Indian Journal of History of Science, 50.2 (2015) 215-226 DOI: 10.

16943/ijhs/2015/v50i2/48237

Allusions to Ancient Indian Mathematical Sciences in an Early

Eighth Century Chinese Compilation by Gautama Siddha
Vijaya J Deshpande*
(Received 04 December 2014; revised 20 April 2015)

Abstract
Gautama Siddha belonged to one of the three prominent Indian families of expert-astronomers
settled in China during Tang dynasty (618-906 AD). Members of this family held important positions in
the successive astronomical bureaus of Tang dynasty. Gautama, once President of the bureau, was assigned
the task of writing down a compendium Datang Kaiyuan Zhanjing ( ) since he was very
well acquainted with both systems, Chinese and Indian. He devoted one chapter out of hundred and twenty
altogether, to Indian calendar-making method, popularly known as the Jiuzhili or Navagraha method.
At the outset Gautama explained the decimal notation system as employed in arithmetical
operations in India at that time. He recorded symbols for numbers one to nine and also zero. He went on
to explain the division of earths orbit into 360 degrees as against more than 365 in the Chinese system
and further proposed algorithms for calendar making and prediction of lunar and solar
eclipses. Trigonometric functions were also officially introduced to China through this work.
Key words: Ancient Indian astronomy, Calendar making, Eclipse-equinox prediction, Gautama
Siddha, Jiuzhili, Navagraha, Siddhntic astronomy, Tang China

1. INTRODUCTION infrequent. Babylonian, Greek, Arabian cultures

successively influenced both Indian and Chinese
Study of the skies or the heavens was a
topic of great interest even to the ancients. It was astronomy.
useful in navigation at night to begin with. Likewise Indian astronomy substantially
Monthly rotation of the moon and yearly rotation influenced both Arabian and Chinese astronomy
of the earth were studied to predict seasons, during medieval period.
making accurate calculations of the calendar day
As Buddhism established itself in China,
and predicting celestial events like equinoxes and
eclipses that sometimes had religious significance. alongside Buddhist monks, experts of other fields
Ancients also observed and recorded relative like astronomy, medicine etc often visited the
position of the planets as against the sun and Chinese capital, especially during Tang dynasty.
distant constellations, to understand their motion. Three Indian families of expert astronomers are
Every ancient culture developed their individual mentioned in Chinese historical records. Among
system of celestial observation, recording, them one Gautama family was outstanding in
calculations and prediction based on their the positions they held in court and their scholarly
indigenous celestial map with characteristic work in the field of making new calendar system,
nomenclature for stars, planets and constellations. writing/compiling books. They advised the ruler
Yet, transmission of ideas and techniques were not in astrological matters too. They were highly

*76/37A, Erandawana, Pune, 411004; Email: vijaya.deshpande@gmail.com

216 INDIAN JOURNAL OF HISTORY OF SCIENCE

Table 1. Approximate parallels to Nakatras are listed below

Rohi B Kttik Mao Bhara Wi Avin Lu
Puya Gu Punarvasu Jng rdr Shn Mgairas Z
Uttara-Phlgun Y Prva-Phlgun Zhang Magh Xng Ale Liu
Vikh D Svti Kng Citr Jiao Hasta Zhen
Prva-Adha J Mla Wei Jyesth Xn Anurdh Fng
Dhanih X ravaa N Abhijit Ni Uttara-Adh Do u
Revat Ku Uttarbhadrapad Bi Purvbhadrapad Shi atatrak Wi

respected for their mastery over both Indian and nakatra/mansion are different since they depend
Chinese theories and techniques, and overall upon the position of the observer and therefore
contribution they made in transmitting ancient are defined in a different way in each culture.
Indian astronomical-mathematical knowledge into Again, when the stars in the constellation are not
China. This article studies contribution by exactly alike, their overall shape, chief star in that
Gautama Siddha in some detail. constellation differs too.2
The twenty-eight mansions of
2. ANCIENT ASTRONOMY - INDIAN AND Chinese astronomy are divided into four groups
CHINESE of seven each referred to as East or Spring; South
Ancient Chinese and ancient Indians both or Summer; West or Autumn; and North or Winter.
had their separate astronomical theories and Chinese zodiac is tropical i.e. it relies on suns
practices that were in use long before they position in a particular constellation, and hence
developed close contacts through Buddhism from mansions are related to specific seasons.
second century AD onwards. These systems were Furthermore, the beginning of the year does not
largely similar since they both were studying change with precession of equinoxes but remains
identical celestial phenomena. Variations were due fixed since it is related to particular lunar mansion
to dissimilar assumptions and other geographic i.e. a distant constellation. Thus Chinese year
and cultural factors. begins when the sun enters the lunar mansion jiao
, which is the first mansion in the section east
A nakatra or a lunar mansion in Chinese of the lunar mansions. Nakatra Citr which
is the group of stars the moon moves through in means bright, clear or variegated corresponds to
twenty four hours. Since the moon revolves round Chinese lunar mansion jiao which means horn.
the earth in about twenty eight days, number of Both correspond to the star spica in western
nakatras or mansions is also the same.1 In fact, astronomy. Here correspondence is as regards
apart from the number twenty eight, all other location which is measured as longitude with
factors are different e.g. number of stars in each respect to the equatorial plane.

