志第十七上(shang) 历三上(shang)
开元九年，《麟德历》署日蚀比不效，诏僧一行作新历，推大衍数立术以应之，较经史所书气朔、日名、宿度可考者皆合。十五年，草成而一行卒，诏特进张说与历官陈玄景等次为《历术》七篇、《略例》一篇、《历议》十篇，玄宗顾访者则称制旨。明年，说表上之，起十七年颁于有司。时善算瞿坛譔者，怨不得预改历事，二十一年，与玄景奏：“《大衍》写《九执历》，其术未尽。”太子右司御率南宫说亦非之。诏侍御史李麟、太史令桓执圭较灵台候簿，《大衍》十得七、八，《麟德》才三、四，九执一、二焉。乃罪说等，而是否决。
自《太(tai)初(chu)》至(zhi)《麟德》，历有(you)二十(shi)(shi)三家，与天虽(sui)近而未密也。至(zhi)一行，密矣(yi)，其(qi)倚数立法固无以(yi)易也。后世虽(sui)有(you)改作者，皆依仿而已，故(gu)详录之(zhi)。《略(lve)例》，所以(yi)明述作本旨也；《历议(yi)》，所以(yi)考(kao)古今得失也。其(qi)说皆足以(yi)为将来折衷(zhong)。略(lve)其(qi)大要，著于篇者十(shi)(shi)有(you)二。
其一《历本议》曰：
《易》：“天(tian)(tian)数(shu)(shu)(shu)(shu)五(wu)，地(di)(di)(di)数(shu)(shu)(shu)(shu)五(wu)，五(wu)位相(xiang)得(de)而(er)(er)各(ge)有合(he)，所以(yi)成变化(hua)而(er)(er)行鬼(gui)神也(ye)。”天(tian)(tian)数(shu)(shu)(shu)(shu)始于(yu)(yu)(yu)(yu)一(yi)，地(di)(di)(di)数(shu)(shu)(shu)(shu)始于(yu)(yu)(yu)(yu)二(er)(er)，合(he)二(er)(er)始以(yi)位刚(gang)柔。天(tian)(tian)数(shu)(shu)(shu)(shu)终(zhong)(zhong)于(yu)(yu)(yu)(yu)九，地(di)(di)(di)数(shu)(shu)(shu)(shu)终(zhong)(zhong)于(yu)(yu)(yu)(yu)十(shi)(shi)(shi)，合(he)二(er)(er)终(zhong)(zhong)以(yi)纪闰余。天(tian)(tian)数(shu)(shu)(shu)(shu)中(zhong)(zhong)(zhong)于(yu)(yu)(yu)(yu)五(wu)，地(di)(di)(di)数(shu)(shu)(shu)(shu)中(zhong)(zhong)(zhong)于(yu)(yu)(yu)(yu)六(liu)(liu)(liu)(liu)(liu)，合(he)二(er)(er)中(zhong)(zhong)(zhong)以(yi)通律(lv)(lv)(lv)历(li)。天(tian)(tian)有五(wu)音，所以(yi)司日也(ye)。地(di)(di)(di)有六(liu)(liu)(liu)(liu)(liu)律(lv)(lv)(lv)，所以(yi)司辰也(ye)。参伍相(xiang)周，究于(yu)(yu)(yu)(yu)六(liu)(liu)(liu)(liu)(liu)十(shi)(shi)(shi)，圣人以(yi)此见天(tian)(tian)地(di)(di)(di)之(zhi)(zhi)(zhi)心也(ye)。自(zi)(zi)五(wu)以(yi)降，为(wei)五(wu)行生(sheng)(sheng)数(shu)(shu)(shu)(shu)；自(zi)(zi)六(liu)(liu)(liu)(liu)(liu)以(yi)往，为(wei)五(wu)材成数(shu)(shu)(shu)(shu)。错而(er)(er)乘(cheng)之(zhi)(zhi)(zhi)，以(yi)生(sheng)(sheng)数(shu)(shu)(shu)(shu)衍(yan)成位。一(yi)、六(liu)(liu)(liu)(liu)(liu)而(er)(er)退极(ji)，五(wu)、十(shi)(shi)(shi)而(er)(er)增极(ji)；一(yi)、六(liu)(liu)(liu)(liu)(liu)为(wei)爻位之(zhi)(zhi)(zhi)统，五(wu)、十(shi)(shi)(shi)为(wei)大衍(yan)之(zhi)(zhi)(zhi)母。成数(shu)(shu)(shu)(shu)乘(cheng)生(sheng)(sheng)数(shu)(shu)(shu)(shu)，其(qi)算六(liu)(liu)(liu)(liu)(liu)百，为(wei)天(tian)(tian)中(zhong)(zhong)(zhong)之(zhi)(zhi)(zhi)积。生(sheng)(sheng)数(shu)(shu)(shu)(shu)乘(cheng)成数(shu)(shu)(shu)(shu)，其(qi)算亦(yi)六(liu)(liu)(liu)(liu)(liu)百，为(wei)地(di)(di)(di)中(zhong)(zhong)(zhong)之(zhi)(zhi)(zhi)积。合(he)千(qian)有二(er)(er)百，以(yi)五(wu)十(shi)(shi)(shi)约(yue)之(zhi)(zhi)(zhi)，则四象(xiang)周六(liu)(liu)(liu)(liu)(liu)爻也(ye)；二(er)(er)十(shi)(shi)(shi)四约(yue)之(zhi)(zhi)(zhi)，则太极(ji)包四十(shi)(shi)(shi)九用也(ye)。综成数(shu)(shu)(shu)(shu)，约(yue)中(zhong)(zhong)(zhong)积，皆(jie)十(shi)(shi)(shi)五(wu)。综生(sheng)(sheng)数(shu)(shu)(shu)(shu)，约(yue)中(zhong)(zhong)(zhong)积，皆(jie)四十(shi)(shi)(shi)。兼而(er)(er)为(wei)天(tian)(tian)地(di)(di)(di)之(zhi)(zhi)(zhi)数(shu)(shu)(shu)(shu)，以(yi)五(wu)位取之(zhi)(zhi)(zhi)，复得(de)二(er)(er)中(zhong)(zhong)(zhong)之(zhi)(zhi)(zhi)合(he)矣。蓍数(shu)(shu)(shu)(shu)之(zhi)(zhi)(zhi)变，九、六(liu)(liu)(liu)(liu)(liu)各(ge)一(yi)，乾坤(kun)之(zhi)(zhi)(zhi)象(xiang)也(ye)。七、八各(ge)三，六(liu)(liu)(liu)(liu)(liu)子之(zhi)(zhi)(zhi)象(xiang)也(ye)。故(gu)爻数(shu)(shu)(shu)(shu)通乎六(liu)(liu)(liu)(liu)(liu)十(shi)(shi)(shi)，策数(shu)(shu)(shu)(shu)行乎二(er)(er)百四十(shi)(shi)(shi)。是以(yi)大衍(yan)为(wei)天(tian)(tian)地(di)(di)(di)之(zhi)(zhi)(zhi)枢，如环(huan)之(zhi)(zhi)(zhi)无端，盖律(lv)(lv)(lv)历(li)之(zhi)(zhi)(zhi)大纪也(ye)。
夫数(shu)象(xiang)(xiang)微(wei)(wei)于(yu)三(san)(san)(san)、四(si)(si)(si)(si)，而(er)(er)(er)章于(yu)七(qi)(qi)、八。卦有(you)(you)(you)三(san)(san)(san)微(wei)(wei)，策(ce)有(you)(you)(you)四(si)(si)(si)(si)象(xiang)(xiang)，故(gu)(gu)二(er)(er)(er)微(wei)(wei)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)合，在始(shi)中(zhong)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)际(ji)(ji)焉。蓍以(yi)七(qi)(qi)备，卦以(yi)八周，故(gu)(gu)二(er)(er)(er)章之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)合，而(er)(er)(er)在中(zhong)终之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)际(ji)(ji)焉。中(zhong)极居五六间，由辟阖之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)交，而(er)(er)(er)在章微(wei)(wei)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)际(ji)(ji)者(zhe)，人神之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)极也。天地(di)中(zhong)积(ji)，千有(you)(you)(you)二(er)(er)(er)百(bai)，揲之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)以(yi)四(si)(si)(si)(si)，为爻率三(san)(san)(san)百(bai)；以(yi)十(shi)(shi)位(wei)乘(cheng)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)，而(er)(er)(er)二(er)(er)(er)章之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)积(ji)三(san)(san)(san)千；以(yi)五材乘(cheng)八象(xiang)(xiang)，为二(er)(er)(er)微(wei)(wei)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)积(ji)四(si)(si)(si)(si)十(shi)(shi)。兼章微(wei)(wei)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)积(ji)，则气朔之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)分(fen)母(mu)也。