1
古先哲王，受命而帝天下者，必先觀象以垂法，治曆以明時，使萬物服其化風，四海同其正朔，然後能允釐下土，欽若上天。 故虞舜之紹唐堯，先齊七政； 武王之得箕子，首敘九疇。 皇極由是而允興，人時以之而不忒。 歷代已降，何莫由斯。
The sage-kings of antiquity who received the Mandate and ruled the world always began by reading the heavens to establish law, and by fixing the calendar to mark the seasons, so that all creation bowed to their civilizing influence and the four seas kept a single calendar—only then could they truly govern the earth below and stand in reverent harmony with Heaven. Thus when Shun succeeded Yao, his first act was to align the seven luminaries; and when King Wu received Jizi, he began by expounding the Nine Categories. The royal norm was thereby truly established, and the seasons of human affairs kept true to it without deviation. Every dynasty since has followed this same path.
2
粵自軒黃，肇正天統，歲躔辛卯，曆法時成。 故黃帝始用《辛卯曆》，顓頊次用《乙卯曆》，虞用《戊午曆》，夏用《丙寅曆》，商用《甲寅曆》，周用《丁巳曆》，魯用《庚子曆》，秦用《乙卯曆》。 漢用《太初曆》、《四分曆》、《三統曆》，凡三本。 魏用《黃初曆》、《景初曆》，凡二本。 晉用《元始曆》、《合元萬分曆》，凡二本。 宋用《大明曆》、《元嘉曆》，凡二本。 齊用《天保曆》、《同章曆》、《正象曆》，凡三本。 後魏用《興和曆》、《正光曆》、《正元曆》，凡三本。 梁用《大同曆》、《乾象曆》、《永昌曆》，凡三本。 後周用《天和曆》、《丙寅曆》、《明元曆》，凡三本。 隋用《甲子曆》、《開皇曆》、《皇極曆》、《大業曆》，凡四本。 唐用《戊寅曆》、《麟德曆》、《神龍曆》、《大衍曆》、《元和觀象曆》、《長慶宣明曆》、《寶應曆》、《正元曆》、《景福崇元曆》，凡九本。
From the age of the Yellow Emperor, the celestial order was first set right; when the year reached xinmao, the calendar was brought to completion. The Yellow Emperor first adopted the Xinmao Calendar; Zhuanxu next the Yimao; the Yu dynasty the Wuwu; Xia the Bingyin; Shang the Jiayin; Zhou the Dingsi; Lu the Gengzi; and Qin the Yimao. Han employed the Taichu, Sifen, and Santong calendars—three in all. Wei used the Huangchu and Jingchu calendars—two in all. Jin used the Yuanshi and Heyuan Wanfen calendars—two in all. Song used the Daming and Yuanjia calendars—two in all. Qi used the Tianbao, Tongzhang, and Zhengxiang calendars—three in all. Northern Wei used the Xinghe, Zhengguang, and Zhengyuan calendars—three in all. Liang used the Datong, Qianxiang, and Yongchang calendars—three in all. Northern Zhou used the Tianhe, Bingyin, and Mingyuan calendars—three in all. Sui used the Jiazi, Kaihuang, Huangji, and Daye calendars—four in all. Tang employed the Wuyin, Linde, Shenlong, Dayan, Yuanhe Guanxiang, Changqing Xuanming, Baoying, Zhengyuan, and Jingfu Chongyuan calendars—nine in all.
3
洎梁氏之應運也，乘唐室陵遲之後，黃巢離亂之餘，眾職未修，三辰孰驗。 故當時歲曆，猶用《宣明》、《崇元》二法，參而成之。
When the Liang came to power, in the wake of Tang's decline and Huang Chao's rebellion, government functions lay in disarray and no one could reliably track the heavens. The court calendar of the day still drew on the Xuanming and Chongyuan systems, blending the two into one.
4
及晉祖肇位，司天監馬重績始造新曆，奉表上之，云：「臣聞為國者，正一氣之元，宣萬邦之命，爰資曆以立章程。 《長慶宣明》，雖氣朔不渝，即星躔罕驗； 《景福崇元》，縱五曆甚正，而年差一日。 今以《宣明》氣朔，《崇元》星緯，二曆相參，方得符合。 自古諸曆，皆以天正十一月為歲首，循太古甲子為上元，積歲彌多，差闊至甚。 臣改法定元，創為新曆一部二十一卷，七章上下經二卷，算草八卷，立成十二卷，取唐天寶十四載乙未，立為近元，以雨水正月朔為歲首。 謹詣閣門上進。」 〈（《玉海》：《調元曆》，蓋仿曹士蒍小曆之舊。 唐建中時，曹士蒍始變古法，以顯慶五年為上元，雨水為歲首。 世謂之小曆。）〉 晉高祖命司天少監趙仁锜、張文皓，秋官正徐皓，天文參謀趙延乂、杜升、杜崇龜等，以新曆與《宣明》、《崇元》考核得失。 俾有司奉而行之，因賜號《調元曆》，仍命翰林學士承旨和凝撰序。
When the Jin founder ascended the throne, Ma Chongji of the Directorate of Astronomy devised a new calendar and presented a memorial, writing: "I have heard that to rule a state is to fix the origin of cosmic breath and proclaim the mandate of all peoples—and for this one must rely on the calendar to set the standards of government. The Changqing Xuanming calendar kept its solar terms and new moons steady, yet its star positions seldom matched observation; while the Jingfu Chongyuan, though its five reckonings were largely sound, drifted a full day in the annual count. Only by taking the solar terms and new moons from Xuanming and the star tracks from Chongyuan, and cross-checking the two, could a satisfactory fit be achieved. Since antiquity every calendar had taken the eleventh month as the year's beginning and traced its origin back to the primordial jiazi year—yet as centuries piled up, the error grew enormous. I have revised the constants and fixed a new origin, composing a calendar in twenty-one scrolls—two of canonical text in upper and lower parts, eight of computational drafts, and twelve of ready tables—taking the yiwei year of Tianbao 14 as the near origin and making the new moon of the first month at Rain Water the start of the year. I respectfully present it at the Gate of the Imperial Secretariat." (Jade Sea: The Tiaoyuan Calendar largely followed the tradition of Cao Shuxun's small calendar. In Tang's Jianzhong era, Cao Shuxun first broke with ancient practice, taking Xianqing 5 as the superior origin and Rain Water as the year's beginning. Contemporaries called this the small calendar.)〉 Jin Gaozu ordered Vice Directors Zhao Renqi and Zhang Wenhao of the Astronomy Bureau, Xu Hao of the Ministry of Rites, and astronomical advisers Zhao Yanyi, Du Sheng, and Du Chonggui to compare the new calendar against Xuanming and Chongyuan and judge its merits. The responsible offices were ordered to adopt and implement it; it was given the name Tiaoyuan Calendar, and Academician Expositor He Ning was commissioned to write its preface.
