن سو‬‫مح سن خایی‬‫مط ژم ژه‬‫ن کوی چیو‬‫ان اک ی‬‫نب یی ماو‬‫جن پنی چن‬‫ند تنی ص‬‫نه وو وو‬‫نو یک وی‬‫نز کن شن‬‫حن سن یوو‬‫نط ژم سو‬‫س کوی خایی‬‫(‪ 3‬اب) فصل [سوم]‬‫‪3‬‬‫در معرفت سالهای [قتاییان]‪ 4‬و اقسام هر سال‬‫سالهای [قتاییان]‪ 5‬مشیس ابشد‪ .‬و أن از وقت رس یدن أفتاب ابشد به موضعی از فلکالربوج‪ 6‬ات‬‫وقت ابز رس یدن او اب هامجنایئ‪ .‬و أن نزدیک ایشان در س یصد و شصت و پنج روز و دو هزار و‬‫‪.‬أن ‪; BoL:‬این ‪BL, SB, DK, BN, NK, KDT and BML:‬‬‫‪1‬‬‫‪; not in BoL.‬که در این جدول هناده است ‪; KDT and BML:‬که در جدول هناده شد‪ ،‬و جدول این است ‪; NK:‬که در جدول هناده شد ‪; SB:‬که در این جدول هناده شد ‪BL, DK and BN:‬‬‫‪2‬‬‫‪.‬س می ‪; BoL, SB, DK and NK:‬سوم ‪BL, BN, KDT and BML:‬‬‫‪3‬‬‫‪.‬خطاییان ‪; BoL and DK:‬قتاییان ‪BL, SB, BN, NK, KDT and BML:‬‬‫‪4‬‬‫‪.‬ختاییان ‪; BoL:‬قتاییان ‪BL, SB, DK, BN, NK, KDT and BML:‬‬‫‪5‬‬‫‪Not in SB and NK.‬‬‫‪6‬‬

‫‪219‬‬‫‪The Tārīkh-i Qitā in the Zīj-i Īlkhānī‬‬‫‪SCIAMVS 14‬‬‫چهار صد و یس و شش فنک ابشد که ارقام أن بعد از رفع فنکها بر این گونه ابشد شسه ‪٠‬ملو‪ .‬و‬‫[به]‪ 1‬زابن ایشان أن را «س یجو»‪ 2‬خوانند‪ .‬و چنانکه منجامن ما سال به دوازده قسم‪ 3‬میکنند‪ ،‬ایشان‬‫مدت یک سال به بیست و چهار قسم متساوی میکنند‪ 4.‬هر قسمی پانزده روز‪ 5‬و دو هزار و صد و‬‫هش تاد و چهار فنک ابشد و پنج سدس از یک فنک‪ ،‬و ارقام مرفوع أن چننی ابشد‪ :‬یه‪ ٠‬لوکدن‪ .‬و‬‫هر قسمی‪ 6‬را به زابن ایشان یک «کیجه»‪ 7‬خوانند‪ .‬پس هر فصیل‪ 8‬از سال شش کیجه ابشد‪ .‬و اوایل‬‫فصلهای سال ما اواسط فصلهای سال‪ 9‬ایشان ابشد‪ .‬پس اول فصل هبار نزدیک ایشان در حدود‬‫نمیۀ دلو ابشد‪ .‬و نقطۀ انقالب اربعه [در]‪ 10‬اواسط فصول سال ایشان ابشد‪ 11.‬و اسامی اقسام‬‫[سال]‪ 12‬به لغت ایشان و عدد اایم و فنکهای مرفوع از اول سال ات أخر در این جدول هناده شد‪.‬‬‫‪.‬بر ‪; BoL:‬به ‪BL, SB, DK, BN, NK, KDT and BML:‬‬‫‪1‬‬‫‪.‬س پجو ‪; DK, BN and NK:‬س پحو ‪; SB and BML:‬سینجور ‪; BL:‬سـجو ‪; BoL:‬س یجو ‪KDT:‬‬‫‪2‬‬‫‪.‬قسمت ‪; BL:‬قسم ‪BoL, SB, DK, BN, NK, KDT and BML:‬‬‫‪3‬‬‫‪.‬قسمت میکنند متساوی ‪; BL:‬قسم متساوی میکنند ‪BoL, SB, DK, BN, NK, KDT and BML:‬‬‫‪4‬‬‫‪Not in BL.‬‬‫‪5‬‬‫‪.‬قسم ‪; DK, SB, BN, NK and BML:‬قسمی ‪BoL, BL and KDT:‬‬‫‪6‬‬‫‪.‬کیچه ‪; NK:‬کنجه ‪; BN:‬کـجه ‪; BL, KDT and BML:‬کـحه ‪; BoL and DK:‬کیجه ‪SB:‬‬‫‪7‬‬‫‪.‬فصل ‪; BL:‬فصیل ‪BoL, SB, DK, BN, NK, BML and KDT:‬‬‫‪8‬‬‫‪Not in BL.‬‬‫‪9‬‬‫‪Not in BoL.‬‬‫‪10‬‬‫‪; not in NK and KDT.‬و نقطۀ انقالب اربعه در اواسط فصول سال ایشان ابشد ‪BoL, BL, SB, DK, BN and BML:‬‬‫‪11‬‬‫‪Not in BoL.‬‬‫‪12‬‬

‫‪SCIAMVS 14‬‬‫‪220‬‬‫‪Yoichi ISAHAYA‬‬‫جدول مبادی هر قسمیت از اقسام سال به حسب روزها و فنکهای مرفوع شصت شصت‬‫د‬‫شونفوند‬‫ه‬‫شینکمینک‬‫و‬‫کووو‬‫‪16‬‬‫اعداد اقسام‬‫روزها‬‫اعداد اقسام‬‫روزها‬‫‪12‬‬‫ل‬‫ایبمطم‬‫ط‬‫منجن‬

‫‪9‬‬

‫قاک‬

‫مه‬

‫امطیدل‬‫ی‬‫شاجر‬‫‪13‬‬‫قلو‬‫بماجل‬‫س‬‫بکهلطک‬‫ای‬‫س یاوشو‬‫قنب‬‫‪٠‬لمحک‬‫عو‬‫‪٠‬یهکدی‬‫یب‬‫‪20‬‬‫دایشو‬‫‪17‬‬‫انهمای فسمها‬‫اعداد اقسام‬‫ج‬‫کنجه‬

‫‪8‬‬

‫قو‬

‫اکحجین‬‫ید‬‫چیوشو‬‫بدحلم‬‫یه‬‫بَیلو‬‫‪10‬‬‫یو‬‫س یوفَن‬‫یز‬‫‪18‬‬‫قزس‬‫ازجیی‬‫حی‬‫خَنلو‬‫‪6‬‬‫‪14‬‬‫شونکون‬‫‪21‬‬‫قفب‬‫امجحل‪٠‬‬‫یط‬‫لیتون‬

‫رجع‬

‫قزص‬

‫بکبن‬‫ک‬‫س یاوشه‬‫رجی‬‫‪٠‬طمزم‬‫اک‬‫دایشه‬‫‪11‬‬

‫شد‬

‫رکح‬

‫‪٠‬یویبل‬‫کب‬‫دوجنن‬‫‪15‬‬‫ش یط‬‫احلال‬‫رمج‬‫اکبلزک‬‫کج‬‫س یوخن‬‫‪19‬‬‫شدل‬‫بیدکوک‬‫روزها‬‫انمهای قسمها‬‫ب‬‫وویش‬

‫‪4‬‬

‫به‬

‫‪٠‬لوکدن‬‫ح‬‫س یومَن‬

‫‪5‬‬

‫صا‬

‫‪٠‬انمط‪٠‬‬‫جی‬‫لیجوو‬‫اعداد اقسام‬‫ا‬‫لیجن‬‫‪٠‬‬‫‪٠٠٠٠‬‬‫ز‬‫لیخَه‬‫‪3‬‬‫انهمای فسمها‬

‫‪1‬‬

‫‪2‬‬

‫فصل پایزی‬‫روزها‬‫فصل هبار‬‫انهمای قسمها‬‫فصل اتبس تان‬‫فصل زمس تان‬‫رحن‬‫انطبی‬‫کد‬‫داخین‬‫لیجن‬‫‪22‬‬‫‪7‬‬‫بهلکز‪٠‬‬‫رفط‬‫‪٠‬کهاین‬‫االوم‬‫شن‬‫‪٠‬دایی‬‫شسه‬‫‪٠‬ملو‪٠‬‬‫‪.‬لیحن ‪; NK:‬لـجن ‪; DK and BN:‬لیجن ‪; BL and KDT:‬لـحن ‪; BoL, SB:‬لیجن ‪BML:‬‬‫‪1‬‬‫‪.‬لیخه ‪; BML:‬لیخه ‪; NK:‬لـخه ‪; BL, SB, DK and BN:‬لـحه ‪; BoL:‬لیخَه ‪KDT:‬‬‫‪2‬‬‫‪.‬ل َیجور ‪; BML:‬لپجوو ‪; KDT:‬لیحوو ‪; NK:‬لـحوو ‪; SB and DK:‬لـجوو ‪; BoL:‬لیجوو ‪BL and BN:‬‬‫‪3‬‬‫‪.‬وویش ‪; NK:‬وویس ‪; SB and BN:‬وویش ‪; BoL, BL and DK:‬وویش ‪KDT and BML:‬‬‫‪4‬‬‫‪.‬س پومن ‪; BN:‬س یومن ‪; DK:‬سـوفن ‪; SB:‬س یوفن ‪; BL and NK:‬سـومن ‪; BoL:‬س یو َمن ‪KDT and BML:‬‬‫‪5‬‬‫‪.‬جیوشه ‪; NK:‬حیوشو ‪; BN:‬حیوش یو ‪; DK:‬حیوشه ‪; SB:‬جیوسینو ‪; BL:‬جیوشـو ‪; BoL:‬چیوشو ‪KDT and BML:‬‬‫‪6‬‬‫‪;.‬س یاوسه ‪; DK, BN and NK:‬سـاوسه ‪; SB:‬س یاوشه ‪BoL, BL, KDT and BML:‬‬‫‪7‬‬‫‪.‬کیخه ‪; NK:‬کنحه ‪; SB:‬کنجه ‪; BoL, BL, DK, BN and KDT:‬کنجه ‪BML:‬‬‫‪8‬‬‫‪.‬منچن ‪; KDT:‬منجون ‪; BN:‬منحن ‪; SB:‬ـتجن ‪; BL:‬منجن ‪; BoL, DK and NK:‬منجن ‪BML:‬‬‫‪9‬‬‫‪.‬بیلو ‪; BN and KDT:‬بـلو ‪; DK:‬ییلو ‪; BL and BML:‬ــلو ‪; BoL and SB:‬بَیلو ‪NK:‬‬‫‪10‬‬‫‪.‬دایسه ‪; BL, DK and BN:‬داـشه ‪; BoL, SB and NK:‬دایشه ‪KDT and BML:‬‬‫‪11‬‬‫‪.‬شوفوند ‪; KDT:‬شونفنل ‪; BN:‬شونفند ‪; SB and NK:‬شونفوند ‪BoL, BL, DK and BML:‬‬‫‪12‬‬‫‪.‬شاجن ‪; KDT and BML:‬شاجر ‪; NK:‬شاحو ‪; SB:‬شاجن ‪; BL:‬شاجر ‪BoL, DK and BN:‬‬‫‪13‬‬‫‪.‬س یوفن ‪; BML:‬س یوفن ‪; BL, DK and BN:‬سـوفن ‪; BoL and SB:‬س یوفَن ‪NK and KDT:‬‬‫‪14‬‬‫‪.‬دوجنن ‪; BML:‬دوچن ‪; BN:‬دهجنن ‪; BL:‬دوحنن ‪; BoL and SB:‬دوجنن ‪DK, NK and KDT:‬‬‫‪15‬‬‫‪.‬سینکمینک ‪; NK:‬سینکمــک ‪; DK and BN:‬سینکمـنک ‪; SB:‬شینکمنک ‪; BoL and KDT:‬شینکمینک ‪BL and BML:‬‬‫‪16‬‬‫یاوشو ‪; BML:‬ش یاوشو ‪; KDT:‬س یاشو ‪; DK:‬ساوشو ‪; BL and SB:‬س یاوشو ‪BoL, BN and NK:‬‬‫‪.‬س َ‬‫‪17‬‬‫‪.‬خـلو ‪; DK:‬خلو ‪; BL:‬خنلو ‪; BoL, SB, BN:‬خَنلو ‪NK, KDT and BML:‬‬‫‪18‬‬‫‪.‬س یوخن ‪; BML:‬سـوخن ‪; BL, SB and NK:‬س یوحن ‪; BoL and DK:‬س یوخن ‪BL and KDT:‬‬‫‪19‬‬‫‪.‬دایسو ‪; DK:‬داـشو ‪; SB and NK:‬دایشو ‪BL, BN, KDT and BML:‬‬‫‪20‬‬‫‪.‬شونکن ‪; BN:‬شوکون ‪; DK:‬شونکون ‪BL, SB, NK, KDT and BML:‬‬‫‪21‬‬‫‪.‬داجین ‪; NK:‬داجبن ‪; BN and KDT:‬داـخن ‪; DK:‬داـحن ‪; BL and SB:‬داخین ‪BML:‬‬‫‪22‬‬

‫‪221‬‬‫‪The Tārīkh-i Qitā in the Zīj-i Īlkhānī‬‬‫‪SCIAMVS 14‬‬‫فصل چهارم‬‫در اعتبار دورها در سالهای [قتاییان]‪ 1‬و اترخی‪ 2‬ایشان‬‫[قتاییان]‪ 3‬سالها‪ 4‬به دور س تیین میمشرند‪ 4( .‬الف) و دورها مقید کنند به سه انم‪ :‬اول را دور‬‫«شانک َون»‪ 5‬خوانند و میانه را دور «جونک ون» خوانند‪ 6‬و أخرین را دور «خا ون»‪ .‬و مدت هر‬‫سه دور صد و هش تاد سال ابشد‪[ .‬پس]‪ 7‬سالها مقید [میکنند]‪ 8‬به این دورها‪ .‬و اگر خواهند که‬‫تقیید به زایدت از این مبلغ کنند‪ ،‬از ابتدای أفرینش عامل بگریند‪ .‬و به حساب ایشان از أن مبدأ ات‬‫سال اول که چنکز‪ 9‬خان به پادشاهی نشست‪ ،‬هشت هزار و هش تصد و شصت و سه « َون»‪ 10‬متام‬‫گذش ته بود‪— 11‬و هر یک َون ده هزار سال ابشد‪ —12‬و از َون انقصه‪ ،‬نه هزار و ششصد و هفتاد‬‫و نه سال متام گذش ته بود‪ 13‬و سال هش تادم جلوس چنکز خان بود و أن سال کویخایی بود —یعین‬‫سال أخر از دور جونک ون‪ .‬و به حساب پارس یان‪ 14‬سال ششصد و یس و سوم‪ 15‬یزدجردی‪،‬‬‫‪.‬خطاییان ‪; BoL:‬قتاییان ‪BL, SB, DK, BN, NK, KDT and BML:‬‬‫‪1‬‬‫‪.‬توارخی ‪; BL:‬اترخی ‪BoL, SB, DK, BN, NK, KDT and BML:‬‬‫‪2‬‬‫‪.‬خطاییان ‪; BoL:‬قتاییان ‪BL, SB, DK, BN, NK, KDT and BML:‬‬‫‪3‬‬‫‪.‬سالها را ‪; DK:‬سالها ‪BoL, BL, SB, BN, NK, KDT and BML:‬‬‫‪4‬‬‫‪.‬شانکون ‪; BoL, DK and BN:‬شانکون ‪; BL, NK and KDT:‬شانک َون ‪BML:‬‬‫‪5‬‬‫‪.‬خوانند ‪«; SB, DK, BN, NK, KDT and BML:‬جونک ون» خوانند ‪BL and BoL:‬‬‫‪6‬‬‫‪Not in BoL.‬‬‫‪7‬‬‫‪Not in BoL.‬‬‫‪8‬‬‫‪.‬جنکـز ‪; KDT and BML:‬چـکـز ‪; NK:‬حنکزی ‪; DK:‬جنکز ‪; BL, SB and BN:‬چنکز ‪BoL:‬‬‫‪9‬‬‫‪.‬ون ‪; BoL, SB and DK:‬ون ‪;َ BL:‬ون ‪BN, NK, KDT and BML:‬‬‫‪10‬‬‫‪.‬متام شده بود ‪; NK:‬متام گذش ته بود ‪BoL, BL, SB, DK, BN, KDT and BML:‬‬‫‪11‬‬‫‪Not in SB, DK and NK.‬‬‫‪12‬‬‫‪Not in SB, KR and KDT.‬‬‫‪13‬‬‫‪.‬ـارس یان ‪; SB and KDT:‬ابرس یان ‪; BL, DK and BML:‬پارس یان ‪BoL, BN and NK:‬‬‫‪14‬‬‫‪.‬س می ‪; SB, DK and NK:‬سهام ‪; BL:‬سوم ‪BoL, BN, KDT and BML:‬‬‫‪15‬‬

‫‪SCIAMVS 14‬‬‫‪222‬‬‫‪Yoichi ISAHAYA‬‬‫ابتدای دور شانک ون [ابشد]‪ 1.‬و اما تراکن بر دوازدهگانه اقتصار کنند‪ .‬و أن را به انمهایئ که به لغت‬‫ایشان است‪ ،‬میشامرند‪ .‬و قید اترخی ایشان ما را معلوم نیست‪.‬‬‫فصل پنجم‬‫در معرفت مبادی اقسام سالهای مشیس که واقع ابشد در هر [سال]‬‫‪2‬‬‫هر گاه‪ 3‬که خواهمی که مبدأی هر‪ 4‬قسمی از اقسام بیست و چهارگانه در سایل معنی بدانمی‪ ،‬ابید که‬‫در یک سال پیش از أن سال ای بعد از أن سال‪ 5‬دانس ته ابش می که مبدأی [لیجن]‪ 6‬در کدام روز و‬‫چاغ بوده است از دور س تیین‪ .‬و ما أن را اصل اقسام سال‪ 7‬میخوانمی‪ .‬و أن را به لغت [قتاییان]‬‫‪8‬‬‫«کیجو» خوانند‪ .‬و أن در سال اول از دور شانک ون که بعد از جلوس چنکز خان بود‪ ،‬بعد از‬‫‪9‬‬‫ایزده روز و هفت هزار و ششصد و شصت فنک بوده است که ارقام أن‪ 10‬بر این صورت ابشد ای‬‫بزم‪[ 11.‬پس]‪ 1‬چون خواهمی که مبدأی سال‪ 2‬دیگر معلوم کنمی‪ ،‬بنگری ات أن سال پیش از سال اصل‬‫‪.‬بود ‪; BoL:‬ابشد ‪BL, SB, DK, BN, NK, KDT and BML:‬‬‫‪1‬‬‫‪.‬سایل ‪; BoL:‬سال ‪BL, SB, DK, BN, NK, KDT and BML:‬‬‫‪2‬‬‫‪.‬در هرگاه ‪; BoL:‬هرگاه ‪BL, SB, DK, BN, NK, KDT and BML:‬‬‫‪3‬‬‫‪Not in BL.‬‬‫‪4‬‬‫‪Not in BL.‬‬‫‪5‬‬‫‪.‬لـجن ‪; DK, BN and KDT:‬لـچن ‪; SB and NK:‬لیچن ‪; BoL:‬لیجن ‪BL and BML:‬‬‫‪6‬‬‫‪.‬اصل اقسام دور س تیین ‪; BoL:‬اصل اقسام سال ‪BL, SB, DK, BN, NK, KDT and BML:‬‬‫‪7‬‬‫‪.‬خطاییان ‪; BoL:‬قتاییان ‪BL, SB, DK, BN, NK, KDT and BML:‬‬‫‪8‬‬‫‪.‬و بعد از ‪; BoL:‬بعد از ‪BL, SB, DK, BN, NK, KDT and BML:‬‬‫‪9‬‬‫‪.‬أن را ‪; BoL:‬أن ‪BL, SB, DK, BN, NK, KDT and BML:‬‬‫‪10‬‬‫‪Not in BL and DK.‬‬‫‪11‬‬