以(yi)三(san)(san)(san)极参(can)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)，倍六位(wei)除之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)，凡(fan)七(qi)(qi)百(bai)六十(shi)(shi)，是谓(wei)辰法(fa)，而(er)(er)(er)齐于(yu)代轨(gui)。以(yi)十(shi)(shi)位(wei)乘(cheng)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)，倍大(da)衍除之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)，凡(fan)三(san)(san)(san)百(bai)四(si)(si)(si)(si)，是谓(wei)刻法(fa)，而(er)(er)(er)齐于(yu)德(de)运。半气朔之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)母(mu)，千五百(bai)二(er)(er)(er)十(shi)(shi)，得天地(di)出符之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)数(shu)，因而(er)(er)(er)三(san)(san)(san)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)，凡(fan)四(si)(si)(si)(si)千五百(bai)六十(shi)(shi)，当(dang)七(qi)(qi)精(jing)返(fan)初之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)会也。《易》始(shi)于(yu)三(san)(san)(san)微(wei)(wei)而(er)(er)(er)生一象(xiang)(xiang)，四(si)(si)(si)(si)象(xiang)(xiang)成而(er)(er)(er)后八卦章。三(san)(san)(san)变(bian)皆(jie)刚，太(tai)阳之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)象(xiang)(xiang)。三(san)(san)(san)变(bian)皆(jie)柔，太(tai)阴之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)象(xiang)(xiang)。一刚二(er)(er)(er)柔，少阳之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)象(xiang)(xiang)。一柔二(er)(er)(er)刚，少阴之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)象(xiang)(xiang)。少阳之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)刚，有(you)(you)(you)始(shi)、有(you)(you)(you)壮、有(you)(you)(you)究(jiu)。少阴之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)柔，有(you)(you)(you)始(shi)、有(you)(you)(you)壮、有(you)(you)(you)究(jiu)。兼三(san)(san)(san)才(cai)而(er)(er)(er)两之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)，神明动乎其中(zhong)。故(gu)(gu)四(si)(si)(si)(si)十(shi)(shi)九(jiu)象(xiang)(xiang)，而(er)(er)(er)大(da)业之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)用周矣(yi)。数(shu)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)德(de)圆，故(gu)(gu)纪之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)以(yi)三(san)(san)(san)而(er)(er)(er)变(bian)于(yu)七(qi)(qi)。象(xiang)(xiang)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)德(de)方，故(gu)(gu)纪之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)以(yi)四(si)(si)(si)(si)而(er)(er)(er)变(bian)于(yu)八。
人(ren)在(zai)天地中(zhong)(zhong)(zhong)，以(yi)阅盈虚(xu)之(zhi)(zhi)(zhi)(zhi)(zhi)变(bian)，则(ze)闰(run)余之(zhi)(zhi)(zhi)(zhi)(zhi)初，而(er)气朔所(suo)虚(xu)也(ye)。以(yi)终合通大(da)衍(yan)之(zhi)(zhi)(zhi)(zhi)(zhi)母(mu)，亏其地十(shi)(shi)(shi)，凡九(jiu)(jiu)百(bai)四十(shi)(shi)(shi)为通数。终合除(chu)之(zhi)(zhi)(zhi)(zhi)(zhi)，得中(zhong)(zhong)(zhong)率四十(shi)(shi)(shi)九(jiu)(jiu)，余十(shi)(shi)(shi)九(jiu)(jiu)分(fen)之(zhi)(zhi)(zhi)(zhi)(zhi)九(jiu)(jiu)，终岁之(zhi)(zhi)(zhi)(zhi)(zhi)弦(xian)，而(er)斗分(fen)复初之(zhi)(zhi)(zhi)(zhi)(zhi)朔也(ye)。地于(yu)终极之(zhi)(zhi)(zhi)(zhi)(zhi)际，亏十(shi)(shi)(shi)而(er)从天，所(suo)以(yi)远疑阳之(zhi)(zhi)(zhi)(zhi)(zhi)战也(ye)。夫十(shi)(shi)(shi)九(jiu)(jiu)分(fen)之(zhi)(zhi)(zhi)(zhi)(zhi)九(jiu)(jiu)，盈九(jiu)(jiu)而(er)虚(xu)十(shi)(shi)(shi)也(ye)。乾盈九(jiu)(jiu)，隐乎(hu)龙战之(zhi)(zhi)(zhi)(zhi)(zhi)中(zhong)(zhong)(zhong)，故(gu)不(bu)见其首。坤(kun)虚(xu)十(shi)(shi)(shi)，以(yi)导潜龙之(zhi)(zhi)(zhi)(zhi)(zhi)气，故(gu)不(bu)见其成(cheng)。周(zhou)日(ri)之(zhi)(zhi)(zhi)(zhi)(zhi)朔分(fen)，周(zhou)岁之(zhi)(zhi)(zhi)(zhi)(zhi)闰(run)分(fen)，与(yu)一章之(zhi)(zhi)(zhi)(zhi)(zhi)弦(xian)，一蔀(bu)之(zhi)(zhi)(zhi)(zhi)(zhi)月，皆合于(yu)九(jiu)(jiu)百(bai)四十(shi)(shi)(shi)，盖取诸(zhu)中(zhong)(zhong)(zhong)率也(ye)。
一(yi)(yi)策之(zhi)(zhi)(zhi)(zhi)分十(shi)(shi)九，而(er)(er)章法生(sheng)；一(yi)(yi)揲之(zhi)(zhi)(zhi)(zhi)分七(qi)(qi)十(shi)(shi)六(liu)，而(er)(er)蔀(bu)法生(sheng)。一(yi)(yi)蔀(bu)之(zhi)(zhi)(zhi)(zhi)日(ri)二(er)万七(qi)(qi)千七(qi)(qi)百(bai)五十(shi)(shi)七(qi)(qi)，以(yi)通数约之(zhi)(zhi)(zhi)(zhi)，凡二(er)十(shi)(shi)九日(ri)余四百(bai)九十(shi)(shi)九，而(er)(er)日(ri)月(yue)相交于朔，此(ci)六(liu)爻(yao)之(zhi)(zhi)(zhi)(zhi)纪(ji)也。以(yi)卦当(dang)(dang)岁，以(yi)爻(yao)当(dang)(dang)月(yue)，以(yi)策当(dang)(dang)日(ri)，凡三十(shi)(shi)二(er)岁而(er)(er)小终(zhong)，二(er)百(bai)八(ba)十(shi)(shi)五小终(zhong)而(er)(er)与卦运(yun)大终(zhong)，二(er)百(bai)八(ba)十(shi)(shi)五，则参伍(wu)二(er)终(zhong)之(zhi)(zhi)(zhi)(zhi)合也。数象(xiang)既合，而(er)(er)遁行之(zhi)(zhi)(zhi)(zhi)变在(zai)乎其间矣(yi)。