5
其後數載，法度浸差。 至周顯德二年，世宗以端明殿學士、左散騎常侍王樸明於曆算，乃命樸考而正之。 樸奉詔歲餘，撰成《欽天曆》十五卷，上之。 表云：
Within a few years its constants began to slip. In Zhou Xiande 2, Shizong, finding Wang Pu—Academician of the Duanming Hall and Left Regular Attendant—expert in calendrical science, commissioned him to review and revise the calendar. After more than a year at the task, Pu completed the Qintian Calendar in fifteen scrolls and presented it to the throne. His memorial read:
6
臣聞聖人之作也，在乎知天人之變者也。 人情之動，則可以言知之； 天道之動，則當以數知之。 數之為用也，聖人以之觀天道焉。 歲月日時，由斯而成； 陰陽寒暑，由斯而節； 四方之政，由斯而行。 夫為國家者，履端立極，必體其元； 布政考績，必因其歲； 禮動樂舉，必正其朔； 三農百工，必授其時； 五刑九伐，必順其氣； 庶務有為，必從其日月。 六籍宗之為大典，百王執之為要道。 是以聖人受命，必治曆數。 故得五紀有常度，庶征有常應，正朔行之於天下也。
I have heard that what the sage creates rests on knowing how Heaven and humanity change. The movements of human affairs may be known through language; but the movements of Heaven must be known through number. Number is what the sage uses to read the Way of Heaven. Year, month, day, and hour take their form through it; yin and yang, cold and heat, are ordered by it; and the governance of the four quarters proceeds from it. Whoever rules a state, in inaugurating the year and fixing the cosmic pole, must take its origin as foundation; in promulgating policy and reviewing achievement, must follow its annual cycle; in rites and music, must align the new moon; farmers and artisans must be given their proper seasons; punishments and punitive campaigns must follow its cosmic breath; and every undertaking of state must keep to its sun and moon. The Six Classics enshrine it as the supreme canon; the hundred kings have held it as the essential art of rule. Hence when the sage receives the Mandate, he must set the calendar in order. Only then do the Five Regulators keep their proper measures, the portents answer as they should, and the calendar reign throughout the realm.
7
自唐而下，凡曆數朝，亂日失天，垂將百載，天之曆數，汩陳而已矣。 今陛下順考古道，寅畏上天，咨詢庶官，振舉墜典。 以臣薄遊曲藝，嘗涉舊史，遂降述作之命，俾究迎推之要，雖非能者，敢不奉詔。 乃包萬象以立法，齊七政以立元，測圭箭以候氣，審朓朒以定朔，明九道以步月，校遲疾以推星，考黃道之斜正，辨天勢之升降，而交蝕詳焉。
From Tang onward, dynasty after dynasty let the calendar fall into chaos; for nearly a century Heaven's reckoning was nothing but confusion and decay. Now Your Majesty follows the ancient Way, stands in reverent awe of Heaven, consults his ministers, and revives fallen institutions. Finding in me only a modest acquaintance with these minor arts and some reading in the old histories, Your Majesty has charged me to compose a calendar and master the essentials of astronomical calculation—no master of the craft, yet how could I refuse the edict. I have embraced the myriad phenomena to frame the law, aligned the seven luminaries to fix the origin, measured gnomon and clepsydra to track the seasons, refined waxing and waning to set the new moon, clarified the nine paths to pace the moon, calibrated planetary motion to reckon the stars, examined the obliquity of the ecliptic and the incline of the celestial sphere—and so made eclipses calculable in full detail.
