2 : 133, (Johannes Ke2 [10 pler, ), ] [11 ],, :,, ;, [12 ],, ( Ignatius Koegler, ) ;,,, ;,,,, ( ),,,,, 1 ( ) M v ( = v - M) 2,,, v =

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1 24 2 (2003 ) : China Historical Materials of Science and Technology Vol. 24 No. 2(2003) (, ) :, : 1, 11,,,, :, 10, 4 10, : ; ; : P12092 : A : (2003) [1, ] ( ) ( Isaac Newton, ) [2 9 ] : ; : : (1964 ),,, : ( : ),,,, [ 20 ], 20 30, (N. Grammaticus), [2 5 ]

2 2 : 133, (Johannes Ke2 [10 pler, ), ] [11 ],, :,, ;, [12 ],, ( Ignatius Koegler, ) ;,,, ;,,,, ( ),,,,, 1 ( ) M v ( = v - M) 2,,, v = M +,,,,, ( ),,,,,,, v = M +,,,,,

3 (Seth Ward, ) ( Ismael Boulliau, ) [13 ], 18,, (David Gregory, ) [14 ] (William Whiston, ) [15 ],,, 1 1,, AB PH, O, ADPF, S a, b, e L Q, M = AQL, v = ASL QL R, RL = LS, RS, RQS, : RSO + R tg 2 RQ + QS = RSQ - R RQ - QS tg 2, RSQ + R = AQL = M, RSQ - R = LSQ = v ; RQ = 2 a, QS = 2 e : tg M 2 tg v 2 = a + e (1) a - e, M, v = v - M a e, M, (Paul Neile), [13 ] 178,18,

4 2 : 135, , ,,,, 2, AB P, ADP, S, F AFL, L E A P, L E G GF, V, V, v = VS F, M 1 = A FV : tg A FV tg A FL = tgm 1 tgm = a b (2),, M M 1, M 1 M (1), v = v - M,, , 0. 37, ( ), ( ),, (Cassini) ( [1 ], 2, 22 ), ( ) : [2 a ], [2 e ], [ M ], [ b ], [ a ],,,,,,, [ ] ( [1 ], 4, 7ab ) ( [ 1 ], 1,96a 103b ), ( ) 1, RQ, QS, R, QLS = 2 R = p, :, M, E 0 = M E = M + esin E, E 1 = M + esin E 0, E 2 = M + esin E 1, E 3 = M + esin E 2,, E i - E i , E i,,,, 2 a

5 136 24, : (1) v, RSQ + R = M, RSQ - R = v R ;, RQ, S, RS, R : tg R = QSsin A FL RQ + QScos A FL = esin M a + ecosm (3) ( ) 2, (2) M 1, q = V FL = M 1 - M = p q 3,,,,,, 0. 66, 0. 34,, 3 2,, :,, ; (Jeromia Horrocks, ),, [ 20 ] 81 95,,,

6 2 : 137, ,, : [ ],, [ ],,,,, ( [1 ], 2, 22a ), :,,,, ( ), (,, ),,, ( [1 ], 4, 20ab ) ( [ 1 ], 2, 22a 35b ), 4, ABCD, O, A ECF, a, b, e, D, A ECF G, M = AOG, O OH OG, H AC, I, J I, v = ATI 4, GOT, GO = a ( ), OT = e ), GOT = M = M 2 (, ), (3) :,

7 tg G = esin M 2 a - ecosm 2, G, HOT, OH = a, OT = e, HOT = M 2 + HOG = M 2 + G(, ) (3) : tg HTO = esin ( M 2 + G) a - ecos( M 2 + G), HTO,, (2), : tg HTO tg ITO = a (4) b ITO, v, ( ) : = v - M = ITO - GOT, , ;, , 5. 71,,, ( [1 ], 2, 22b ), (Jacques Cassini, ) 1719 [17 [16 ] ] 5, AWP, C, AQJ P, S, AC = a, CS = e L L A P, Q, A P R ; QC, W, JW CQ, ACJ M ; JC, SG CJ, ST QC, QCR, QSC, (4) QSC, QCR = M - QCJ = M - CJN = M - CJS - SJN, CJS,, SJN,, SJN, : SJN sin SJN = SN SJ = NT - ST a aecosm + e 2 NT - ST = JQ - JW = JCQ - sin JCQ ( JCQ ), : SJN = JCQ - sin JCQ ( ) a aecosm + e 2 JCQ JS QC,,, , ;, , ;, ,

8 2 : ,18 S CQ, J 1726 (J. Hermann) [18, ] 18 [19 ],,,, 0. 17, ( 3),, 1 3, (N. Kollerstrom), ( 2 ) 2, 5, ( [ 20 ], ),, ;, ( [ 20 ],74 ),, ,