所谓(wei)遁(dun)行者(zhe)，以(yi)(yi)爻率(lv)(lv)(lv)乘(cheng)朔(shuo)余，为十(shi)(shi)(shi)(shi)(shi)四(si)万九(jiu)(jiu)(jiu)千(qian)(qian)(qian)七(qi)百(bai)，以(yi)(yi)四(si)十(shi)(shi)(shi)(shi)(shi)九(jiu)(jiu)(jiu)用、二十(shi)(shi)(shi)(shi)(shi)四(si)象(xiang)虚之(zhi)(zhi)(zhi)(zhi)，复(fu)以(yi)(yi)爻率(lv)(lv)(lv)约之(zhi)(zhi)(zhi)(zhi)，为四(si)百(bai)九(jiu)(jiu)(jiu)十(shi)(shi)(shi)(shi)(shi)八、微分七(qi)十(shi)(shi)(shi)(shi)(shi)五太半(ban)，则章(zhang)微之(zhi)(zhi)(zhi)(zhi)中率(lv)(lv)(lv)也。二十(shi)(shi)(shi)(shi)(shi)四(si)象(xiang)，象(xiang)有四(si)十(shi)(shi)(shi)(shi)(shi)九(jiu)(jiu)(jiu)蓍，凡千(qian)(qian)(qian)一(yi)百(bai)七(qi)十(shi)(shi)(shi)(shi)(shi)六。故虚遁(dun)之(zhi)(zhi)(zhi)(zhi)数七(qi)十(shi)(shi)(shi)(shi)(shi)三(san)，半(ban)气(qi)(qi)(qi)朔(shuo)之(zhi)(zhi)(zhi)(zhi)母，以(yi)(yi)三(san)极乘(cheng)参伍，以(yi)(yi)两仪乘(cheng)二十(shi)(shi)(shi)(shi)(shi)四(si)变，因而(er)并之(zhi)(zhi)(zhi)(zhi)，得千(qian)(qian)(qian)六百(bai)一(yi)十(shi)(shi)(shi)(shi)(shi)三(san)，为朔(shuo)余。四(si)揲气(qi)(qi)(qi)朔(shuo)之(zhi)(zhi)(zhi)(zhi)母，以(yi)(yi)八气(qi)(qi)(qi)九(jiu)(jiu)(jiu)精遁(dun)其十(shi)(shi)(shi)(shi)(shi)七(qi)，得七(qi)百(bai)四(si)十(shi)(shi)(shi)(shi)(shi)三(san)，为气(qi)(qi)(qi)余。岁(sui)(sui)八万九(jiu)(jiu)(jiu)千(qian)(qian)(qian)七(qi)百(bai)七(qi)十(shi)(shi)(shi)(shi)(shi)三(san)而(er)气(qi)(qi)(qi)朔(shuo)会，是(shi)谓(wei)章(zhang)率(lv)(lv)(lv)。岁(sui)(sui)二亿七(qi)千(qian)(qian)(qian)二百(bai)九(jiu)(jiu)(jiu)十(shi)(shi)(shi)(shi)(shi)万九(jiu)(jiu)(jiu)百(bai)二十(shi)(shi)(shi)(shi)(shi)而(er)无(wu)小余，合于夜(ye)半(ban)，是(shi)谓(wei)蔀(bu)率(lv)(lv)(lv)。岁(sui)(sui)百(bai)六十(shi)(shi)(shi)(shi)(shi)三(san)亿七(qi)千(qian)(qian)(qian)四(si)百(bai)五十(shi)(shi)(shi)(shi)(shi)九(jiu)(jiu)(jiu)万五千(qian)(qian)(qian)二百(bai)而(er)大余与岁(sui)(sui)建俱终(zhong)，是(shi)谓(wei)元率(lv)(lv)(lv)。此不易之(zhi)(zhi)(zhi)(zhi)道也。
策以(yi)纪(ji)日，象以(yi)纪(ji)月(yue)。故乾(qian)坤(kun)之(zhi)(zhi)策三(san)(san)百(bai)六十(shi)(shi)(shi)，为日度之(zhi)(zhi)准。乾(qian)坤(kun)之(zhi)(zhi)用四十(shi)(shi)(shi)九(jiu)象，为月(yue)弦(xian)(xian)之(zhi)(zhi)检。日之(zhi)(zhi)一(yi)度，不盈(ying)全策；月(yue)之(zhi)(zhi)一(yi)弦(xian)(xian)，不盈(ying)全用。故策余万(wan)五千九(jiu)百(bai)四十(shi)(shi)(shi)三(san)(san)，则十(shi)(shi)(shi)有(you)二(er)(er)中(zhong)所(suo)盈(ying)也(ye)(ye)。用差万(wan)七(qi)千一(yi)百(bai)二(er)(er)十(shi)(shi)(shi)四，则十(shi)(shi)(shi)有(you)二(er)(er)朔所(suo)虚也(ye)(ye)。综盈(ying)虚之(zhi)(zhi)数，五岁(sui)而(er)再闰。中(zhong)节相(xiang)距，皆(jie)当(dang)三(san)(san)五；弦(xian)(xian)望相(xiang)距，皆(jie)当(dang)二(er)(er)七(qi)。升绛之(zhi)(zhi)应，发(fa)敛之(zhi)(zhi)候，皆(jie)纪(ji)之(zhi)(zhi)以(yi)策而(er)从日者也(ye)(ye)。表里之(zhi)(zhi)行，朓朒之(zhi)(zhi)变，皆(jie)纪(ji)之(zhi)(zhi)以(yi)用而(er)从月(yue)者也(ye)(ye)。
积算曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)演纪，日(ri)法曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)通法，月(yue)气曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)中(zhong)(zhong)(zhong)朔，朔实(shi)曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)揲法，岁分(fen)曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)策(ce)(ce)(ce)实(shi)，周(zhou)天(tian)(tian)曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)乾实(shi)，余(yu)分(fen)曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)虚分(fen)。气策(ce)(ce)(ce)曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)三元，一元之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)策(ce)(ce)(ce)，则(ze)(ze)天(tian)(tian)一遁行(xing)(xing)也(ye)。月(yue)策(ce)(ce)(ce)曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)四象，一象之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)策(ce)(ce)(ce)，则(ze)(ze)朔、弦、望(wang)相(xiang)距也(ye)。五行(xing)(xing)用事，曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)发敛(lian)。候(hou)策(ce)(ce)(ce)曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)天(tian)(tian)中(zhong)(zhong)(zhong)，卦策(ce)(ce)(ce)曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)地中(zhong)(zhong)(zhong)，半卦曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)贞悔。旬周(zhou)曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)爻数，小分(fen)母(mu)曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)象统(tong)。日(ri)行(xing)(xing)曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)躔，其差(cha)曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)盈缩(suo)，积盈缩(suo)曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)先(xian)后。古者平(ping)朔，月(yue)朝见曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)朒，夕见曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)朓。今以(yi)(yi)日(ri)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)所(suo)盈缩(suo)、月(yue)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)所(suo)迟(chi)疾损益之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)，或进退(tui)(tui)其日(ri)，以(yi)(yi)为(wei)定朔。舒(shu)亟之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)度，乃数使然，躔离(li)相(xiang)错，偕以(yi)(yi)损益，故同谓(wei)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)朓朒。月(yue)行(xing)(xing)曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)离(li)，迟(chi)疾曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)转度，母(mu)曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)转法。迟(chi)疾有衰，其变者势也(ye)。月(yue)逶(wei)迤驯屈(qu)，行(xing)(xing)不(bu)(bu)中(zhong)(zhong)(zhong)道(dao)，进退(tui)(tui)迟(chi)速(su)，不(bu)(bu)率其常(chang)。过(guo)中(zhong)(zhong)(zhong)则(ze)(ze)为(wei)速(su)，不(bu)(bu)及(ji)中(zhong)(zhong)(zhong)则(ze)(ze)为(wei)迟(chi)。积迟(chi)谓(wei)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)屈(qu)，积速(su)谓(wei)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)伸(shen)。阳(yang)，执中(zhong)(zhong)(zhong)以(yi)(yi)出令，故曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)先(xian)后；阴，含(han)章(zhang)以(yi)(yi)听命，故曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)屈(qu)伸(shen)。