8
夫立天之道，曰陰與陽，陰陽各有數，合則化成矣。 陽之策三十六，陰之策二十四，奇偶相命，兩陽三陰，同得七十二，同則陰陽之數合。 七十二者，化成之數也，化成則謂之五之之數。 五之得期之數，過者謂之氣盈，不及謂之朔虛。 至於應變分用，無所不通，所謂包萬象矣。 故以七十二為經法，經者常也，常用之法也。 法者數之節也，隨法進退，不失舊位，故謂之通法。 以通法進經法，得七千二百，謂之統法。 自元入經，先用此法，統曆之諸法也。 以通法進統法，得七十二百萬，氣朔之下，收分必盡，謂之全率。 以通法進全率，得七千二百萬，謂之大率，而元紀生焉。 元者，歲日月時皆甲子，日月五星，合在子正之宿，當盈縮先後之中，所謂七政齊矣。
The Way of Heaven is yin and yang; each has its number, and when they combine, transformation is complete. The yang tally is thirty-six and the yin twenty-four; odd and even are paired by mandate—two parts yang to three yin—both yielding seventy-two, and in that sameness the yin-yang numbers unite. Seventy-two is the number of completed transformation—the number of the Five Phases made whole. When the fivefold count reaches the period number, excess is called surplus of qi and shortfall is called void of new moon. Applied to change and divided for use, nothing lies outside its reach—this is what it means to embrace the myriad phenomena. Seventy-two serves as the canonical constant—the standard method in everyday use. A method is a step of number; advancing and retreating by the method without losing place is called the universal method. Advancing the canonical by the universal method yields seven thousand two hundred—the systematic method. From origin to canonical reckoning, this method is applied first—it governs all methods of the systematic calendar. Advancing the systematic by the universal method yields seven million two hundred thousand; under solar terms and new moons every fractional part is absorbed—this is the complete rate. Advancing the complete rate by the universal method yields seventy-two million—the great rate, from which the origin era is born. The origin is the moment when year, month, day, and hour are all jiazi, when sun, moon, and the five planets conjoin at the zi lodge, at the mean of their varying speeds—this is the alignment of the seven luminaries.
9
古之植圭於陽城者，以其近洛故也，蓋尚慊其中，乃在洛之東偏。 開元十二年，遣使天下候影，南距林邑國，北距橫野軍，中得浚儀之嶽臺，應南北弦，居地之中。 皇家建國，定都於梁。 今樹圭置箭，測嶽臺晷漏，以為中數，晷漏正，則日之所至，氣之所應得之矣。
The ancients set the gnomon at Yangcheng because it lay near Luoyang—yet even then they judged it slightly east of true center. In Kaiyuan 12, observers were sent across the empire to measure shadows, from Linyi in the south to Hengye garrison in the north; at the center they found the Yuetai at Junyi, on the north-south meridian and at the heart of the land. Our dynasty founded the state with its capital at Liang. We now erect the gnomon and set the clepsydra, taking measurements at the Yuetai as our central standard; when sundial and water clock are true, the sun's position and the seasons' response can be read correctly.
10
日月皆有盈縮。 日盈月縮，則後中而朔； 月盈日縮，則先中而朔。 自古朓肭之法，率皆平行之數，入曆既有前次，而又衰稍不倫。 《皇極》舊述，則迂回而難用，降及諸曆，則疏遠而多失。 今以月離朓朒，隨曆較定，日躔朓朒，臨用加減，所得者入離定日也。 一日之中，分為九限，逐限損益，衰稍有倫。 朓朒之法，所謂審矣。
Both sun and moon vary in speed. When the sun is fast and the moon slow, the median hour comes late and so does the new moon; when the moon is fast and the sun slow, both median and new moon come early. Since antiquity, methods for lunar speed have relied on uniform motion; though the calendar marks prior steps, the rates of change do not scale consistently. The old Huangji account is circuitous and impractical; later calendars are crude and error-prone. We now fix lunar speed by comparing waxing and waning against the calendar, and adjust solar speed at the moment of use—yielding the true day of lunar departure. Each day is divided into nine intervals, with incremental adjustments at each step so that the rates of change follow a proper scale. The method of waxing and waning is, in a word, exact.
11
赤道者，天之纮帶也，其勢圓而平，紀宿度之常數焉。 黃道者，日軌也，其半在赤道內，半在赤道外，去赤道極遠二十四度。 當與赤道交，則其勢斜； 當去赤道遠，則其勢直。 當斜則日行宜遲，當直則日行宜速。 故二分前後加其度，二至前後減其度。 九道者，月軌也，其半在黃道內，半在黃道外，去黃道極遠六度。 出黃道謂之正交，入黃道謂之中交。 若正交在秋分之宿，中交在春分之宿，則比黃道益斜。 若正交在春分之宿，中交在秋分之宿，則比黃道反直。 若正交、中交在二至之宿，則其勢差斜。 故較去二至、二分遠近，以考斜正，乃得加減之數。 自古雖有九道之說，蓋亦知而未詳，空有祖述之文，全無推步之用。 今以黃道一周，分為八節，一節之中，分用九道，盡七十二道而復，使日月之軌，無所隱其斜正之勢焉。 九道之法，所謂明矣。
The equator is Heaven's girdle—round and level—and records the constant degrees of the lodges. The ecliptic is the sun's path: half within the equator, half without, reaching twenty-four degrees from it at maximum. Where it crosses the equator, its course is oblique; where it stands farthest from the equator, its course is most direct. At the oblique points the sun should move slowly; at the direct points, quickly. Hence degrees are added around the equinoxes and subtracted around the solstices. The nine paths are the moon's track: half within the ecliptic, half without, deviating up to six degrees at maximum. Emerging from the ecliptic is the ascending node; entering it is the descending node. If the ascending node falls at the autumn-equinox lodge and the descending at the spring-equinox lodge, the moon's path is more oblique than the sun's. If the ascending node is at the spring-equinox lodge and the descending at the autumn-equinox lodge, the moon's path is conversely more direct than the sun's. If both nodes fall at the solstice lodges, the obliquity differs again. By comparing distance from the solstices and equinoxes, one determines obliquity and derives the correction figures. The nine paths have been discussed since antiquity, but only in outline—handed-down words without real computational use. We now divide the ecliptic into eight sections, each section into nine paths—seventy-two in all, cycling back—so that the tracks of sun and moon nowhere conceal their varying obliquity. The method of the nine paths is, in a word, clear.