‫‪223‬‬‫‪The Tārīkh-i Qitā in the Zīj-i Īlkhānī‬‬‫‪SCIAMVS 14‬‬‫است ای بعد از أن و میان هر دو چند سال بوده است؛ پس عدد تفاضل را در مقدار فضل یک سال‬‫مشیس بر س یصد و شصت روز [که]‪ 3‬أن پنج روز و دو هزار و چهارصد و یس و شش فنک ابشد‬‫و رمق أن این است ه ‪٠‬ملو و به لغت ایشان أن‪ 4‬را «یسیو»‪ 5‬خوانند‪ ،‬ضب کنمی؛ و فنکها که از‬‫ده هزار —یعین بموم— زایدت ابشد‪[ 6،‬هر ده هزار را یکی بر عدد روزها افزایمی؛ و أن ده هزار‬‫بیفکنمی ات تفاوت میان سال اصل و سال مطلوب حاصل أید‪.‬‬‫پس اگر سال مطلوب بعد از سال اصل ابشد‪ ،‬أن تفاوت را بر اصل مذکور افزایمی؛ (‪ 4‬اب) و اگر‬‫فنکها از ده هزار —یعین از بموم— زایدت شود]‪ 7،‬این مقدار بیفکنمی؛ و یک روز بر روزها‬‫افزایمی؛ و أن اایم اگر بر شصت زایدت ابشد‪ ،‬شصت میاکهمی‪ 8.‬و اگر سال مطلوب پیش از سال‬‫اصل ابشد‪ ،‬تفاوت را از اصل باکهمی؛ اگر روزها نقصان نتوان کرد‪ ،‬شصت بر روزهای اصل افزایمی و‬‫نقصان کنمی؛ و اگر فنکها نقصان نتوان کرد‪ ،‬یک روز باکهمی؛ و به جای أن‪ ،‬ده هزار —یعین ب‪-‬‬‫موم— بر فنکها افزایمی و فنکها از مجموع باکهمی؛‬‫‪9‬‬‫‪Not in BoL.‬‬‫‪1‬‬‫‪.‬سایل ‪; SB, DK and NK:‬سال ;‪BoL, BL, BN, KDT and BML‬‬‫‪2‬‬‫‪Not in BoL.‬‬‫‪3‬‬‫‪.‬این ‪; BN:‬أن ‪BoL, BN, SB, DK, NK, KDT and BML:‬‬‫‪4‬‬‫‪.‬یسیو ‪; BN and BML:‬س یو ‪; DK:‬یسـو ‪; BoL, SB, NK and KDT:‬یسیو ‪BL:‬‬‫‪5‬‬‫‪.‬شود ‪; BL, SB and KDT:‬ابشد ‪BoL, DK, BN, NK, and BML:‬‬‫‪6‬‬‫هر ده هزار را یکی بر عدد روزها افزایمی؛ و أن ده هزار بیفکنمی ات تفاوت میان سال اصل و سال مطلوب حاصل أید‪ .‬پس اگر سال مطلوب بعد از سال اصل ‪BL, DK, BN, KDT and BML:‬‬‫‪7‬‬‫ده هزار یکی بر عدد روزها افزایمی؛ و أن ده هزار بیفکنمی ات تفاوت میان سال مطلوب و ‪; BoL:‬ابشد‪ ،‬أن تفاوت را بر اصل مذکور افزایمی؛ و اگر فنکها از ده هزار —یعین از بموم— زایدت شود‬‫‪; not in SB and NK.‬سال اصل مطلوب حاصل أید‪ .‬پس اگر سال مطلوب بعد از سال اصل ابشد‪ ،‬أن تفاوت را بر اصل مذکور افزایمی؛ و اگر فنکها از ده هزار —یعین از بموم— زایدت شود‬‫‪; Not in BL, SB, BN, NK, KDT and BML.‬و اایم اگر از شصت زایدت شود‪ ،‬شصت از او بیفکنمی ‪; DK:‬و أن اایم اگر بر شصت زایدت ابشد‪ ،‬شصت میاکهمی ‪BoL:‬‬‫‪8‬‬‫‪; not in BL, SB, DK, BN, NK and BML.‬و فنکها از مجموع باکهمی ‪BoL and KDT:‬‬‫‪9‬‬‫‪SCIAMVS 14‬‬‫‪Yoichi ISAHAYA‬‬‫‪224‬‬‫أچنه حاصل أید بعد از زایدت ای نقصان‪ ،‬مبدأی لیجن ابشد در سال مطلوب؛ أن را از مبدأی دور‬‫س تیین بشمری؛ و فنکها را از حساب یک روز گریی؛ به هر موضع که رسد‪ ،‬مبدأی سال مطلوب‬‫ابشد؛ و متامت أن سال را به أن [انم]‪ 1‬نسبت کنند‪.‬‬‫مثالش خواستمی که مبدأی سال دمه از دور شانک ون که مطابق سال ششصد و چهل و دوم‬‫یزدجردی ابشد و أن سال کوی یوو ابشد به لغت [قتا]‪ 2‬و داقوق ییل به لغت تراکن‪ ،‬معلوم کنمی‪.‬‬‫تفاضل میان سال اصل و سال مطلوب نه عدد بود؛‪ 3‬در «یسیو» ضب [کردی]؛‪ 4‬أمد چهل و پنج‬‫روز و بیست و یک هزار و هنصد و بیست و چهار فنک بر این صورت مه وهکد؛ هجت بیست‬‫هزار فنک —یعین هجلک— دو روز گرفتمی؛ چهل و هفت روز شد؛ و یک هزار و هنصد و بیست‬‫و چهار فنک مباند بر این صورت مز ‪٠‬لبد؛ پس این مبلغ را بر اصل که ایزده روز و هفت هزار و‬‫ششصد و شصت فنک است بر این صورت ای بزم‪ ،‬افزودی‪ ،‬از هبر أنکه سال مطلوب بعد از‬‫سال اصل است؛ حاصل أمد پنجاه و هشت روز و نه هزار و پانصد و هش تاد و چهار فنک بر این‬‫صورت حن بلطمد؛ و این‪ 5‬مبدأی سال مطلوب ابشد؛ فنکها را یکی بر پنجاه و هشت افزودی ات‬‫پنجاه و نه روز‪ 6‬شد؛ و پنجاه و هنم از دور س تیین ژمسو ابشد و به تریک ایت کون‪ 7.‬پس معلوم شد‬‫‪Not in BoL and KDT.‬‬‫‪1‬‬‫‪.‬اهل خطا ‪; BL‬خطا ‪; BoL:‬قتا ‪SB, DK, BN, NK, KDT and BML:‬‬‫‪2‬‬‫‪.‬ایفتمی ‪BN:‬‬‫‪3‬‬‫‪.‬کنمی ‪; BoL:‬کردی ‪BL, SB, DK, BN, NK, KDT and BML:‬‬‫‪4‬‬‫‪.‬أن ‪; BL and DK:‬این ‪BoL, SB, BN, NK, KDT and BML:‬‬‫‪5‬‬‫‪Not in SB, DK and BML.‬‬‫‪6‬‬‫‪Not in BL, DK and NK.‬‬‫‪7‬‬

‫‪225‬‬‫‪The Tārīkh-i Qitā in the Zīj-i Īlkhānī‬‬‫‪SCIAMVS 14‬‬

‫که اول سال کوییوو که سال داقوق است‪ ،‬روز ژمسو است که ایت کون ابشد‪ .‬از مبدأی روز نه‬‫هزار و پانصد و هش تاد و چهار فنک گذش ته بر این صورت بلطمد؛ و چون أن را در جدول‬‫مبادی چاغها و کهها طلب کردی‪ ،‬ایفتمی میان اول و دوم؛ و فضل او بر مبدأی چاغ اول که بلط‪-‬‬‫مجک ابشد‪ ،‬به دو ثلث یک فنک بود‪ .‬پس دانستمی که مبدأی سال کوییوو که داقوق ییل است‪،‬‬‫در که اول ابشد از چاغ ژه که چاغ کسکو ابشد‪ ،‬از روز ژمسو که روز ایت ابشد‪ 5( ،‬الف) بعد از‬‫دو ثلث از یک فنک از أن که‪ .‬ومه بر این قیاس‪.‬‬‫و چون مبدأی سال معلوم شود‪ ،‬اقسام سال برأن مبدأ میافزایمی‪ 1‬ات مبادی‪ 2‬هر [قسم]‪ 3‬که‬‫خواهمی معلوم شود‪ 4.‬مث ًال خواستمی که مبدأی لیخه‪ 5‬از أن سال معلوم کنمی؛ نگاه کردی در جدول‬‫مبادی اقسام سالها از روزها نود و یک و از فنکها ‪٠‬انمط‪ ٠‬بود؛ أن را بر روزها و فنکهای رس‬‫سال افزودی؛ حاصل أمد از روزها‪ ،‬صد و چهل و نه روز و از فنکها‪ ،‬جالجل؛ پس از فنکها یک‬‫روز‪— 6‬یعین بموم— نقصان کردی؛‪ 7‬روزها صد و پنجاه شد؛ و اب فنکها بر این گونه شد قن‪٠‬مد‪-‬‬‫جن؛ از روزها شصت شصت [بیفکندی]؛‪ 8‬مباند یس روز؛‪ 9‬دانستمی که در روز یس و یمک از دور‬‫‪.‬افزایمی ‪; BoL:‬میافزایمی ‪BL, SB, DK, BN, NK, KDT and BML:‬‬‫‪1‬‬‫‪.‬مبدأی ‪; BL:‬مبادی ‪BoL, SB, DK, BN, NK, KDT and BML:‬‬‫‪2‬‬‫‪.‬قسمی ‪; BoL:‬قسم ‪BL, SB, DK, BN, NK, KDT and BML:‬‬‫‪3‬‬‫‪.‬میشود ‪; BL:‬شود ‪BoL, SB, DK, BN:‬‬‫‪4‬‬‫‪.‬لیحه ‪; SB and DK:‬لیخه ‪BoL, BL, BN, NK, KDT and BML:‬‬‫‪5‬‬‫‪.‬روزه ‪BL:‬‬‫‪6‬‬‫‪..‬نقصان کردی؛ و یک روز بر روزها افزودی ‪; BL:‬نقصان کردی ‪BoL, SB, DK, BN, NK, KDT and BML:‬‬‫‪7‬‬‫‪.‬بیفکنمی ‪; BoL:‬بیفکندی ‪BL, SB, DK, BN, NK, KDT and BML:‬‬‫‪8‬‬‫‪Not in BL, DK, NK and BML.‬‬‫‪9‬‬‫‪SCIAMVS 14‬‬‫‪226‬‬‫‪Yoichi ISAHAYA‬‬‫س تیین که روز اکوو ابشد و به تریک روز یوند‪ ،‬در که ششم از چاغ ماو که به تریک طاوشقن ابشد‪،‬‬‫بعد از هش تاد و نه فنک از أن که مبدأی قسم لیخه ابشد در أن سال‪ .‬و بر این قیاس‪.‬‬‫[و]‪ 1‬ما جدویل بنهادی مش متل بر مبادی سالها در بیست و چهار سال از دور شانکون و‬‫جدویل دیگر در مبادی اقسام سال داقوق از هجت مثال را‪ ،‬و أن [جدول] این است‪.‬‬‫‪2‬‬‫‪Not in BoL.‬‬‫‪1‬‬‫از ‪; KDT:‬از هجت مثال‪ ،‬و أن دو جدول این است که در صفحۀ دیگر است ‪; BN:‬از هجت مثال را‪ ،‬و أن جدول این است ‪ ; BL:‬از هجت مثال‪ ،‬و أن این است ‪BoL, SB, DK and NK:‬‬‫‪2‬‬‫‪.‬از هجت امثال‪ ،‬و أن جدول این است که بر ورق دیگر نسبت أید ‪; BML:‬هجت مثال‪،‬و أن جدول این است که بر أن دیگر صفحه است‬‫‪227‬‬‫‪SCIAMVS 14‬‬‫‪The Tārīkh-i Qitā in the Zīj-i Īlkhānī‬‬‫سالهای‬‫یزدجردی‬‫سالهای قتایی‬‫سالهای تریک‬‫روزهای س تیین‬‫انم مبدأی‬‫لیجن به قتایی‬‫خلج‬‫اکزه‬‫کسکو‬

‫ای‬

‫بزم‬

‫یی خایی‬‫طونغوز‬‫خدل‬‫ییچیو‬

‫اوط‬

‫یز‬

‫‪ ٠‬ا لو‬‫سن ص‬‫ییالن‬‫خهل‬‫پنیی‬‫ابرس‬‫کب‬‫‪ ٠‬مب یب‬‫پنی سو‬

‫ایت‬

‫خلو‬

‫تنیماو‬‫طاوشقن‬‫کز‬‫ا کب مح‬‫سن ماو‬‫طاوشقن‬‫خلز‬‫ووچن‬‫لو‬‫لب‬‫ب ج کد‬‫پنی شن‬‫بیجنی‬

‫خلح‬

‫یکص‬

‫ییالن‬‫لز‬‫ب مد ‪٠‬‬‫تنی چیو‬

‫اوط‬

‫خلط‬

‫کنوو‬‫یوند‬‫مج‬‫‪ ٠‬لز نو‬‫تنی وی‬

‫قوی‬

‫مخ‬

‫سنوی‬

‫قوی‬

‫مح‬

‫ا اح لب‬‫ژم ژه‬‫کسکو‬‫خام‬‫ژمشن‬‫بیجنی‬‫جن‬‫ا نط ح‬‫تنی ص‬‫ییالن‬‫مخب کوییوو‬‫داقوق‬‫حن‬‫ب لط مد‬‫ژم سو‬

‫ایت‬

‫مخج‬

‫اکسو‬‫ایت‬‫د‬‫‪ ٠‬جل م‬‫وو چن‬

‫لو‬

‫مجد‬

‫ییخایی‬‫طونغز‬‫ط‬‫ا ید نو‬‫کوی یوو‬‫داقوق‬‫مخه‬‫پنیژه‬‫کسکو‬‫ید‬‫ا ند نب‬‫وو ی‬‫ابرس‬‫مخو‬‫تنیچیو‬

‫اوط‬

‫یط‬

‫ب هل کح‬‫کوی وی‬

‫قوی‬

‫مخز‬

‫ووی‬

‫ابرس‬‫که‬‫‪ ٠‬کط کد‬‫یک چیو‬

‫اوط‬

‫مخح‬

‫یکماو‬‫طاوشقن‬‫ل‬‫ای‪٠‬‬‫اک وو‬‫یوند‬‫مخط‬‫کنچن‬‫لو‬‫هل‬‫ا ن لو‬‫یک خایی‬‫طونغوز‬

‫خنا‬

‫سنص‬

‫ییالن‬‫م‬‫ب ال یب‬‫اک چن‬‫لو‬‫خنب ژموو‬‫یوند‬‫مو‬‫‪ ٠‬که ح‬‫کن سو‬

‫ایت‬

‫خنج‬

‫کویوی‬

‫قوی‬

‫ان‬

‫ا ه مد‬‫یی ماو‬‫طاوشقن‬‫خند‬‫اکشن‬‫بیجن‬‫نو‬‫ا مو ک‬‫کن شن‬‫بیجنی‬‫خنه‬‫یییوو‬‫داقوق‬‫ا‬‫ب کو نو‬‫یی چیو‬

‫اوط‬

‫خند‬

‫پنیسو‬

‫ایت‬

‫ز‬

‫‪ ٠‬ک نب‬‫سن وو‬‫یوند‬‫خنو‬‫تنیخایی‬‫طونغوز‬‫یب‬‫ا ا کح‬‫پنی ژه‬‫کسکو‬‫خزن‬‫ووژه‬‫کسکو‬‫یز‬‫ا مب د‬‫سن ص‬‫ییالن‬‫لیجن به تریک‬‫انم مبدأی‬‫جدول مبادی لیجن در سایل چند‬

‫‪SCIAMVS 14‬‬‫‪228‬‬‫‪Yoichi ISAHAYA‬‬‫اسامی اقسام‬‫اایم دور س تیین‬‫اسامی مبادی‬‫اقسام به قتایی‬‫اوقات اقسام‬‫از موضع أفتاب‬‫جدول مبادی اقسام سال داقوق موافق مخب یزدجردی‬‫لیجن‬‫حن‬‫ب لط مد‬‫ژمسو ایت‬‫اواسط ادللو‬‫وویش‬‫ید‬‫‪ ٠‬کط کط‬‫ووی ابرس‬‫اوایل احلوت‬‫کنجه‬‫کط‬‫ا ه ند‬‫کویص ییالن‬‫اواسط احلوت‬‫شونفوند‬‫مد‬‫ا مب یط‬‫ووشن بیجنی‬‫اولیل امحلل‬‫سینکمینک‬‫نط‬‫ب حی مج‬‫کویخایی طونغوز‬‫اواسط امحلل‬‫کووو‬‫یه‬‫‪ ٠‬ح کح‬‫یکماو طاوشقن‬‫اوایل الثور‬‫لیخه‬‫ل‬‫‪ ٠‬مد جن‬‫اکوو یوند‬‫اواسط الثور‬‫س یومن‬‫مه‬‫ا اک حی‬‫یکیوو داقوق‬‫اوایل اجلوزا‬‫منجن‬‫‪٠‬‬‫ا نز مج‬‫اکژه کسکو‬‫اواسط اجلوزا‬‫شاجر‬‫یه‬‫ب دل ح‬‫یکماو طاوشقن‬‫اوایل الرسطان‬‫س یاوشو‬‫ال‬‫‪ ٠‬کج نب‬‫ییوی قوی‬‫اواسط الرسطان‬‫دایشو‬‫مو‬‫ا ‪ ٠‬یز‬‫کنسو ایت‬‫اوایل الاسد‬‫لیجوو‬‫ا‬‫ا لو مب‬‫ییچیو اوط‬‫اواسط الاسد‬‫چیوشو‬‫یو‬‫ب جی ز‬‫کنچن لو‬‫اوایل السنبهل‬‫بیلو‬‫لب‬‫‪ ٠‬ب نب‬‫پنیشن بیجنی‬‫اواسط السنبهل‬‫س یوفن‬‫مز‬‫‪ ٠‬لط یز‬‫سنخایی طونغوز‬‫اوایل املزیان‬‫خنلو‬‫ب‬‫ا یه مب‬‫پنیی ابرس‬‫اواسط املزیان‬‫شونکن‬‫یز‬‫ا نب و‬‫سنص ییالن‬‫اوایل العقرب‬‫لیتون‬‫لب‬‫ب کح ال‬‫پنیشن بیجنی‬‫اواسط العقرب‬‫س یاوشه‬‫مح‬‫‪ ٠‬حی یو‬‫ژمژه کسکو‬‫اوایل القوس‬‫دایشه‬‫ج‬‫‪ ٠‬ند ما‬‫تنیماو طاوشقن‬‫اواسط القوس‬‫دوجنن‬‫حی‬‫ا ال و‬‫ژموو یوند‬‫اوایل اجلدی‬‫س یوخن‬

