《御制历象考成》的交食理论
The Theory of Eclipse in
Yuzhi Lixiang Kaocheng (1725)
Dr. Lu Dalong
Institute for the History of Natural Science (IHNS),
Chinese Academy of Sciences (CAS)
28 June 2010, Beijing for 12th ICHSC
Paper for the 12th International Conference on the History of
Science in China (12th ICHSC)
26-30 June 2010, Beijing, China
The author gratefully acknowledges the supports of:
National Science Foundation of China (NSFC),
K. C. Wong Education Foundation, CAS,
The China-Portugal Center for the History of Sciences.
Part 1 The Brief History of Chinese Calendars in Qing Dynasty
(1644-1911)
Part 2 The Theory of Eclipse in Yuzhi Lixiang Kaocheng
(YZLXKC)
Part 3 Discussion and Conclusions Related to YZLXKC
Part 1 The Brief History of Chinese Calendars
In the early period of the Qing Dynasty (1644-1911), The
four calendars had been put into use.
Xiyang Xinfa Lishu (Treatise on Mathematics (Astronomy and
Calendrical Science) according to the Western method, this
encyclopaedia was issued in the Ming (1635) as Chongzhen
reign-period Treatise on (Astronomy and) Calendrical
Science, first form of the Jesuit astronomical encyclopaedia,
reissued as the former by Johann Adam Schall von Bell
(1591-1666) in 1645, 1628-1827, and the year of 1628 was
selected as the epoch of the Calendar).
Part
1 The Brief History of Chinese Calendars
一、清代历法早期发展概略
Kangxi Yongnian Lifa (The Eternal Calendar of Kangxi Emperor,
compiled by Ferdinand Verbiest (1623-1688) in 1669, 18283827).
Yuzhi Lixiang Kaocheng (Complete Studies on Astronomy and
Calendar, 1725, 1684-1983).
Yuzhi Lixiang Kaocheng Houbian (The Supplement to Complete
Studies on Astronomy and Calendar, 1742, 1723-2022).
Part 1 The Brief History of Chinese Calendars
1、《西洋新法历书》，传教士汤若望（Johann Adam Schall
von Bell，1591—1666）根据明末《崇祯历书》改编，1645
年行用，200年（1628—1827）闰年特点。
2、《康熙永年历法》，传教士南怀仁（Ferdinand Verbiest，
1623—1688）主持编修，1669年行用，2000年（1828—
3827）交食表。
3、《御制历象考成》，传教士与中国宫廷天文学家主持编修，
1725年行用， 300年（1684—1983）闰年特点。
4、《御制历象考成后编》，传教士戴进贤（Ignace Kögler，
1680—1746）、徐懋德（André Pereira，1690—1743）等
与中国宫廷天文学家主持编修，1743年行用， 300年
（1723—2022）闰年特点。
Part 1 The Brief History of Chinese Calendars
The Characters of Leap Years in XYXFLS for 200 years (16281827), in YZLXKC for 300 years (1684-1983) , and in Kangxi
Yongnian Lifa for 2000 years (1828-3827)
1644* 1677 1710 1743 1776 1809 1842 1875 1908 1941 1974
1648 1681
14 47 80 13 46 79 12 45 78
1652 1685
18 51 84 17 50 83 16 49 822)
1656 1689
22 55 88 21 54 87 20 53
86
1660 1693
26 59 92 251) 58 91 24 57 90
1631 1664 1697
30 63 96 293) 62 95 1929*1962*1995*
1635 1668 1701
34 67 1801*1834*1867*1900* 33 66
99
1639 1673* 1706* 1739* 1772* 05 38 71 04 37 70 2003
1) For XYXFLS 200 years from 1628 to 1827
2) In red color for YZLXKC 300 years from 1684 to 1983
3)For KXYNLF 2000 years, based on the 4 volumes of the Ecliptic Tables
Part 1 The Brief History of Chinese Calendars
2007 2040 2073 2106 2139 2172 2205 2238 2271 2304 2337 2370 2403 2436
11 44 77 10 43
76 09 42 75 08 41 74 07 2441*
15 48 81 14 47
80 13 46 79 2313*2346*2379*2412* 45
19 52 85 18 51 2185*2218*2251*2284* 17 50
83 16 49
23 2057*2090*2123*2156* 89 22 55 88 21 54
87 20 53
2028* 61 94 27 60