1
The number was revised to 27 in later Indian works from 5/6th century AD onwards. Nakatra Abhijit was dropped since it was
not necessary. The division of the zodiac in 27 Nakatras was accepted to account for the period of 27.32 days taken by the
moon to complete one rotation through the zodiac i.e. 360 degrees.
2
Niu weixing. (1997/98), p119-129
Stra on Majur Bodhisattva and the Sages Teaching on Auspicious and Inauspicious Times, Days, Good and Evil Constel-
lations and Luminaries , translated by Amoghavajra (705-774 AD)
in 759 and revised in 764 by disciple Yang Jing Feng under his masters guidance.
 EARLY EIGHTH CENTURY CHINESE COMPILATION BY GAUTAMA SIDDHA 217

On the contrary, a major difference lay in nine heavenly bodies as Jiu zhi, the nine
calculating angles, since Indians divided the grahas, seizers or upholders, also written as Jiu
celestial orbit in 360 degrees whereas the Chinese yao or nine luminaries or planets.
into little more than 365 which is based on their The nine luminaries mentioned are:
assumption that the sun moves one degree per ditya - the sun, Sma - the moon, five planets
calendar day of twenty four hours. They divided are- Agraka - Mars, Budha Mercury,
the whole zodiac by number 365.25 hence their Bhaspati Jupiter, ukra Venus, and
single smallest unit is smaller than a degree.3 anaicara - Saturn; also Louhou - Rhu,
and Jidu - Ketu, the demons that were
3. ANCIENT INDIAN ASTRONOMY IN
supposed to cause eclipses.6
CHINESE BUDDHIST WORKS
Earliest indication of the entry of Indian 4. ANCIENT INDIAN ASTRONOMY IN
astronomy is found in Buddhist canonical works. CHINESE HISTORICAL RECORDS
Ideas related to cosmology, constellations, the sun,
Several allusions to ancient Indian
the moon, planets; also names and categories of
astronomy, visiting Indian astronomers and their
months like lunar, solar, intercalary months,
skills are found in Chinese historical records too.
changes in the lengths of day and night, noon
Titles of works related to mathematics and
shadow method for determining latitude of a place
astronomy were also included in the Polomen
etc. are recorded in these works.4
or Brahmin books listed in the
Following three sutras allude to the noon bibliography of Sui dynasty (581-618 AD). These
shadow method for determining latitude of a books are no more extant though. Their titles
place.5 mention Jivaka, Nagarjuna, Brahmins or western
Modengjia jing, Mtagastra (TT sages as their authors suggesting their Indian
1300) the Chinese translation of rdlakara- connection. Among these, one by the name
avadna, translated into Chinese in 230 AD, Polomen tian wen jing , was
probably related to astronomy and calendar
Fo shuo shi fei shi jing (TT794) science.
When time was non-time stra as told by Buddha
Later in the year 759 AD Amoghavajra, a
Dafang deng daji jing (TT 397) - well-known Tantrik author and translator of
Mahvaipulya mahsamghta stra Buddhist canonical works, wrote Xiu yao jing
Siddhtic astronomy appeared in later i.e. Lunar mansion and planet stra. A
Buddhist stras. Buddhist stra Brahma- commentary to this work by Yang Jingfeng
hornavagraha written around 751 AD, alluded mentioned the three Indian schools of astronomy
to navagraha defined by the Indian tradition, the in following words.
3
Ho Pengyoke (1985)
4
Four definitions of month are given in Volume 48 of Great Treatise on the Perfection of Wisdom namely Solar Month,
Karma Month, Lunation Month, Nakatra Month. Therein, Solar Month is one-twelfth the length of the tropical year,
Karma Month is an ideal year (360 days as an ideal year), Lunation Month is namely the synodic month and Nakatra
Month is the sidereal month. See Encyclopedia of India-China cultural contacts, MaXposure Media Group, New Delhi, 2014,
part 1, p 74
5
Niu weixing (1997/98), p199-129
Also see, Niu Weixing and Jiang xiaoyun, (1998).
6
Niu Weixing (2005) p329.
218 INDIAN JOURNAL OF HISTORY OF SCIENCE