‫جل‬

‫بزل‬

‫تنییوو داقوق‬‫اواسط اجلدی‬‫داخین‬‫مح‬‫ب مج نه‬‫ژمژه کسکو‬‫اوایل ادللو‬‫لیجن‬‫د‬‫‪ ٠‬جل م‬‫ووچن لو‬‫اواسط ادللو‬‫‪229‬‬‫‪The Tārīkh-i Qitā in the Zīj-i Īlkhānī‬‬‫‪SCIAMVS 14‬‬‫(‪ 5‬اب) فصل ششم‬‫در معرفت مبدأی أرام ای به حسب امر وسط در هر سال‬‫اول ابید که در یک سال مابنی اول أرام‪ 1‬ای که رس سال است‪ ،‬و مابنی مبدأی وویش که قسم دوم‬‫است از اقسام سال مشیس‪ ،‬معلوم ابشد؛ و أن در اول دور شانکون موافق خلج یزدجردی بعد از‬‫چهارده روز و چهار هزار و ششصد و هفتاد و شش فنک بوده است که ارقام أن بر این صورت ید‬‫ایزنو‪ ،‬و أن بر جدول که خواهد أمد‪ ،‬مذکور است؛‪ 2‬و أن را به لغت [قتا]‪« 3‬شوجنن»‪ 4‬خوانند و ما‬‫أن را اصل رس سالها‪ 5‬میخوانمی؛‬‫‪6‬‬‫پس تفاوت میان أن سال و سال مطلوب بگریی که چندی است؛‪ 7‬و أن را در فضل یک سال‬‫مشیس بر یک سال مقری که أن ده روز و هشت هزار و هفتصد و شصت و چهار فنک ابشد و‬‫ارقامش ی بکود‪ 8،‬و أن را به لغت [قتا]‪« 9‬سوجیا»‪ 10‬خوانند‪ ،‬ضب کنمی؛ پس حاصل را بر اصل‬‫‪.‬اورام ‪; SB:‬ارام ‪; BoL, BL, KM, BN, NK and KDT:‬أرام ‪DK and BML:‬‬‫‪1‬‬‫در اول دور شانکون موافق خلج یزدجردی بعد از چهارده روز و چهار هزار و ششصد و هفتاد و شش فنک بوده است که ارقام أن بر این صورت ید ایزنو‪ ،‬و أن بر جدول که خواهد أمد‪BoL: ،‬‬‫‪2‬‬‫‪; not in BL, KM, SB, KDT and BML.‬و أن جدویل که خواهند أمدن‪ ،‬مذکور است ‪; NK:‬مذکور است‬‫‪.‬خطا ‪; BoL and BL:‬قتا ‪KM, SB, DK, BN, KDT and BML:‬‬‫‪3‬‬‫‪.‬شوـجن ‪; DK:‬شوـحن ‪; SB and NK:‬شوحنن ‪; BL:‬شوجنن ‪BoL, BN and BML:‬‬‫‪4‬‬‫‪..‬اصل رس سال ‪; BoL and DK:‬اصل رس سالها ‪BL, KM, SB, BL, KR, KDT and BML:‬‬‫‪5‬‬‫;و أن در اول شانکون موافق خلج ید روز و ایزنو فنک بوده است ‪; DK:‬پس تفاوت میان أن سال و سال مطلوب بگریی که چند است ‪ and‬و ما أن را «اصل رس سال» میخوانمی ‪Between‬‬‫‪6‬‬‫و أن در سال اول از دور شانکون بعد از چهارده روز و ‪; NK:‬و أن در اول شانکون موافق خلج چهارده روز و چهار هزار و ششصد و هفتاد و شش فنک بوده و ارقامش این است ید ایزنو ‪BN:‬‬‫و أن در جدویل که خواهند أمدن مذکور است در اول دور شانکون موافق خلج چهارده روز و ‪; KDT:‬چهار هزار و ششصد و هفتاد و شش فنک بوده است که ارقام أن بر این صورت بود ید ایزنو‬‫‪.‬چهار هزار و ششصد و هفتاد و شش فنک بوده و ارقامش أن است ید ایزنو‬‫‪; not in BN.‬چند است ‪; KDT and BML:‬چندی است ‪BoL, BL, KM, SB, DK and NK:‬‬‫‪7‬‬‫‪.‬ی بکود ابشد ‪; BN:‬ی بکود ‪BoL, BL, KM, SB, DK, NK, KDT and BML:‬‬‫‪8‬‬‫‪.‬ختا ‪; BoL:‬قتا ‪BL, KM, SB, DK, BN, NK, KDT and BML:‬‬‫‪9‬‬‫‪.‬شوـجا ‪; DK:‬سوـحا ‪; SB:‬سوحیا ‪; KM and NK:‬سوـجا ‪BoL, BL, BN, KDT and BML:‬‬‫‪10‬‬

‫‪Yoichi ISAHAYA‬‬‫‪SCIAMVS 14‬‬‫‪230‬‬‫رس [سالها] افزایمی‪ ،‬اگر سال مطلوب بعد از أن [سال] بود؛‪ 1‬و مدت یک ماه مقری اوسط و أن‬‫بیست و نه روز و پنج هزار س یصد و شش فنک ابشد بر این صورت کط اکحکو و به لغت [قتا]‬‫‪2‬‬‫[أن را]‪« 3‬شوجه»‪ 4‬خوانند؛ اگر از حاصل ضب اب شوجنن‪ 5‬نقصان توان کرد‪ ،‬نقصان میکنمی ات مکرت از‬‫مدت یک ماه مباند؛ و هر یک ابر که تقصان کنمی‪ ،‬در أن سالها که تفاوت ابشد میان سال اصل و‬‫سال مطلوب‪ ،‬یک ابر ماه «شون» افتده ابشد؛‪ -‬و سال سزیده ماه شده‪.‬‬‫و اگر پیش از أن ابشد‪ ،‬أن را از اصل رس [سالها] –اگر نقصان توان کرد—نقصان کنمی؛ و اگر‬‫نقصان نتوان کرد‪ ،‬چندان ابر مدت یک ماه بر اصل رس [سالها] افزایمی که چون حاصل ضب از او‬‫نقصان کنمی‪ ،‬مکرت از یک ماه مباند‪.‬‬‫‪6‬‬‫پس أچنه مباند مکرت از مدت یک ماه‪ ،‬مابنی اول أرام ای و اول وویش ابشد در سال مطلوب؛ و‬‫أن اصل رس أن سال ابشد؛ پس اایم وویش بگریی در هر سال؛‪ 7‬و مابنی اول أرام و اول وویش از‬‫از «شوجنن» ‪; NK:‬و حاصل را بر اصل رس سالها افزایمی‪ ،‬اگر سال مطلوب بعد از أن سال ابشد ‪; BN:‬پس حاصل را بر اصل رس سال افزایمی‪ ،‬اگر سال مطلوب بعد از أن سال بود ‪BoL:‬‬‫‪1‬‬‫باکهمی‪ ،‬اگر سال مطلوب بر سال اصل مقدم ابشد؛ و اگر از «شوجنن» نتوان اکست‪ ،‬مقدار یک ماه مقری اوسط را بر «شوجنن» افزای؛ یک ابر ای بیشرت ای چندان گردد که حاصل ضب از او توان‬‫[و] «شوجنن» ‪; KDT and BML:‬اکست؛ پس از فناکت زاید بر بموم تضاعیف بموم میاکهمی؛ و به عدد هر یک ابر که باکهمی‪ ،‬روزی بر اایم میافزایمی ات فناکت مکرت از فناکت ش بانروزی گردد‬‫‪; not in BL, KM, SB and DK.‬بر او افزایمی‬‫‪.‬قتایئ ‪; BML:‬خطاییان ‪; BoL:‬قتا ‪BL, KM, SB, DK, BN, NK and KDT:‬‬‫‪2‬‬‫‪Not in BoL.‬‬‫‪3‬‬‫‪.‬سوجه ‪; BoL:‬شوجه ‪; SB, DK, BN, NK and KDT:‬شو َجه ‪BL, KM and BML:‬‬‫‪4‬‬‫‪.‬أن مجموع ‪ ; SB, BN and NK:‬حاصل ضب ‪; BL, KM, DK, KDT and BML:‬از حاصل ضب اب «شوجنن» ‪BoL:‬‬‫‪5‬‬‫و هر یک ابر که تقصان کنمی‪ ،‬در أن سالها که تفاوت ابشد میان سال اصل و سال مطلوب‪ ،‬یک ابر ماه شون افتده ابشد؛ و سال سزیده ماه شده؛ و اگر پیش از أن ابشد‪ ،‬أن را از اصل ‪BoL:‬‬‫‪6‬‬‫اگر سال ‪; BN:‬رس سال –اگر نقصان توان کرد—نقصان کنمی؛ و اگر نقصان نتوان کرد‪ ،‬چندان ابر مدت یک ماه بر اصل رس سال افزایمی که چون حاصل ضب از او نقصان کنمی‪ ،‬مکرت از یک ماه مباند‬‫مطلوب پیش از أن ابشد‪ ،‬چندان ابر مدت یک ماه مقری بر اصل رس سال افزایمی که چون حاصل ضب از أن اکهمی‪ ،‬ابیق مکرت از مدی یک ماه بود؛ به هر یک ابر که نقصان کرده ابیش می‪ ،‬به این افزوده‬‫و اگر پیش از أن ‪; not in BL, KM, SB, DK, NK, KDT and BML after‬در أن سالها که تفاوت ابشد میان سال اصل و سال مطلوب‪ ،‬یک ابر ماه شون افزوده ابشد‪ ،‬و سال سزیده ماه شده‬‫ابشد‪ ،‬أن را از اصل رس سال –اگر نقصان توان کرد—نقصان کنمی؛ و اگر نقصان نتوان کرد‪ ،‬چندان ابر مدت یک ماه بر اصل رس سال افزایمی که چون حاصل ضب از او نقصان کنمی‪ ،‬مکرت از یک ماه‬‫‪.‬مباند‬‫‪.‬در سال مطلوب ‪; NK:‬در أن سال ‪; BN:‬در هر سال ‪BoL, BL, KM, DK, KDT and BML:‬‬‫‪7‬‬

‫‪231‬‬‫‪The Tārīkh-i Qitā in the Zīj-i Īlkhānī‬‬‫‪SCIAMVS 14‬‬‫او نقصان کنمی؛ اگر نقصان توان کرد‪ ،‬و ا ّال شصت بر اایم وویش افزایمی؛ و از مبلغ (‪ 6‬الف) نقصان‬‫کنمی؛ أچنه ابیق ابشد‪ ،‬مدخل مبدأی أرام ابشد به حسب امر اوسط از دور س تیین؛ پس أن را اب‬‫مدخل مبدأی لیجن در أن سال نگاه کنمی ات معلوم شود که کدام مقدم ابشد چه تفاوت میان هر دو‬‫مبدأ الحماهل مکرت از [مدت یک قسم سال مشیس ابشد]‪.‬‬‫‪1‬‬‫فصل هفمت‬‫در معرفت حصۀ أفتاب و حصۀ ماه در اول هر سال‬‫اما حصۀ أفتاب را مابنی اول أرام و اول وویش در هر سال از سدس مدت یک سال مشیس که أن‬‫شصت روز هشت هزار و هفتصد و چهل فنک ابشد و به ارقام س بکهم و أن را «کیجا»‪ 2‬خوانند‪،‬‬‫نقصان کنمی؛ أچنه مباند‪ ،‬حصۀ أفتاب ابشد به‪ 3‬اول أن سال‪.‬‬‫و اما حصۀ ماه را ابید که اصل حصۀ ماه‪ 4‬در مبدأی یک سال معلوم ابشد؛ و أن در اول سال‬‫شانکون موافق خلج هفتاد و هشت روز و سه هزار وهنصد و چهل و هشت فنک بوده است‪،‬‬‫‪.‬مدت قسم یک سال مشیس ابشد ‪; BoL:‬مدت یک قسم سال مشیس ابشد ‪BL, KM, SB, DK, BN, NK, KDT and BML:‬‬‫‪1‬‬‫‪.‬کـجا ‪; DK and BN:‬کنجا ‪; SB:‬کیخا ‪; BoL:‬کیجا ‪BL, KM, NK, KDT and BML:‬‬‫‪2‬‬‫‪.‬ات ‪; BN:‬به ‪BoL, BL, KM, SB, DK, NK, KDT and BML:‬‬‫‪3‬‬‫‪.‬اصل حصۀ ماه را که حمفوظ اول خوانمی ‪; NK:‬اصل حصۀ ماه ‪BoL, BL, KM, SB, DK, BN, KDT and BML:‬‬‫‪4‬‬

‫‪SCIAMVS 14‬‬‫‪Yoichi ISAHAYA‬‬‫‪232‬‬‫ارقام أن عح اهمح ‪ 1‬و به لغت [قتا]‪ 2‬أن را «جوجنوناک»‪ 3‬خوانند؛ پس تفاوت‪ 4‬میان أن سال و سال‬‫مطلوب بگریی؛ و أن را در هفت روز و س یصد و یس و هشت فنک که ارقام أن این است ز‪٠‬هحل‬‫و أن را به لغت [قتا]‪« 5‬جوجنا»‪ 6‬خوانند— و ظن من أن است که أن فضل مدت یک سال مشیس‬‫است بر سزیده دور مقری اوسط—‪ 7‬ضب کنمی؛ [و حاصل را بر اصل حصۀ ماه افزایمی‪ ،‬اگر سال‬‫مطلوب بعد از أن ابشد؛ و ا ّال باکهمی‪ ،‬به أن طریق که در فصل ششم گفته ای أچنه حاصل أید‪ ،‬أن را‬‫حمفوظ اول خوانمی؛]‪ 8‬پس مابنی اول أرام و اول وویش را‪ 9‬از أن مبلغ نقصان کنمی؛ اگر نقصان نتوان‬‫کرد‪ ،‬شصت‪ 10‬بر روزها افزایمی و نقصان کنمی؛ أچنه حاصل أید‪ 11،‬أن را حمفوظ دوم خوانمی؛ پس مدت‬‫یک دور حصۀ ماه که مقدار أن بیست و هفت روز و پنج هزار و پانصد و پنجاه و شش فنک ابشد‬‫و ارقامش این است کز البلو و أن را «جنجون»‪ 12‬خوانند‪ ،‬از حمفوظ دوم نقصان میکنمی ات مکرت از‬‫و أن در اول شانکون که موافق خلج یزدجردی ‪; DK:‬و أن در اول سال شانکون موافق خلج هفتاد و هشت روز و سه هزار وهنصد و چهل و هشت فنک بوده است‪ ،‬ارقامش عح اهمح ‪BoL:‬‬‫‪1‬‬‫و أن در اول شانکون ‪; KDT:‬و أن در اول شانکون بیست و سه روز و دو هزار و هش تصد و یس و شش فنک بوده و ارقامش کج ‪٠‬مزیو ‪; BN:‬است‪ ،‬کج روز و ‪٠‬مزیو فنک بوده است‬‫‪; not in BL, KM, SB, NK and BML.‬بیست و سه روز و دو هزار و هش تصد و یس و شش بود و ارقامش این است کج ‪٠‬مزیو‬‫‪; not in BN.‬خطاییان ‪; BoL:‬قتا ‪BL, KM, DK, SB, NK, KDT and BML:‬‬‫‪2‬‬‫‪.‬جوحنوناک ‪; BL, KM and SB:‬خوحنوناک ‪; BoL:‬جوجنوناک ‪DK, BN, NK, KDT and BML:‬‬‫‪3‬‬‫‪.‬و هجت دیگر سالها‪ ،‬عدد تفاوت ‪; BN:‬پس تفاوت ‪BoL, BL, KM, SB, DK, NK, KDT and BML:‬‬‫‪4‬‬‫‪.‬خطاییان ‪; BoL:‬قتا ‪BL, KM, SB, DK, BN, NK, KDT and BML:‬‬‫‪5‬‬‫‪.‬جوحنا ‪; BN:‬جوـجا ‪; DK:‬حوجنا ‪: SB:‬جوچنا ‪; BL:‬خوجنا ‪; BoL:‬جوجنا ‪KM, NK, KDT and BML:‬‬‫‪6‬‬‫و ظن من أن است که أن فضل ‪ ; BL, KM, SB, DK, BN, NK and KDT:‬و ظن من أن است که أن فضل مدت یک سال مشیس است بر سزیده دور مقری اوسط ‪BoL and BML:‬‬‫‪7‬‬‫‪.‬سزیده دور مقری اوسط است بر مدت سال مشیس‬‫‪; BoL, NK, KDT,‬و حاصل را بر اصل حصۀ ماه افزایمی‪ ،‬اگر سال مطلوب بعد از أن ابشد؛ و ا ّال باکهمی‪ ،‬به أن طریق که در فصل ششم گفته ای أچنه حاصل أید‪ ،‬أن را حمفوظ اول خوانمی‪BN:‬‬‫‪8‬‬‫‪.‬أچنه حاصل أید‪ ،‬أن را حمفوظ اول خوانمی ‪; BL, KM, SB and DK:‬أچنه حاصل أید؛ حصۀ اصل ماه بر او افزایمی؛ و أن را حمفوظ اول خوانمی ‪and BML:‬‬‫‪.‬مابنی اول أرام و اول وویش را –یعین سوجنن‪; BML: --‬مابنی اول أرام و اول وویش را ;‪BoL: BL, KM, SB, DK, BN, NK and KDT‬‬‫‪9‬‬‫‪.‬دور مقری ‪; DK:‬شصت ‪BoL, BL, KM, SB, BN, NK, KDT and BML:‬‬‫‪10‬‬‫‪.‬مباند ‪; BL:‬حاصل أید ‪BoL, KM, SB, DK, BN, NK, KDT and BML:‬‬‫‪11‬‬‫‪.‬حـجون ‪; DK:‬جنحون ‪; KM and NK:‬حنجون ‪; BoL:‬جنجون ‪BL, BN and BML:‬‬‫‪12‬‬

‫‪233‬‬‫‪SCIAMVS 14‬‬‫‪The Tārīkh-i Qitā in the Zīj-i Īlkhānī‬‬‫یک دور مباند؛ أچنه مباند‪ ،‬تسع اصل حصۀ [ماه]‪ 1‬ابشد؛ أن را در نه ضب کنمی ات حصۀ ماه در اول‬‫سال مطلوب حاصل شود؛ [اگر از دویست و چهل و هشت روز زایدت ابشد‪ ،‬أن را از او نقصان‬‫کنمی‪ .‬أچنه مباند‪ ،‬حصۀ ماه ابشد در اول سال مطلوب‪].‬‬‫‪2‬‬‫(‪ 6‬اب) و ما جنجون را در اعداد ضب کرده‪ ،‬در جدول هنادی ات به أساین از أجنا بر میگریند‪ .‬و نزی‬‫متامیت أچنه در فصل ششم و در این فصل گفته أمد‪ ،‬در مدت دو دور از ادوار دوازدهگانه از مبدأی‬‫دور شانکون در جدول هنادی از هجت مثال‪ .‬و جدول این است‪.‬‬

‫‪3‬‬

‫حدل‬

‫ییجیو‬

‫اوط‬

‫که‬

‫‪٠‬نزک‬‫لب‬‫‪٠‬حلا‬‫و‬‫بکزاک‬‫خهل‬‫پنیی‬‫ابرس‬‫و‬‫اندحن‬‫لز‬‫احیلز‬‫ل‬‫بییط‬‫خلو‬‫تنیماو‬‫طاوشقن‬‫یز‬‫ادلکب‬‫مب‬‫انطجی‬‫که‬‫‪٠‬کدان‬