93 26 59 92 25 58
91 24 57
32 65 98 31 64
97 30 63 96 29 62
95 28 61
36 69 2102 35 68 2201 34 67 2300 33 66
99 32 65
2469 2502 2535 2569*2602*2635*2668*2701 2734 2767 2800 2833 2866 2899
2474*2507*2540* 73 06 39 72 05 38 71 04 37 70 2903
78 11
44 77 10 43 76 09 42 75 08 41 74 07
82 15
48 81 14 47 80 13 46 79 12 45 78 11
86 19
52 85 18 51 84 17 50 83 16 49 82 15
90 23
56 89 22 55 88 21 54 87 20 53 86 19
94 27
60 93 26 59 92 25 58 91 2825*2858*2891*2924*
98 31
64 97 30 63 2697*2730*2763*2769* 29 62 95 28
Part 1 The Brief History of Chinese Calendars
2932 2965 2998 3031 3064 3097 3130 3163 3196 3229 3262 3295 3328 3361
36 69 3002 35 68 3101 34
67 3200 33 66 99 32 65
40 73 06 39 72
05 38
71 04 37 70 3303 36 69
44 77 10 43 76
09 42
75 08 41 3275*3308*3341*3374*
48 81 14 47 3081*3114*3147* 3180*3213*3246* 79 12 45 78
2953*2986*3019* 3052* 85
18 51
84 17
50 83 16 49 82
57 90 23
56 89
22 55
88 21
54 87 20 53 86
61 94 27
60 93
26 59
92 25
58 91 24 57 90
3394 3427 3460 3493 3526 3559 3592 3625 3659*3692*3725*3758*3791 3824
98 31 64
97 3531*3564*3597*3630* 63 96 29 62 95
3403*3436*3469* 3502* 35 68 3601 34 67 3700 33 66 99
07 40 73
06 39 72 05 38 71 04 37 70 3803
11 44 77
10 43 76 09 42 75 08 41 74 07
15 48 81
14 47 80 13 46 79 12 45 78 11
18 52 85
18 51 84 17 50 83 16 49 82 15
23 56 89
20 55 88 21 54 87 20 53 3787*3820*
Part 1 The Brief History of Chinese Calendars
The historical vicissitudes of the Chinese calendar will, indeed,
remain a matter of some difficulty, as the definitive monograph on
this subject has not yet been written, either in Chinese or a Western
language . Fortunately, however, it is not of primary scientific
importance. The various shifts to which the calendar experts were
put by their inaccurate knowledge of precession, planetary cycles,
etc., need not delay us too much. What seem really interesting in Chinese
astronomy are such questions as the ancient and medieval cosmic theories, the
mapping of the heavens and the coordinates used, the understanding of the great
circles of the celestial sphere, the use of circumpolar stars as indicators of the
meridian passages of invisible equatorial constellations, the study of eclipses, the
gradual development of astronomical instruments (which by the +13th century
had attained a level much higher than that of Europe), and the through recording
of observations of important celestial phenomena.
Joseph Needham, Vol.3 of Science and Civilisation in China, Cambridge: at the
University Press, 1959, p. 173.
Part 1 The Brief History of Chinese Calendars
Seven branches of the research field in the History of Chinese
Astronomy:
1. the ancient and medieval cosmic theories;
2. the mapping of the heavens and the coordinates used;
3. the understanding of the great circles of the celestial sphere;
4. the use of circumpolar stars as indicators of the meridian
passages of invisible equatorial constellations;
5. the study of eclipses,
6. The gradual development of astronomical instruments (which by
the +13th century had attained a level much higher than that of
Europe); and
7. the through recording of observations of important celestial
phenomena.