Those who wish to know the positions explains the division of degrees in Indian method
of the five planets adopt Indian as sixty minutes of fen making one degree and
calendrical methods. One can thus predict
what hsiu7 (a planet will be traversing).
thirty degrees making one zodiacal sign called
So we have the three clans of Indian hsiang and further that, signs filled to twelve
calendar experts, Chia yeh (Jia ye should be cancelled. (Naturally, since they
Kyapa), Chhu than (Qu tan complete one circle). Gautama writes,
Gautama) and Chu mo lo (Jiu
The hsiang is called loshih ( r) in
mo lo Kumra), all of them hold office at Sanskrit, which means collection.
the Bureau of Astronomy. But now most Formerly it was translated as tzu, and
use is made of the calendrical methods of now hsiang is adopted.
Master Chhu than chuan (Qutan zhuan)8
together with his Great Art.9 We can see here that Chinese astronomers
Here the author states that positions of five before Gautamas time itself replaced the
planets can be determined using Indian methods. transliterated word loshi to its Chinese counterpart
Probably they were part of earlier calendars hsiang.
Jingweili and Guangzaili Again, in the sub-section no. 7, while
composed by Gautama Rahula, father of Gautama calculating the anomaly of the moon
Siddha or in the methods taught by experts of other Gautama Siddha states,
clans viz. Kayapa and Kumra. Formerly yuehtsan (yuecang) was
Also, Xintangshu, New History of Tang sometimes translated as yueh-sun-i-shuai
dynasty (10th century AD) records that Temolo, an (candra-ra-dhana in
Indian transmitted the method of solar eclipse Sanskit)11
prediction.10 When ideas or substances came from
In order to translate Buddhist works related outside, related terminology was transmitted too.
to astronomy and astrology into Chinese and to As new substances or ideas became familiar their
express Indian ideas correctly, new terminology foreign sounding names were dropped for more
was developed in Chinese. It was formulated either homogeneous terms. This is observed even in
by translating Sanskrit words into Chinese or other disciplines like chemistry, alchemy and
transliterating them using Chinese characters with medicine.12
similar sounds e.g. A shi bi ni for avin,
A shi li sha for Ale and A 5. GAUTAMA CLAN OF ASTRONOMERS
nu luo tuo for Anurdh. This terminology The long tradition of having Indian
changed with time as Gautama Siddha specifically scholar-astronomers in prominent positions in the
mentioned in his work. Tang court began in mid sixth century AD and
In the sub-section no. 4 while calculating Jiaye xiaowei was probably the first among them.
the mean longitude of the sun, Gautama Siddha Jiaye or Kyapa, Jiumolo or Kumra and Qudan
7
Hsiu or Xiu in Pinyin or the modern system of transliteration means (lunar) mansion.
8
Son of Gautama Siddha
9
Xiuyao jing p 350, see Sen Tansen (1995) p197
10
Yabuuti, K. (1979) p2
11
Yabuuti, K. (1979) p 18 (Translation by Yabuuti K.)
12
Nao sha for ammonium chloride or Sal ammoniac was written with different characters in succeeding periods which suggested
that it was a transliterated word from some foreign language. The word was in fact derived from Sanskrit Navasra. It was later
changed to Lu hua an or Muriate of ammonia.
 EARLY EIGHTH CENTURY CHINESE COMPILATION BY GAUTAMA SIDDHA 219