‫ق‬

‫خلز‬

‫ووجن‬‫لو‬‫کح‬‫اجبمو‬‫مز‬‫بلطمط‬‫یط‬‫اکوج‬

‫ق‬

‫خلح‬

‫یکص‬

‫ییالن‬‫ط‬‫بایکد‬‫جن‬‫‪٠‬جلمه‬

‫مج‬

‫اطا‬

‫خلط‬

‫کنوو‬‫یوند‬‫ک‬‫انکح‬‫حن‬‫ایداک‬‫لز‬‫بیجل‬

‫شون‬

‫شون‬

‫شون‬

‫ق‬

‫ق‬

‫مدخل وویش‬‫مدخل أرام به حسب امر اوسط‬‫حصۀ أفتاب در رس سالها‬‫سالهای یزدجردی‬‫سالهای قتا‬‫سالهای تریک‬‫خلج‬‫اکزه‬‫کسکو‬‫ید‬‫ایزنو‬‫کو‬‫بمده‬‫یب‬‫اکزط‬‫سالها که أرام بر لیجن مقدم بود‬‫مابنی اول أرام و وویش و أن اصل‬‫رس سالها است‬‫جدول دو دور مذکور از مبدأی شانکون که به هجت مثال هناده شد‬‫مو‬‫ازمد‬‫هل‬‫اکحک‬‫ند‬‫‪٠‬لمب‬‫مج‬‫‪٠‬انحی‬‫لب‬‫اایند‬‫ان‬‫‪٠‬یدیو‬‫م‬‫‪٠‬هلیب‬‫‪Not in BoL.‬‬‫‪1‬‬‫‪; not in BoL, BL, KM, SB, BN and BML.‬اگر از دویست و چهل و هشت روز زایدت ابشد‪ ،‬أن را از او نقصان کنمی‪ .‬أچنه مباند‪ ،‬حصۀ ماه ابشد در اول سال مطلوب ‪DK and NK:‬‬‫‪2‬‬‫‪; not‬از هجت مثال؛ و أن جدول این است که بر صفحۀ دیگر است ‪; BML:‬از هجت مثال؛ و أن جدول این است ‪; KM, SB, DK and NK:‬از هجت مثال؛ و جدول این است ‪BoL and BL:‬‬‫‪3‬‬‫‪in BN.‬‬‫‪SCIAMVS 14‬‬

‫شون‬

‫شون‬

‫شون‬

‫شون‬

‫شون‬

‫شون‬

‫‪234‬‬‫‪Yoichi ISAHAYA‬‬‫مخ‬‫شنوی‬‫قوی‬‫ب‬‫‪٠‬امو‬‫ج‬‫اندنز‬‫ا‬‫اجنای‬‫حن‬‫بکجند‬‫خام‬‫ژمشن‬‫بیجنی‬‫یب‬‫بکزن‬‫ح‬‫بهلجل‬‫نو‬‫‪٠‬زمج‬‫مز‬‫بمدل‬‫مخب‬‫کوییوو‬‫داقوق‬‫کج‬‫بزبد‬‫ید‬‫‪٠‬کطکط‬‫ن‬‫احنه‬‫لز‬‫‪٠‬حیکو‬‫مخج‬‫اکسو‬‫ایت‬‫ه‬‫‪٠‬حییب‬

‫یط‬

‫ایه‬

‫ید‬

‫‪٠‬انجن‬‫نه‬‫بزکح‬‫مخد‬‫ییخایی‬‫طونغوز‬‫یه‬‫بمدیو‬‫کد‬‫ااناک‬‫ح‬‫اجنمه‬‫ق‬‫مد‬‫بکحد‬‫مخه‬‫پنیزه‬‫کسکو‬‫کو‬‫بکجم‬‫کط‬‫بالیز‬‫ج‬‫‪٠‬زلز‬

‫ق‬

‫دل‬

‫‪٠‬ب‪٠‬‬‫مخو‬‫تنیجیو‬

‫اوط‬

‫ح‬

‫‪٠‬دلحل‬‫هل‬‫‪٠‬کهجی‬‫کو‬‫بلزیه‬‫نب‬‫اانب‬

‫مخز‬

‫ووی‬

‫ابرس‬‫یط‬‫‪٠‬یدب‬‫م‬‫اهمط‬‫اک‬‫‪٠‬انمز‬‫ما‬‫بایحل‬‫مخح‬‫یکماو‬‫طاوشقن‬‫‪٠‬‬‫اایم‬‫مه‬‫اموکه‬‫مه‬‫‪٠‬دلمه‬‫س‬‫اید‪٠‬‬‫مخط‬‫کنجن‬‫لو‬‫ای‬‫‪٠‬اند‬‫ن‬‫بکزا‬‫لط‬‫الزنز‬‫مط‬‫ادللو‬

‫خن‬

‫شنص‬

‫ییالن‬‫کب‬‫‪٠‬لکح‬‫نو‬‫‪٠‬کنز‬‫جل‬‫بلزط‬‫حل‬‫انهیب‬‫خنا‬‫ژموو‬‫یوند‬‫ج‬‫اکحو‬‫ا‬‫ااجل‬

‫نز‬

‫بکز‬

‫نز‬

‫‪٠‬نزدل‬‫خنب‬‫کویوی‬

‫قوی‬

‫ید‬

‫از ل‬‫و‬‫امبط‬‫نب‬‫‪٠‬دللط‬‫مو‬‫احیی‬‫خنج‬‫اکسن‬‫بیجنی‬‫که‬‫‪٠‬موند‬‫ای‬‫بکبمه‬‫مو‬‫اهلان‬‫هل‬‫احلمز‬‫خند‬‫یییوو‬‫داقوق‬‫و‬‫امدلب‬‫یز‬‫‪٠‬یوما‬‫ی‬‫احیمط‬‫ند‬‫‪٠‬ماح‬‫خنه‬‫پنیسو‬

‫ایت‬

‫یز‬

‫اکجنو‬‫کب‬‫‪٠‬نزیز‬

‫د‬

‫بکا‬

‫ق‬

‫مج‬

‫اامد‬‫خنو‬‫تنیخایی‬‫طونغوز‬

‫کح‬

‫اجک‬

‫کز‬

‫الزجن‬‫نط‬‫‪٠‬دلجل‬

‫ق‬

‫لب‬

‫اکبک‬‫خزن‬‫ووزه‬‫کسکو‬‫ط‬‫ب‪٠‬حل‬‫لب‬‫بحیکط‬‫کج‬‫‪٠‬یزال‬‫ان‬‫‪٠‬کدمب‬‫خنح‬‫یکجیو‬

‫اوط‬

‫ک‬

‫امکب‬‫لز‬‫بنطه‬‫یز‬‫احیمج‬‫م‬‫‪٠‬مهحی‬

‫ق‬

‫ق‬

‫ق‬

‫ق‬

‫ق‬

‫‪235‬‬‫‪SCIAMVS 14‬‬‫حمفوظ دوم‬‫سالهای یزدجردی‬
‫حدل‬

‫فه‬

‫‪5‬‬

‫‪3‬‬

‫بدللب‬

‫‪6‬‬

‫س‬

‫‪7‬‬

‫‪٠‬یدو‬‫‪8‬‬‫‪10‬‬‫اهمح‬‫اایکو‬

‫‪2‬‬

‫جس‬

‫خهل‬

‫صب‬

‫‪9‬‬

‫ایزد‬

‫خلو‬

‫صط‬

‫‪13‬‬‫اکبمب‬

‫خلز‬

‫قو‬

‫خلح‬

‫قیج‬

‫ح‬

‫بیو‪٠‬‬‫عط‬‫‪٠‬نزک‬‫د‬‫بمبید‬‫مد‬‫بومو‬‫‪11‬‬‫بحمو‬‫‪12‬‬‫ج‬‫‪٠‬یزحل‬‫کز‬‫‪15‬‬‫بهل‪٠‬‬‫‪16‬‬‫کو‬‫بیوکح‬‫رما‬‫‪20‬‬‫فه‬‫‪14‬‬‫فا‬‫‪18‬‬‫اکحک‬‫‪19‬‬‫عح‬‫‪24‬‬‫‪25‬‬‫‪1‬‬‫اجلحن‬‫‪4‬‬‫حصۀ مقر‬‫حمفوظ اول‬

‫خلج‬

‫عح‬

‫‪1‬‬

‫تشع اصل حصۀ مقر‬‫‪The Tārīkh-i Qitā in the Zīj-i Īlkhānī‬‬‫جف‬‫‪٠‬یددل‬‫بحلمب‬‫‪17‬‬‫االب‬‫‪21‬‬‫کب‬‫بمبمب‬‫رو‬‫‪22‬‬‫بیحن‬

‫‪2‬‬

‫‪3‬‬

‫‪٠‬حیو‬

‫ط‬

‫‪4‬‬

‫بمبند‬‫بطید‬‫ا‬‫‪23‬‬‫‪.‬کج ‪SB and NK:‬‬‫‪1‬‬‫‪۰.‬مزیو ‪SB and NK:‬‬‫‪2‬‬‫‪.‬ح ‪SB and NK:‬‬‫‪3‬‬‫‪.‬بیو‪SB and NK: ۰‬‬‫‪4‬‬‫‪.‬ل ‪SB and NK:‬‬‫‪5‬‬‫‪۰.‬نبند ‪SB and NK:‬‬‫‪6‬‬‫‪.‬د ‪SB and NK:‬‬‫‪7‬‬‫‪.‬بمبید ‪SB and NK:‬‬‫‪8‬‬‫‪.‬لز ‪SB and NK:‬‬‫‪9‬‬‫‪۰.‬حنلب ‪SB and NK:‬‬‫‪10‬‬‫‪.‬ل ‪SB and NK:‬‬‫‪11‬‬‫‪.‬انید ‪SB and NK:‬‬‫‪12‬‬‫‪.‬مد ‪SB and NK:‬‬‫‪13‬‬‫‪.‬ادی ‪SB and NK:‬‬‫‪14‬‬‫‪.‬کو ‪SB and NK:‬‬‫‪15‬‬‫‪.‬بیوکح ‪SB and NK:‬‬‫‪16‬‬‫‪.‬یه ‪SB and NK:‬‬‫‪17‬‬‫‪.‬ان ‪SB and NK:‬‬‫‪18‬‬‫‪.‬اطمح ‪SB and NK:‬‬‫‪19‬‬‫‪.‬کب ‪SB and NK:‬‬‫‪20‬‬‫‪.‬بمبمب ‪SB and NK:‬‬‫‪21‬‬‫‪.‬قف ‪SB, NK and BML:‬‬‫‪22‬‬‫‪.‬بیحل ‪SB and NK:‬‬‫‪23‬‬‫‪.‬حن ‪SB and NK:‬‬‫‪24‬‬‫‪.‬ایهکو ‪SB and NK:‬‬‫‪25‬‬

‫‪SCIAMVS 14‬‬‫‪Yoichi ISAHAYA‬‬‫‪5‬‬‫الطلو‬

‫‪6‬‬

‫صط‬

‫‪7‬‬

‫بهلمح‬

‫‪8‬‬

‫یز‬

‫مخ‬

‫قکز‬

‫‪10‬‬‫امهید‬‫‪11‬‬‫قکه‬‫‪12‬‬‫امجکح‬‫‪13‬‬

‫خام‬

‫قدل‬

‫‪14‬‬‫اننب‬‫‪15‬‬‫قاک‬‫‪16‬‬‫بطمب‬

‫مخب‬

‫مقا‬

‫‪18‬‬‫انول‬‫‪19‬‬

‫قزی‬

‫خلط‬

‫قک‬

‫یه‬

‫اوکد‬

‫قلح‬

‫ای‬

‫البحل‬‫قد‬‫‪٠٠‬کب‬‫‪20‬‬‫بهلنو‬‫‪21‬‬‫ز‬‫احننب‬‫سط‬‫اطمح‬‫‪22‬‬‫‪25‬‬‫امجنو‬‫‪26‬‬‫ه‬‫بکنو‬‫نب‬‫امامد‬‫‪29‬‬‫بیی‬‫‪30‬‬‫ب‬‫‪٠٠‬ل‬‫حی‬‫‪٠‬دل‬

‫‪3‬‬

‫که‬

‫مخج‬

‫مقح‬

‫‪23‬‬‫ببح‬‫‪24‬‬

‫مخد‬

‫قنه‬

‫‪27‬‬‫‪28‬‬

‫قلط‬

‫مخه‬

‫قسب‬

‫‪1‬‬

‫‪2‬‬

‫‪31‬‬‫بجیکد‬

‫قهل‬

‫قنه‬

‫اهم‬
‫الزلو‬‫مقج‬‫بزمو‬‫‪٠‬مدم‬‫‪9‬‬‫‪236‬‬‫بلوکد‬‫‪17‬‬‫انطک‬‫رال‬‫اید‪٠‬‬‫‪.‬مح ‪SB and NK:‬‬‫‪1‬‬‫‪.‬انمب ‪SB and NK:‬‬‫‪2‬‬‫‪.‬اک ‪BL, KM, SB, DK, BN, NK and BML:‬‬‫‪3‬‬‫‪.‬قصط ‪BL, KM, SB, DK, BN, NK and BML:‬‬‫‪4‬‬‫‪.‬سه ‪SB and NK:‬‬‫‪5‬‬‫‪.‬ااکد ‪SB and NK:‬‬‫‪6‬‬‫‪.‬مد ‪SB and NK:‬‬‫‪7‬‬‫‪.‬بیزیو ‪SB and NK:‬‬‫‪8‬‬‫‪۰.‬مدک ‪BL, KM, SB, DK, BN, NK and BML:‬‬‫‪9‬‬‫‪.‬عب ‪SB and NK:‬‬‫‪10‬‬‫‪.‬اکومه ‪SB and NK:‬‬‫‪11‬‬‫‪.‬ع ‪SB and NK:‬‬‫‪12‬‬‫‪.‬اکدنز ‪SB and NK:‬‬‫‪13‬‬‫‪.‬عط ‪SB and NK:‬‬‫‪14‬‬‫‪.‬ا لبک ‪SB and NK:‬‬‫‪15‬‬‫‪.‬مو ‪SB and NK:‬‬‫‪16‬‬‫‪.‬اانی ‪SB and NK:‬‬‫‪17‬‬‫‪.‬فو ‪SB and NK:‬‬‫‪18‬‬‫‪.‬الزحن ‪SB and NK:‬‬‫‪19‬‬‫‪.‬سب ‪SB and NK:‬‬‫‪20‬‬‫بیبکد ‪SB and NK:‬‬‫‪21‬‬‫‪.‬اهمح ‪SB, DK and NK:‬‬‫‪22‬‬‫‪.‬جص ‪SB and NK:‬‬‫‪23‬‬‫‪.‬امجلو ‪SB and NK:‬‬‫‪24‬‬‫‪.‬حف ‪SB and NK:‬‬‫‪25‬‬‫‪.‬اکهکد ‪SB and NK:‬‬‫‪26‬‬‫‪.‬ق ‪SB and NK:‬‬‫‪27‬‬‫‪.‬امطید ‪SB and NK:‬‬‫‪28‬‬‫‪.‬فد ‪SB and NK:‬‬‫‪29‬‬‫‪.‬اانمح ‪SB and NK:‬‬‫‪30‬‬‫‪.‬قز ‪SB and NK:‬‬‫‪31‬‬SCIAMVS 14

237

The Tārīkh-i Qitā in the Zīj-i Īlkhānī‫امهنو‬‫رید‬‫باککد‬

7

‫کج‬
11

‫امدکد‬6‫بیحل‬

10‫احیحل‬

14

‫ح‬

29

28

‫را‬

27

‫د‬

2

‫قزص‬

31

‫صد‬

‫ایهل‬‫ی‬

25‫مدمو‬٠‫عز‬‫الزدل‬SB and NK: ‫اکهنب‬.
SB and NK: ‫قاک‬.

9

SB and NK: ‫بوح‬.

10

SB and NK: ‫قب‬.

11

SB and NK: ‫انبو‬.

12

SB and NK: ‫قکح‬.

13

SB and NK: ‫بایمو‬.

14

SB and NK: ‫قکح‬.

15

SB and NK: ‫و‬۰‫ا‬.

16

SB and NK: ‫قهل‬.

17

SB and NK: ‫بیزکد‬.

18

SB and NK: ‫قکد‬.

19

SB and NK: ‫اکوک‬.

20

BL, KM, SB, DK, BN, NK and BML: ‫ید‬.

21

BL, KM, SB, DK, BN, NK and BML: ‫قکح‬.

22

SB and NK: ‫مقب‬.

23

SB and NK: ‫بکجب‬.

24

SB and NK: ‫قک‬.

25

SB and NK: ‫انبدل‬.

26

BL, KM, DK and BN: ‫ ;رد‬SB and NK: ‫مقط‬.

27

BL, KM, DK and BN: ‫ ;بمزیب‬SB and NK: ‫ ;بکحم‬not in BML.

28

SB and NK: ‫مقو‬.

29

SB and NK: ‫دل‬٠‫ا‬.

30

BL, KM, DK and BN: ‫ ;رای‬SB and NK: ‫ ;قنو‬not in BML.

31

BL, KM, DK and BN: ‫ ;بنبن‬SB and NK: ‫ ;بدلحی‬not in BML.

‫خنب‬

22

‫یبن‬٠

8‫ریب‬‫بمادل‬18

SB and NK: ‫قو‬.

‫خنا‬

23

‫امدنب‬

7

‫ره‬

‫قعه‬

19

SB and NK: ‫ل‬٠‫ب‬.

26

24

‫کد‬

6

‫خن‬

‫بایو‬‫مطیو‬٠SB and NK: ‫قید‬.

‫قزص‬

16

‫قیح‬

5

‫مخط‬

‫بهلنو‬21

SB and NK: ‫بیزنب‬.

‫قص‬

17

‫اند‬

4

‫مخح‬

‫قفط‬

15

SB and NK: ‫ف‬.

‫قفج‬

12

‫حی‬

3

‫مخز‬

‫بلحی‬‫کجب‬٠

SB and NK: ‫اندنب‬.

‫قعو‬

13

‫قسج‬

2

‫مخو‬

‫قفج‬

‫محل‬٠

1‫قسط‬‫بکدم‬‫ک‬‫بجمح‬

4‫قزن‬‫حن‬٠٠

‫مب‬‫بیطب‬

8‫قف‬‫اندیب‬59‫حمب‬٠

20‫قسا‬‫ایطو‬‫امهک‬

1‫لب‬٠٠
‫وی‬٠

30

238

Yoichi ISAHAYA‫یوحن‬٠
10

‫بلب‬

٠

5

‫بایدل‬‫قصج‬

4‫ایطدل‬

8

‫ریط‬

7

‫امهمح‬

13

‫ریه‬

12

‫بیبب‬

17

‫رای‬

‫خنج‬

‫یزکو‬٠

6

‫رکو‬

‫خند‬

‫کجد‬٠

11

‫رجل‬

‫خنه‬

‫کحمب‬٠

15

‫رم‬

‫خنو‬

‫رلز‬

20

‫دلک‬٠

19

‫رمز‬

‫خزن‬

‫قطج‬

24

‫لطحن‬٠

23

‫خنح‬

‫رلط‬

‫احلب‬‫کو‬‫احنکد‬‫رد‬‫بدیو‬‫کب‬

14‫اکی‬٠

‫قع‬

‫بلل‬

‫حی‬

‫جنو‬٠

‫قنج‬‫هند‬٠

‫یز‬

22

‫اکب‬

21

‫ببلو‬

29‫بدمو‬

27

26

25

‫و‬

1

SB and NK: ‫مقب‬.

2

SB and NK: ‫اکومح‬.

3

BL, KM, DK, BN: ‫ ;رحی‬SB and NK: ‫قسج‬.

4

BL, KM, DK, BN and BML: ‫ ;بحنکح‬SB and NK: ‫بلطنو‬.

5

SB and NK: ‫اجنب‬.

6

BL, KM, DK, BN and BML: ‫ ;رکه‬SB and NK: ‫قع‬.

7

BL, KM, DK, BN and BML: ‫ ;جدو‬SB and NK: ‫بمهدل‬.

8

SB and NK: ‫قسد‬.

9

SB and NK: ‫ااب‬.

10

BL, KM, SB, DK, NK and BML: ‫رحل‬.

11

BL, KM, DK, BN and BML: ‫ ;رلب‬SB and NK: ‫قعح‬..

12

BL, KM, DK, BN and BML: ‫ ;جطمد‬SB and NK: ‫دلب‬٠.

13

SB and NK: ‫قس‬.

14

SB and NK: ‫اکزیو‬.

15

BL, KM, DK, BN and BML: ‫ ;رلط‬SB and NK: ‫قفه‬.

16

BL, KM, DK, BN and BML: ‫ ;ریهکب‬SB and NK: ‫یی‬٠.

17

SB and NK: ‫قنو‬.

18

SB and NK: ‫اجنم‬.

19

BL, KM, DK, BN and BML: ‫ ;رمو‬SB and NK: ‫قصب‬.