日(ri)不(bu)(bu)及(ji)中(zhong)(zhong)(zhong)则(ze)(ze)损之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)，过(guo)则(ze)(ze)益之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)。月(yue)不(bu)(bu)及(ji)中(zhong)(zhong)(zhong)则(ze)(ze)益之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)，过(guo)则(ze)(ze)损之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)，尊卑之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)用睽，而(er)及(ji)中(zhong)(zhong)(zhong)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)志同。观晷景之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)进退(tui)(tui)，知(zhi)轨(gui)道(dao)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)升降。轨(gui)与晷名(ming)(ming)舛(chuan)而(er)义合(he)，其差(cha)则(ze)(ze)水(shui)漏之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)所(suo)从也(ye)。总名(ming)(ming)曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)轨(gui)漏。中(zhong)(zhong)(zhong)晷长(zhang)短谓(wei)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)陟降。景长(zhang)则(ze)(ze)夜(ye)短，景短则(ze)(ze)夜(ye)长(zhang)。积其陟降，谓(wei)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)消息。游交(jiao)曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)交(jiao)会，交(jiao)而(er)周(zhou)曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)交(jiao)终(zhong)。交(jiao)终(zhong)不(bu)(bu)及(ji)朔，谓(wei)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)朔差(cha)。交(jiao)中(zhong)(zhong)(zhong)不(bu)(bu)及(ji)望(wang)，谓(wei)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)望(wang)差(cha)。日(ri)道(dao)表曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)阳(yang)历，其里曰(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)(yue)阴历。五星见伏周(zhou)，谓(wei)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)终(zhong)率。以(yi)(yi)分(fen)从日(ri)谓(wei)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)终(zhong)日(ri)，其差(cha)为(wei)进退(tui)(tui)。
其二《中气议》曰：
历(li)(li)(li)(li)(li)(li)气始于(yu)(yu)(yu)冬至(zhi)(zhi)，稽其实，盖(gai)取(qu)诸晷(gui)景。《春(chun)秋传》僖公(gong)五年正(zheng)月(yue)(yue)辛(xin)亥(hai)(hai)朔(shuo)，日(ri)(ri)(ri)南(nan)至(zhi)(zhi)。以(yi)《周(zhou)历(li)(li)(li)(li)(li)(li)》推之(zhi)(zhi)(zhi)，入壬子(zi)蔀第四章(zhang)，以(yi)辛(xin)亥(hai)(hai)一(yi)分(fen)合(he)朔(shuo)冬至(zhi)(zhi)，《殷(yin)历(li)(li)(li)(li)(li)(li)》则(ze)(ze)壬子(zi)蔀首(shou)也。昭公(gong)二(er)十(shi)(shi)年二(er)月(yue)(yue)己(ji)(ji)丑(chou)朔(shuo)，日(ri)(ri)(ri)南(nan)至(zhi)(zhi)。鲁史失闰，至(zhi)(zhi)不在(zai)正(zheng)。左氏记之(zhi)(zhi)(zhi)，以(yi)惩司历(li)(li)(li)(li)(li)(li)之(zhi)(zhi)(zhi)罪(zui)。《周(zhou)历(li)(li)(li)(li)(li)(li)》得(de)(de)己(ji)(ji)丑(chou)二(er)分(fen)，《殷(yin)历(li)(li)(li)(li)(li)(li)》得(de)(de)庚寅(yin)一(yi)分(fen)。《殷(yin)历(li)(li)(li)(li)(li)(li)》南(nan)至(zhi)(zhi)常在(zai)十(shi)(shi)月(yue)(yue)晦(hui)，则(ze)(ze)中(zhong)气后(hou)天也。《周(zhou)历(li)(li)(li)(li)(li)(li)》蚀(shi)朔(shuo)差《经(jing)》或二(er)日(ri)(ri)(ri)，则(ze)(ze)合(he)朔(shuo)先(xian)天也。《传》所据者(zhe)《周(zhou)历(li)(li)(li)(li)(li)(li)》也，《纬》所据者(zhe)《殷(yin)历(li)(li)(li)(li)(li)(li)》也。气合(he)于(yu)(yu)(yu)《传》，朔(shuo)合(he)于(yu)(yu)(yu)《纬》，斯(si)得(de)(de)之(zhi)(zhi)(zhi)矣(yi)。《戊寅(yin)历(li)(li)(li)(li)(li)(li)》月(yue)(yue)气专合(he)于(yu)(yu)(yu)《纬》，《麟德(de)历(li)(li)(li)(li)(li)(li)》专合(he)于(yu)(yu)(yu)《传》，偏取(qu)之(zhi)(zhi)(zhi)，故两(liang)失之(zhi)(zhi)(zhi)。又(you)《命历(li)(li)(li)(li)(li)(li)序(xu)》以(yi)为(wei)孔子(zi)修《春(chun)秋》用(yong)《殷(yin)历(li)(li)(li)(li)(li)(li)》，使(shi)其数(shu)可传于(yu)(yu)(yu)后(hou)。考其蚀(shi)朔(shuo)不与《殷(yin)历(li)(li)(li)(li)(li)(li)》合(he)，及开(kai)元(yuan)十(shi)(shi)二(er)年，朔(shuo)差五日(ri)(ri)(ri)矣(yi)，气差八(ba)日(ri)(ri)(ri)矣(yi)。上不合(he)于(yu)(yu)(yu)《经(jing)》，下(xia)不足以(yi)传于(yu)(yu)(yu)后(hou)代，盖(gai)哀、平(ping)间治甲(jia)(jia)寅(yin)元(yuan)历(li)(li)(li)(li)(li)(li)者(zhe)托(tuo)之(zhi)(zhi)(zhi)，非古也。又(you)汉太(tai)史令张寿王说黄帝《调(diao)历(li)(li)(li)(li)(li)(li)》以(yi)非《太(tai)初》。有司劾：“官有黄帝《调(diao)历(li)(li)(li)(li)(li)(li)》不与寿王同，寿王所治乃《殷(yin)历(li)(li)(li)(li)(li)(li)》也。”汉自中(zhong)兴以(yi)来，图谶(chen)漏泄，而《考灵曜》、《命历(li)(li)(li)(li)(li)(li)序(xu)》皆有甲(jia)(jia)寅(yin)元(yuan)，其所起在(zai)《四分(fen)历(li)(li)(li)(li)(li)(li)》庚申元(yuan)后(hou)百一(yi)十(shi)(shi)四岁。延光初中(zhong)谒者(zhe)亶诵、灵帝时五官郎中(zhong)冯(feng)光等，皆请用(yong)之(zhi)(zhi)(zhi)，卒不施行。《纬》所载壬子(zi)冬至(zhi)(zhi)，则(ze)(ze)其遗术也。《鲁历(li)(li)(li)(li)(li)(li)》南(nan)至(zhi)(zhi)又(you)先(xian)《周(zhou)历(li)(li)(li)(li)(li)(li)》四分(fen)日(ri)(ri)(ri)之(zhi)(zhi)(zhi)三，而朔(shuo)后(hou)九百四十(shi)(shi)分(fen)日(ri)(ri)(ri)之(zhi)(zhi)(zhi)五十(shi)(shi)一(yi)，故僖公(gong)五年辛(xin)亥(hai)(hai)为(wei)十(shi)(shi)二(er)月(yue)(yue)晦(hui)，壬子(zi)为(wei)正(zheng)月(yue)(yue)朔(shuo)。又(you)推日(ri)(ri)(ri)蚀(shi)密(mi)于(yu)(yu)(yu)《殷(yin)历(li)(li)(li)(li)(li)(li)》，其以(yi)闰余一(yi)为(wei)章(zhang)首(shou)，亦取(qu)合(he)于(yu)(yu)(yu)当时也。