Part 1 The Brief History of Chinese Calendars
5. the study of eclipses
1) The Theory of the Solar Motion;
2) The Theory of the Lunar Motion;
3) The Calculations of the Solar and Lunar Eclipses
three divisions:
the calculations of the Solar and Lunar Eclipses - Prediction
the observation of the Solar and Lunar Eclipsed - Records
the calculations by modern astronomical theory - Accuracy
Part 2 The Theory of Eclipse in YZLXKC
The calculations of the Eclipses - Prediction
Yuzhi Lixiang Kaocheng was composed by three parts:
1. Shang Bian (16 volumes) – LiLi (The theories of calendar)
2. Xia Bian (10 volumes) – LiFa (The calendrical sciences)
3. Biao (16volumes, Astronomical tables)
Part 2 The Theory of Eclipse in YZLXKC
The Theory of the solar motion in Yuzhi Lixiang Kaocheng was
derived from the model of eccentrical circle, and illustrated in
the model of epicycle- oblique circle (Benlun- Junlun). The
diameters of the epicycle and oblique circle are supposed to be
268,812 and 89,604 respectively when the mean distance
between the Earth and the Moon was supposed as 10,000,000.
The annual equation of the mean motion of the Sun depends on the
eccentricity of the Earth’s orbit round the Sun, which is 179208
of such parts, as that the Earth’s mean distance from the Sun
shall be 10,000,000. The greatest of the Equation of the Sun’s
center is 2º03'11".
the equation of the center = arctg [0.0358416 sinα÷(1－
0.0179208 cosα)]
Isaac Newton, Principia (1713, the second edition): 1º56' 20".
Yuzhi Lixiang Kaocheng Houbian (1742): 1º56 '13".
Part 2 The Theory of Eclipse in YZLXKC
御制历象考成 上编，卷四·日躔历理：求两心差及最高：
新法历书用春分、秋分、立夏三节气相距日时，推得两心差
为三五八四一六，最高在夏至后五度三十分，然而未详何
年月日。
永年表载康熙丁酉年最卑在冬至后七度四十三分四十九秒。
今以丁酉年实测节气时刻，依法推算，得两心差三五八九七
七，最卑在冬至后八度三十八分二十五秒五十五微，皆与
原数不合。
今以丁酉年实测日躔度分，求得最高过夏至、最卑过冬至各
七度四十四分三十六秒四十八微。又自太阳过最高之日分，
加周岁四分之一，求其时刻之实行，不及中距二度零三分
零九秒四十微，检其正切得三五八四一六，皆与历书所载
相合。 ( tg 2º03'09"40'" = 0.0358415059)
Part 2 The Theory of Eclipse in YZLXKC
The theory of the lunar motion in Yuzhi Lixiang Kaocheng was
derived from the model of epicycle- oblique circle- subepicycle- sub-oblique circles (Benlun- Junlun- Cilun- Cijunlun).
The diameters of the epicycle, oblique circle, sub-epicycle and
sub-oblique circle were 1,160,000, 580,000, 434,000 and
235,000 respectively when the mean distance between the
Earth and the Moon was supposed as 10,000,000.
R1 = 10,000,000, R2 = 290,000, R3 = 217,000, R4 = 117,500.