20

BL, KM, DK, BN and BML: ٠‫ ;جاک‬SB and NK: ‫یهمح‬٠.

21

SB and NK: ‫قفب‬.

22

SB and NK: ‫اال‬.

23

Not in SB and NK.

24

Not in SB and NK.

25

Not in SB and NK.

26

Not in SB and NK.

27

Not in BL, KM, SB, DK, BN, NK and BML.

28

Not in BL, KM, SB, DK, BN, NK and BML.

29

Not in BL, KM, SB, DK, BN, NK and BML.

30

Not in BL, KM, SB, DK, BN, NK and BML.

28

٠

18

‫امویو‬16‫ایمح‬٠

3

‫ریط‬

9

‫مححن‬٠30‫ح‬SCIAMVS 14‫رید‬‫‪239‬‬‫‪The Tārīkh-i Qitā in the Zīj-i Īlkhānī‬‬‫‪SCIAMVS 14‬‬‫فصل هش مت‬‫در اس تخراج تعدیل أفتاب‬‫حصۀ أفتاب به اول سال بگریی؛ و مدت یک ماه مقری‪ —1‬و أن بیست و نه روز و پنج هزار و‬‫س یصد و شش فنک ابشد و ارقامش‪ 2‬کط اکحکو و به لغت [قتا]‪ 3‬أن را «شوجه» خوانند— بر او‬‫حصۀ ماههای [یکی بعد از دیگر]‪ 4‬معلوم میشود؛ و هرچه حصه از مدت یک مشیس که‬‫میافزایمی ات ّ‬‫شسه‪٠‬ملو است زایدت گردد‪ ،‬این مبلغ از او باکهمی؛ أچنه مباند‪ ،‬حصه ابشد؛‪ 5‬و اگر از میانۀ سال‬‫حصۀ ماهی معنی خواهمی‪ ،‬عدد ماهها که مابنی اول سال و ماه مطلوب ابشد‪ ،‬در شوجه ضب کنمی؛‬‫و حاصل بر حصۀ أفتاب [به]‪ 6‬اول سال افزایمی ات حصۀ رس أن ماه حاصل شود‪ .‬ما حاصل ضب‬‫شوجه در اعداد تفاوت ضب کرده‪ ،‬در جدول هنادی ات از أجنا برمیگریند‪.‬‬‫و چون حصۀ أفتاب معلوم شود‪ ،‬اگر عدد روزهای یباعتبار فنکها از نمیۀ دور که أن صد و‬‫هش تاد و دو [است]‪ 7‬که أن را «بیجوتن»‪ 8‬خوانند مکرت ابشد‪ ،‬أن را از صد و هش تاد و دو باکهمی ات‬‫‪.‬مقری اوسط ‪; DK:‬مقری ‪BoL, BL, KM, SB, BN, NK and BML:‬‬‫‪1‬‬‫‪.‬این است ‪BML:‬‬‫‪2‬‬‫‪.‬خطا ‪; BoL:‬قتا ‪BL, KM, SB, DK, BN, NK and BML:‬‬‫‪3‬‬‫‪.‬یکی بعد از دیگری ‪; SB and NK:‬یکی از بعد از یکی دیگر ‪; BoL:‬یکی بعد از دیگر ‪BL, KM, DK, BN and BML:‬‬‫‪4‬‬‫‪; not in BL, KM, SB, DK, BN and BML.‬و هرچه حصه از مدت یک مشیس که شسه‪٠‬ملو است زایدت گردد‪ ،‬این مبلغ (را) از او باکهمی؛ أچنه مباند‪ ،‬حصه ابشد ‪BoL and NK:‬‬‫‪5‬‬‫‪.‬اب ‪; BoL:‬به ‪BL, KM, SB, DK, BN, NK, KDT and BML:‬‬‫‪6‬‬‫‪Not in BoL, KM, DK, BN and NK.‬‬‫‪7‬‬‫‪.‬ــجوتن ‪; DK and BN:‬ــحوـن ‪; SB and NK:‬ــحوتن ‪; KM:‬تــجوتن ‪; BoL:‬بیجوتن ‪BL and BML:‬‬‫‪8‬‬‫‪SCIAMVS 14‬‬‫‪240‬‬‫‪Yoichi ISAHAYA‬‬‫متامش مباند؛ پس حصه را در متام حصه ضب کنمی؛ و حاصل را مضاعف کنمی؛ و تسع مبلغ بگریی؛‬‫حاصل تعدیل أفتاب ابشد؛ و زاید ابشد و زاید را‪« 1‬نو» خوانند‪.‬‬‫و اگر روزهای حصه از صد و هش تاد و دو زایدت ابشد‪ ،‬فضلش بر صد و هش تاد و دو بگریی؛‬‫و حصه را از ضعف صد و هش تاد و دو که متام دور ابشد‪ ،‬نقصان کنمی؛ و فضل را در ابیق از نقصان‬‫ضب کنمی؛ و حاصل را مضاعف کنمی؛ و تسع مبلغ بگریی؛ أچنه حاصل أید‪ ،‬تعدیل أفتاب ابشد؛ و‬‫انقص ابشد و أن را «تیاوو» خوانند یعین انقص‪ .‬و تعدیل أفتاب را «اتاینکژیک»‪ 2‬خوانند‪.‬‬‫و ما تعدیل أفتاب را جدویل‪ 3‬هبادی و فنکهای مرفوع تعدیل به ازای حصه در أن جدول هنادی ات‬‫به ازای حصۀ رس ماهها از أن جدول برمیگریند‪.‬‬‫فصل هنم‬‫در اس تخراج تعدیل ماه‬‫حصۀ ماه به اول سال بنهمی؛ و أن را به لغت [قتا]‪« 4‬جوجنوناک»‪ 5‬خوانند؛ و هجت دیگر ماهها‪ ،‬هفده‬‫روز و هفت هزار و هفتصد و پنجاه و چهار فنک [که]‪ 6‬ارقامش این ست بز بطید و أن را‬‫‪Not in DK.‬‬‫‪1‬‬‫‪.‬اتـانکژیک ‪; DK and BN:‬اتاینکزیک ‪; BL:‬اتاینکژیک ‪; BL and BML:‬اتاینکژیک ‪BoL, KM, SB and NK:‬‬‫‪2‬‬‫‪.‬در جدویل ‪; BL:‬در جدول ‪; BoL:‬جدویل ‪KM, SB, DK, BN, NK and BML:‬‬‫‪3‬‬‫‪.‬خطا ‪; BoL:‬قتا ‪BL, KM, SB, DK, BN, NK and BML:‬‬‫‪4‬‬‫‪.‬جوـجوـاک ‪; DK:‬حوحوـاک ‪; SB:‬حوحوناک ‪; KM:‬جوجوناک ‪; BL:‬جوجنوناک ‪BN, NK and BML:‬‬‫‪5‬‬‫‪Not in BoL.‬‬‫‪6‬‬‫‪241‬‬‫‪The Tārīkh-i Qitā in the Zīj-i Īlkhānī‬‬‫‪SCIAMVS 14‬‬‫«جنجونشا»‪ 1‬خوانند‪ ،‬بر حصۀ رس سال [میافزایمی]‪ 2‬و چون حصه از رمح زایدت گردد‪ ،‬رمح [را] از‬‫او ابید اکست‪ ،‬و ابیق را ثبت کرد‪ 3‬ات حصۀ رس یک [یک]‪ 4‬ماه حاصل میشود‪ .‬و ما جدویل مش متل‬‫بر ضب أن در هر عدد هنادی ات أچنه به ازای عدد تفاوت [ایبند]‪ 5،‬بر حصۀ رس سال [میافزایند]‪ 6‬ات‬‫حصۀ رس ماه که خواهند‪ ،‬حاصل [میشود]؛‬‫‪7‬‬‫و اایم حصه اگر از صد و بیست و چهار که أن را «بنجوشا»‪ 8‬خوانند‪ ،‬مکرت بود‪ ،‬أن را از صد و‬‫بیست و چهار نقضان کنمی ات متامش مباند؛ و اایم را در متامش ضب کنمی؛ أچنه حاصلأید‪ ،‬تعدیل ماه‬‫ابشد؛ و «نو» ابشد یعین زاید‪ .‬و اگر از صد و بیست و چهار زایدت ابشد‪ ،‬فضلش بر صد و بیست‬‫و چهار در متامش بعد از نقصان از دویست و چهل و هشت ضب کنمی؛ أچنه حاصل أید‪ ،‬تعدیل ماه‬‫ابشد؛ و «تیاوو» ابشد یعین انقص‪ .‬و تعدیل ماه را «اتاینکژچون»‪ 9‬خوانند‪ .‬و ما تعدیل ماه را‬‫جدویل هنادی (‪ 7‬الف) ات به ازای حصۀ رس ماهها از أن جدول برمیگریند و جدولها این است‪.‬‬‫‪10‬‬‫‪.‬حـحونشا ‪; BN:‬حـجونشا ‪; DK:‬حنحونشا ‪; SB and NK:‬حوحنونشا ‪; KM:‬جوحنونشا ‪; BL:‬حنچویشا ‪; BoL:‬جنجونشا ‪BML:‬‬‫‪1‬‬‫‪.‬افزایمی ‪; BoL:‬میافزایمی ‪BL, KM, SB, DK, BN, NK and BML:‬‬‫‪2‬‬‫‪; not in BL, KM, SB, DK, BN and BML.‬و چون حصه از رمح زایدت گردد‪ ،‬رمح را از او ابید اکست‪ ،‬و ابیق را ثبت کرد ‪BoL and NK:‬‬‫‪3‬‬‫‪Not in BoL.‬‬‫‪4‬‬‫‪.‬ـاـند ;‪; NK‬ـاــد ‪; DK and BN:‬ابشد ‪; SB:‬مبانند ‪; BoL:‬ایبند ‪BL, KM and BML:‬‬‫‪5‬‬‫‪.‬میافزایمی ‪; BoL:‬میافزایند ‪BL, KM, SB, DK, BN, NK and BML:‬‬‫‪6‬‬‫‪.‬شود ‪; BoL:‬میشود ‪BL, KM, SB, DK, BN, NK and BML:‬‬‫‪7‬‬‫‪.‬بینجوشا ‪; BML:‬ــجوشا ‪; BN:‬ـنحوشا ‪; SB:‬ــنجوشا ‪; BL, KM and DK:‬تـنجوشا ‪; BoL:‬بنجوشا ‪NK:‬‬‫‪8‬‬‫‪.‬اتاینکرجون ‪; NK:‬اتایـکژحون ‪; DK:‬اتاینکرجون ‪; SB:‬اتـانکژجون ‪; KM:‬اتاینکژجون ‪; BL and BML:‬اتاینکژچون ‪BoL and BN:‬‬‫‪9‬‬‫‪; not in SB and NK.‬أن جدولها این است که بر ورقهای دیگری است ‪; BML:‬جدولها در صفحۀ دیگر است ‪ ; BN:‬این است ;جدولها این است ‪BoL, BL and DK:‬‬‫‪10‬‬

‫‪SCIAMVS 14‬‬‫‪242‬‬‫‪Yoichi ISAHAYA‬‬‫جدول تعدیل أفتاب که أن را اتاینکژیک میخوانند‬‫حصۀ أفتاب‬‫تفدیل أفتاب‬‫حصۀ أفتاب‬‫حصۀ أفتاب‬‫حصۀ أفتاب‬‫تعدیل أفتاب‬‫زاید‬‫حصۀ أفتاب‬‫تعدیل أفتاب‬‫انقص‬‫زاید‬‫انقص‬‫زاید‬‫انقص‬‫حصۀ أفتاب‬

‫‪٠‬‬

‫قفب‬

‫‪٠٠٠‬‬

‫قفب‬

‫شسد‬

‫ل‬

‫قنب‬

‫‪ ٠‬یو جن‬

‫ریب‬

‫شدل‬

‫س‬

‫قکب‬

‫‪ ٠‬کز ز‬

‫رمب‬

‫شد‬

‫ا‬

‫قفا‬

‫‪٠٠‬م‬

‫قفج‬

‫شسج‬

‫ال‬

‫قنا‬

‫‪ ٠‬یز ک‬

‫رجی‬

‫شلج‬

‫سا‬

‫قاک‬

‫‪ ٠‬کز ک‬

‫رمج‬

‫جش‬

‫ب‬

‫قف‬

‫‪٠‬اک‬

‫قفد‬

‫شسب‬

‫لب‬

‫قن‬

‫‪ ٠‬یز مز‬

‫رید‬

‫شلب‬

‫سب‬

‫قک‬

‫‪ ٠‬کز جل‬

‫رمد‬

‫شب‬

‫ج‬

‫قعط‬

‫‪ ٠‬ا نط‬

‫قفه‬

‫شسا‬

‫جل‬

‫مقط‬

‫‪ ٠‬حی جی‬

‫ریه‬

‫شال‬

‫جس‬

‫قیط‬

‫‪ ٠‬کز مو‬

‫رمه‬

‫شا‬

‫د‬

‫قعح‬

‫‪ ٠‬ب حل‬

‫قفو‬

‫شس‬

‫دل‬

‫مقح‬

‫‪ ٠‬حی حل‬

‫ریو‬

‫شل‬

‫سد‬

‫قیح‬

‫‪ ٠‬کز حن‬

‫رمو‬

‫ش‬

‫ه‬

‫قعز‬

‫‪ ٠‬ج یز‬‫قفز‬‫ش نط‬

‫هل‬

‫مقز‬

‫‪ ٠‬یط ج‬

‫ریز‬

‫شکط‬

‫سه‬

‫قزی‬

‫‪ ٠‬کح ی‬

‫رمز‬

‫رصط‬

‫و‬

‫قعو‬

‫‪ ٠‬ج نه‬‫قفح‬‫ش نح‬

‫لو‬

‫مقو‬

‫‪ ٠‬یط کح‬

‫رحی‬

‫شکح‬

‫سو‬

‫قیو‬

‫‪ ٠‬کح اک‬

‫رمح‬

‫رحص‬

‫ز‬

‫قعه‬

‫‪ ٠‬د لب‬

‫قفط‬

‫شزن‬

‫لز‬

‫مقه‬

‫‪ ٠‬یط نب‬

‫ریط‬

‫شکز‬

‫زس‬

‫قیه‬

‫‪ ٠‬کح لب‬

‫رمط‬

‫رص‬

‫ح‬

‫قعد‬

‫‪٠‬هط‬‫قص‬‫ش نو‬

‫حل‬

‫مقد‬

‫‪ ٠‬ک یو‬

‫رک‬

‫شکو‬

‫حس‬

‫قید‬

‫‪ ٠‬کح مج‬

‫رن‬

‫رصو‬

‫ط‬

‫قعج‬

‫‪ ٠‬ه مو‬‫قصا‬‫ش نه‬

‫لط‬

‫مقج‬

‫‪ ٠‬ک لط‬

‫راک‬

‫شکه‬

‫سط‬

‫قیج‬

‫‪٠‬کح جن‬

‫ران‬

‫رصه‬

‫ی‬

‫قعب‬

‫‪ ٠‬و کب‬‫قصب‬‫ش ند‬‫م‬‫مقب‬‫‪ ٠‬اک ب‬

‫‪2‬‬

‫رکب‬

‫شکد‬

‫ع‬

‫قیب‬

‫‪ ٠‬کط ب‬

‫رنب‬

‫رصد‬

‫ای‬

‫قعا‬

‫‪ ٠‬و حن‬‫قصج‬‫ش نج‬

‫ما‬

‫مقا‬

‫‪ ٠‬اک که‬

‫‪3‬‬

‫رکج‬

‫شکج‬

‫عا‬

‫قیا‬

‫‪ ٠‬کط ای‬

‫رجن‬

‫رجص‬

‫یب‬

‫قع‬

‫‪ ٠‬ز جل‬

‫قصد‬

‫شنب‬

‫مب‬

‫مق‬

‫‪ ٠‬اک مز‬

‫رکد‬

‫شکب‬

‫عب‬

‫یق‬

‫‪ ٠‬کط ک‬

‫رند‬

‫رصب‬

‫جی‬

‫قسط‬

‫‪٠‬حح‬‫قصه‬‫ش نا‬

‫مج‬

‫قلط‬

‫‪ ٠‬کب ح‬

‫رکه‬

‫شاک‬

‫جع‬

‫قط‬

‫‪ ٠‬کط کح‬

‫رنه‬

‫رصا‬

‫ید‬

‫قسح‬

‫‪ ٠‬ح مج‬

‫قصو‬

‫شن‬

‫مد‬

‫قلح‬

‫‪ ٠‬کب کط‬

‫رکو‬

‫شک‬

‫عد‬

‫حق‬

‫‪ ٠‬کط لو‬

‫رنو‬

‫رص‬

‫یه‬

‫قزس‬

‫‪ ٠‬ط یز‬

‫قزص‬

‫مشط‬

‫مه‬

‫قلز‬

‫‪ ٠‬کب ن‬‫رکز‬‫ش یط‬‫عه‬‫قز‬‫‪ ٠‬کط مج‬

‫رنز‬

‫رفط‬

‫یو‬

‫قسو‬

‫‪٠‬طن‬

‫قصح‬

‫مشح‬

‫مو‬

‫قلو‬

‫‪ ٠‬کج ی‬‫رکح‬‫ش یح‬‫عو‬‫قو‬‫‪ ٠‬کط ن‬

‫رحن‬

‫رحف‬

‫یز‬

‫قسه‬

‫‪ ٠‬ی کج‬

‫قصط‬

‫مشز‬

‫مز‬

‫قهل‬

‫‪ ٠‬کج ل‬

‫رکط‬

‫شزی‬

‫عز‬

‫قه‬

‫‪ ٠‬کط نز‬

‫رنط‬

‫رفز‬

‫حی‬

‫قسد‬

‫‪ ٠‬ی نو‬

‫ر‬

‫مشو‬

‫مح‬

‫قدل‬

‫‪ ٠‬کج مط‬‫رل‬‫ش یو‬‫عح‬‫قد‬‫‪٠‬لج‬

‫رس‬

‫رفو‬

‫یط‬

‫قسج‬

‫‪ ٠‬ای کح‬

‫را‬

‫مشه‬

‫مط‬

‫قلج‬

‫‪ ٠‬کد ح‬‫رال‬‫ش یه‬‫عط‬‫قج‬‫‪٠‬لح‬

‫رسا‬

‫رفه‬

‫ک‬

‫قسب‬

‫‪ ٠‬یب ‪٠‬‬

‫رب‬

‫مشد‬

‫ن‬

‫قلب‬

‫‪ ٠‬کد کز‬‫رلب‬‫ش ید‬‫ف‬‫قب‬‫‪ ٠‬ل جی‬

‫رسب‬

‫رفد‬

‫اک‬

‫قسا‬

‫‪ ٠‬یب ال‬

‫رج‬

‫مشج‬

‫ان‬

‫قال‬

‫‪ ٠‬کد مه‬‫رجل‬‫ش یج‬‫فا‬‫قا‬‫‪ ٠‬ل حی‬

‫رجس‬

‫رجف‬

‫کب‬

‫قس‬

‫‪ ٠‬جی ب‬

‫رد‬

‫مشب‬

‫نب‬

‫قل‬

‫‪ ٠‬که ب‬

‫ردل‬

‫شیب‬

‫فب‬

‫ق‬

‫‪ ٠‬ل کب‬

‫رسد‬

‫رفب‬

‫کج‬

‫قنط‬

‫‪ ٠‬جی جل‬

‫ره‬

‫شام‬

‫جن‬

‫قکط‬

‫‪ ٠‬که یط‬‫رهل‬‫ش یا‬‫جف‬‫صط‬‫‪ ٠‬ل کو‬

‫رسه‬

‫رفا‬

‫کد‬

‫قنح‬

‫‪ ٠‬ید ج‬

‫رو‬

‫مش‬

‫ند‬

‫قکح‬

‫‪ ٠‬که لو‬

‫رلو‬

‫یش‬

‫فد‬

‫حص‬

‫‪ ٠‬ل کط‬

‫رسو‬

‫رف‬

‫‪1‬‬

‫‪۰.‬کم ‪BL, KM, SB, DK, BN, NK and BML:‬‬‫‪1‬‬‫‪۰.‬اکج ‪BL, KM, SB, DK, BN, NK and BML:‬‬‫‪2‬‬‫‪۰.‬اککب ‪BL, KM, DK and BN:‬‬‫‪3‬‬‫‪243‬‬‫‪SCIAMVS 14‬‬‫‪The Tārīkh-i Qitā in the Zīj-i Īlkhānī‬‬