or Gautama, these three were major astronomical included all earlier rare texts of Chinese astronomy
schools of Indian origin at that time. Qudan xida in this compilation thus making the otherwise
or Gautama Siddha belonged to the Gautama clan extinct works available to posterity. For this
settled in China.13 Four/five generations of this reason, he is a highly respected figure in the
clan were high officers in astronomical bureaus History of Chinese astronomy.
of Tang dynasty. When Gautama familys tomb
Kaiyuan zhanjing devoted chapter 104
was excavated in Chang an in the year 1977,
inscriptions therein provided more information (hereafter KYZJ-104) to the so-called navagraha
about the clan. or jiuzhi method of calendar making. It was
initially introduced into China through the
Gautama family was originally from Mtagastra translated in third century AD.
Banares. One named Gautama yi went to China These navagraha or Nine upholders refer to the
sometime in the sixth century. He worked as a sun, the moon, five planets and Rhu and Ketu
translator of Buddhist classics. His son Gautama that were the terms given to the two nodes,
Rhula was the director of astronomy
ascending and descending respective of the moon.
between 627 to 649 AD. He compiled two
Scholars believe the contents of (KYZJ-104) as
calendars viz. Jingweili and
derived from, and not a direct translation of,
Guangzaili. As the family settled down in China
famous sixth/seventh century Indian astronomical
they married Chinese women so later generations
works Pacasiddhntik by Varhamihira and
are not mentioned as Indian in Chinese records.14
Khaakhdyaka of Brahmagupta of AD 575 and
Gautama Siddha was born 665 respectively.15
sometime after 650 AD. He was the head of the
Bureau of Astronomy from 712 to 718 AD. Gautama Siddha wrote advanced
Between 712 and 713 AD he was in charge of algorithms in KYZJ-104 for calculations for
repairing the armillary sphere. In 718 AD he predicting various astronomical events. Jiuzhili or
translated the Navagraha Siddhnta - Jiuzhili into the navagraha system did not get much popularity
Chinese. Being well acquainted with Chinese though. Knowing its importance the manuscript
astronomical development till the time, he was was secretly preserved. Therefore it was forgotten
given the task of compiling astronomical works. over a long period till accidentally in 1616 AD
Gautama Siddha compiled a book named Cheng Mingshan discovered the
Datang Kaiyuan Zhanjing - The manuscript inside the stomach of a Buddha statue,
Great Tang Treatise on Astrology of the Kaiyuan most probably hidden there for safe keeping by
Era between the years 718 and 728 AD. He some unknown Buddhist monk-scholar.16

Tang and early Song names of eye disease pterygium are Nurou panjing spoilt flesh spreading over the eye, and
Nurou qinjingwaizhang i.e. The external obstacle due to the spoilt flesh invading the eye. They appear to be
derived from the Sanskrit term Prastri arma - A spreading (over the eye) spoilt flesh. This was the time when there occurred
major transmission of ophthalmic ideas to China from India. Pre-Tang name for the same disease was Xi rou or polypus in
general. In modern terminology, pterygium is now called Yizhuang nurou or Wing-shaped spoilt flesh. This name
is derived from the English name of the disease pterygium which means wing-shaped. It is in turn derived from Greek
pterygion meaning wing.
13
Sen Tansen (1995)
14
Jean-Claude Martzloff- Le Calendrier Chinois
15
Li Hui and Niu Weixing(2014) (2010)
16
Yabuuti, K. (1979) p 9
220 INDIAN JOURNAL OF HISTORY OF SCIENCE

5.1 The zero symbol and decimal place value the right (i.e. aforesaid) is Indian counting
system method. Using the above nine symbols,
multiplication and divisions are carried.
In Indian scientific literature from the sixth All these characters are single stroked,
century AD onwards one frequently comes across and are written cursively. While counting
the zero symbol and its application in the decimal when the number reaches ten then it is
place value. In the year 498 AD, when ryabhaa entered in the front (row). In each vacant
wrote his ryabhayam, he introduced the place is then placed one dot. In this way
decimal place value system. Even before that time there is a mark/symbol in each place so
there cannot be any error. The calculation
a Jain work Lokavibhga of 458 AD referred to it.
is necessarily easy to the eye, so it is (we
In China, however, both these concepts were have described it) before the calendrical
unknown at the time of writing of KYZJ. The methods.
KYZJ -104 clearly mentioned both, the symbol
of zero and its use in decimal value system for the Although, perhaps the symbols for the
first time. The text elaborated the new concepts numbers were written by the original author
in following words. Gautama Siddha, they were dropped by successive
copyists and now we have only the mention of
them in KYZJ that is preserved in a 18th century
compilation that is oldest available source of this
work now.17
Method of the Counting symbols:
symbol for 1 - for 2 - for 3 - for 4 - for 5 - KYZJ is available separately too in new
for 6 - for 7 - for 8 - for 9 and a dot. On editions.18
17
Here is the page from Siku quanshu, a eighteenth century collection which contains KYZJ. The column second from
left keeps the places of symbols blank. See the page below. It actually says character/symbol (for) 1, character (for) 2, and so
on, without actually writing symbols. It is followed by the character in Chinese for dot which is dian or in the simplified
version in modern compilations dian as quoted in the passage above.