9 , ( [ 13 ], 193 ) ; ( , ), (,annual equation),, (, the 7 th Equation), ( ), ( [ 20 ],124 ), 1732 [21 ] [22 ],,, 1 3,,,, :, ;, WENDING( ) J INXIAN( ),,,,,, (A. Gaubil) 1734,,,,,,, 1726 ( ), , (La Hire), [ 30 ], (Joseph2Nicholas Delisle),, ( [20 ], 211 ;[31 ], ), ( ) ( [31 ],268 ),,, ( ),,,, ( ),, Newtonian Astronomy for Chinese Use ( )

10 2 : 141, ( ),,,,, WENDING J INXIAN ( ) ( ), ( ), ( - ),,, [23 (Jean Meeus) VSOP82 ], , 2 (M. Chapront2Touz ) EPL,, 8. 2, 1. 3 [24 ],,, (UT), ,, 8. 31, ; , ; , , ; , ; 2. 70, 0. 75, 6 7 8,, 6

11 ,,, 0. 78, ; , ,,,,,, [23 ] 151 ; [24 ] 12

12 2 : 143, ;, ( [25 ] ),,, 4, (F. R. Stephenson) (L. J. Fatoohi) ] [26, :, , 15, , 6 ;, , 10 20, , :1750 ( ),1745 ( ),, [28, ],,, 1742 ( ),,,,,,, 20 4, 10,, 2, 4 8,,,, ( [13 ] ),

13 144 24,,,,,,,,,1629, (Charles Leadbetter) [29, ] : (Dibner Institute of the History of Science and Technology), (Owen Gingerich) ( George Smith), : [1 ],,. [M]. [ Z]. 7. :, [2 ] Pfister L. Notices Biographiques et Bibliographiques sur les J suites de l Ancienne Mission de Chine, [ M]. San Francisco : Chinese Materials Center [3 ] Dehergne J. R pertoire des J suites de Chine de [M]. Roma :Institutum historicum S. I. ; Paris : Letouzey &An, [4 ]. [A].. [ C].. :, [5 ] : [A].. [ C]. :, [6 ]. [A]. [ Z]. 7. :, [7 ]. [M]. :, [8 ]. [J ].,1997, (4) : [9 ] Lu Dalong. Guimao yuan Calendar ( ) and Isaac Newton s Theory of the Moon s Motion, in Celina A. L rtora Mendoza et al. [A]. The Spread of the Scientific Revolution in the European Periphery, Latin America and Eastern Asia, Pre2 ceedings of the XXth International Congress of History of Science (Li ge, July 1997) [ C]. Volume V. Turnhout, Bel2 gium : Brepolis publishers, [11 ]. [A]. [ C]. 3. :, [12 ] Newton I. The Principia : Mathematical Principles of Natural Philosophy, a New Translation by I. Bernard Cohen and Anne Whitman, Assisted by Julia Budenz ; Preceded by a Guide to Newton s Principia by I. Bernard Cohen[M]. Berkeley : Uni2 versity of California Press, [13 ] Taton R,Wilson C (eds). Planetary Astronomy from the Renaissance to the Rise of Astrophysics, Part A : Tycho Brahe to New2 ton[m]. Cambridge, UK: Cambridge University Press,