‫که‬

‫قزن‬

‫‪ ٠‬ید لب‬

‫رز‬

‫شلط‬

‫نه‬

‫قکز‬

‫‪ ٠‬که نب‬

‫رلز‬

‫شط‬

‫فه‬

‫ص‬

‫‪ ٠‬ل لب‬

‫رزس‬

‫رعط‬

‫کو‬

‫قنو‬

‫‪ ٠‬یه ا‬

‫رح‬

‫شلح‬

‫نو‬

‫قکو‬

‫‪ ٠‬کو ح‬

‫رحل‬

‫حش‬

‫فو‬

‫صو‬

‫‪ ٠‬ل هل‬

‫رحس‬

‫رعح‬

‫کز‬

‫قنه‬

‫‪ ٠‬یه ل‬

‫رط‬

‫شلز‬

‫نز‬

‫قکه‬

‫‪ ٠‬کوکج‬

‫رلط‬

‫زش‬

‫فز‬

‫صه‬

‫‪ ٠‬ل لز‬

‫رسط‬

‫رعز‬

‫کح‬

‫قند‬

‫‪ ٠‬یه حن‬

‫ری‬

‫شلو‬

‫حن‬

‫قکد‬

‫‪ ٠‬کو حل‬

‫رم‬

‫شو‬

‫حف‬

‫صد‬

‫‪ ٠‬ل حل‬

‫رع‬

‫رعو‬

‫کط‬

‫قنج‬

‫‪ ٠‬یو کو‬

‫رای‬

‫شهل‬

‫نط‬

‫قکج‬

‫‪ ٠‬کو جن‬

‫رما‬

‫شه‬

‫فط‬

‫جص‬

‫‪ ٠‬ل لط‬

‫رعا‬

‫رعه‬

‫ص‬

‫صب‬

‫‪٠‬لم‬

‫رعب‬

‫رعد‬

‫صا‬

‫صا‬

‫‪٠‬لم‬

‫رجع‬

‫رجع‬

‫حصۀ ماه‬‫انقص‬‫زاید‬‫حصۀ ماه‬‫حصۀ ماه‬‫انقص‬‫تعدیل ماه‬‫زاید‬‫تعدیل ماه‬‫جدول تعدیل ماه و أن را اتاینکژچون خوانند‬‫حصۀ ماه‬

‫‪٠‬‬

‫قکد‬

‫‪٠٠٠‬‬

‫قکد‬

‫رمح‬

‫لب‬

‫صب‬

‫‪ ٠‬مط د‬

‫قنو‬

‫ریو‬

‫ا‬

‫قکج‬

‫‪٠‬بج‬

‫قکه‬

‫رمز‬

‫جل‬

‫صا‬

‫‪٠‬نج‬

‫قزن‬

‫ریه‬

‫ب‬

‫قکب‬

‫‪٠‬دد‬

‫قکو‬

‫رمو‬

‫دل‬

‫ص‬

‫‪ ٠‬ان ‪٠‬‬

‫قنح‬

‫رید‬

‫ج‬

‫قاک‬

‫‪٠‬وج‬

‫قکز‬

‫رمه‬

‫هل‬

‫فط‬

‫‪ ٠‬ان نه‬

‫قنط‬

‫رجی‬

‫د‬

‫قک‬

‫‪٠‬ح‪٠‬‬

‫قکح‬

‫رمد‬

‫لو‬

‫حف‬

‫‪ ٠‬نب مح‬

‫قس‬

‫ریب‬

‫ه‬

‫قیط‬

‫‪ ٠‬ط نط‬

‫قکط‬

‫رمج‬

‫لز‬

‫فز‬

‫‪ ٠‬جن لط‬

‫قسا‬

‫رای‬

‫و‬

‫قیح‬

‫‪ ٠‬ای مح‬

‫قل‬

‫رمب‬

‫حل‬

‫فو‬

‫‪ ٠‬ند کح‬

‫قسب‬

‫ری‬

‫ز‬

‫قزی‬

‫‪ ٠‬جی لط‬

‫قال‬

‫رما‬

‫لط‬

‫فه‬

‫‪ ٠‬نه یه‬

‫قسج‬

‫رط‬

‫ح‬

‫قیو‬

‫‪ ٠‬یه کح‬

‫قلب‬

‫رم‬

‫م‬

‫فد‬

‫‪ ٠‬نو ‪٠‬‬

‫قسد‬

‫رح‬

‫ط‬

‫قیه‬

‫‪ ٠‬یز یه‬

‫‪4‬‬

‫قلج‬

‫رلط‬

‫ما‬

‫جف‬

‫‪ ٠‬نو مج‬

‫قسه‬

‫رز‬

‫ی‬

‫قید‬

‫‪ ٠‬یط ‪٠‬‬

‫قدل‬

‫رحل‬

‫مب‬

‫فب‬

‫‪ ٠‬نز کد‬

‫قسو‬

‫رو‬

‫ای‬

‫قیج‬

‫‪ ۰‬کمج‬

‫قهل‬

‫رلز‬

‫مج‬

‫فا‬

‫‪ ٠‬حن ج‬

‫قزس‬

‫ره‬

‫یب‬

‫قیب‬

‫‪ ٠‬کب کد‬

‫قلو‬

‫رلو‬

‫مد‬

‫ف‬

‫‪ ٠‬حن م‬

‫قسح‬

‫رد‬

‫جی‬

‫قیا‬

‫‪٠‬کدج‬

‫قلز‬

‫رهل‬

‫مه‬

‫عط‬

‫‪ ٠‬نط یه‬

‫قسط‬

‫رج‬

‫ید‬

‫یق‬

‫‪ ٠‬که م‬

‫قلح‬

‫ردل‬

‫مو‬

‫عح‬

‫‪ ٠‬نط مح‬

‫قع‬

‫رب‬

‫‪1‬‬

‫‪2‬‬

‫‪3‬‬

‫‪۰.‬دب ‪BL, KM, SB, DK, BN, NK, and BML:‬‬‫‪1‬‬‫‪۰.‬وا ‪BL, KM, SB, DK, BN, NK, and BML:‬‬‫‪2‬‬‫‪۰.‬طنه ‪BL, KM, SB, DK, BN, NK and BML:‬‬‫‪3‬‬‫‪۰.‬یویه ‪BL, KM, SB and NK:‬‬‫‪4‬‬‫‪SCIAMVS 14‬‬‫‪244‬‬‫‪Yoichi ISAHAYA‬‬

‫یه‬

‫قط‬

‫‪ ٠‬کز یه‬

‫قلط‬

‫رجل‬

‫مز‬

‫عز‬

‫ا ‪ ٠‬یط‬

‫قعا‬

‫را‬

‫یو‬

‫حق‬

‫‪ ٠‬کح مح‬

‫مق‬

‫رلب‬

‫مح‬

‫عو‬

‫ا‪ ٠‬مح‬

‫قعب‬

‫ر‬

‫یز‬

‫قز‬

‫‪ ٠‬ل یط‬

‫مقا‬

‫رال‬

‫مط‬

‫عه‬

‫ا ا یه‬

‫قعج‬

‫قصط‬

‫حی‬

‫قو‬

‫‪ ٠‬ال مح‬

‫مقب‬

‫رل‬

‫ن‬

‫عد‬

‫اام‬

‫قعد‬

‫قصح‬

‫یط‬

‫قه‬

‫‪ ٠‬جل یه‬

‫مقج‬

‫رکط‬

‫ان‬

‫جع‬

‫ابج‬

‫قعه‬

‫قزص‬

‫ک‬

‫قد‬

‫‪ ٠‬دل م‬

‫مقد‬

‫رکح‬

‫نب‬

‫عب‬

‫ا ب کد‬

‫قعو‬

‫قصو‬

‫اک‬

‫قج‬

‫‪ ٠‬لو ج‬

‫مقه‬

‫رکز‬

‫جن‬

‫عا‬

‫ا ب مج‬

‫قعز‬

‫قصه‬

‫کب‬

‫قب‬

‫‪ ٠‬لز کد‬

‫‪1‬‬

‫مقو‬

‫رکو‬

‫ند‬

‫ع‬

‫اج‪٠‬‬

‫قعح‬

‫قصد‬

‫کج‬

‫قا‬

‫‪ ٠‬حل مج‬

‫مقز‬

‫رکه‬

‫نه‬

‫سط‬

‫ا ج یه‬

‫قعط‬

‫قصج‬

‫کد‬

‫ق‬

‫‪٠‬م‪٠‬‬

‫مقح‬

‫رکد‬

‫نو‬

‫حس‬

‫ا ج کح‬

‫قف‬

‫قصب‬

‫که‬

‫صط‬

‫‪ ٠‬ما یه‬

‫مقط‬

‫رکج‬

‫نز‬

‫زس‬

‫ا ج لط‬

‫قفا‬

‫قصا‬

‫کو‬

‫حص‬

‫‪ ٠‬مب کح‬

‫قن‬

‫رکب‬

‫حن‬

‫سو‬

‫ا ج مح‬

‫قفب‬

‫قص‬

‫کز‬

‫ص‬

‫‪ ٠‬مج لط‬

‫قنا‬

‫راک‬

‫نط‬

‫سه‬

‫ا ج نه‬

‫قفج‬

‫قفط‬

‫کح‬

‫صو‬

‫‪ ٠‬مد مح‬

‫قنب‬

‫رک‬

‫س‬

‫سد‬

‫اد‪٠‬‬

‫قفد‬

‫قفح‬

‫کط صه‬‫‪ ٠‬مه نه‬

‫قنج‬

‫ریط‬

‫سا‬

‫جس‬

‫ادج‬

‫قفه‬

‫قفز‬

‫ل‬

‫صد‬

‫‪ ٠‬مز ‪٠‬‬

‫قند‬

‫رحی‬

‫سب‬

‫سب‬

‫ادد‬

‫قفو‬

‫قفو‬

‫ال‬

‫جص‬

‫‪ ٠‬مح ج‬

‫قنه‬

‫ریز‬

‫‪۰.‬لوکد ‪DK:‬‬‫‪1‬‬‫‪245‬‬‫‪SCIAMVS 14‬‬‫‪The Tārīkh-i Qitā in the Zīj-i Īlkhānī‬‬‫تضاعیف شوجه یعین مدت یک ماه مقری تضاعیف جنجون یعین سری یک ماهۀ مفری‬‫اعداد‬‫روزها‬‫مرفوع مرین‬‫مرفوع مره‬‫فنکها‬‫مرفوع مرین‬‫مرفوع مره‬‫فنکها‬‫اعداد‬‫فنکها‬‫روزها‬‫فنکها‬

‫ا‬

‫کط‬

‫ا‬

‫کح‬

‫کو‬

‫ا‬

‫کز‬

‫ا‬

‫لب‬

‫لو‬

‫ب‬

‫نط‬

‫‪٠‬‬

‫ی‬

‫یب‬

‫ب‬

‫نه‬

‫‪٠‬‬

‫حی‬

‫لب‬

‫ج‬

‫حف‬

‫ا‬

‫حل‬

‫حل‬

‫ج‬

‫فب‬

‫ا‬

‫ان‬

‫ح‬

‫د‬

‫قیح‬

‫‪٠‬‬

‫ک‬

‫کد‬

‫د‬

‫یق‬

‫‪٠‬‬

‫لز‬

‫د‬

‫ه‬

‫مقز‬

‫ا‬

‫مح‬

‫ن‬

‫ه‬

‫قلز‬

‫ب‬

‫ط‬

‫م‬

‫و‬

‫قعز‬

‫‪٠‬‬

‫ل‬

‫لو‬

‫و‬

‫قسه‬

‫‪٠‬‬

‫نه‬

‫لو‬

‫ز‬

‫رو‬

‫ا‬

‫نط‬

‫ب‬

‫ز‬

‫قصب‬

‫ب‬

‫کح‬

‫یب‬

‫ح‬

‫رلو‬

‫‪٠‬‬

‫م‬

‫حن‬

‫ح‬

‫رک‬

‫ا‬

‫ید‬

‫ح‬

‫ط‬

‫رسه‬

‫ب‬

‫ط‬

‫ید‬

‫ط‬

‫رمح‬

‫‪٠‬‬

‫‪٠‬‬

‫د‬

‫ی‬

‫رصه‬

‫‪٠‬‬

‫ان‬

‫‪٠‬‬

‫ای‬

‫شکد‬

‫ب‬

‫یط‬

‫کو‬

‫یب‬

‫ش ند‬

‫ا‬

‫ا‬

‫یب‬

‫مقدار مجموع نمیشب یک نمیروز در‬‫هر ماه تقریب‬‫فنکها‬‫ماهها‬‫روزها‬‫مرفوع مرین‬‫مرفوع مره‬‫ایکندی‬‫طوقسوجن‬‫بجک‬‫اوجوجن‬‫سکسینج‬

‫بوم‬

‫ا‬

‫یز‬

‫ب‬

‫ط‬

‫ید‬

‫تورتوجن‬‫یتینج‬‫بی‪٠‬‬

‫ب‬

‫هل‬

‫ا‬

‫ال‬

‫مح‬

‫ج‬

‫جن‬

‫‪٠‬‬

‫ند‬

‫کب‬

‫د‬

‫عا‬

‫‪٠‬‬

‫یو‬

‫نو‬

‫ه‬

‫حف‬

‫ب‬

‫کو‬

‫ی‬

‫بیشینج‬‫التینج‬‫ب جی ک‬‫تضاعیف فنکهای‬‫ش بانروز‬‫اعداد‬‫اعداد‬‫أرام‬‫اونوجن‬‫ب‪٠٠‬‬‫فنکها‬‫تضاعیف جوجنونشا یعین سری حصۀ مقر‬‫در یک ماه‬‫جقشاابط‬‫بریکزمنج‬‫ا نو م‬

‫و‬

‫قو‬

‫ا‬

‫مح‬

‫مد‬

‫ا‬

‫ب‬

‫مو‬

‫م‬

‫ز‬

‫قکد‬

‫ا‬

‫ای‬

‫حی‬

‫ب‬

‫ه‬

‫جل‬

‫ک‬

‫ح‬

‫مقب‬

‫‪٠‬‬

‫جل‬

‫نب‬

‫ج‬

‫ح‬

‫ک‬

‫‪٠‬‬

‫ط‬

‫قنط‬

‫ب‬

‫مج‬

‫و‬

‫د‬

‫ای‬

‫و‬

‫م‬

‫ی‬

‫قعز‬

‫ب‬

‫ه‬

‫م‬

‫ه‬

‫جی‬

‫جن‬

‫ک‬

‫ای‬

‫قصه‬

‫ا‬

‫کح‬

‫ید‬

‫و‬

‫یو‬

‫م‬

‫‪٠‬‬

‫‪SCIAMVS 14‬‬‫‪246‬‬‫‪Yoichi ISAHAYA‬‬

‫یب‬

‫رجی‬

‫‪٠‬‬

‫ن‬

‫مح‬

‫ز‬

‫یط‬

‫کو‬

‫م‬

‫جی‬

‫رال‬

‫‪٠‬‬

‫جی‬

‫کب‬

‫ح‬

‫کب‬

‫جی‬

‫ک‬

‫ید‬

‫رمح‬

‫ب‬

‫کب‬

‫لو‬

‫ط‬

‫که‬

‫‪٠‬‬

‫‪٠‬‬

‫(‪ 7‬اب) فصل دمه‬‫در معرفت اوایل ماهها از هر سال‪ 1‬که خواهمی‪ ،‬و تعینی ماه شون [در سایل] که واقع ابشد‬‫‪2‬‬‫از حصۀ أفتاب در اوایل ماهها تعدیل او معلوم کنمی‪ .‬و زاید و انقص بدانمی‪ .‬و از حصۀ ماه در اوایل‬‫ماهها تعدیل ماه نزی معلوم کنمی‪ .‬و زاید و انقص بدانمی‪ .‬و هردو تعدیل اگر زاید ای انقص ابش ند‪ ،‬مجع‬‫کنمی‪ .‬و االّ فضل یکی بر دیگری‪ 3‬بگریی و أن را تعدیل مرکب‪ 4‬خوانمی‪ .‬اگر‪ 5‬هردو زاید بوده ابش ند ای‬‫فضل زاید را ابشد‪ ،‬تعدیل مرکب زاید ابشد‪[ .‬و اگر هردو انقص بوده ابش ند ای فضل انقص را ابشد‪،‬‬‫تعدیل مرکب انقص ابشد‪ 6].‬پس مدخل أرام به حسب امر اوسط در اول [سال]‪ 7‬بگریی؛ و مقدار‬‫یک ماه که بیست و نه روز و پنج هزار و س یصد و شش فنک است و ارقامش یطاکحکو یعین‬‫«شوجه»‪ ،‬بر مدخل [أرام میافزایمی؛ و هرچه اایم از شصت زایدت ابشد‪ ،‬شصت میافکنمی ات‬‫‪.‬سایل ‪; KM and DK:‬سال ‪BoL, BL, SB, BN, NK and BML:‬‬‫‪1‬‬‫ماه شون ‪; BML:‬ماه شون در سال که واقع ابشد ‪; SB and KR:‬ماه شون در سایل که واقع شود ‪; KM:‬ماه شون که واقع ابشد ‪; BoL:‬ماه شون در سایل که واقع ابشد ‪BL, DK and BN:‬‬‫‪2‬‬‫‪.‬که واقع ابشد در سال‬‫‪.‬دیگر ‪; BL, KM, BN and BML:‬دیگری ‪BoL, SB, DK and NK:‬‬‫‪3‬‬‫‪.‬مرکت ‪; BL:‬مرکب ;‪BoL, KM, SB, DK, BN, NK and BML‬‬‫‪4‬‬‫‪.‬پس اگر ‪; BL:‬اگر ‪BoL, KM, SB, DK, BN, NK and BML:‬‬‫‪5‬‬‫;اگر هردو زاید بوده ابش ند ای فضل زاید را ابشد‪ ،‬تعدیل مرکب زاید ابشد‪ .‬و اگر هردو انقص بوده ابش ند ای فضل انقص را ابشد‪ ،‬تعدیل مرکب انقص ابشد ‪BL, KM, DK, BN, NK and BML:‬‬‫‪6‬‬‫‪.‬اگر هر دو زاید بوده ابش ند ای فضل انقص را ابشد‪ ،‬تعدیل مرکب اتقص ابشد ‪; SB:‬اگر هردو زاید بوده ابش ند ای فضل زاید را ابشد‪ ،‬تعدیل مرکب زاید ابشد ‪BoL:‬‬‫‪; not in BoL.‬سال ‪BL, KM, SB, DK, BN, NK and BML:‬‬‫‪7‬‬