12
星之行也，近日而疾，遠日而遲，去日極遠，勢盡而留。 自古諸曆，分段失實，隆降無準，今日行分尚多，次日便留，自留而退，唯用平行，仍以入段行度為入曆之數，皆非本理，遂至乖戾。 今校定逐日行分，積逐日行分以為變段。 於是自疾漸而遲，勢盡而留，自留而行，亦積微而後多。 別立諸段變曆，以推變差，俾諸段變差際會相合，星之遲疾，可得而知之矣。
A planet moves fastest near the sun, slowest far from it; at greatest distance its momentum is spent and it stations. Earlier calendars misjudged the segments, with no proper scale for acceleration and deceleration—a planet still moving quickly one day would station the next, and from station to retrograde only uniform motion was assumed, using segment degrees as calendar entries. None of this matched nature, and error piled on error. We now fix the daily motion part by part, accumulating them into variable segments. Thus speed gradually gives way to slowness, momentum is spent and the planet stations; from station to direct motion, minute increments build until motion is swift again. Separate variable tables are set up for each segment to calculate the discrepancies, so that segment by segment the figures align—and the planet's varying speed can be known with precision.
13
自古相傳，皆謂去交十五度以下，則日月有蝕，殊不知日月之相掩，與暗虛之所射，其理有異焉。 今以日月徑度之大小，校去交之遠近，以黃道之斜正，天勢之升降，度仰視旁視之分數，則交虧得其實矣。
Tradition held that within fifteen degrees of nodal departure, sun and moon would eclipse—yet they did not grasp that mutual occultation of sun and moon and casting of the dark void follow different principles. By comparing sun and moon diameters, calibrating nodal distance, ecliptic obliquity, celestial disposition, and overhead versus side-view fractions, eclipse magnitude is obtained in reality.
14
乃以一篇步日，一篇步月，一篇步星， 〈（案：以下脫「一篇步發斂」五字。 下云「以卦候沒滅，為之下篇」者，言為步發斂之下篇。 《歐陽史》約其文，稱「謹以步日、步月、步星、步發斂為四篇」，是也。）〉 以卦候沒滅，為之下篇，都四篇，為曆經一卷，曆十一卷，草三卷，《顯德三年七政細行曆》一卷。
He then set one chapter to pace the sun, one to pace the moon, and one to pace the stars, (Note: The five characters "one chapter pacing emergence and retraction" are missing below. The phrase below, "taking hexagram periods and extinction as the lower chapter," refers to the lower chapter on pacing emergence and retraction. The Ouyang History condenses the text to read, "respectfully taking pacing the sun, moon, stars, and emergence and retraction as four chapters"—which is correct.)〉 With hexagram periods and extinction as the lower chapter, four chapters in all formed one scroll of the calendar classic, eleven of calendar, three of draft, and one scroll of the Detailed Motion of the Seven Regulators for Xiande 3.
15
臣檢討先代圖籍，今古曆書，皆無蝕神首尾之文，蓋天竺胡僧之祆說也。 近自司天卜祝小術，不能舉其大體，遂為等接之法。 蓋從假用以求徑捷，於是乎交有逆行之數，後學者不能詳知，便言曆者有九道，以為註曆之恒式，今並削而去之。
I have examined charts and calendar books old and new and found none with text on the head and tail of the eclipse spirit—likely a Zoroastrian doctrine from Indian monks. Recently, minor techniques of the Astronomy Bureau and court diviners, unable to grasp the whole, devised a method of equal connection. Adopted provisionally for convenience, it gave crossing a retrograde number; later students, ignorant of the details, said calendars had nine paths as the standard annotating form—all of which are now cut away.
16
昔在唐堯，欽若昊天。 陛下親降聖謨，考曆象日月星辰。 唐堯之道也，其曆謹以「顯德欽天」為名。 天道元遠，非微臣之所盡知，但竭兩端，以奉明詔。 疏略乖謬，甘俟罪戾。
Of old, Yao of Tang reverently conformed to august Heaven. Your Majesty has personally bestowed sacred counsel, examining the calendar and the images of sun, moon, stars, and constellations. This is the Way of Yao of Tang; the calendar is respectfully named "Xiande Qintian." The Heavenly Way is profoundly remote—beyond your humble servant's full knowledge; I can only give my utmost to serve the enlightened edict. If it is coarse or mistaken, I willingly await punishment.
17
世宗覽之，親為制序，仍付司天監行用，以來年正旦為始，自前諸曆並廢。 〈（《玉海》：《欽天》於朔分之下，立小分謂之杪。 說者謂前代謂曆朔余未有杪者。 若可用杪，何待求日法以齊朔分也。）〉 其曆經一卷，今聊紀於後，以備太史氏之周覽焉。
Shizong reviewed it, composed the preface himself, and ordered the Astronomy Bureau to implement it from new year's dawn of the coming year, abolishing all previous calendars. (Jade Sea: The Qintian Calendar, below the new-moon parts, establishes small parts called miao. Commentators say that in former ages calendar new-moon remainders had no miao. If miao sufficed, why seek the day method to align new-moon parts?)〉 Its one-scroll calendar classic is briefly recorded below for the Grand Astrologer's comprehensive review.
18
《顯德欽天曆經》
The 《Xiande Qintian Calendar Classic》
19
演紀上元甲子，距今顯德三年丙辰，積七千二百六十九萬八千四百五十二。 《欽天》統法：七千二百《欽天》經法：七十二
Projecting the era from supreme origin jiazi to the present Xiande 3 bingchen: accumulated 72,698,452. 《Qintian》 comprehensive method: 7,200. 《Qintian》 canonical method: 72.
