1
志第十歷四
Treatise Ten: Calendrics, Part Four.
2
大統曆法二立成
▲ Grand Concordance Calendar Method, Part Two: Ready Reckoners.
3
立成者，以日月五星盈縮遲疾之數，預爲排定，以便推步取用也。 《元志》、《曆經》步七政盈縮遲疾，皆有二術。 其一術以三差立算者，即布立成法也。 其又術雲，以其下盈縮分，乘入限分萬約之，以加其下盈縮積者，用立成法也。 而遣立成未載，無從入算。 今依《大統歷通軌》具錄之。 其目四：曰太陽盈縮，曰晨昏分，曰太陰遲疾，曰五星盈縮。 餘詳《法原》及《推步》卷中。 按《元史》，至正十七年《授時曆》成。 十九年王恂卒，時歷雖頒，然立成之數尚皆有定藁。 郭守敬比類編次，整齊分秒，裁爲二卷。 而今欽天監本，載嘉議大夫太史令臣王恂奉敕撰。 意者王先有藁，而郭卒成之歟？
Ready reckoners tabulate the expansion–contraction and slow–rapid values of the sun, moon, and five planets in advance, arranged for ready retrieval in stepwise computation. In the Yuan History and the Calendar Classic, the procedures for the seven regulators' expansion–contraction and slow–rapid motion each take two forms. One establishes the calculation through the three differences—this is the arrayed ready-reckoner method. The other reads: multiply the underlying expansion–contraction increment by the degrees entered into the limit, scale by ten thousand, and add it to the underlying expansion–contraction accumulation—this is the ready-reckoner method. Yet the transmitted ready reckoners were never recorded, leaving no basis for the calculation. They are reproduced here in full from the Comprehensive Track of the Grand Concordance Calendar. There are four sections: solar expansion–contraction, morning and evening divisions, lunar slow–rapid motion, and planetary expansion–contraction. Further particulars appear in Origins of the Method and in the Stepwise Computation fascicle. Note: According to the Yuan History, the Season Granting Calendar was completed in the seventeenth year of Zhizheng. Wang Xun died in the nineteenth year. The calendar had been promulgated, but the ready-reckoner constants still existed only as settled drafts. Guo Shoujing drew analogies among the drafts, harmonized the minutes and seconds, and reduced the work to two fascicles. The Imperial Astronomical Bureau edition now in use, however, credits Raised-Proposal Grandee and Grand Astrologer Wang Xun as having composed it by imperial commission. Perhaps Wang prepared the drafts and Guo brought them to completion?
4
太陽盈初縮末限立成冬至前後二象限同用
Ready reckoners for the solar expansion-initial and contraction-final interval: the two quadrants before and after the winter solstice share the same table.
5
表格略
[Table omitted.]
6
晨分加二百五十分，爲日出分。 日週一萬分，內減晨分爲昏分。 昏分減二百五十分，爲日入分，又減五千分，爲半晝分。 故立成只列晨昏分，則出入及半晝分皆具，不必盡列也。
Add 250 parts to the morning division to obtain the sunrise division. From the solar circuit of 10,000 parts, subtract the morning division to obtain the evening division. Subtract 250 parts from the evening division for sunset, and a further 5,000 parts for half-daylight. The ready reckoners therefore list only the morning and evening divisions; sunrise, sunset, and half-daylight follow from them without need for separate columns.
7
以下表格略
[Tables below omitted.]