M‘ (初均数) = arctg [3R2 sinM ÷ (R1 + R2 cosM)]; M (自行)
a = √( 3R2 sinM )2 + (R1 + R2 cosM )2
b = 2R3 sin (S – A ) ; S – A (月距日)
c = √a2 + b2 – 2abcos [90 + (S – A ) – (M – M' )]
Part 2 The Theory of Eclipse in YZLXKC
M" (二均数) = arcsin (b sinM ÷ c)
d = √c2 + R4 2 – 2 c R4 cos [360 – 2 (S – A )]
M'"(三均数) = arcsin (R4 sin [360 – 2 (S – A )] ÷ d)
Mend (实行) = M – M' – M" – M'"
M the distance of the center of oblique circle from the apogee
Lunar equation of the center (M' + M" + M'"):7º33'03"/4º58'28".
The Moon’s greatest distance from the Earth, the parallaxes of the
Moon and the apparent diameters of the Moon given by
Claudius Ptolemaeus (c.90-168) Nicolaus Copernicus (14731543), Tycho Brahe (1546-1601), Yuzhi Lixiang Kaocheng and
Johannes Kepler (1571-1630) were tabulated.
Part 2 The Theory of Eclipse in YZLXKC
Ptolemaeus/ Copernicus/ Tycho/ Kaocheng/ Kepler
(Greatest distance) Pto/ Cop/ Tyc/ Kaocheng (parallaxes) Pto/ Cop/ Tyc/ Kaocheng
(apparent diameters) Pto/ Cop/ Tyc/ Kaocheng/ Kepler
The greatest [altitudinal] elongation of the half moon
64P09′/ 68P21′/ 60P36′/ 61.98P
0º54′/ 50′19″/ 57′44″/ 55′27″
0º29′/ 27′40″/
/ (29′49″) / 29′30″
The greatest distance from the Earth at new moon and full moon
53P50′/ 65P30′/ 58P08′/ 58.16P
1º58′/ 52′24″/ 59′09″/ (59′06″)
32′08″/ 30′10″/ 30′30″/ 31′47″/ 31′12″
The distance of the center of the epicycle from the Earth
48P51′/ 60P19′/ 56P50′/ 56.72P
1º01′/ 58′25″/ 60′51″/ (60′36″)
38′42″/ 32′44″/ 32′34″/ (32′35″)/
The least distance from the Earth at new moon and full moon
43P51′/ 55P08′/ 54P50′/ 54.84P
1º04′/ 62′21″/ 62′39″/ (62′41″)
38′08″/ 35′40″/ 34′40″/ 33′42″/ 32′
The Least [altitudinal] elongation of the half moon
33P33′/ 52P17′/ 52P14′/ 53.71P 1º24′/ 65′44″/ 65′36″/ 64′51″
55′ / 36′08″/
/ (34′52″)/ 34′18″
The difference between the greatest and the least elongations of the half moon
30P37′/ 16P/
8P/
9P
0º30′/ 12′25″/ 8′53″/ 9′24″
Part 2 The Theory of Eclipse in YZLXKC
The Parallaxes Tables (Taiyin Dibanjingcha Biao) were composed
by 10 tables, which are related to the distances of 53P, 54P, 55P,
56P, 57P, 58P, 59P, 60P, 61P, 62P. The parallaxes of the moon in
Yuzhi Lixiang Kaocheng, which were different from the values
given by the four Western astronomers, are rather precise.
Had been compared with the theory of the lunar motion in Xiyang
Xifa Lishu, the theory in Yuzhi Lixiang Kaocheng, compiled by
Jesuits, Court Astronomers and stimulated by
nongovernmental astronomers, has a relative completeness,
though the modern theory of the lunar motion had been put
forward in Isaac Newton’s 1702 Theory of the Moon’s Motion
and the second edition of Principia (1713).