开(kai)元十(shi)二年(nian)十(shi)一月，阳城测(ce)景，以癸未(wei)极(ji)长，较其前后(hou)所(suo)差，则夜半前尚(shang)有(you)余分(fen)。新(xin)历(li)大余十(shi)九(jiu)(jiu)，加时九(jiu)(jiu)十(shi)九(jiu)(jiu)刻，而(er)《皇极(ji)》、《戊寅》、《麟德(de)历(li)》皆得甲申，以《玄始历(li)》气分(fen)二千(qian)四(si)(si)百四(si)(si)十(shi)三为(wei)率，推(tui)而(er)上之，则失(shi)《春(chun)秋》辛(xin)亥，是减分(fen)太多(duo)也(ye)。以《皇极(ji)历(li)》气分(fen)二千(qian)四(si)(si)百四(si)(si)十(shi)五为(wei)率，推(tui)而(er)上之，虽合《春(chun)秋》，而(er)失(shi)元嘉十(shi)九(jiu)(jiu)年(nian)乙巳冬至及开(kai)皇五年(nian)甲戌冬至、七年(nian)癸未(wei)夏至；若用(yong)《麟德(de)历(li)》率二千(qian)四(si)(si)百四(si)(si)十(shi)七，又失(shi)《春(chun)秋》己丑，是减分(fen)太少(shao)也(ye)。故新(xin)历(li)以二千(qian)四(si)(si)百四(si)(si)十(shi)四(si)(si)为(wei)率，而(er)旧(jiu)所(suo)失(shi)者皆中(zhong)矣。
汉会稽(ji)东部(bu)尉刘(liu)(liu)洪以(yi)(yi)《四(si)分》疏阔，由(you)斗分多，更(geng)(geng)以(yi)(yi)五百(bai)八十(shi)九(jiu)为(wei)纪法(fa)，百(bai)四(si)十(shi)五为(wei)斗分，减(jian)余(yu)(yu)太(tai)甚，是(shi)(shi)以(yi)(yi)不及四(si)十(shi)年(nian)而(er)(er)加(jia)时(shi)渐觉(jue)先天。韩(han)翊(yi)、杨伟、刘(liu)(liu)智等(deng)皆(jie)稍损益，更(geng)(geng)造新术(shu)，而(er)(er)皆(jie)依谶纬(wei)“三百(bai)岁(sui)改宪”之文，考《经》之合朔多中，较《传》之南(nan)至(zhi)则否(fou)。《玄始历》以(yi)(yi)为(wei)十(shi)九(jiu)年(nian)七闰(run)，皆(jie)有(you)余(yu)(yu)分，是(shi)(shi)以(yi)(yi)中气渐差。据浑天，二(er)分为(wei)东西之中，而(er)(er)晷景不等(deng)；二(er)至(zhi)为(wei)南(nan)北之极，而(er)(er)进退不齐。此古人所未(wei)达也。更(geng)(geng)因(yin)刘(liu)(liu)洪纪法(fa)，增十(shi)一年(nian)以(yi)(yi)为(wei)章岁(sui)，而(er)(er)减(jian)闰(run)余(yu)(yu)十(shi)九(jiu)分之一。春秋后五十(shi)四(si)年(nian)，岁(sui)在甲(jia)寅，直应(ying)钟(zhong)章首，与(yu)《景初历》闰(run)余(yu)(yu)皆(jie)尽。虽减(jian)章闰(run)，然中气加(jia)时(shi)尚差，故未(wei)合于(yu)《春秋》。其斗分几得中矣。
后代(dai)历(li)(li)(li)家，皆(jie)因(yin)循《玄始(shi)》，而(er)损益或过(guo)差。大(da)抵古历(li)(li)(li)未(wei)减斗分，其(qi)(qi)(qi)率(lv)自(zi)二(er)千(qian)五百以(yi)上(shang)(shang)。《乾(qian)象》至(zhi)于《元(yuan)(yuan)嘉历(li)(li)(li)》，未(wei)减闰(run)余，其(qi)(qi)(qi)率(lv)自(zi)二(er)千(qian)四(si)百六十(shi)(shi)以(yi)上(shang)(shang)。《玄始(shi)》、《大(da)明》至(zhi)《麟德历(li)(li)(li)》皆(jie)减分破章，其(qi)(qi)(qi)率(lv)自(zi)二(er)千(qian)四(si)百二(er)十(shi)(shi)九以(yi)上(shang)(shang)。较前(qian)代(dai)史(shi)官注记(ji)，惟元(yuan)(yuan)嘉十(shi)(shi)三年(nian)(nian)十(shi)(shi)一(yi)月(yue)甲戌景长(zhang)(zhang)(zhang)，《皇极》、《麟德》、《开(kai)元(yuan)(yuan)历(li)(li)(li)》皆(jie)得癸(gui)酉，盖(gai)日(ri)度变常尔。祖冲之既(ji)失(shi)(shi)(shi)甲戌冬(dong)至(zhi)，以(yi)为(wei)加时太(tai)早，增小(xiao)余以(yi)附(fu)会之。而(er)十(shi)(shi)二(er)年(nian)(nian)戊辰(chen)景辰(chen)，得己(ji)(ji)巳；十(shi)(shi)七年(nian)(nian)甲午景长(zhang)(zhang)(zhang)，得乙(yi)未(wei)；十(shi)(shi)八(ba)年(nian)(nian)己(ji)(ji)亥(hai)景长(zhang)(zhang)(zhang)，得庚子。合一(yi)失(shi)(shi)(shi)三，其(qi)(qi)(qi)失(shi)(shi)(shi)愈多。刘(liu)孝孙(sun)、张胄玄因(yin)之，小(xiao)余益强，又以(yi)十(shi)(shi)六年(nian)(nian)己(ji)(ji)丑景长(zhang)(zhang)(zhang)为(wei)庚寅矣。治历(li)(li)(li)者(zhe)纠合众同，以(yi)稽(ji)其(qi)(qi)(qi)所(suo)异(yi)，苟独(du)异(yi)焉，则失(shi)(shi)(shi)行(xing)(xing)可(ke)知。今曲就其(qi)(qi)(qi)一(yi)，而(er)少者(zhe)失(shi)(shi)(shi)三，多者(zhe)失(shi)(shi)(shi)五，是舍常数而(er)从失(shi)(shi)(shi)行(xing)(xing)也。周建德六年(nian)(nian)，以(yi)壬(ren)辰(chen)景长(zhang)(zhang)(zhang)，而(er)《麟德》、《开(kai)元(yuan)(yuan)历(li)(li)(li)》皆(jie)得癸(gui)巳。开(kai)皇七年(nian)(nian)，以(yi)癸(gui)未(wei)景短，而(er)《麟德》、《开(kai)元(yuan)(yuan)历(li)(li)(li)》皆(jie)得壬(ren)午。先(xian)后相戾，不可(ke)叶也，皆(jie)日(ri)行(xing)(xing)盈缩使然。
凡历(li)术在(zai)于常数，而不在(zai)于变行(xing)。既叶中行(xing)之(zhi)率(lv)，则可以两齐先(xian)后之(zhi)变矣。《麟德(de)》已前，实录所记，乃(nai)依(yi)时(shi)历(li)书(shu)之(zhi)，非候景所得。又(you)比年候景，长短(duan)不均，由加时(shi)有早晏，行(xing)度有盈缩也。
自春秋(qiu)以来(lai)，至(zhi)开(kai)(kai)元十二年，冬、夏至(zhi)凡三(san)十一事，《戊寅历》得十六，《麟(lin)德历》得二十三(san)，《开(kai)(kai)元历》得二十四。
其三《合朔议》曰：
日(ri)(ri)月(yue)合(he)度谓之(zhi)(zhi)朔。无所(suo)取之(zhi)(zhi)，取之(zhi)(zhi)蚀也。《春(chun)秋》日(ri)(ri)蚀有甲乙者(zhe)(zhe)三十(shi)(shi)四。《殷历》、《鲁历》先(xian)(xian)一日(ri)(ri)者(zhe)(zhe)十(shi)(shi)三，后一日(ri)(ri)者(zhe)(zhe)三；《周历》先(xian)(xian)一日(ri)(ri)者(zhe)(zhe)二(er)(er)十(shi)(shi)二(er)(er)，先(xian)(xian)二(er)(er)日(ri)(ri)者(zhe)(zhe)九(jiu)。其伪可知矣。
庄公(gong)(gong)(gong)(gong)(gong)(gong)三(san)(san)(san)十(shi)(shi)(shi)(shi)年(nian)(nian)(nian)(nian)九(jiu)(jiu)月(yue)(yue)庚午(wu)(wu)朔(shuo)(shuo)(shuo)，襄(xiang)公(gong)(gong)(gong)(gong)(gong)(gong)二十(shi)(shi)(shi)(shi)一年(nian)(nian)(nian)(nian)九(jiu)(jiu)月(yue)(yue)庚戌朔(shuo)(shuo)(shuo)，定(ding)(ding)公(gong)(gong)(gong)(gong)(gong)(gong)五(wu)年(nian)(nian)(nian)(nian)三(san)(san)(san)月(yue)(yue)辛(xin)亥(hai)(hai)朔(shuo)(shuo)(shuo)，当(dang)以(yi)盈缩、迟速为定(ding)(ding)朔(shuo)(shuo)(shuo)。《殷(yin)历(li)》虽合(he)(he)，适然耳，非(fei)正也(ye)。僖公(gong)(gong)(gong)(gong)(gong)(gong)五(wu)年(nian)(nian)(nian)(nian)正月(yue)(yue)辛(xin)亥(hai)(hai)朔(shuo)(shuo)(shuo)，十(shi)(shi)(shi)(shi)二月(yue)(yue)丙子朔(shuo)(shuo)(shuo)，十(shi)(shi)(shi)(shi)四年(nian)(nian)(nian)(nian)三(san)(san)(san)月(yue)(yue)己(ji)丑(chou)朔(shuo)(shuo)(shuo)；文(wen)公(gong)(gong)(gong)(gong)(gong)(gong)元年(nian)(nian)(nian)(nian)五(wu)月(yue)(yue)辛(xin)酉朔(shuo)(shuo)(shuo)，十(shi)(shi)(shi)(shi)一年(nian)(nian)(nian)(nian)三(san)(san)(san)月(yue)(yue)甲(jia)申晦(hui)；襄(xiang)公(gong)(gong)(gong)(gong)(gong)(gong)十(shi)(shi)(shi)(shi)九(jiu)(jiu)年(nian)(nian)(nian)(nian)五(wu)月(yue)(yue)壬辰(chen)晦(hui)；昭公(gong)(gong)(gong)(gong)(gong)(gong)元年(nian)(nian)(nian)(nian)十(shi)(shi)(shi)(shi)二月(yue)(yue)甲(jia)辰(chen)朔(shuo)(shuo)(shuo)，二十(shi)(shi)(shi)(shi)年(nian)(nian)(nian)(nian)二月(yue)(yue)己(ji)丑(chou)朔(shuo)(shuo)(shuo)，二十(shi)(shi)(shi)(shi)三(san)(san)(san)年(nian)(nian)(nian)(nian)正月(yue)(yue)壬寅(yin)(yin)朔(shuo)(shuo)(shuo)、七月(yue)(yue)戊(wu)(wu)辰(chen)晦(hui)：皆与(yu)《周(zhou)历(li)》合(he)(he)。