20
《欽天》通法：一百《欽天》步日躔術歲率：二百六十二萬九千七百六十 〈（四十）〉 軌率：二百六十二萬九千八百四十四 〈（八十）〉
《Qintian》 universal method: 100. 《Qintian》 method for pacing the sun's motion, year rate: 2,629,760. Emended calendrical figure 40 in editorial brackets.〉 Track rate: 2,629,844. Emended calendrical figure 80 in editorial brackets.〉
21
朔率：二十一萬二千六百二十二 〈（十八）〉 歲策：三百六十五一千七百六十 〈（四十）〉 軌策：三百六十五一千八百四十四 〈（八十）〉 歲中：一百八十三四千四百八十 〈（二十）〉
New-moon rate: 212,622. Emended calendrical figure 18 in editorial brackets.〉 Year tally: 365, 1,760. Emended calendrical figure 40 in editorial brackets.〉 Track tally: 365, 1,844. Emended calendrical figure 80 in editorial brackets.〉 Year median: 183, 4,480. Emended calendrical figure 20 in editorial brackets.〉
22
軌中：一百八十二四千五百二十二 〈（四十）〉 朔策：二十九三千八百二十 〈（二十八）〉 氣策：一十五一千五百七十三 〈（三十五）〉
Track median: 182, 4,522. Emended calendrical figure 40 in editorial brackets.〉 New-moon tally: 29, 3,820. Emended calendrical figure 28 in editorial brackets.〉 Qi tally: 15, 1,573. Emended calendrical figure 35 in editorial brackets.〉
23
象策：七二千七百五十五 （七） 周紀：六十歲差：八十四 〈（四十）〉 辰則：六百八刻二十四分
Image tally: 7, 2,755. fraction 7 Cycle era: 60. Precession: 84. Emended calendrical figure 40 in editorial brackets.〉 Double-hour rule: 600, eight quarters and twenty-four minutes.
24
〈（案：以上題稱步日躔術及後步月離術、步五星術，合為曆經四篇者之三，又皆僅列用數而不及推步。 據《歐陽史》云：「舊史亡其步發斂一篇，而在者三篇，簡略不完。」 然則《薛史》原文固已闕矣。）〉
(Note: The headings above—the sun-pacing method and the later lunar-departure and five-planet methods, three of the four calendar-classic chapters—only list constants and give no computational procedures. The Ouyang History states: "The old history lost the chapter on pacing emergence and retraction; the three that survive are brief and incomplete. Thus the original text of the Xue History was already deficient.)〉
25
《欽天》步月離術離率：一十九萬八千三百九十三 （九） 交率：一十九萬五千九百三十七 〈（九十七五十六）〉 離策：一十七三千九百九十三 （九）
《Qintian》 method for pacing lunar departure, departure rate: 198,393. fraction 9 Crossing rate: 195,937. Emended calendrical figures 97 and 56 in editorial brackets.〉 Departure tally: 17, 3,993. fraction 9
26
交策：二十七一千五百二十七 〈（九十七五十六）〉 望策：一十四五千五百一十一 〈（十四）〉 交中：一十三四千三百六十三 〈（九十八七十八）〉
Crossing tally: 27, 1,527. Emended calendrical figures 97 and 56 in editorial brackets.〉 Full-moon tally: 14, 5,511. Emended calendrical figure 14 in editorial brackets.〉 Crossing median: 13, 4,363. Emended calendrical figures 98 and 78 in editorial brackets.〉
27
離朔：一七千二十七 〈（一十九）〉 交朔，二二千二百九十二 〈（三十四十四）〉 中準：一千七百三十六中限：四千七百八十
Departure new moon: 1, 7,027. Emended calendrical figure 19 in editorial brackets.〉 Crossing new moon: 2, 2,292. Emended calendrical figures 34 and 44 in editorial brackets.〉 Median standard: 1,736. Median limit: 4,780.
28
平離：九百六十三程節：八百
Level departure: 963. Procedure node: 800.