Fig. 1 See Siku Quanshu Wen yuan ge si ku quan shu dian zi ban. [Catalog] [electronic resource] / Di zhi wen hua chu
ban you xian gong si. . [Catalog] [electronic resource] . Hong
Kong [1999?]
18
Kai yuan zhan jing (2012)
 EARLY EIGHTH CENTURY CHINESE COMPILATION BY GAUTAMA SIDDHA 221

Other Chinese Buddhist works written do not agree with this but propose an alternative
around eighth century that refer to Indian numerals method that Yi xing might have used. In a nutshell,
may give an idea as to how Gautama Siddha might there exists controversy regarding the extent to
have had written the numbers. which Indian methods/theories were incorporated
in Dayanli but all agree that although Yixing used
6. LATER GENERATIONS OF THE GAUTAMA traditional Chinese methods in his calendar
FAMILY AND DAYANLI CONTROVERSY making, he was acquainted with Indians theories
Yi xing (683727 AD), a contemporary and he made use of them too.
of Gautma Siddha, was a mathematician, Before Yixing there were astronomers like
astronomer and also a translator-commentator of Cao Shikui of mid-Tang dynasty who developed
Buddhist canonical works. He was in charge of their own methods and algorithms to calculate
the terrestrial astronomical board and under his astronomical events. In his Futianli calendar Cao
direction was carried out the gigantic task of Shikui used the terms or concepts like Louhou
measuring shadow lengths and longitude of pole Rhu and Jidu Ketu but stuck to the measure of
star at thirteen places between latitude 29 to 52 Suns rotation as one degree a day, again an
degrees North. These observations were used in a integration of two systems.
variety of astronomical calculations and eventually
in writing a new calendar Dayanli. He Yabuuti Kiyosi translated KYZJ 104 i.e.
created an armillary sphere in Chang an. Yi xing Jiuzhili or the Navagraha calendar into English.
was the most prominent Buddhist monk of the He wrote an article based on his studies in the
time. year 1963.20 Later in the year 1979 he revised the
translation with Michio Yano and published an
Gautama Siddhas son, Gautama Duan
article that included a commentary to Yabuutis
(712-776 AD) was a scholar astronomer as well translations by Yano who is an expert of ancient
as a soldier. He later held the office of Vice Indian astronomy.21 Yano explained Gautama
Director of the bureau of astronomy as the post Siddhas algorithms in terms of Siddhtic
was called in the Tang. Gautama Duan criticized astronomical methods of calculations,
Dayanli calendar made by Yi xing in 727 AD after simultaneously elucidating parallel terms from
the latters death, pointing out that portions from Sanskrit. Together Yabuuti and Yano translated and
Jiuzhili calendar were incorporated in Dayanli. He discussed all 37 sub-sections of the KYZJ-104
accused Yi xing of plagiarism. Since Yi xing was which are,
highly respected, and also that Gautama Duans
astrological predictions sometimes failed, he was 1. Numerals
banished from the court and the kingdom. Later, 2. Degrees in Astronomical System
after the regime change he was reinstated and 3. Chapter on the chijih (jiri), sum of days
many honors were conferred upon him. from the epoch, dyugaa or ahargaa in
Some scholars are of the opinion that Sanskrit and the hsiaoyu (xiaoyu), its
certain tangent tables documented by Yi xing were fraction
most probably an outcome of calculations made 4. Chapter on the Calculation of the chungjih -
using sine tables method stated in Jiuzhili than (zhongri) mean latitude of the sun
actual observations.19 Again, some other scholars madhyasrya in Sanskrit
19
Cullen, Christopher (1982)
20
Yabuuti, Kiyosi. (1963)
21
Yabuuti, K.(1979)
222 INDIAN JOURNAL OF HISTORY OF SCIENCE