其(qi)所记多(duo)周(zhou)、齐(qi)、晋事，盖周(zhou)王所颁，齐(qi)、晋用之。僖公(gong)(gong)(gong)(gong)(gong)(gong)十(shi)(shi)(shi)(shi)五(wu)年(nian)(nian)(nian)(nian)九(jiu)(jiu)月(yue)(yue)己(ji)卯(mao)晦(hui)，十(shi)(shi)(shi)(shi)六年(nian)(nian)(nian)(nian)正月(yue)(yue)戊(wu)(wu)申朔(shuo)(shuo)(shuo)；成公(gong)(gong)(gong)(gong)(gong)(gong)十(shi)(shi)(shi)(shi)六年(nian)(nian)(nian)(nian)六月(yue)(yue)甲(jia)午(wu)(wu)晦(hui)；襄(xiang)公(gong)(gong)(gong)(gong)(gong)(gong)十(shi)(shi)(shi)(shi)八年(nian)(nian)(nian)(nian)十(shi)(shi)(shi)(shi)月(yue)(yue)丙寅(yin)(yin)晦(hui)，十(shi)(shi)(shi)(shi)一月(yue)(yue)丁卯(mao)朔(shuo)(shuo)(shuo)，二十(shi)(shi)(shi)(shi)六年(nian)(nian)(nian)(nian)三(san)(san)(san)月(yue)(yue)甲(jia)寅(yin)(yin)朔(shuo)(shuo)(shuo)，二十(shi)(shi)(shi)(shi)七年(nian)(nian)(nian)(nian)六月(yue)(yue)丁未朔(shuo)(shuo)(shuo)：与(yu)《殷(yin)历(li)》、《鲁历(li)》合(he)(he)。此(ci)非(fei)合(he)(he)蚀，故仲尼因循(xun)时史，而所记多(duo)宋、鲁事，与(yu)齐(qi)、晋不同可知矣。
昭(zhao)公(gong)十(shi)二(er)(er)(er)年十(shi)月(yue)壬(ren)申朔，原舆人(ren)(ren)逐原伯绞，与(yu)《鲁(lu)历(li)(li)(li)》、《周(zhou)历(li)(li)(li)》皆(jie)差(cha)一(yi)(yi)日，此(ci)丘明(ming)即其所(suo)闻书之(zhi)(zhi)(zhi)(zhi)也。僖公(gong)二(er)(er)(er)十(shi)二(er)(er)(er)年十(shi)一(yi)(yi)月(yue)己巳朔，宋、楚战(zhan)于泓(hong)。《周(zhou)》、《殷(yin)》、《鲁(lu)历(li)(li)(li)》皆(jie)先(xian)一(yi)(yi)日，楚人(ren)(ren)所(suo)赴也。昭(zhao)公(gong)二(er)(er)(er)十(shi)年六月(yue)丁巳晦，卫侯与(yu)北宫(gong)喜(xi)盟；七月(yue)戊午朔，遂(sui)盟国人(ren)(ren)。三(san)历(li)(li)(li)皆(jie)先(xian)二(er)(er)(er)日，卫人(ren)(ren)所(suo)赴也。此(ci)则(ze)列国之(zhi)(zhi)(zhi)(zhi)历(li)(li)(li)不可以(yi)(yi)(yi)一(yi)(yi)术齐矣。而(er)《长历(li)(li)(li)》日子不在其月(yue)，则(ze)改易(yi)闰(run)余，欲以(yi)(yi)(yi)求合(he)。故(gu)闰(run)月(yue)相距，近则(ze)十(shi)余月(yue)，远或(huo)七十(shi)余月(yue)，此(ci)杜预所(suo)甚缪也。夫合(he)朔先(xian)天(tian)，则(ze)《经》书日蚀以(yi)(yi)(yi)纠之(zhi)(zhi)(zhi)(zhi)。中气后(hou)天(tian)，则(ze)《传》书南至以(yi)(yi)(yi)明(ming)之(zhi)(zhi)(zhi)(zhi)。其在晦、二(er)(er)(er)日，则(ze)原乎定朔以(yi)(yi)(yi)得之(zhi)(zhi)(zhi)(zhi)。列国之(zhi)(zhi)(zhi)(zhi)历(li)(li)(li)或(huo)殊，则(ze)稽于六家之(zhi)(zhi)(zhi)(zhi)术以(yi)(yi)(yi)知之(zhi)(zhi)(zhi)(zhi)。此(ci)四者，皆(jie)治历(li)(li)(li)之(zhi)(zhi)(zhi)(zhi)大端，而(er)预所(suo)未晓故(gu)也。
新历本《春秋》日蚀、古史(shi)交会加时(shi)及史(shi)官候簿所详，稽其(qi)(qi)进退之(zhi)中(zhong)(zhong)，以立常率。然后以日躔(chan)、月离、先后、屈伸之(zhi)变(bian)，偕损益之(zhi)。故经(jing)朔虽得其(qi)(qi)中(zhong)(zhong)，而躔(chan)离或失其(qi)(qi)正；若(ruo)(ruo)躔(chan)离各(ge)得其(qi)(qi)度，而经(jing)朔或失其(qi)(qi)中(zhong)(zhong)，则参求(qiu)累(lei)代，必(bi)有差矣。三(san)者迭相(xiang)为经(jing)，若(ruo)(ruo)权衡(heng)相(xiang)持，使千有五百年间朔必(bi)在昼，望(wang)必(bi)在夜，其(qi)(qi)加时(shi)又合，则三(san)术之(zhi)交，自(zi)然各(ge)当其(qi)(qi)正，此最微者也。若(ruo)(ruo)乾度盈虚，与(yu)时(shi)消息，告谴(qian)于经(jing)数(shu)之(zhi)表，变(bian)常于潜遁之(zhi)中(zhong)(zhong)，则圣(sheng)人且犹不(bu)质，非筹历之(zhi)所能及矣。
昔人(ren)考天事，多不(bu)(bu)知定(ding)(ding)朔(shuo)(shuo)(shuo)。假蚀在二(er)(er)(er)日(ri)(ri)，而(er)(er)常(chang)朔(shuo)(shuo)(shuo)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)晨，月(yue)(yue)见(jian)东(dong)方；食在晦(hui)(hui)(hui)(hui)日(ri)(ri)，则常(chang)朔(shuo)(shuo)(shuo)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)夕，月(yue)(yue)见(jian)西(xi)方。理数(shu)(shu)然也(ye)(ye)(ye)(ye)。而(er)(er)或(huo)以(yi)(yi)为(wei)朓(tiao)朒变(bian)行(xing)，或(huo)以(yi)(yi)为(wei)历术疏阔，遇常(chang)朔(shuo)(shuo)(shuo)朝(chao)见(jian)则增朔(shuo)(shuo)(shuo)余，夕见(jian)则减朔(shuo)(shuo)(shuo)余，此纪历所以(yi)(yi)屡(lv)迁也(ye)(ye)(ye)(ye)。汉编䜣、李梵(fan)等(deng)又以(yi)(yi)晦(hui)(hui)(hui)(hui)犹(you)(you)月(yue)(yue)见(jian)，欲令蔀首(shou)先大(da)。贾逵(kui)曰：“《春秋》书朔(shuo)(shuo)(shuo)、晦(hui)(hui)(hui)(hui)者，朔(shuo)(shuo)(shuo)必(bi)有朔(shuo)(shuo)(shuo)，晦(hui)(hui)(hui)(hui)必(bi)有晦(hui)(hui)(hui)(hui)，晦(hui)(hui)(hui)(hui)、朔(shuo)(shuo)(shuo)必(bi)在其月(yue)(yue)前也(ye)(ye)(ye)(ye)。先大(da)，则一(yi)月(yue)(yue)再朔(shuo)(shuo)(shuo)，后(hou)月(yue)(yue)无(wu)朔(shuo)(shuo)(shuo)，是(shi)朔(shuo)(shuo)(shuo)不(bu)(bu)可必(bi)也(ye)(ye)(ye)(ye)。䜣、梵(fan)等(deng)欲谐偶(ou)十六(liu)日(ri)(ri)、月(yue)(yue)朓(tiao)昏、晦(hui)(hui)(hui)(hui)当灭而(er)(er)已(yi)。又晦(hui)(hui)(hui)(hui)与合朔(shuo)(shuo)(shuo)同时(shi)，不(bu)(bu)得(de)异日(ri)(ri)。”考逵(kui)等(deng)所言，盖知之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)矣。晦(hui)(hui)(hui)(hui)朔(shuo)(shuo)(shuo)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)交(jiao)，始终相际(ji)，则光尽明(ming)生之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)限，度数(shu)(shu)宜均。故合于(yu)(yu)子正(zheng)，则晦(hui)(hui)(hui)(hui)日(ri)(ri)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)朝(chao)，犹(you)(you)朔(shuo)(shuo)(shuo)日(ri)(ri)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)夕也(ye)(ye)(ye)(ye)，是(shi)以(yi)(yi)月(yue)(yue)皆不(bu)(bu)见(jian)；若合于(yu)(yu)午正(zheng)，则晦(hui)(hui)(hui)(hui)日(ri)(ri)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)晨，犹(you)(you)二(er)(er)(er)日(ri)(ri)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)昏也(ye)(ye)(ye)(ye)，是(shi)以(yi)(yi)月(yue)(yue)或(huo)皆见(jian)。