29
《欽天》步五星術◎歲星周率：二百八十七萬一千九百七十六 （六） 變率：二十四萬二千二百一十五 〈（六十六）〉
《Qintian》 procedure for the five planets ◎ Jupiter circuit rate: 2,871,976. fraction 6 Variation rate: 242,215. Emended calendrical figure 66 in editorial brackets.〉
30
曆率：二百六十二萬九千七百六十一 〈（七十八）〉 周策：三百九十八六千三百七十六 （六） 曆中：一百八十二四千四百八十 〈（九十六）〉
Calendar rate: 2,629,761. Emended calendrical figure 78 in editorial brackets.〉 Circuit tally: 398, 6,376. fraction 6 Circuit median: 182, 4,480. Emended calendrical figure 96 in editorial brackets.〉
31
〈（案：《歐陽史》小分作八十九，此雲九十六，非也。 據曆中倍之為曆率，倍九十六，適得大分一，小分七十八）〉 變段變日變度變曆
(Note: Ouyang Shi's History gives the minor fraction as 89, but this text has 96, which is wrong. Doubling the circuit median (96) for the calendar rate yields 1 major fraction and 78 minor fractions.)〉 Variable segment, variable days, variable degrees, variable calendar
32
晨見一十七三 〈（三十七）〉 二 〈（二十四）〉 順遲二十五二 （九） 一 〈（二十九）〉 退遲一十四一 〈（一十二）〉 空 〈（二十八）〉
Morning appearance: 17 days, 3 parts Emended calendrical figure 37 in editorial brackets.〉 2 Emended calendrical figure 24 in editorial brackets.〉 Direct slow motion: 25, 2. fraction 9 1 Emended calendrical figure 29 in editorial brackets.〉 Retrograde slow motion: 14, 1. Emended calendrical figure 12 in editorial brackets.〉 — Emended calendrical figure 28 in editorial brackets.〉
33
退疾二十七四 〈（三十八）〉 一 〈（三十七）〉 後留二十六 〈（三十二）〉
Retrograde fast motion: 27, 4. Emended calendrical figure 38 in editorial brackets.〉 1 Emended calendrical figure 37 in editorial brackets.〉 Station after retrograde: 26. Emended calendrical figure 32 in editorial brackets.〉
34
順疾九十一十六 〈（六十三）〉 一十一 〈（一十三）〉
Swift direct motion: 91 days, 16 parts Emended calendrical figure 63 in editorial brackets.〉 11 Emended calendrical figure 13 in editorial brackets.〉
35
順疾九十一十六 〈（六十三）〉 一十一 〈（一十三）〉 前留二十六 〈（三十二）〉 退疾二十七四 〈（三十八）〉 一 〈（三十七）〉
Direct fast motion: 91, 16. Emended calendrical figure 63 in editorial brackets.〉 11 Emended calendrical figure 13 in editorial brackets.〉 Station before retrograde: 26. Emended calendrical figure 32 in editorial brackets.〉 Retrograde fast motion: 27, 4. Emended calendrical figure 38 in editorial brackets.〉 1 Emended calendrical figure 37 in editorial brackets.〉
36
退遲一十四一 〈（一十二）〉 空 〈（二十八）〉 順遲二十五二 （九） 一 〈（二十九）〉
Retrograde slow motion: 14, 1. Emended calendrical figure 12 in editorial brackets.〉 — Emended calendrical figure 28 in editorial brackets.〉 Direct slow motion: 25, 2. fraction 9 1 Emended calendrical figure 29 in editorial brackets.〉
37
夕伏一十七三 〈（三十七）〉 二 〈（二十四）〉 ◎熒惑周率：五百六十一萬五千四百二十二 〈（一十一）〉 變率：二百九十八萬五千六百六十一 〈（七十一）〉
Evening disappearance: 17, 3. Emended calendrical figure 37 in editorial brackets.〉 2 Emended calendrical figure 24 in editorial brackets.〉 ◎ Mars orbital cycle rate: 5,615,422. Emended calendrical figure 11 in editorial brackets.〉 Mutation rate: 2,985,661. Emended calendrical figure 71 in editorial brackets.〉
38
曆率：二百六十二萬九千七百六十周策：七百七十九六千六百二十二一 〈（十一）〉 曆中：百八十二四千四百八十變段變日變度變曆
Calendar rate: 2,629,760; circuit tally: 779, 6,622, remainder 1. Emended calendrical figure 11 in editorial brackets.〉 Circuit median: 182, 4,480; variable segment, variable days, variable degrees, variable calendar
39
晨見七十三五十三 〈（六十八）〉 五十 〈（五十八）〉 順疾七十三五十一 （一） 四十八 （三） 次疾七十一四十六 〈（六十九）〉 四十四 〈（一十七）〉
Morning appearance: 73, 53. Emended calendrical figure 68 in editorial brackets.〉 50 Emended calendrical figure 58 in editorial brackets.〉 Direct fast motion: 73, 51. fraction 1 48 fraction 3 Second direct-fast phase: 71, 46. Emended calendrical figure 69 in editorial brackets.〉 44 Emended calendrical figure 17 in editorial brackets.〉
40
次遲七十一四十五 〈（三十三）〉 四十二 〈（五十八）〉 順遲六十二一十九 〈（二十九）〉 一十八 〈（二十）〉 前留八 〈（六十九）〉
Second direct-slow phase: 71, 45. Emended calendrical figure 33 in editorial brackets.〉 42 Emended calendrical figure 58 in editorial brackets.〉 Direct slow motion: 62, 19. Emended calendrical figure 29 in editorial brackets.〉 18 Emended calendrical figure 20 in editorial brackets.〉 Station before retrograde: 8. Emended calendrical figure 69 in editorial brackets.〉
41
退遲一十一 〈（五十八）〉 空 〈（四十四）〉 退疾二十一七 〈（四十六）〉 二 〈（四十）〉 退疾二十一七 〈（四十六）〉 二 〈（四十）〉
Retrograde slow motion: 11, 1. Emended calendrical figure 58 in editorial brackets.〉 — Emended calendrical figure 44 in editorial brackets.〉 Retrograde fast motion: 21, 7. Emended calendrical figure 46 in editorial brackets.〉 2 Emended calendrical figure 40 in editorial brackets.〉 Retrograde fast motion: 21, 7. Emended calendrical figure 46 in editorial brackets.〉 2 Emended calendrical figure 40 in editorial brackets.〉