5. Chapter on the Calculation of the chungyueh 18. Chapter on the Calculation of the chunfen
(zhongyue), mean longitude of the moon, (junfen), longitude of the moon and the
madhyacadra sun at syzygy, samalipta in Sanskrit
6. Chapter on the Calculation of the kaoyueh 19. Chapter on the Calculation of the ahsiu
(gaoyue), longitude of the lunar apogee, (axiu), the moons node, asura in Sanskrit
cadra-ucca in Sanskrit
20. Chapter on the Calculation of the chienliang-
7. Chapter on the Calculation of the yuehtsang fu (jianliangfu), longitude of an
(yuecang), anomaly of the moon, eclipsed body counted from moons node
cadrakendra in Sanskrit
21. Chapter on the Calculation of the yueh-
8. Chapter on the Calculation of the jihtsan
chienliang-ming (yuejianli-
(jicang), anomaly of the sun, sryakendra in
angming) half the cord of the chienliang-fu
Sanskrit
(jianliangfu) i.e. sine table
9. Chapter on the Calculation of the tingjih
(dingri), true longitude of the sun in Sanskrit 22. Method on the calculation of the yueh-
chienliang (yuejianliang), moons
10. Chapter on the Calculation of the tingyueh latitude
(dingyue), true longitude of the moon,
sphuacandra in Sanskrit 23. Method on the calculation of the yuehliang
(yueliang), apparent diameter of the
11. Chapter on the Calculation of the Daytime and
moon
Night
12. Chapter on the Computation of yuehyu 24. Method on the calculation of the ahsiu-liang
(yueyu), moons boundary i.e. true daily (axiuliang), diameter of the earths
motion of the moon shadow

13. Chapter on the Calculation of the jihyu 25. Method on the calculation of the chuanwei
(riyu), difference between the daily motion of (quanwei) or panwei (banwei) of
the moon and the sun the ahsiu (axiu) and the moon (sum of
the diameters of the earths shadow and of the
14. Chapter on the Calculation of the hsio-ko
moon
(xiaoke), nakatra-kla in Sanskrit: a time
interval since moons entrance into the current 26. Method on the calculation of the Duration of
nakatra to its present position at midnight a (lunar) Eclipse
15. Chapter on the Calculation of the hsiutuan 27. Method on the calculation of the yueh-kuei
(suduan), nakatra-cutting i.e. time when (yuegui), moons disc i.e. magnitude of
moon enters the nakatra, nakatra-ccheda in a lunar eclipse
Sanskrit
28. Method on the calculation of the shihshen
16. Chapter on the Calculation of the chiehko (shishen), middle of eclipses i.e. vimarda
(jieke), time of joint i.e. time interval between in Sanskrit
syzygy and midnight before and after,
parvakla in Sanskrit 29. Method on the calculation of the shihhsiang
(shixing), direction of the obscuration
17. Chapter on the Calculation of the chiehtuan
(jieduan), joint cutting, parva-ccheda in 30. Method on the calculation of the jih-liang
Sanskrit (jiliang), apparent diameter of the sun
 EARLY EIGHTH CENTURY CHINESE COMPILATION BY GAUTAMA SIDDHA 223