若阴阳迟速，轨(gui)漏(lou)加时(shi)不(bu)(bu)同，举其中数(shu)(shu)率，去日(ri)(ri)十三(san)度以(yi)(yi)上而(er)(er)月(yue)(yue)见(jian)，乃(nai)其常(chang)也(ye)(ye)(ye)(ye)。且晦(hui)(hui)(hui)(hui)日(ri)(ri)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)光未(wei)尽也(ye)(ye)(ye)(ye)，如二(er)(er)(er)日(ri)(ri)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)明(ming)已(yi)生也(ye)(ye)(ye)(ye)。一(yi)以(yi)(yi)为(wei)是(shi)，一(yi)以(yi)(yi)为(wei)非。又常(chang)朔(shuo)(shuo)(shuo)进退，则定(ding)(ding)朔(shuo)(shuo)(shuo)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)晦(hui)(hui)(hui)(hui)、二(er)(er)(er)也(ye)(ye)(ye)(ye)。或(huo)以(yi)(yi)为(wei)变(bian)，或(huo)以(yi)(yi)为(wei)常(chang)。是(shi)未(wei)通(tong)于(yu)(yu)四三(san)交(jiao)质之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)论也(ye)(ye)(ye)(ye)。
综近代诸历，以百万为率(lv)齐之(zhi)(zhi)(zhi)，其(qi)所(suo)差，少或一分，多至十数失一分。考《春秋(qiu)》才(cai)差一刻，而(er)百数年间(jian)不足成朓朒之(zhi)(zhi)(zhi)异。施(shi)行未几，旋复疏阔，由(you)未知躔(chan)离经朔相求耳。李(li)业兴、甄鸾等欲求天验，辄加(jia)减月分，迁革不已，朓朒相戾，又未知昏明之(zhi)(zhi)(zhi)限(xian)与定朔故(gu)也(ye)。杨伟采《乾(qian)象(xiang)》为迟疾(ji)阴阳历，虽知加(jia)时后天，蚀(shi)不在朔，而(er)未能有(you)以更之(zhi)(zhi)(zhi)也(ye)。
何承天欲以(yi)(yi)(yi)盈(ying)缩定(ding)(ding)朔(shuo)(shuo)望(wang)小(xiao)(xiao)余。钱乐之(zhi)(zhi)以(yi)(yi)(yi)为：“推(tui)(tui)交(jiao)会时(shi)刻虽审(shen)，而(er)月(yue)频(pin)三大(da)(da)二小(xiao)(xiao)。日(ri)(ri)(ri)蚀(shi)不(bu)唯在朔(shuo)(shuo)，亦有(you)在晦(hui)、二者。”皮(pi)延宗(zong)又(you)以(yi)(yi)(yi)为：“纪(ji)(ji)首(shou)合朔(shuo)(shuo)，大(da)(da)小(xiao)(xiao)余当(dang)尽，若每(mei)月(yue)定(ding)(ding)之(zhi)(zhi)，则纪(ji)(ji)首(shou)位(wei)盈(ying)，当(dang)退一(yi)日(ri)(ri)(ri)，便应以(yi)(yi)(yi)故(gu)岁(sui)之(zhi)(zhi)晦(hui)为新纪(ji)(ji)之(zhi)(zhi)首(shou)。立法之(zhi)(zhi)制，如为不(bu)便。”承天乃(nai)止。虞(yu)广(guang)刂(dao)曰(yue)(yue)：“所(suo)谓朔(shuo)(shuo)在会合，苟(gou)躔次既同，何患于(yu)频(pin)大(da)(da)也(ye)(ye)(ye)？日(ri)(ri)(ri)月(yue)相离，何患于(yu)频(pin)小(xiao)(xiao)也(ye)(ye)(ye)？”《春秋》日(ri)(ri)(ri)蚀(shi)不(bu)书(shu)朔(shuo)(shuo)者八(ba)，《公(gong)羊》曰(yue)(yue)：“二日(ri)(ri)(ri)也(ye)(ye)(ye)。”《谷梁》曰(yue)(yue)：“晦(hui)也(ye)(ye)(ye)。”《左氏》曰(yue)(yue)：“官失之(zhi)(zhi)也(ye)(ye)(ye)。”。刘(liu)孝孙(sun)推(tui)(tui)俱得(de)朔(shuo)(shuo)日(ri)(ri)(ri)，以(yi)(yi)(yi)丘明为是，乃(nai)与刘(liu)焯皆议定(ding)(ding)朔(shuo)(shuo)，为有(you)司所(suo)抑不(bu)得(de)行。傅仁均始为定(ding)(ding)朔(shuo)(shuo)，而(er)曰(yue)(yue)“晦(hui)不(bu)东见，朔(shuo)(shuo)不(bu)西朓”，以(yi)(yi)(yi)为昏晦(hui)当(dang)灭，亦䜣、梵之(zhi)(zhi)论。淳风因循《皇极(ji)》，《皇极(ji)》密于(yu)《麟德》，以(yi)(yi)(yi)朔(shuo)(shuo)余乘三千四(si)十(shi)(shi)(shi)，乃(nai)一(yi)万(wan)除之(zhi)(zhi)，就(jiu)全数得(de)千六百一(yi)十(shi)(shi)(shi)三。又(you)以(yi)(yi)(yi)九百四(si)十(shi)(shi)(shi)乘之(zhi)(zhi)，以(yi)(yi)(yi)三千四(si)十(shi)(shi)(shi)而(er)一(yi)，得(de)四(si)百九十(shi)(shi)(shi)八(ba)秒七十(shi)(shi)(shi)五太强(qiang)，是为《四(si)分(fen)》余率。
刘洪以古历(li)斗分太强，久当后(hou)天(tian)，乃(nai)(nai)先正(zheng)斗分，而(er)后(hou)求朔(shuo)法(fa)，故朔(shuo)余之(zhi)母(mu)烦(fan)矣(yi)(yi)。韩翊以《乾象》朔(shuo)分太弱(ruo)，久当先天(tian)，乃(nai)(nai)先考朔(shuo)分，而(er)后(hou)覆求度法(fa)，故度余之(zhi)母(mu)烦(fan)矣(yi)(yi)。何承天(tian)反覆相求，使气朔(shuo)之(zhi)母(mu)合简易之(zhi)率，而(er)星数不得(de)同(tong)元矣(yi)(yi)。李业兴、宋(song)景(jing)业、甄鸾、张宾(bin)欲使六甲之(zhi)首众术(shu)同(tong)元，而(er)气朔(shuo)余分，其细甚矣(yi)(yi)。《麟德历(li)》有总法(fa)，《开元历(li)》有通法(fa)，故积岁(sui)如月分之(zhi)数，而(er)后(hou)闰余偕尽。
考汉元光(guang)已来史(shi)官注记，日蚀有加时者凡(fan)三十七事，《麟德历(li)》得(de)(de)五，《开元历(li)》得(de)(de)二(er)(er)十二(er)(er)。
其四(si)《没灭略(lve)例》曰：
古者(zhe)以中(zhong)气所盈(ying)之(zhi)日为(wei)没(mei)(mei)(mei)，没(mei)(mei)(mei)分(fen)偕尽(jin)者(zhe)为(wei)灭；《开元(yuan)历》以中(zhong)分(fen)所盈(ying)为(wei)没(mei)(mei)(mei)，朔分(fen)所虚(xu)为(wei)灭。综终岁(sui)没(mei)(mei)(mei)分(fen)，谓之(zhi)策余；终岁(sui)灭分(fen)，谓之(zhi)用差。皆归于揲易再扌力而后挂也。
其五《卦候议》曰：
七十(shi)二候，原于周公《时(shi)训》。《月令》虽颇有增益，然先后之次(ci)则同(tong)。自后魏始(shi)载于历(li)，乃依(yi)《易轨(gui)》所传，不(bu)合经(jing)义。今改从古。
其六《卦议》曰：
十(shi)二月卦(gua)(gua)出于《孟氏(shi)章句》，其说《易(yi)》本于气(qi)，而(er)后以人(ren)事(shi)明之(zhi)。京(jing)氏(shi)又以卦(gua)(gua)爻(yao)配期之(zhi)日(ri)(ri)，坎、离、震、兑，其用事(shi)自分、至(zhi)(zhi)之(zhi)首，皆(jie)得八十(shi)分日(ri)(ri)之(zhi)七(qi)(qi)十(shi)三。颐、晋(jin)、井(jing)、大畜，皆(jie)五日(ri)(ri)十(shi)四分，余皆(jie)六日(ri)(ri)七(qi)(qi)分，止于占灾眚(sheng)与吉凶(xiong)善败之(zhi)事(shi)。至(zhi)(zhi)于观阴阳之(zhi)变(bian)，则错乱(luan)而(er)不明。自《乾象历》以降，皆(jie)因京(jing)氏(shi)。惟(wei)《天保(bao)历》依(yi)《易(yi)通统轨图》。自八十(shi)有(you)二节、五卦(gua)(gua)、初(chu)爻(yao)，相次用事(shi)，及上爻(yao)而(er)与中气(qi)偕终，非京(jing)氏(shi)本旨(zhi)及《七(qi)(qi)略》所传。按郎顗所传，卦(gua)(gua)皆(jie)六日(ri)(ri)七(qi)(qi)分，不以初(chu)爻(yao)相次用事(shi)，齐历谬矣。又京(jing)氏(shi)减七(qi)(qi)十(shi)三分，为四正之(zhi)候(hou)，其说不经，欲附会(hui)《纬》文《七(qi)(qi)日(ri)(ri)来复》而(er)已。