‫‪247‬‬‫‪The Tārīkh-i Qitā in the Zīj-i Īlkhānī‬‬‫‪SCIAMVS 14‬‬‫مدخل]‪ 1‬هر ماهی به حسب امر اوسط حاصل میشود؛ [پس]‪ 2‬تعدیل مرکب اگر زاید ابشد‪ ،‬در اول‬‫هرماهی بر مدخل أن ماه میافزایمی؛ و اگر انقص ابشد‪ ،‬میاکهمی ات مدخل هرماه به حتقیق معلوم می‪-‬‬‫شود؛ و فنکها را اگر از مقدار نمی شب و یک روز مکرت ابشد‪ ،‬أن را یکی میگریی؛ و بر روزها‬‫میافزایمی؛ و اگر زایدت ابشد‪ ،‬أن را دو میگریی؛ و بر روزها میافزایمی‪ .‬پس حاصل را در جدول‬‫[دور]‪ 3‬س تیین میأوری‪ 4‬ات مدخل هرماه از أن دور معلوم میشود؛ و از مدخل هر ماه و مدخل‬‫ماهی که بعد از او ابشد‪ ،‬معلوم شود که ماه اول یس روز ابشد ای بیست و نه روز؛ و ابید که زایدت‬‫از دو ماه متوایل بیست و نه نگریند‪ ،‬و زایدت از سه ماه متوایل یس نگریند‪ .‬پس مدخل اقسام سال‬‫مشیس [را]‪ 5‬که واقع ابشد در هر ماه‪ ،‬اعتبار میکنند؛ اگر سال شون ابشد که سزیده ماه در وی‬‫افتاد‪ ،‬هر ماه که مدخل یک قسم از اقسام سال مشیس تنها در وی افتاد‪ ،‬ماه‪ 6‬شون ابشد؛ و هر ماه‬‫که مدخل دو قسم در وی افتاد‪ ،‬شون نباشد‪.‬‬‫و ما از هجت مثال ماههای سال دمه از دور شانکون که أن سال کوییو ابشد و به تریک داقوق‬‫ییل و به حساب فاریس‪ 7‬سال ششصد و چهل و دوم یزدجردی ابشد‪ 1،‬اس تخراج کردی‪ .‬و این معل‪-‬‬‫ها به تفصیل در این جدول هنادی ات بر أن قیاس میکنند‪ .‬و أن جدول این است‪.‬‬‫أرام میافزایمی؛ و هرچه اایم از شصت زایدت شود‪ ،‬شصت میافکنمی ‪; DK:‬أرام میافزایمی؛ و هرچه اایم از شصت زایدت ابشد‪ ،‬شصت میافکنمی ات مدخل ‪BL, KM, SB, BN, NK and BML:‬‬‫‪1‬‬‫‪; not in BoL.‬ات مدخل‬‫‪Not in BoL.‬‬‫‪2‬‬‫‪Not in BoL.‬‬‫‪3‬‬‫‪.‬میأری ‪; BN:‬میأوری ‪BoL, BL, KM, SB, DK, NK and BML:‬‬‫‪4‬‬‫‪Not in BoL.‬‬‫‪5‬‬‫‪.‬أن ماه ‪; BL, KM, DK, BN, KR and BML:‬ماه ‪BoL and SB:‬‬‫‪6‬‬‫‪.‬ابریس ‪; NK and BML:‬پاریس ‪; BN:‬ـاریس ‪; BL, KM and DK:‬فاریس ‪BoL and SB:‬‬‫‪7‬‬‫‪SCIAMVS 14‬‬‫‪248‬‬‫‪Yoichi ISAHAYA‬‬‫جدول تقوی سال دمه که أن کوییو ابشد که داقوق ییل است موفق‬‫شهور‬‫حصۀ مشس‬‫تعدیلالشمس‬‫حصۀ مقر‬‫ایکندی‬‫سو‬‫ا مو نب‬‫کح اک‬‫فز‬‫‪ ٠‬لب کب‬‫اوجنج‬‫صو‬‫‪ ٠‬کح حل‬‫ل هل‬

‫‪8‬‬

‫قد‬

‫ب ما لو‬‫تورتوجن‬‫قکه‬‫ا نز د‬‫کو کج‬

‫قکب‬

‫بدی‬

‫بیشینج‬‫قنه‬‫‪ ٠‬حل ن‬‫یه ل‬‫مق‬‫ا کو مد‬‫التینج‬‫قفد‬‫ب ز یو‬

‫اک‬

‫قنح‬

‫‪ ٠‬مط حی‬

‫شون‬

‫رید‬

‫‪ ٠‬مط ب‬‫یز مز‬‫قعو‬‫‪ ٠‬ای نب‬‫یتینج‬‫رمج‬‫ب یز کح‬‫کز ک‬‫قصج‬‫‪17‬‬‫‪5‬‬‫تعدیل مقر‬‫أرام‬‫لز‬‫‪ ٠‬حی کو‬‫یط نب‬‫سط‬‫ا ط مح‬‫‪3‬‬‫تعدیل مرکب‬‫مخب یزدجردی که به هجت مثال هناده شد‬‫‪2‬‬‫ا ج یه‬‫ا کج ز‬‫‪ ٠‬جن نط‬

‫‪6‬‬

‫‪4‬‬

‫ا کب ک‬‫‪9‬‬‫‪ ٠‬دل م‬‫‪11‬‬‫‪٠‬دد‬‫‪14‬‬‫‪ ٠‬کح مح‬‫‪ ٠‬جی حی‬‫‪15‬‬‫‪ ٠‬ان ‪٠‬‬‫‪ ٠‬نب ک‬‫‪16‬‬‫ا ب کد‬‫ا ک ای‬‫‪18‬‬‫ا ج یه‬‫‪19‬‬‫ا ل هل‬‫ب اک و‬‫‪12‬‬‫ا ه یه‬‫‪7‬‬‫‪10‬‬‫‪ ٠‬ل کز‬‫‪13‬‬‫‪1‬‬‫‪Not in BL.‬‬‫‪1‬‬‫‪.‬جدول سال تقوی سال دمه که أن کوییو ابشد که داقوق ییل است موفق مخب یزدجردی که به هجت مثال هناده شد ‪BN:‬‬‫‪2‬‬‫‪.‬اهمح ‪SB and DK:‬‬‫‪3‬‬‫‪.‬اکجو ‪BL, KM, SB, DK and BML:‬‬‫‪4‬‬‫‪۰.‬کجکب ‪BL, KM, SB and DK:‬‬‫‪5‬‬‫‪۰.‬جنلط ‪۰; BN:‬جندل ‪SB, DK and BML:‬‬‫‪6‬‬‫‪.‬اکب‪BL, KM, SB, DK, BN and BML: ۰‬‬‫‪7‬‬‫‪.‬لجن ‪BL, KM, SB, DK and BML:‬‬‫‪8‬‬‫‪.‬بلزلو ‪BL, KM, SB and DK:‬‬‫‪9‬‬‫‪.‬اهجل ‪BL, KM, SB, DK, BN and BML:‬‬‫‪10‬‬‫‪.‬ب‪۰‬ی ‪; SB and DK:‬ب‪۰‬ط ‪BL:‬‬‫‪11‬‬‫‪۰.‬دب ‪۰; BN and BML:‬وی ‪۰; DK:‬ود ‪۰; SB:‬دی ‪BL and KM:‬‬‫‪12‬‬‫‪۰.‬کبکز ‪۰; SB, DK and BN:‬دلکز ‪۰; KM:‬لبکز ‪BL:‬‬‫‪13‬‬‫‪.‬اکبمد ‪BL, KM, SB and DK:‬‬‫‪14‬‬‫‪۰.‬مهحی ‪BL, KM, SB and DK:‬‬‫‪15‬‬‫‪۰.‬زنب ‪BL, KM, SB and DK:‬‬‫‪16‬‬‫‪.‬قصد ‪BL, KM and SB:‬‬‫‪17‬‬‫‪.‬بیزو ‪BL, KM, SB and DK:‬‬‫‪18‬‬‫‪.‬اج‪BL, KM, SB, DK and BN: ۰‬‬‫‪19‬‬

‫‪249‬‬‫‪SCIAMVS 14‬‬‫‪The Tārīkh-i Qitā in the Zīj-i Īlkhānī‬‬‫ا مج م‬‫سکسینج‬‫رجع‬‫‪ ٠‬نط ید‬

‫لم‬

‫‪2‬‬

‫رای‬

‫طوقسوجن‬‫شب‬‫ب کز م‬‫کز جل‬‫رکط‬‫اونوجن‬‫شلب‬‫ا ط کو‬‫‪11‬‬‫یز مز‬‫رمز‬‫‪ ٠‬کح مح‬‫بریکزمنج‬‫شسا‬‫ب لز نب‬‫ا نط‬‫یو‬‫ب حل ب‬‫جقشاابط‬‫کو‬‫‪ ٠‬لط ب‬‫یه ا‬‫دل‬‫ب ‪ ٠‬لو‬‫أرام‬‫نه‬‫ب ز کح‬‫که نب‬‫نب‬‫ا کج ی‬

‫‪3‬‬

‫‪7‬‬

‫ا و ید‬‫‪4‬‬‫‪ ٠‬جن لط‬‫‪8‬‬‫‪ ٠‬جل یه‬‫ا کد یط‬‫‪5‬‬‫ا‪٠‬مح‬‫‪9‬‬‫‪12‬‬‫‪٠‬بج‬‫‪14‬‬‫‪ ٠‬کح مح‬‫‪17‬‬‫‪ ٠‬ان ‪٠‬‬‫‪19‬‬‫ا ب کد‬‫‪18‬‬‫‪6‬‬‫‪10‬‬‫‪ ٠‬یط ن‬‫‪15‬‬‫‪13‬‬‫‪ ٠‬کو مط‬‫‪16‬‬‫اوا‬‫ا کح یو‬‫‪20‬‬‫‪.‬الک ‪BL, KM, SB, DK and BN:‬‬‫‪1‬‬‫‪.‬لحل ‪BL, KM, SB, DK and BN:‬‬‫‪2‬‬‫‪.‬ریب ‪BL, KM and SB:‬‬‫‪3‬‬‫‪.‬اطم ‪; SB:‬الطم ‪BL, KM and DK:‬‬‫‪4‬‬‫‪۰.‬نبمح ‪BL, KM; SB, DK and BN:‬‬‫‪5‬‬‫‪.‬اکجکو ‪BL, KM, SB, DK and BN:‬‬‫‪6‬‬‫‪.‬رکح ‪SB and DK:‬‬‫‪7‬‬‫‪.‬ابید ‪BL, KM, SB and DK:‬‬‫‪8‬‬‫‪۰.‬المح ‪BL, KM, SB, DK and BN:‬‬‫‪9‬‬‫‪۰.‬نطاک ‪BL, KM, SB, DK and BN:‬‬‫‪10‬‬‫‪.‬اهکو ‪BML:‬‬‫‪11‬‬‫‪۰.‬کحمد ‪۰; DK:‬کدمح ‪BL, KM and SB:‬‬‫‪12‬‬‫‪۰.‬یطان ‪DK:‬‬‫‪13‬‬‫‪۰.‬ی‪۰; BN: ۰‬طنو ‪BL, KM, SB, DK and BML:‬‬‫‪14‬‬‫‪۰.‬لیط ‪BL, KM, SB, BN and BML:‬‬‫‪15‬‬‫‪۰.‬کحک ‪BL, KM, SB, DK, BN and BML:‬‬‫‪16‬‬‫‪.‬بیطمد ‪; BN:‬بیطی ‪BL, KM, SB, DK and BML:‬‬‫‪17‬‬‫‪۰.‬انو ‪SB:‬‬‫‪18‬‬‫‪.‬امامد ‪BL, KM, DK, BN and BML:‬‬‫‪19‬‬‫‪.‬اکحو ‪; BML‬ابکد ‪SB:‬‬‫‪20‬‬

‫اوجنج‬‫مط‬‫ا یط ز‬‫مط‬‫ب کد کب‬‫تورتوجن‬‫یط‬‫‪ ٠ ٠‬جن‬‫یط‬‫‪ ٠‬ال ک‬‫بیشینج‬‫مح‬‫ا کط یط‬‫مح‬‫ا یو ا‬‫التینج‬‫حی‬‫‪ ٠‬ای ه‬‫یز‬‫ب ه که‬

‫شون‬

‫مز‬

‫ا لط ال‬

‫‪9‬‬

‫مز‬

‫‪ ٠‬یط ک‬‫یتینج‬‫یز‬‫‪ ٠‬اک یز‬‫یو‬‫ا لز کب‬‫سکسینج‬‫مو‬‫ا مط مج‬‫مو‬‫‪ ٠‬که کد‬‫طوقسوجن‬‫یو‬‫‪ ٠‬ال کط‬‫یه‬‫ب یز اک‬‫اونوجن‬‫مه‬‫ا نط نه‬

‫مه‬

‫امه‬

‫بریکزمنج‬‫یه‬‫‪ ٠‬ما ما‬

‫یه‬

‫احل‬

‫جقشاابط‬

‫مد‬

‫بیز‬

‫مه‬

‫‪ ٠‬کط مح‬‫أرام‬‫ید‬‫‪ ٠‬ان جن‬

‫ید‬

‫بکط‬

‫کط‬

‫ییماو‬‫ح‬‫ژمسو‬‫کج‬‫ل‬‫اکشن‬‫ی‬‫کویص‬‫که‬‫ووشن‬

‫کط‬

‫اکی‬

‫ی‬

‫کویخایی‬‫کو‬‫یکماو‬‫کط‬‫کویوی‬‫یب‬‫اکوو‬‫کز‬‫یکیوو‬

‫‪8‬‬

‫ل‬

‫ژمژه‬‫جی‬‫اکژه‬‫کح‬‫یکماو‬‫کط‬‫ژموو‬‫ید‬‫ییوی‬‫کط‬‫یکسو‬‫کط‬‫سنخایی‬‫یه‬‫ییچیو‬‫مدخل شهور حقیقی‬‫اعداد اایم شهور‬‫ایکندی‬‫یط‬‫ب لز اک‬‫ک‬‫ا جی ا‬‫اسامی مدخل‬‫أرام‬‫ن‬‫ا ح نه‬‫ن‬‫ب لب ب‬‫أچنه مقادیر سال مشیس‬‫در هر ماه واقع ابشد‬‫شهور‬‫‪Yoichi ISAHAYA‬‬‫مدخل شهور به حسب‬‫امر اوسط‬‫‪SCIAMVS 14‬‬‫‪7‬‬‫‪15‬‬‫‪250‬‬

‫‪1‬‬

‫‪4‬‬

‫‪5‬‬

‫‪6‬‬

‫‪10‬‬‫‪2‬‬‫ووچیو‬‫‪3‬‬‫‪11‬‬‫ل‬‫کنچن‬‫ا‬‫کنچن‬‫یز‬‫پنیشن‬‫‪12‬‬‫ل‬‫کنسو‬‫ب‬‫سنخایی‬‫یز‬‫پنیی‬‫‪13‬‬‫کط‬‫کنچن‬

‫ب‬

‫سنص‬

‫یز‬

‫پنیشن‬‫ل‬‫یکیوو‬‫د‬‫ژمژه‬‫یط‬‫تنیماو‬‫ل‬‫یکماو‬‫د‬‫ژموو‬‫یط‬‫تنییوو‬‫ل‬‫یکیوو‬‫د‬‫ژمژه‬‫ک‬‫ووچن‬‫‪14‬‬‫‪16‬‬‫یکماو‬‫‪.‬بلبا ‪BL, KM, SB, DK and BML:‬‬‫‪1‬‬‫‪.‬کد ‪BL, KM, SB, DK, BN and BML:‬‬‫‪2‬‬‫‪.‬ووی ‪BL, KM, SB, DK, NK and BML:‬‬‫‪3‬‬‫‪.‬انبما ‪; KM:‬ایبما ‪BL, SB, DK, BN and BML:‬‬‫‪4‬‬‫‪.‬بکدم ‪BL, KM, SB, DK, BN and BML:‬‬‫‪5‬‬‫‪۰.‬جلک ‪BL, KM, SB, DK and BN:‬‬‫‪6‬‬‫‪.‬اکطیو ‪SB:‬‬‫‪7‬‬‫‪.‬امبلز ‪SB, DK and BN:‬‬‫‪8‬‬‫‪.‬اکطال ‪SB and DK:‬‬‫‪9‬‬‫‪۰.‬طک ‪SB and DK:‬‬‫‪10‬‬‫‪.‬الزلو ‪BL, KM, SB, DK and BN:‬‬‫‪11‬‬‫‪۰.‬کویز ‪BL, KM, SB, DK and BN:‬‬‫‪12‬‬‫‪.‬بحیمح ‪BL, KM, SB, DK and BN:‬‬‫‪13‬‬‫‪.‬ایا ‪BL, KM, SB, DK, BN and BML:‬‬‫‪14‬‬‫‪.‬بیـد ‪BL, KM, SB, DK and BML:‬‬‫‪15‬‬‫‪۰.‬کطل ‪BL, KM, SB, DK and BML:‬‬‫‪16‬‬

‫‪251‬‬‫‪The Tārīkh-i Qitā in the Zīj-i Īlkhānī‬‬‫‪SCIAMVS 14‬‬‫(‪ 8‬الف) فصل ایزدمه‬‫در معرفت دور چهارم‬‫اهل [قتا]‪[ 1‬را]‪ 2‬دوری دیگر است که در اختیار روزها برأن اعامتد میکنند‪ .‬و أن دور مه بردوازده‬‫میگردد‪ .‬و انمهای أن دوازده این است‪ :‬ا کن‪ 3‬ب چو‪ 4‬ج َمن د پن‪ 5‬ه تن و چه‪ 6‬ز پو‪ 7‬ح وی ط‬‫چن‪ 8‬ی ش یو ای خایی یب پیی‪ 9.‬از این مجهل‪ ،‬چهار عدد «خ»‪ 10‬ابشد یعین س یاه‪ .‬و أن مایل ابشد‬‫به تباهی‪ ،‬و أن کن و من و پن و ش یو ابشد‪ .‬و چهار «خونک»‪ 11‬ابشد یعین زرد‪ .‬و أن مایل به نیکی‬‫ابشد‪ ،‬و أن چو و تن و چه و وی ابشد‪ .‬و دو «پ َه»‪ 12‬ابشد یعین سفید‪ .13‬و أن به غایت نیک ابشد‪،‬‬‫و أن چن و خایی ابشد‪ .‬و دو «هون» ابشد یعین به غایت تباه‪ 14،‬و أن پو و پیی ابشد‪ .‬و روزهای‬‫اقسام سال مشیس بر هامن ترتیب که به اول‪ 15‬گفتمی‪[ ،‬میمشرند]‪ 16.‬و چون‪ 17‬نوبت به اقسام طاق‬‫‪.‬خطاء ‪; BoL and BL:‬قتا ‪KM, SB, DK, BN, NK and BML:‬‬‫‪1‬‬‫‪Not in BoL.‬‬‫‪2‬‬‫‪.‬کن ‪; SB, DK, NK and BML:‬کَن ‪; BN and BoL:‬کن ‪BL and KM:‬‬‫‪3‬‬‫‪.‬جیو ‪; BN and BML:‬جو ‪; BoL and DK‬چو ‪; SB and NK:‬چو ‪BL and KM:‬‬‫‪4‬‬‫‪.‬بن ‪; BoL, DK and NK :‬بن ‪; KM:‬پن ‪; SB:‬پن ‪BL, BN and BML:‬‬‫‪5‬‬‫‪.‬جه ‪; DK and BN:‬چه ‪; BoL, SB:‬چه ‪BL, KM, NK and BML:‬‬‫‪6‬‬‫‪.‬پوو ‪; BN:‬ـو ‪; DK:‬پو ‪; BoL and SB:‬پو ‪BL, KM, NK and BML:‬‬‫‪7‬‬‫‪..‬حن ‪; DK:‬جن ‪; KM, BN and BML:‬چن ‪; BoL, SB and NK:‬چن ‪BL:‬‬‫‪8‬‬‫‪.‬ـی ‪; KM and DK:‬یی ‪; BL:‬پو ‪; BoL:‬پیی ‪SB, BN, NK and BML:‬‬‫‪9‬‬‫َ‪.‬خ ‪; NK:‬خ ‪; BoL, SB, DK, BN and BML:‬خ ‪BL and KM:‬‬‫‪10‬‬‫‪.‬خوـک ‪; DK:‬خونک ‪; SB, BN, NK and BML:‬حزیک ‪; BoL:‬خونک ‪BL and KM:‬‬‫‪11‬‬‫;په ‪; KM:‬په ‪; BoL, SB, DK, BN, NK and BML:‬پَه ‪BL:‬‬‫‪12‬‬‫‪.‬سپید ‪; BML:‬سـید ‪; KM, DK and DK:‬سبید ‪; BL, SB and KR:‬سفید ‪BoL:‬‬‫‪13‬‬‫‪.‬یعین به غایت تباه است ‪; BN and BML:‬یعین اغرب‪ .‬و أن به غایت تباه ابشد ‪; DK:‬یعین به غایت تباه ‪BoL, BL, KM, SB and NK:‬‬‫‪14‬‬‫‪.‬اول ‪; BL:‬به اول ‪BoL, KM, SB, DK, BN, KR and BML:‬‬‫‪15‬‬‫‪.‬میشامرند ‪; BoL, BL, BN, NK and BML:‬میمشرند ‪KM, SB and DK:‬‬‫‪16‬‬‫‪.‬و أن چون ‪; BoL:‬و چون ‪BL, KM, SB, DK, BN, NK and BML:‬‬‫‪17‬‬