42
退遲一十一 〈（五十八）〉 空 〈（四十四）〉 後留八 〈（六十九）〉 順遲六十二一十九 〈（二十九）〉 一十八 〈（二十）〉 次遲七十一四十五 〈（三十三）〉 四十二 〈（五十八）〉
Retrograde slow motion: 11, 1. Emended calendrical figure 58 in editorial brackets.〉 — Emended calendrical figure 44 in editorial brackets.〉 Station after retrograde: 8. Emended calendrical figure 69 in editorial brackets.〉 Direct slow motion: 62, 19. Emended calendrical figure 29 in editorial brackets.〉 18 Emended calendrical figure 20 in editorial brackets.〉 Second direct-slow phase: 71, 45. Emended calendrical figure 33 in editorial brackets.〉 42 Emended calendrical figure 58 in editorial brackets.〉
43
次疾七十一四十六 〈（六十九）〉 四十四 〈（一十七）〉 順疾七十三五十一 （一） 四十八 （三）
Second direct-fast phase: 71, 46. Emended calendrical figure 69 in editorial brackets.〉 44 Emended calendrical figure 17 in editorial brackets.〉 Direct fast motion: 73, 51. fraction 1 48 fraction 3
44
夕伏七十三五十三 〈（六十八）〉 五十 〈（五十八）〉 ◎鎮星周率：二百七十二萬二千一百七十六 〈（九十）〉 變率：九萬二千四百一十六 〈（五十）〉
Evening disappearance: 73, 53. Emended calendrical figure 68 in editorial brackets.〉 50 Emended calendrical figure 58 in editorial brackets.〉 ◎ Saturn orbital cycle rate: 2,722,176. Emended calendrical figure 90 in editorial brackets.〉 Variation rate: 92,416. Emended calendrical figure 50 in editorial brackets.〉
45
曆率：二百六十二萬九千七百五十九 〈（八十）〉 周策：三百七十八五百七十六 〈（九十）〉 曆中：一百八十二四千四百七十九 〈（九十）〉 變段變日變度變曆
Calendar rate: 2,629,759. Emended calendrical figure 80 in editorial brackets.〉 Circuit tally: 378, 576. Emended calendrical figure 90 in editorial brackets.〉 Circuit median: 182, 4,479. Emended calendrical figure 90 in editorial brackets.〉 Variable segment, variable days, variable degrees, variable calendar
46
晨見一十九二 （七） 一 〈（一十四）〉 順疾六十五六 〈（三十八）〉 三 〈（五十一）〉 順遲一十九空 〈（六十三）〉 空 〈（三十五）〉
Morning appearance: 19, 2. fraction 7 1 Emended calendrical figure 14 in editorial brackets.〉 Direct fast motion: 65, 6. Emended calendrical figure 38 in editorial brackets.〉 3 Emended calendrical figure 51 in editorial brackets.〉 Direct slow motion: 19; — Emended calendrical figure 63 in editorial brackets.〉 — Emended calendrical figure 35 in editorial brackets.〉
47
前留三十七 （三） 退遲一十六空 〈（四十三）〉 空 〈（一十四）〉 退疾三十三二 〈（三十五）〉 空 〈（六十）〉 退疾三十三二 〈（三十五）〉 空 〈（六十）〉
Station before retrograde: 37. fraction 3 Retrograde slow motion: 16; — Emended calendrical figure 43 in editorial brackets.〉 — Emended calendrical figure 14 in editorial brackets.〉 Retrograde fast motion: 33, 2. Emended calendrical figure 35 in editorial brackets.〉 — Emended calendrical figure 60 in editorial brackets.〉 Retrograde fast motion: 33, 2. Emended calendrical figure 35 in editorial brackets.〉 — Emended calendrical figure 60 in editorial brackets.〉
48
退遲一十六空 〈（四十三）〉 空 〈（一十四）〉 後留三十七 （三） 順遲一十九空 〈（六十三）〉 空 〈（三十五）〉 順疾六十五六 〈（三十八）〉 三 〈（五十一）〉
Retrograde slow motion: 16; — Emended calendrical figure 43 in editorial brackets.〉 — Emended calendrical figure 14 in editorial brackets.〉 Station after retrograde: 37. fraction 3 Direct slow motion: 19; — Emended calendrical figure 63 in editorial brackets.〉 — Emended calendrical figure 35 in editorial brackets.〉 Direct fast motion: 65, 6. Emended calendrical figure 38 in editorial brackets.〉 3 Emended calendrical figure 51 in editorial brackets.〉
49
夕伏一十九二 （七） 一 〈（一十四）〉 ◎太白周率：四百二十萬四千一百四十三 〈（九十六）〉 變率：四百二十萬四千一百四十三 〈（九十六）〉
Evening disappearance: 19, 2. fraction 7 1 Emended calendrical figure 14 in editorial brackets.〉 ◎ Venus orbital cycle rate: 4,204,143. Emended calendrical figure 96 in editorial brackets.〉 Variation rate: 4,204,143. Emended calendrical figure 96 in editorial brackets.〉
50
曆率：二百六十二萬九千七百五十 〈（五十六）〉 周策：五百八十三六千五百四十三 〈（九十六）〉 曆中：一百八十二四千四百七十五 〈（二十八）〉
Calendar rate: 2,629,750. Emended calendrical figure 56 in editorial brackets.〉 Circuit tally: 583, 6,543. Emended calendrical figure 96 in editorial brackets.〉 Circuit median: 182, 4,475. Emended calendrical figure 28 in editorial brackets.〉
51
變段變日變度變曆
Variable segment, variable days, variable degrees, variable calendar
52
夕見四十二五十三 〈（四十）〉 五十一 〈（一十七）〉
Evening appearance: 42, 53. Emended calendrical figure 40 in editorial brackets.〉 51 Emended calendrical figure 17 in editorial brackets.〉
53