14 2 : 145 [14 ] Gregory D. The Elements of Physical and Geometrical Astronomy (an English translation of the Latin version first published in 1702) [M]. vol. 1. London :Three Crowns, [15 ] Whiston W. Astronomical Lectures ( English translation from the Latin version of 1707) [M]. London :J. Senex,W. and J. Os2 bome,and T.Longman, [16 ] Cassini J. M thode de Determiner la Premiere Equation des Plan tes Suivant l Hypothese de Kepler [ A ]. Acad mie Royale des Sciences ( Paris) [M] M moires de l [17 ] Colwell P. Solving Kepler s Equation over Three Centuries[M]. Richmond, Virginia : Willmann2Bell, Inc., [ 18 ] Hermann J. Geminus Modus Dividendi Semicircvlvm in data ratione : Quibus Keplerianum Problema De Inveniendis Planearvm Locis ad datum quodvis tempus Solutum exhibetur [J ]. Commentarii Academiae Scientiarum Imperialis1726,1 : [19 ]. [ M ]. :, [20 ] Kollerstrom N. Newton s forgotten lunar theory : his contribution to the quest for longitude, including the complete text of Isaac Newton s Theory of the moon s motion, 1702[M]. Santa Fe, N. M. : Green Lion Press, [21 ],. [M] a 44b. [22 ] Grammaticus N. Tabulae Lunares ex Theoria et Geometrae Celeberrimi domini Isaaci Newtoni [ M]. Ingolstadt : Typis Viduae Grassianae Typogr. Acad, [23 ] Meeus J. Astronomical Algorithms[M]. Richimond, Virginia :Willmann2Bell, [24 ] Chaprot2Touz M,Chapront J. Lunar Tables and Programs from 4000 B. C. to A. D. 8000[M]. Richimond, Virginia :Will2 mann Bell,1991. [25 ] Nauenberg M. Newton and the Lunar Motion, Essay Review of Newton s forgotten Lunar Theory [J ]. Journal for History of Astronomy, 2001,32 : [26 ] Stephenson F R, Fatoohi L J. Accuracy of Solar Eclipse observations made by Jesuit Astronomers in China [J ]. Journal for the History of Astronomy, 1995,xxvi : [ 27 ] Fatoohi L J,Stephenson F R. Accuracy of Lunar Eclipse Observations Made by Jesuit Astronomers in China[J ]. Journal for the History of Astronomy, 1996, xxvii : [28 ] Shi Yunli. The Eclipse Observations Made by Jesuit Astronomers in China : a Reconsideration[J ]. Journal for the History of Astronomy,2000,xxxi : [29 ] Leadbetter C. Astronomy of the Satellites of the Earth, Jupiter and Saturn : Grounded upon Sir Issac Newton s Theory of the Earth s Satellite[M]. London : printed for J. Wilcox, at the Green2Dragon, in Little2Britain, [30 ] Gaubil G. Correspondance de P kin[m]. Gen ve :Droz, ,246, ,211,213. [31 ] Shaffer S. Halley,Delisle,and the Making of the Comet[A]. In Norman J. W. Thrower (eds). Standing on the Shoulders of Giants a Long View of Newton and Halley[ C]. Berkeley,Los Angles,Oxford :University of California Press,

15 The Calculation of the Equation of Center in the Lixiang Kaocheng Houbian and the Accuracy of the Theory of the Sun and Moon in the Book In Memory of Professor Bo Shuren SHI Yun2li ( Dept. of Scientific History and Archaeometry, University of Science and Technology of China, Hefei , China) Abstract: This paper discusses the Western sources of the methods employed in the Lixiang Kaocheng Houbian (Later Edition of the Established System of Calendrical Astronomy) to resolve the Ke2 pler Equation in calculating the solar and lunar equations of center. Meanwhile, it also analyzes the preci2 sion of these methods and the overall accuracy of the lunisolar theory of the book in positional calculations. The methods, as applied to the equation of center of the sun and the moon respectively, are found to be simplified versions of the procedures of I. Boulliau and J. Cassini. While the former can be correct to within 1 arcsecond in calculating the equation of solar center, the latter displays an error not exceeding 11 arcseconds as used to calculate the equation of lunar center. The Jesuit authors selection of these two methods turns out to be very reasonable with respect to the overall precision level of the lunisolar theory of the book, although it was not the best choice of the time as seen from the present point of view. Since the book appropriated the most important European achievements from the time of Kepler to thet of Newton like the two methods, the positional astronomy of the sun and moon thus witnessed a very remarkable advance2 ment in the Qing dynasty : as compared with the theory of the old Lixiang Kaocheng, the precision of the positional calculation of the sun enhanced more than ten times, whereas the lunar theory became over four times more accurate in the longitudinal calculation and nearly ten times more accurate in the latitudinal calculation, thus laying a sound foundation for improvement in the predictive calculation of solar and lunar eclipses. Key words : Lixiang Kaocheng Houbian, theory of the sun and moon, equation of center, Kepler equation, I. Kggler :

2004 1 / ( ),,,, ;,? ( 311 ),,, 25 9,, 1 2, [8 ] : ( 1637 ),, ( 1636 ), [6 ] 2 ( 8, 1651 ) [9 ],,, 1644 ( 22 ),,, ( ), 4 ( ) 6,,, ( 5 ),, :,,,,,,, ( 1

2004 1 / ( ),,,, ;,? ( 311 ),,, 25 9,, 1 2, [8 ] : ( 1637 ),, ( 1636 ), [6 ] 2 ( 8, 1651 ) [9 ],,, 1644 ( 22 ),,, ( ), 4 ( ) 6,,, ( 5 ),, :,,,,,,, ( 1 ( ) 10 1 JOURNAL OF GUANGXI UNIVERSITY FOR NATIONALITIES Vol 10 No 1 2004 2 ( Natural Science Edition) Feb 2004 ( ) Ξ (, 230026) : 17 18,,,, : ; ; : P1-0931312 : A :1007-0311 (2004) 01-0030 - 09 0 17,,,