Part 2 The Theory of Elipse in YZLXKC
御制历象考成 上编，卷八·交食历理三，专论日食：
新法历书因日食近两交，黄白二道相距不远，故止用黄道为省
算。究之，必用白道，方为密合。
太阳实行在春分后一十五度为三宫十五度，食甚用时为申正初
刻，求黄平象限诸数和白平象限诸数。
太阳黄道ecliptic longitude l0 = 105º ； 黄赤交角obliquity of the
eclipticε= 23º29'30"；黄赤距度ecliptic latitudeδ；北极出地
astronomical latitude of Beijing h = 39º55'。
本时正午距春分（黄道经度）75º05'10".34142
75º05'10"
（日躔黄赤升度表 leaves 35-38, vol.1 of the Biao；
The headlines of the ecliptic longitude and right ascension
should be exchanged）
日躔黄道赤经交角
83º37'02".497728
83º37'04"
（黄道赤经交角表 leaf 40, vol.1 of the Biao）
Part 2 The Theory of Eclipse in YZLXKC
本时正午黄赤相距纬度
22º39'19".477512
22º39'19"
（黄赤距度表 leaves 31-33, vol.1 of the Biao）
黄平象限距地平之度
72º50'56".093604
72º50'56"
黄平象限距正午东之度
1º58'41".659356
1º58'42"
太阳实行黄道经度
167º03'52".13664
167º03'52"
太阳距黄平象限西之度之余 27º56'08".000124
27º56'08"
（黄平象限表 vol.6 and vol.7 of the Biao, total 196 leaves）
黄道高弧交角
19º15'19".479276
（黄道高弧交角表 leaves 3-23, vol.8 of the Biao）
太阳高弧
26º35'33".703152
（太阳高弧表 leaves 25-45, vol.8 of the Biao）
19º15'19"
26º35'30"
Part 2 The Theory of Eclipse in YZLXKC
朔望时黄白大距四度五十八分三十秒
The minimum of the lunar equation of the center
白平象限距地平之高
77º28'19".290144
太阴距白平象限西之度
62º34'27".99354
白道高弧交角
14º03'17".383536
太阴高弧
26º43'11".558136
4º58'30"
77º28'19"
62º34'28"
14º03'16"
16º43'12“
东西差 = arctg ( cos 白道高弧交角 × tg 高下差 )
南北差 = arcsin ( sin 白道高弧交角 × sin 高下差 )
（东西南北差表 leaves 47-57, vol.8 of the Biao）
纬差角 = arcsin ( sin 距纬 ÷ sin 併经 )
（纬差角表 leaves 59-67, vol.8 of the Biao; The end of vol.8）
Part 3 Discussion and Conclusions Related to YZLXKC
The Compilation of YZLXKC
《御制历象考成》原名《钦若历书》上编16卷、下编10卷、表
16卷。据陶湘先生考言，初为杨文言纂修于诚王府，书未
成而文言卒。允祉、允禄等人续加编纂。康熙六十一年刊
刻告成，有康熙年铜活字印本行世。是年十月前后，何国
宗、梅珏成、王蓝生等奏请颁发《律历渊源》御制序文时，
仍称为《钦若历书》。然而，在雍正二年刊刻《御制律历
渊源》全书时，便将该书的正文卷端及书口处所题《钦若
历书》的书名，皆挖改为“历象考成”四字。而其它行款
字数等项内容未变。此书共有上下二编。上编16卷，题曰
“揆天察纪”，论述了天体运行轨迹的原理；下编10卷，
题曰“明时正度”，介绍观测天体的计算方法；末附运算
表16卷。
Part 3 Discussion and Conclusions Related to YZLXKC
该书是在明末徐光启等人所编《崇祯历书》（亦名《新法历
书》）的基础上加以修订而成的。整体上虽采用了第谷体
系理论及其数据，但在编纂和精确度上，却较《新法历书》
高。在“推阐微茫，穷究正变”上，亦是《新法历书》所
不能及的。故而《四库全书总目提要》高度评价，说该书
“集中西之大不同，建天地而不悖，精微广大，殊非管蠡
之见所能测”。这部书实系通过系统整理中西古典天文学
的理论，并经具体实测而修正了黄赤交角等错误数据，消
除了原图表诸多不合之舛误，成为一部代表当时天文学最
高水平的科学著作。
齐秀梅、杨玉良等著，《清宫藏书》，紫禁城出版社，2005年
4月第1版，第185—186页。
Part 3 Discussion and Conclusions Related to YZLXKC
Had based on the volume 24, 25 and 26, three volumes of the Xinfa
Suanshu, the paper reveals the method of the intercalary year
(see Table 1), outlines the calculating formula for the Solar
Equation and explains the secular variation of the obliquity of
the ecliptic in Xinfa Suanshu.