31. Method on the calculation of the Solar Eclipses An analogous phenomenon was observed
when Nagarjunas ophthalmic works were written
32. Method on the calculation of the jih-
in Chinese between ninth and twelfth century AD.
shangsussu (jishangxusi)
Although these works are based on
33. Method on the calculation of the chiehtuan- Surutasamhit and Atghdaya, they
cho (jieduanke) , the ecliptic point on essentially depict an integration of ancient Indian
the eastern horizon at the time of a solar and Chinese ophthalmology.22
eclipse, parvaklalagna in Sanskrit
Following factors must have made the
34. Method on the calculating the jih-chienliang- writing of KY-104 tricky.
ming (jijianliangming)
1. Different methods for the division of circle into
35. Method on the calculation of houming degrees
(houming)
2. New concepts introduced e.g. trigonometric
36. Method on the calculation of the jih-chienliang concepts and the sexagesimal system for
(jijianliang), moons parallax in division of degrees, i.e. a degree is divided
latitude into 60 minutes
37. Calculation of a solar eclipse 3. Dissimilar epochs used in Chinese and Indian
calculations23
7. CONTRIBUTION OF GAUTAMA SIDDHA
4. Sanskrit terminology unknown to the Chinese
TO CHINESE ASTRONOMY
and its forever changing Chinese parallels as
Gautama Siddha must have faced seen in section 4.
enormous difficulties when he compiled KYZJ
5. Changing the standard latitudes to those of the
and particularly when he wrote the chapter on
Chinese capital Chang an for further
Jiuzhili. It was not an easy or straightforward task
calculations (see sub-section 11)24
to write this chapter for several reasons. For that
matter, the task of translating Buddhist works in 6. Theoretical considerations behind the
general into Chinese must have been challenging construction of these algorithms were difficult
in itself. It either involved word to word to comprehend for the Chinese since they
translations, or in the case of scientific texts when knew neither language nor tradition,
basic concepts were unfamiliar to the Chinese, the All this must have made writing of KY-
author either explained or simplified them. While 104 very complex. Yet for the fact that predictions
dealing with topics like astronomy and medicine, made on the basis of actual observations as done
the writer who would be a subject expert as well in the Chinese system were found to be more
as linguist just as Gautama Siddha was, essentially accurate than those using Indian methods, the
wrote a new book altogether. The outcome foreign system was ignored; irrespective of the
typically would be a simplified version of original fact that they were based on genuine scientific
Indian work and an integration of two systems to theory. A paragraph from the New history of Tang
some extent. dynasty quoted by Cullen (1982) makes the whole
22
Deshpande Vijaya Jayant with Fan Ka Wai (2012),
Also see Deshpande Vijaya Jayant (1999), (2000)
23
- first day of the second month in the second year of Hsienching reign period, March 20th of 657AD, Julian calendar) and
Indian- March 20/21, 505 A.D. or Saka 427/428)
24
Yabuuti, K.(1979) p25
224 INDIAN JOURNAL OF HISTORY OF SCIENCE

scenario apparent.25 Leaving aside the veracity of graphical representation, and parallax
their judgment we surmise that Jiu zhi li was computations for solar eclipses were all recorded
officially judged to be less precise and ignored. in this book.28 Yano further quotes Yabuuti Kiyosi,
Importance of the Indian system was Such theoretical methods are far more advanced
acknowledged by certain Arab travelers in Tang compared with the calendars in the Tang dynasty
China. Needham writes, Contemporaries such as that used so called experimental methods, in other
Sulaimn al - Tjir recorded the impression that words, methods of induction exclusively from the
Indian astronomy was more advanced than the ancient records.29
Chinese. Sulaimn al - Tjir states, Physic and Li Hui summarized the contribution made
Philosophy are cultivated among the Indians, and by Siddhtic astronomy in following words,
the Chinese have some skill in medicine, hot irons
or cauteries, they also have some smattering of In terms of astronomical calculation,
astronomy; but therein the Indians surpass the Jiuzhi Calendar, at least, introduces six western
Chinese.26 (Indian) astronomical elements to China:

It was Yabuuti who recognized the true 1. 360circumference division

contribution of ancient Indian astronomy. Yano, 2. Counting method for 60 binary
Michio states, Indian astronomy represented by
3. Ecliptic coordinates system
Jiuzhili was not highly regarded in China. Chinese
records often refer to the Jiuzhili as a crude 4. Definition of distinctions between perigee and
calendar in comparison with Chinese calendars.27 winter as well as between apogee and summer
Yabuuti, however, correctly pointed out solstice
importance of the very theoretical nature of Indian
5. Method for calculating the visible diameter
astronomy even though it was not very accurate
change of the Moon
from the practical point of view. For instance the
decimal notation system with the symbol of zero, 6. Sine function calculation method and sine-
the sine function, spherical astronomy with function table.30