順疾九十六一百二十一 〈（五十）〉 一百一十六 〈（三十九）〉 次疾七十三八十 〈（三十七）〉 七十七 （一）
Direct fast motion: 96, 121. Emended calendrical figure 50 in editorial brackets.〉 116 Emended calendrical figure 39 in editorial brackets.〉 Second direct-fast phase: 73, 80. Emended calendrical figure 37 in editorial brackets.〉 77 fraction 1
54
次遲三十三三十四 （一） 三十二 〈（四十）〉
Second direct-slow phase: 33, 34. fraction 1 32 Emended calendrical figure 40 in editorial brackets.〉
55
順遲二十四一十一 〈（六十一）〉 一十一 〈（二十四）〉 前留六 〈（六十九）〉 退遲四一 〈（二十二）〉 空 〈（三十一）〉
Direct slow motion: 24, 11. Emended calendrical figure 61 in editorial brackets.〉 11 Emended calendrical figure 24 in editorial brackets.〉 Station before retrograde: 6. Emended calendrical figure 69 in editorial brackets.〉 Retrograde slow motion: 4, 1. Emended calendrical figure 22 in editorial brackets.〉 — Emended calendrical figure 31 in editorial brackets.〉
56
退疾六三 〈（六十五）〉 一 〈（二十二）〉 夕伏七四 〈（四十）〉 一 〈（三十七）〉 晨見七四 〈（四十）〉 一 〈（三十七）〉
Retrograde fast motion: 6, 3. Emended calendrical figure 65 in editorial brackets.〉 1 Emended calendrical figure 22 in editorial brackets.〉 Evening disappearance: 7, 4. Emended calendrical figure 40 in editorial brackets.〉 1 Emended calendrical figure 37 in editorial brackets.〉 Morning appearance: 7, 4. Emended calendrical figure 40 in editorial brackets.〉 1 Emended calendrical figure 37 in editorial brackets.〉
57
退疾六三 〈（六十五）〉 一 〈（二十二）〉 退遲四一 〈（二十二）〉 空 〈（三十一）〉 後留六 〈（六十九）〉
Retrograde fast motion: 6, 3. Emended calendrical figure 65 in editorial brackets.〉 1 Emended calendrical figure 22 in editorial brackets.〉 Retrograde slow motion: 4, 1. Emended calendrical figure 22 in editorial brackets.〉 — Emended calendrical figure 31 in editorial brackets.〉 Station after retrograde: 6. Emended calendrical figure 69 in editorial brackets.〉
58
順遲二十四一十一 〈（六十一）〉 一十一 〈（二十四）〉
Direct slow motion: 24, 11. Emended calendrical figure 61 in editorial brackets.〉 11 Emended calendrical figure 24 in editorial brackets.〉
59
次遲三十三三十四 （一） 三十二 〈（四十）〉 次疾七十三八十三 〈（十七）〉 七十七 （一）
Second direct-slow phase: 33, 34. fraction 1 32 Emended calendrical figure 40 in editorial brackets.〉 Second direct-fast phase: 73, 83. Emended calendrical figure 17 in editorial brackets.〉 77 fraction 1
60
順疾九十六一百二十一 〈（五十七）〉 一百一十六 〈（三十九）〉
Direct fast motion: 96, 121. Emended calendrical figure 57 in editorial brackets.〉 116 Emended calendrical figure 39 in editorial brackets.〉
61
晨伏四十二五十三 〈（四十）〉 五十一 〈（一十七）〉 ◎辰星周率：八十三萬四千三百三十五 〈（五十二）〉 變率：八十三萬四千三百三十五 〈（五十二）〉
Morning disappearance: 42, 53. Emended calendrical figure 40 in editorial brackets.〉 51 Emended calendrical figure 17 in editorial brackets.〉 ◎ Mercury orbital cycle rate: 834,335. Emended calendrical figure 52 in editorial brackets.〉 Variation rate: 834,335. Emended calendrical figure 52 in editorial brackets.〉
62
曆率：二百六十二萬九千七百六十 〈（四十四）〉 周策：一百一十五六千三百三十五 〈（五十二）〉 曆中：一百八十二四千四百八十 〈（二十二）〉
Calendar rate: 2,629,760. Emended calendrical figure 44 in editorial brackets.〉 Circuit tally: 115, 6,335. Emended calendrical figure 52 in editorial brackets.〉 Circuit median: 182, 4,480. Emended calendrical figure 22 in editorial brackets.〉
63
變段變日變度變曆
Variable segment, variable days, variable degrees, variable calendar
64
夕見一十七三十四 （一） 二十九 〈（五十四）〉
Evening appearance: 17, 34. fraction 1 29 Emended calendrical figure 54 in editorial brackets.〉
65
順疾一十一一十八 〈（二十四）〉 一十六 （四）
Direct fast motion: 11, 18. Emended calendrical figure 24 in editorial brackets.〉 16 fraction 4
66
順遲一十六一十一 〈（四十三）〉 一十 〈（一十）〉 前留二 〈（六十八）〉 夕伏一十一六二晨見一十一六二
Direct slow motion: 16, 11. Emended calendrical figure 43 in editorial brackets.〉 10 Emended calendrical figure 10 in editorial brackets.〉 Station before retrograde: 2. Emended calendrical figure 68 in editorial brackets.〉 Evening disappearance: 11, 6, fraction 2; morning appearance: 11, 6, fraction 2.
67
後留二 〈（六十八）〉
Station after retrograde: 2. Emended calendrical figure 68 in editorial brackets.〉
68
順遲一十六一十一 〈（四十三）〉 一十 〈（一十）〉
Direct slow motion: 16, 11. Emended calendrical figure 43 in editorial brackets.〉 10 Emended calendrical figure 10 in editorial brackets.〉
69
順疾一十一一十八 〈（二十四）〉 一十六 （四）
Prograde, swift: 11 days, 18 degrees. Emended calendrical figure 24 in editorial brackets.〉 16 Fraction 4
70
晨伏一十七三十四 （一） 二十九 〈（五十四）〉
Morning concealment: 17 days, 34 degrees. Fraction 1 29 Emended calendrical figure 54 in editorial brackets.〉