Part 3 Discussion and Conclusions Related to YZLXKC
In Xinfa Suanshu, the concept of the Jiajiancha, one of the basic
concepts in traditional Chinese astronomy, is equivalent to the
concept of the solar equation in modern western astronomy,
has the calculating formula for itself:
Jiajiancha = arcsin (e SinM)
+ arctg{e SinM ÷ [Cos(arcsin (e SinM)) – 2e CosM]}
Part 3 Discussion and Conclusions Related to YZLXKC
The model of the solar motion in Xinfa Suanshu is the equidistantly
eccentric orbit, of which the eccentricity e is 0.01792, Yinshu M
is the arc between the apogee and the Sun, and the maxium of
the Jiajiancha is 2º03' 12", which is different from 2º03' 15" in
Tychonis Brahe Astronomiae Instauratae Progymnasmata
(Bragae Bohemiae, M. DC. II., pp. 60-61).
Part 3 Discussion and Conclusions Related to YZLXKC
The secular variation of the obliquity of the ecliptic was distinctly
expressed in Xinfa Suanshu, of which the retarding rate is
45˝.454545 per 100 years, being slightly smaller than the
numerical value 46˝. The secular periodicity of the obliquity of
the ecliptic of Nicolaus Copernicus (1473-1543) and that the
corresponding values of Profatius (c.1236-1305, Ibn Tibbon,
Jacob ben Machir) is 23º32', of George von Peurbach (14231461) is 23º28', of N. Copernicus is 23º28' 24" and of T. Brahe
(1546-1610) is 23º31'30" had been involved, Xinfa Suanshu did
not mentioned the reasons for its mention of the variation,
though its value for the obliquity of the ecliptic is 23º31'30 ".
Part 3 Discussion and Conclusions Related to YZLXKC
总之，《历象考成》在天文体系上仍沿用第谷的体系，只是反
复进行观测，提高了精度，并改进了一些天文数据，使得
日月食的预报更为精确。和《西洋新法历书》相比，《历
象考成》在图和表以及文字方面配合得比较好，逻辑比较
合理。从内容上看，《西洋新法历书》、《灵台仪象志》、
《康熙永年历法》等清初天文历算著作是《历象考成》的
必要基础。由于《历象考成》在理论上没有多大改进，因
此在日、月食的预报上，误差仍然不小。
陈美东著，《中国科学技术史·天文学卷》，科学出版社，
2003年1月第一版，第669—670页。
桥本敬造，“《历象考成》の成立——清代初期の天文算学”，
载薮内清、吉田光邦编，《明清时代の科学技术史》，京
都大学人文科学研究所，1970年。
Part 3 Discussion and Conclusions Related to YZLXKC
1、《西洋新法历书》、《康熙永年历法》和《御制历象考成》
闰年特点存在一致性。
2、 依据《钦定四库全书会要·御制历象考成》（简称《考
成》）上编卷五“月离历理”，对照《考成》表卷二“月
离表一”、表卷三“月离表二”、表卷四“月离表三”，
复原“二三均”完整的推算公式。
3、《钦定四库全书·新法算书》（简称《算书》）月球运动
理论中计算“第一均数”的模型是“偏心圆”，关于“二
均”、“三均”的模型“未加介绍”（江晓原、纽卫星著，
《天文西学东渐集》，上海书店出版社，2001年，第279
页）； 《考成》月球运动理论依据的则是“本轮—均
轮—次轮—次均轮”模型；两种模型所获得的“太阴自行
加减”最大值为4º58'27"（《算书》卷三十二·月离表卷二
“自行加减表”，叶二；788：577）、“初均数”最大值
是4º58'28"（《考成》表卷二“太阴初均表”，叶二十三；
265：406）。
Part 3 Discussion and Conclusions Related to YZLXKC
值得注意的是，两者列表给出的“二三均”最大值分别为
2º48'（《算书》卷三十五·月离表卷四“太阴二三均总数加
减表上”，叶三十一；788：622—623）和2º48'16"（《考
成》表卷四之二“二三均数表下之二”，叶二十；265：
500）