‫‪SCIAMVS 14‬‬‫‪252‬‬‫‪Yoichi ISAHAYA‬‬‫رسد مانند لیجن که اول است‪ ،‬و کنجه که سوم‪ 1‬است‪ ،‬و سینک مینک که پنجم است‪ ،‬روز‬‫مبدأی أن قسم و روز مقدم بر أن قسم هر دو را یکی [مشرند]‪ :2‬یعین أچنه در روز مقدم نوبت به او‬‫رس یده ابشد‪ ،‬در روز مبدأی قسم مکرر [شود]‪ 3.‬ابیق بر ترتیب ابشد‪.‬‬‫و ما أچنه در اوایل سالهای دو دور‪ 4‬از اول دور شانکون نوبت به أن رس یده ابشد‪ ،‬اید کنمی ات‬‫از أجنا بر ترتیب میشامرند‪ .‬و برابر هر سال أچنه نوبت به او رس یده ابشد روز اول لیجن هنادی‪ .‬و هر‬‫سال که بعد از أن ابشد‪ ،‬در ششم أن انم روز نوبت به او رس ید‪ .‬و اگر سال کبیسه ابشد‪ ،‬در هفمت‬‫نوبت به او رس ید‪ .‬و سالهای کبیسه را عالمت «ک»‪ 5‬در برابر هنادی‪ .‬و بر این قیاس ابید کرد‪.‬‬‫‪.‬س می ‪: SB, DK and KR:‬سوم ‪BoL, BL, KM, BN and BML:‬‬‫‪1‬‬‫‪.‬میمشرند ‪; BML:‬میشامرند ‪; BoL:‬مشرند ‪BL, KM, SB, DK, BN and KR:‬‬‫‪2‬‬‫‪.‬میشود ‪; BoL:‬شود ‪BL, KM, SB, DK, BN, KR and BML:‬‬‫‪3‬‬‫‪.‬در دو دور ‪; BN:‬دو دور ‪BoL, BL, KM, SB, DK, KR and BML:‬‬‫‪4‬‬‫‪Not in BN.‬‬‫‪5‬‬‫‪253‬‬‫‪SCIAMVS 14‬‬‫سالهای یزدجردی‬‫سالهای تریک‬‫نوبت اول سال دور‬‫خلط‬‫یوند‬‫چه‬‫لیجن‬‫سالها که کبیسه‬‫خلح‬‫ییالن‬

‫پیی‬

‫ک‬

‫‪8‬‬

‫افتد‬

‫خلز‬

‫لو‬

‫پو‬

‫‪7‬‬

‫خن‬

‫ییالن‬‫سالهای یزدجردی‬‫خلو‬‫طاوشقن‬

‫چو‬

‫مخط‬

‫لو‬

‫سالهای تریک‬‫خهل‬‫ابرس‬

‫چن‬

‫مخح‬

‫نوبت اول سال دور‬

‫خدل‬

‫اوط‬

‫پن‬

‫‪4‬‬

‫لیجن‬‫سالها که کبیسه‬‫خلج‬‫کسکو‬‫ش یو‬

‫ک‬

‫‪1‬‬

‫‪2‬‬

‫‪3‬‬

‫مخو‬

‫اوط‬

‫چه‬

‫مخز‬

‫ابرس‬

‫پیی‬

‫‪5‬‬

‫طاوشقن‬

‫تن‬

‫‪6‬‬

‫ش یو‬
‫من‬

‫ک‬

‫خنا‬

‫یوند‬

‫چن‬

‫خنب‬

‫قوی‬

‫چو‬

‫مخ‬

‫قوی‬

‫خایی‬‫خنج‬‫بیجنی‬

‫پو‬

‫خام‬

‫بیجنی‬‫پن‬‫‪12‬‬‫مخب‬‫داقوق‬

‫چن‬

‫ک‬

‫مخج‬

‫ایت‬

‫من‬

‫‪16‬‬‫مخد‬‫طونغوز‬

‫وی‬

‫مخه‬

‫کسکو‬

‫کن‬

‫‪9‬‬

‫‪10‬‬‫‪15‬‬‫خند‬‫داقوق‬

‫پیی‬

‫خنه‬

‫ایت‬

‫چه‬

‫ک‬

‫افتد‬‫‪The Tārīkh-i Qitā in the Zīj-i Īlkhānī‬‬‫‪11‬‬‫‪13‬‬‫خنو‬‫طونغوز‬‫خایی‬‫خزن‬‫کسکو‬‫پن‬‫ک‬‫‪14‬‬‫‪17‬‬‫‪18‬‬‫‪Not in DK and BN.‬‬‫‪1‬‬‫‪.‬پیی ‪BL:‬‬‫‪2‬‬‫‪Not in SB and BN.‬‬‫‪3‬‬‫‪.‬ک ‪; BN:‬کبیسه ‪DK:‬‬‫‪4‬‬‫‪.‬کبیسه ‪BN:‬‬‫‪5‬‬‫‪.‬کبیسه ‪SB:‬‬‫‪6‬‬‫‪.‬ک ‪BN:‬‬‫‪7‬‬‫‪Not in BN.‬‬‫‪8‬‬‫‪.‬چن ‪KM:‬‬‫‪9‬‬‫‪.‬ک ‪BN:‬‬‫‪10‬‬‫‪.‬ک ‪BN:‬‬‫‪11‬‬‫‪.‬تن ‪SB:‬‬‫‪12‬‬‫‪.‬من ‪BL:‬‬‫‪13‬‬‫‪Not in BN.‬‬‫‪14‬‬‫‪Not in SB.‬‬‫‪15‬‬‫‪.‬کبیسه ‪SB:‬‬‫‪16‬‬‫‪.‬ک ‪BN:‬‬‫‪17‬‬‫‪.‬ک ‪BN:‬‬‫‪18‬‬

‫‪SCIAMVS 14‬‬‫‪254‬‬‫‪Yoichi ISAHAYA‬‬‫فصل دوازدمه‬‫در معرفت اترخی قتایی‪ 1‬از اترخی عریب‬‫چون نزدیک منجامن ما اترخی جهری مشهورتر است‪ ،‬از اول عهد جنکز‪ 2‬خان ات مدت صد سال‪،‬‬‫سالها و ماههای جهری در جدول هنادی‪ .‬سال از جانب راست‪ ،‬و ماهها بر رس جدول‪ ،‬و ماههای‬‫مغویل در میان جدول به رقوم‪ ،‬و انم سال تریک گشاده‪ ،‬و شون گشاده‪ ،‬و بر ابالی جدول مدخل ماه‬‫عریب‪ ،‬و در شصت مدخل ماه [قتایی]‪ 3،‬و عدد روزهای ماه‪ 4.‬و جدول این ست که در صفحۀ دیگر‬‫است‪.‬‬‫‪5‬‬‫‪.‬ختایی ‪; BoL:‬قتایی ‪BL, KM, BL, KM, SB, DK, BN, NK and BML:‬‬‫‪1‬‬‫‪.‬جنکزی ‪; BML:‬جنکـز ‪; NK:‬حـکـر ‪; DK:‬حـکر ‪; SB:‬حنکز ‪; KM:‬حنکـر ‪; BL and BN:‬جنکز ‪BoL:‬‬‫‪2‬‬‫‪.‬خطایی ‪; BoL:‬قتایی ‪BL, KM, SB, DK, BN, NK and BML:‬‬‫‪3‬‬‫‪; not in KM.‬و عدد روزهای ماه‬‫‪4‬‬‫‪; not in KM, SB, DK, BN and NK.‬که بر صفحات ورقهای دیگر است ‪ ; BML:‬که در صفحۀ دیگر است ‪BoL and BL:‬‬‫‪5‬‬

SCIAMVS 14

The Tārīkh-i Qitā in the Zīj-i Īlkhānī

255

Appendix: Chinese Technical Terms
Here, the Persian transcriptions of the Chinese terms are listed in arphabetical order,
along with the Chinese characters and meanings.
Banjūshā: ban zhou-xian 半周限 (puɜan tʂiau-hian), the parts of the half-cycle, or 124. The cycle of ananomalistic month is divided into 248 parts in this calendar, so that the half-cycle consists of 124 parts(section 9).
Baylū: bai-lu 白露 (pai-lu), the fifteenth solar division (section 3).
Bījūtin: ban zhou-tian 半周天 (puɜan tʂiau-thiɛn), or the Celestial Half-Circle. The approximate half-periodof the solar anomaly, 182 days (section 8).
Chih: zhi 執 (tʂi), the sixth of the twelve-presage cycle (section 11).
Chin: chen 辰 (tʂhian), the fifth terrestrial branch (section 1).
Chin: cheng 成 (tʂiaŋ), the ninth of the twelve-presage cycle (section 11).
Chīu: chou 丑 (tʂhiau), the second terrestrial branch (section 1).
Chīu-Shū: chu-shu 處暑 (tʂhiu-ʂiu), the fourteenth solar division (section 3).
Chū: chu 除 (tʂhiu), the second of the twelve-presage cycle (section 11).
Dāy-Khan: da-han 大寒 (tai-han), the twenty-fourth solar division (section 3).
Dāy-Shih: da-xue 大雪 (tai-siuɛ), the twenty-first solar division (section 3).
Dāy-Shū: da-shu 大暑 (tai-ʂiu), the twelfth solar division (section 3).
Dūnjin: dong-zhi 冬至 (tuŋ-tʂɪ), the twenty-second solar division (section 3).
Funk: fen 分 (fuan), a ten-thousandth of a day (section 1).
Jūnjā: zhuan-chai 轉差 (tʂiuɛn-tʂha) means the excess of a solar year over thirteen anomalistic months,
7.0338 days (section 7).
Junjūn: zhuan-zhong 轉 終 (tʂiuɛn-tʂiuŋ) literally means the Revolution Terminal Constant, i.e., ananomalistic month (section 7).
Jūnjūnkā: zhuan-zhong ying 轉終應 (tʂiuɛn-tʂiuŋ iaŋ), the time from the beginning of the last anomalisticmonth preceding the wūshī to the wūshī itself. The value is 78.3948 days in the epoch year (section 7).
Junjūnshā: zhuan-zhong chai 轉終差 (tʂiuɛn-tʂiuŋ tʂha) means nine times the excess of a lunar month overan anomalistic month (27.5556 days, in this case), i.e., 17.7754 days (section 9).
Jūnk-Wan: zhong-yuan 中元 (tʂiuŋ-iuɛn), the Middle Epoch, the middle of the three sixty-year cycles(section 4).
Kā: jia 甲 (kia), the first heavenly stem (section 2).
Khā’ī: hai 亥 (hai), the twelfth terrestrial branch (section 1).
Khā’ī: kai 開 (khai), the eleventh of the twelve-presage cycle (section 11).

256

Yoichi ISAHAYASCIAMVS 14

Khanlū: han-lu 寒露 (han-lu), the seventeenth solar division (section 3).
Khā-Wan: xia-yuan 下元 (hia-iuɛn), the Inferior Epoch, the last of the three sixty-year cycles (section 4).
Kī: ji 己 (ki), the sixth heavenly stem (section 2).
Kih: ke 刻 (khiai), a unit of time equal to one eighth of a chāgh, a double-hour (section 1).
Kīja: qi-ce 氣策 (khi-tʂhai), the length of the twenty-four equal divisions of a solar year, each 15.21848333...
days long (section 3).
Kījā: qi-chai 氣差 (khi-tʂha) is the interval between the twenty-second solar division (the winter solstice)and the wūshī, namely one-sixth of a solar year, is 60.8740 days (section 7).
Kījū: qi-shou 氣首 (khi-ʂiau) denotes the beginning of the first division of any solar year (section 5).
Kin: geng 庚 (kiaŋ), the seventh heavenly stem (section 2).
Kin: jian 建 (kiɛn), the first of the twelve-presage cycle (section 11).
Kin-Jih: jing-zhe 驚蟄 (kiŋ-tʂi), the third solar division (section 3).
Kūwū: gu-yu 穀雨 (ku-iu), the sixth solar division (section 3).
Kūy: gui 癸 (kui), the tenth heavenly stem (section 2).
Lījun: li-chun 立春 (li-tʂhiuan), the first solar division (section 3).
Lījū’u: li-qiu 立秋 (li-tshiau), the thirteenth solar division (section 3).
Līkha: li-xia 立夏 (li-hia), the seventh solar division (section 3).
Lītūn: li-dong 立冬 (li-tuŋ), the nineteenth solar division (section 3).
Māh-i Shūn: a combination of the Persian term māh with Chinese run 閏 (ɽiuan), which means anintercalary month (section 6).
Man: man 滿 (muɜn), the third of the twelve-presage cycle (section 11).
Manjun: mang-zhong 芒種 (muaŋ-tʂiuŋ), the ninth solar division (section 3).
Māu: mao 卯 (mau), the forth terrestrial branch (section 1).
Nū: nu 朒 is used for the slow phase of the luminaries. Here, it means “additive,” as applied to the solar andlunar equations (section 8).
Pī: bi 閉 (pi), the twelfth of the twelve-presage cycle (section 11).
Pīn: bing 丙 (piaŋ), the third heavenly stem (section 2).
Pin: ping 平 (phiaŋ), the fourth of the twelve-presage cycle (section 11).
Pū: po 破 (phuɜ), the seventh of the twelve-presage cycle (section 11).
Shājir: xia-zhi 夏至 (hia-tʂɪ), the tenth solar division (section 3).
Shānk-Wan: shang-yuan 上元 (ʐĭaŋ-iuɛn), the Superior Epoch, the first of the three sixty-year cycles(section 4).
Shin: shen 申 (ʂian), the ninth terrestrial branch (section 1).
Shīnk-Mīnk: qing-ming 清明 (tshiaŋ-miaŋ), the fifth solar division (section 3).

SCIAMVS 14

The Tārīkh-i Qitā in the Zīj-i Īlkhānī

257

Shīu: shou 收 (ʂiau), the tenth of the twelve-presage cycle (section 11).
Shūja: shuo-ce 朔策 (ʂau-tʂhai), a mean synodic month, 29.5306 days (section 6).
Shūn-Fūnd: chun-fun 春分 (tʂhiuan-fuan), the fourth solar division (section 3).
Shūnjan: run-ying 閏應 (ɽiuan-iaŋ) represents the interval from the mean first month (ārām ay) to the wūshī
for any particular year (section 6).
Shūn-Kūn: shuang-jiang 霜降 (ʂaŋ-kiaŋ), the eighteenth solar division (section 3).
Sin: xin 辛 (sian), the eighth heavenly stem (section 2).
Siyāu-Shih: xiao-xue 小雪 (siau-siuɛ), the twentieth solar division (section 3).
Siyāu-Shū: xiao-shu 小暑(siau-ʂiu), the eleventh solar division (section 3).
Siyū-Fan: qiu-fun 秋分 (tshiau-fuan), the sixthteenth solar division (section 3).
Siyū-Khan: xiao-han 小寒 (siau-han), the twenty-third solar division (section 3).
Siyū-Man: xiao-man 小滿 (siau-muan), the eighth solar division (section 3).
Ṣiz: si 巳 (sï), the sixth terrestrial branch (section 1).
Sū: xu 戌 (ʂiu), the eleventh terrestrial branch (section 1).
Suijā: sui-chai 歳差 (sui-tʂha) denotes the difference between the solar year and twelve mean lunar months,
10.8764 days (section 6).
Suijū: sui-zhou 歳周 (sui-tʂiau), the length of a solar year, taken as 365.2436 days (section 3).
Suiyū: sui-yu 歳餘 (sui-iu) indicates the excess of a solar year over 360, specifically 5.2436 days (section 5).
Tāyānk-Zhichūn: tai-yin ru-zhuan 太陰入轉 (thai-iam ɽi-tʂiuɛn) is the lunar equation (section 9).
Tāyānk-Zhikī: tai-yang ru-qi 太陽入氣 (thai-iaŋ ɽi-khi) is the solar equation (section 8).
Tīn: ding 丁 (tiaŋ), the fourth heavenly stem (section 2).
Tin: ding 定 (tiaŋ), the fifth of the twelve-presage cycle (section 11).
Tiyā’ū: tiao 朓 is used for the fast phase of the luminaries. Here, it means “subtractive,” as applied to thesolar and lunar equations (section 8).
Wī: wei 未 (vui), the eighth terrestrial branch (section 1).
Wī: wei 危 (ui), the eighth of the twelve-presage cycle (section 11).
Wū: wu 午 (u), the seventh terrestrial branch (section 1).
Wū: wu 戊 (vu), the fifth heavenly stem (section 2).
Wūshī: yu-sui 雨水 (iu-ʂui), the second solar division (section 3).
Yī: yi 乙 (i), the second heavenly stem (section 2).
Yim: yin 寅 (ian), the third terrestrial branch (section 1).
Yū’u: you 酉 (iau), the tenth terrestrial branch (section 1).
Zhih: zi 子 (tsï), the first terrestrial branch (section 1).
Zhim: ren 壬 (ɽiam), the ninth heavenly stem (section 2).

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Yoichi ISAHAYASCIAMVS 14

Acknowledgements
First of all, my greatest debt of gratitude goes to my doctoral advisor, Masashi Haneda
who opened my eyes to the importance of reconsidering existing frameworks fromvarious perspectives, theoretical, geographical, and so on. Without his strict but kind
instruction, I would never have realized how this multi-lingual material holds thepossibility of crossing cultural boundaries. This article was the result of my research in
the last winter at the Warburg Institute, which was made possible thanks to Charles
Burnett. He facilitated my stay and introduced me to professors in the UK, such as
Raymond Mercier, who gave me advice on the draft of this article. Just as indispensable
was the constant help of Benno van Dalen who has deepened understanding of the Qitai
calendar, allowing me to deal with the source. In addition, this article would not exist
without his computer program SCTR, which enabled me to recompute values in theentries of the tables in this calendar. I am lucky to have seen a draft of the English
translation of the Qitai calendar by Javad Hamadani-Zadeh, which was quite useful,
especially for analyzing the tables. Before that, the work was prepared through roughly
two years of research (2010–2012) in Iran under the supervision of Mohammad Bagheri,
whose attention and advice were an essential aid to me over the course of my stay in thatcountry. Of course, I was benefited so much from all my Iranian professors andcolleagues at the Institute for the History of Science, the University of Tehran, to which I
belonged as a visiting scholar. My thanks are due to Asghar Qaedan, the director of theinstitute, who has always been supportive to me. Christopher Atwood’s knowledgeableadvice directed my attention to a “true” critical edition and the linguistic viewpoints ofthe source. Satoshi Ogura and Susan Asili kindly provided me with precious information
about the Bodleian and Florence manuscripts respectively. I am also grateful to Kazuo
Morimoto, who instructed me to deal with Persian materials and gave me a chance todiscuss the draft of this article in his class, in which I got useful feedback. Finally, I must
express my deep appreciation to the editors and anonymous referees of this journal,
whose reviews clarified many points to be revised and encouraged me to complete thisarticle. This work is supported by a Grant-in-Aid for JSPS Fellows.
(Received: March 27, 2013)(Revised: December 24, 2013)