25
Cullen (1982), p 30-33)
The author quotes from Xin tang shu (New history of Tang dynasty of 1060 AD
In the twenty-first year (of Kaiyuan era i.e. 733 AD) he (Qutan zhuan) memorialized jointly with Chen Hsuan-ching (Chen
Xuan-jing) The Ta Yen li (Da yan li) plagiarizes the Chiu Chih li (Jiu zhi li), and its methods are incomplete. A similar
condemnation came from Nan-Kung Yueh (Nan-gong Yue), the Right Guardian of the Heir Apparent. The Imperial Clerk Li Lin
and the Astronomer Royal Huan Chih-Kuei (Huan Zhigui) were then instructed to check the register of observations of the
Imperial Observatory. It was found that the Ta yen li (Da yan li) was correct seven or eight times out of ten, the Lin te li (Lin de
li) three or four times, and the Chiu Chih li (Jiu zhi li) once or twice only. Thus Nan-Kung Yueh (Nan-gong Yue) and others were
seen to be in the wrong, and the dispute was settled. Hsin Tang Shu (Xin tang shu)(28A, 587). Again, a brief note on the Chiu
Chih li (Jiu zhi li) follows the full description of the Ta yen li (Da yan li). It concludes, The methods of Chiu Chih li (Jiu zhi li)
were overelaborate, and although they were sometimes fortuitously correct they could not be taken as standard. The terms and
quantities employed were strange, and at first no one could make sense of them. Chen Hsuan-ching (Chen Xuan-jing) and
others took advantage of this to deceive their contemporaries, saying that I-hsing (Yi xing) has plagiarized (the Jiu Zhi li) and
that the methods (of Da yan li). This was nonsense. Hsin Tang Shu (Xin tang shu) 28B:692).
26
Needham Joseph, Wang Ling. (1959), p 203
Also see, Al-Srf, Ab Zayd $asan ibn Yazd, (1733)
27
See FN 24 above.
28
Yano Michio (2001)
29
Yabuuti Kiyosi. (1944)
 EARLY EIGHTH CENTURY CHINESE COMPILATION BY GAUTAMA SIDDHA 225

7.1 Planetary Motion Cullen, Christopher. An eighth century Chinese table of

tangents, Chinese Science, 5:1, 1982.
The translated contents of Jiuzhi Calendar
Deshpande, Vijaya Jayant. Indian influences on early
include the motions of the Sun and the Moon and Chinese ophthalmology: Glaucoma as a case study, in
calculations of magnitude and durations of lunar Bulletin of the School of Oriental and African Studies,
and solar eclipses, but are not related to planetary 62/2, June 1999, pp.306-322.
motion.31 Again, in an earlier quote an eight Deshpande, Vijaya Jayant. Ophthalmic Surgery - A chapter
century author states that positions of five planets in the history of Sino-Indian medical contacts - in
can be determined using Indian methods. These Bulletin of the School of Oriental and African Studies,
methods are not found in KY-104. To investigate 63/3 (October 2000):370-88.
whether they were part of earlier calendars Deshpande, Vijaya Jayant with Fan Ka Wai. Restoring the
Jingweili and Guangzaili will again make an Dragons vision, Nagarjuna and Medieval Chinese
Ophthalmology, published by Chinese Civilization
interesting and worthwhile study. Centre, City University of Hong Kong, Hong Kong,
2012.
8. CONCLUDING REMARKS
Duan, Yao-Yong and Li, Wen-Lin. The Influence of Indian
Gautama Siddha was a scholar, a linguist Trigonometry on Chinese Calendar-Calculations in the
Tang Dynasty, B.S. Yadav and M. Mohan (eds.),
and a historian. He stands high in the list of ancient Ancient Indian Leaps into Mathematics, 45, DOI
Indian scholars who carried out the task of 10.1007/978-0-8176-4695-0 3, _c Springer
introducing ancient Indian scientific thought to the Science+Business Media, LLC 2011, pp 45-54.
new land, thus enabling it to take root there and Encyclopedia of India-China cultural contacts, Ma Xposure
develop thereafter. It was not possible to translate Media Group, New Delhi, 2014, part 1&2
Indian texts verbatim. Therefore the scholars Ho Pengyoke. Li, Qi and Shu: An Introduction to Science
studied corresponding Chinese systems and and Civilization in China. Hong Kong University
modified Indian material so as to make it digestible Press, Hong Kong, 1985.
to the Chinese palate. Gautama was instrumental Jean-Claude Martzloff- Le Calendrier Chinois. Webpage
in the comparative study of two systems and their http://chinesereferenceshelf.brillonline.com/grand-
integration to some extent. ricci/files/calendrier-chinoi.pdf;jsessionid=
2357FC3C6BC11256CD5AE2895F2F9441
ACKNOWLEDGEMENTS Kai yuan zhan jing by Gautama Siddha
, ,: Jiuzhou book publishing
Thanks are due to the referees whose house. Beijing, 2012.
valuable suggestions led to an improved version
Lu hui. Jiuzhi Calendar, Encyclopedia of India-China
of this paper. cultural contacts, MaXposure Media Group, New
Delhi, 2014, part 1, p 82.
BIBLIOGRAPHY Li Hui and Niu Weixing. From Rhu and Ketu to Four
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30
Li Hui and Niu Weixing (2014) p 96
Also see, Duan Yao-Yong and Li Wen-Lin (2011) p 45-54
31
Lu hui (2014) part 1, p 82
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