4、应用“二三均”的8个推算公式，不仅可以得到《考成》的
“二三均数表”（《考成》表卷三、卷四；265：419—
523）、而且在“分”上取值得到《算书》“二三均总数加
减表”（《算书》卷三十四、卷三十五；788：590—632 。
5、根据“月距诸率为地半径”、“地半径视差”和“月视径”
数据，可以认定，《御制历象考成》所取的地球直径与月
球直径之比约为3.72，不同于哥白尼的3.5，目前测定值为
3.66528229（= 6371.004km ×2 ÷3476.4km）。
6、《考成》交食理论基础是地平坐标系和黄白交角；与其相
关的“表”卷六、卷七和卷八的几何计算公式得以复原。
Part 3 Discussion and Conclusions Related to YZLXKC
Conclusions:
1. The characters of leap years in Xiyang Xinfa Lishu (1645),
Kangxi Yongnian Lifa (1669) and Yuzhi Lixiang Kaocheng
(1725) had a common continuity.
2. The theory of the lunar motion in Yuzhi Lixiang Kaocheng was
based on the model of epicycle- oblique circle- sub-epicyclesub-oblique circles (Benlun- Junlun- Cilun- Cijunlun).
3. The Ersan Junshu Biao in Yuzhi Lixiang Kaocheng, and Ersan
Junshu Zongshu Jiajian Biao in Xiyang Xinfa Lishu as well,
could be derived by the above mentioned model as the result of
the eight calculating formula.
Part 3 Discussion and Conclusions Related to YZLXKC
4. The Moon’s greatest distance from the Earth, the parallaxes of the
Moon and the apparent diameters of the Moon in Yuzhi Lixiang
Kaocheng were different from the values given by Claudius
Ptolemaeus (c.90-168), Nicolaus Copernicus (1473-1543), Tycho
Brahe (1546-1601), and Johannes Kepler (1571-1630).
5. The ratio of the diameter of Earth and the diameter of the Moon in
YZLXKC is 3.72 and 1, which is different from the value of 3.5
and 1 given by Nicolaus Copernicus and appeared in Xiyang
Xinfa Lishu.
6. The modern theory of the lunar motion, put forward in Issac
Newtion’s 1702 Theory of the Moon’s Motion and the second
edition of Principia (1713) was not introduced in YZLXKC,
which was slightly revised and incorporated in Yuzhi Lixiang
Kaocheng Houbian (The Supplement to Complete Studies on
Astronomy and Calendar, 1723-2022).
Part 3 Discussion and Conclusions Related to YZLXKC
7. The theory of eclipse in Yuzhi Lixiang Kaocheng was slightly
different from that in Xiyang Xinfa Lishu (1645) and Kangxi
Yongnian Lifa (1669), and based on the horizontal coordinate
system and the angle of intersection between the Moon’s circle
and the ecliptic.
8. The vol.6, vol.7 and vol.8 of the astronomical tables related to
the eclipsed prediction in Yuzhi Lixiang Kaocheng Houbian
have been interpreted in some geometrical formula.
Thanks for your suggestions and comments!
The author gratefully acknowledges the support of
National Science Foundation of China
K. C. Wong Education Foundation, CAS,
The China-Portugal Center for the History of Sciences (CPCHS)