佛祖歷代通載 2.15

2.15

大古以還。四時既序。晝夜長短。分至斯興。書曰。朞三百有六旬有六日。以閏月定四時成歲（天體至圓。周圍三百六十五度四分度之一。繞地左旋。常一日一周而過一度。日麗天而少遲。故日行一日亦繞地一周。而在天為不及一度。積三百六十五日九百四十分日之二百三十五而與天會。是一歲日行之數也。月麗天而尤遲。一日常不及天十三度十九分度之七。積二十九日九百四十分日之四百九十九而與日會。十二會得全日三百四十八餘分之積。又五千九百八十八如日法。九百四十而一得六不盡三百四十八。通計得日三百五十四九百四十分日之三百四十八。是一歲月行之數也。歲有十二月。月有三十日。三百六十者。一藏之常數也。故日與天會而多五日九百四十分日之二百三十五者。為氣盈月與日會而少五日九百四十分日之五百九十二者為朔虛而閏生焉。故一歲閏率則十日九百四十分日之八百二十七。三歲一閏則三十二日九百四十分日之六百單一。五歲再閏則五十四日九百四十分日之三百七十五。十有九歲七閏則氣朔分齊。是為一章也。故三年不置閏。則春之一月入于夏。而時漸不定矣。子之一月入于丑。而歲漸不成矣。積之之久至於三失閏。則春皆入夏。而時全不定矣。十二次失閏。子皆入丑。歲全不成矣）。

From high antiquity onward, the four seasons were ordered, the length of days and nights was measured, and the equinoxes and solstices arose. The Book of Documents says: 'A year consists of three hundred and sixty-six days; by an intercalary month the four seasons are fixed and the year is completed.' (The body of Heaven is perfectly round, circumscribing 365 and 1/4 degrees. Reversing its rotation westward around the Earth, it regularly completes one circuit a day and exceeds it by one degree. The sun adheres to Heaven but moves slightly slower; thus the sun's travel in one day also completes one circuit around the Earth, yet relative to Heaven falls short by one degree. Accumulating 365 days and 235/940ths of a day, it meets with Heaven: this is the figure for the sun's travel in one year. The moon adheres to Heaven and moves still slower; in one day it regularly falls short of Heaven by 13 and 7/19ths degrees. Accumulating 29 days and 499/940ths of a day, it meets with the sun. Twelve meetings yield 348 whole days and an accumulated remainder of fractions; further, 5,988 divided by the day-divisor 940 yields 6 with a remainder of 348. Taken altogether, this yields 354 days and 348/940ths of a day: this is the figure for the moon's travel in one year. A year has twelve months; a month has thirty days; 360 is the regular number of a single storage. Thus, when the sun meets with Heaven and exceeds it by 5 days and 235/940ths of a day, this is the solar excess; when the moon meets with the sun and falls short by 5 days and 592/940ths of a day, this is the lunar deficit; and from this the intercalation arises. Hence the intercalary rate for one year is 10 days and 827/940ths of a day; in three years there is one intercalation of 32 days and 601/940ths of a day; in five years there are two intercalations of 54 days and 375/940ths of a day; in nineteen years there are seven intercalations, whereupon the solar terms and new moons coincide evenly: this constitutes one cycle. Therefore, if no intercalation is inserted for three years, one month of spring slips into summer, and the seasons gradually become unfixed; the month of zi slips into chou, and the year gradually becomes incomplete. If this accumulates for long until three intercalations are missed, all of spring slips into summer, and the seasons become entirely disordered. If twelve intercalations are missed, all of zi slips into chou, and the year becomes entirely incomplete.)