夫(fu)阳(yang)精道(dao)消，静(jing)(jing)而(er)(er)无迹(ji)，不过极(ji)(ji)(ji)其(qi)正数，至(zhi)七(qi)(qi)而(er)(er)通矣。七(qi)(qi)者(zhe)，阳(yang)之(zhi)(zhi)(zhi)(zhi)正也，安在益(yi)其(qi)小余，令(ling)七(qi)(qi)日而(er)(er)后雷(lei)动地(di)中(zhong)乎？当据孟氏(shi)，自冬至(zhi)初，中(zhong)孚用(yong)事，一月之(zhi)(zhi)(zhi)(zhi)策，九(jiu)(jiu)六、七(qi)(qi)八(ba)，是为(wei)三(san)十(shi)。而(er)(er)卦以(yi)地(di)六，候以(yi)天五(wu)，五(wu)六相乘，消息一变，十(shi)有(you)(you)二(er)(er)(er)变而(er)(er)岁(sui)复初。坎(kan)(kan)、震、离(li)(li)(li)(li)、兑(dui)，二(er)(er)(er)十(shi)四气(qi)，次主(zhu)(zhu)一爻(yao)，其(qi)初则二(er)(er)(er)至(zhi)、二(er)(er)(er)分也。坎(kan)(kan)以(yi)阴包阳(yang)，故自北(bei)正，微阳(yang)动于(yu)(yu)下，升(sheng)而(er)(er)未(wei)达，极(ji)(ji)(ji)于(yu)(yu)二(er)(er)(er)月，凝涸之(zhi)(zhi)(zhi)(zhi)气(qi)消，坎(kan)(kan)运(yun)终焉(yan)。春分出于(yu)(yu)震，始(shi)(shi)据万物之(zhi)(zhi)(zhi)(zhi)元，为(wei)主(zhu)(zhu)于(yu)(yu)内(nei)，则群阴化而(er)(er)从之(zhi)(zhi)(zhi)(zhi)，极(ji)(ji)(ji)于(yu)(yu)南正，而(er)(er)丰大之(zhi)(zhi)(zhi)(zhi)变穷(qiong)，震功(gong)究焉(yan)。离(li)(li)(li)(li)以(yi)阳(yang)包阴，故自南正，微阴生(sheng)于(yu)(yu)地(di)下，积(ji)而(er)(er)未(wei)章，至(zhi)于(yu)(yu)八(ba)月，文明之(zhi)(zhi)(zhi)(zhi)质衰，离(li)(li)(li)(li)运(yun)终焉(yan)。仲秋阴形于(yu)(yu)兑(dui)，始(shi)(shi)循(xun)万物之(zhi)(zhi)(zhi)(zhi)末，为(wei)主(zhu)(zhu)于(yu)(yu)内(nei)，群阳(yang)降(jiang)而(er)(er)承之(zhi)(zhi)(zhi)(zhi)，极(ji)(ji)(ji)于(yu)(yu)北(bei)正，而(er)(er)天泽之(zhi)(zhi)(zhi)(zhi)施穷(qiong)，兑(dui)功(gong)究焉(yan)。故阳(yang)七(qi)(qi)之(zhi)(zhi)(zhi)(zhi)静(jing)(jing)始(shi)(shi)于(yu)(yu)坎(kan)(kan)，阳(yang)九(jiu)(jiu)之(zhi)(zhi)(zhi)(zhi)动始(shi)(shi)于(yu)(yu)震，阴八(ba)之(zhi)(zhi)(zhi)(zhi)静(jing)(jing)始(shi)(shi)于(yu)(yu)离(li)(li)(li)(li)，阴六之(zhi)(zhi)(zhi)(zhi)动始(shi)(shi)于(yu)(yu)兑(dui)。故四象(xiang)之(zhi)(zhi)(zhi)(zhi)变，皆(jie)兼六爻(yao)，而(er)(er)中(zhong)节(jie)之(zhi)(zhi)(zhi)(zhi)应备矣。《易》爻(yao)当日，十(shi)有(you)(you)二(er)(er)(er)中(zhong)，直全卦之(zhi)(zhi)(zhi)(zhi)初；十(shi)有(you)(you)二(er)(er)(er)节(jie)，直全卦之(zhi)(zhi)(zhi)(zhi)中(zhong)。齐历又以(yi)节(jie)在贞，气(qi)在悔，非是。
其七《日度议》曰：
古(gu)历(li)，日有常度(du)(du)，天周(zhou)为(wei)岁(sui)(sui)终，故(gu)系星度(du)(du)于(yu)(yu)节气。其(qi)说似是而非，故(gu)久而益差。虞喜(xi)觉之，使天为(wei)天，岁(sui)(sui)为(wei)岁(sui)(sui)，乃(nai)立差以追其(qi)变，使五(wu)十(shi)(shi)年退(tui)一(yi)度(du)(du)。何承(cheng)天以为(wei)太(tai)过，乃(nai)倍其(qi)年，而反(fan)不及。《皇极》取二家中数为(wei)七(qi)十(shi)(shi)五(wu)年，盖近(jin)之矣(yi)(yi)。考古(gu)史及日官候簿，以通法(fa)之三十(shi)(shi)九(jiu)分太(tai)为(wei)一(yi)岁(sui)(sui)之差。自帝尧演纪(ji)之端(duan)，在虚一(yi)度(du)(du)。及今开元甲子，却三十(shi)(shi)六度(du)(du)，而乾策复(fu)初矣(yi)(yi)。日在虚一(yi)，则鸟(niao)、火、昴、虚皆以仲月昏中，合于(yu)(yu)《尧典》。
刘炫依《大(da)(da)明历(li)》四(si)(si)十(shi)五年差(cha)一(yi)度(du)(du)(du)(du)(du)，则(ze)(ze)冬至(zhi)在(zai)虚(xu)(xu)、危，而(er)(er)夏(xia)(xia)(xia)至(zhi)火(huo)已过中(zhong)(zhong)(zhong)(zhong)(zhong)矣(yi)。梁武帝据虞(yu)广刂历(li)，百八(ba)(ba)十(shi)六年差(cha)一(yi)度(du)(du)(du)(du)(du)，则(ze)(ze)唐、虞(yu)之(zhi)(zhi)(zhi)(zhi)(zhi)际(ji)，日(ri)(ri)在(zai)斗、牛(niu)间，而(er)(er)冬至(zhi)昴(mao)(mao)尚(shang)未中(zhong)(zhong)(zhong)(zhong)(zhong)。以(yi)(yi)为皆承闰后节前(qian)，月却(que)使然。而(er)(er)此经终始(shi)一(yi)岁(sui)之(zhi)(zhi)(zhi)(zhi)(zhi)事，不(bu)(bu)容顿有(you)四(si)(si)闰，故(gu)淳风因为之(zhi)(zhi)(zhi)(zhi)(zhi)说(shuo)曰：“若(ruo)冬至(zhi)昴(mao)(mao)中(zhong)(zhong)(zhong)(zhong)(zhong)，则(ze)(ze)夏(xia)(xia)(xia)至(zhi)秋(qiu)分星(xing)火(huo)、星(xing)虚(xu)(xu)，皆在(zai)未正(zheng)(zheng)(zheng)(zheng)(zheng)之(zhi)(zhi)(zhi)(zhi)(zhi)西(xi)。若(ruo)以(yi)(yi)夏(xia)(xia)(xia)至(zhi)火(huo)中(zhong)(zhong)(zhong)(zhong)(zhong)，秋(qiu)分虚(xu)(xu)中(zhong)(zhong)(zhong)(zhong)(zhong)，则(ze)(ze)冬至(zhi)昴(mao)(mao)在(zai)巳正(zheng)(zheng)(zheng)(zheng)(zheng)之(zhi)(zhi)(zhi)(zhi)(zhi)东(dong)(dong)(dong)(dong)。互有(you)盈缩，不(bu)(bu)足以(yi)(yi)为岁(sui)差(cha)证。”是(shi)(shi)又(you)不(bu)(bu)然。今以(yi)(yi)四(si)(si)象分天，北正(zheng)(zheng)(zheng)(zheng)(zheng)玄枵中(zhong)(zhong)(zhong)(zhong)(zhong)，虚(xu)(xu)九(jiu)度(du)(du)(du)(du)(du)；东(dong)(dong)(dong)(dong)正(zheng)(zheng)(zheng)(zheng)(zheng)大(da)(da)火(huo)中(zhong)(zhong)(zhong)(zhong)(zhong)，房(fang)二(er)(er)度(du)(du)(du)(du)(du)；南(nan)正(zheng)(zheng)(zheng)(zheng)(zheng)鹑火(huo)中(zhong)(zhong)(zhong)(zhong)(zhong)，七星(xing)七度(du)(du)(du)(du)(du)；西(xi)正(zheng)(zheng)(zheng)(zheng)(zheng)大(da)(da)梁中(zhong)(zhong)(zhong)(zhong)(zhong)，昴(mao)(mao)七度(du)(du)(du)(du)(du)。总昼夜刻(ke)以(yi)(yi)约周天，命距(ju)中(zhong)(zhong)(zhong)(zhong)(zhong)星(xing)，则(ze)(ze)春(chun)(chun)分南(nan)正(zheng)(zheng)(zheng)(zheng)(zheng)中(zhong)(zhong)(zhong)(zhong)(zhong)天，秋(qiu)分北正(zheng)(zheng)(zheng)(zheng)(zheng)中(zhong)(zhong)(zhong)(zhong)(zhong)天。冬至(zhi)之(zhi)(zhi)(zhi)(zhi)(zhi)昏(hun)，西(xi)正(zheng)(zheng)(zheng)(zheng)(zheng)在(zai)午(wu)东(dong)(dong)(dong)(dong)十(shi)八(ba)(ba)度(du)(du)(du)(du)(du)；夏(xia)(xia)(xia)至(zhi)之(zhi)(zhi)(zhi)(zhi)(zhi)昏(hun)，东(dong)(dong)(dong)(dong)正(zheng)(zheng)(zheng)(zheng)(zheng)在(zai)午(wu)西(xi)十(shi)八(ba)(ba)度(du)(du)(du)(du)(du)：轨漏使然也(ye)。冬至(zhi)，日(ri)(ri)在(zai)虚(xu)(xu)一(yi)度(du)(du)(du)(du)(du)，则(ze)(ze)春(chun)(chun)分昏(hun)张一(yi)度(du)(du)(du)(du)(du)中(zhong)(zhong)(zhong)(zhong)(zhong)；秋(qiu)分虚(xu)(xu)九(jiu)度(du)(du)(du)(du)(du)中(zhong)(zhong)(zhong)(zhong)(zhong)；冬至(zhi)胃二(er)(er)度(du)(du)(du)(du)(du)中(zhong)(zhong)(zhong)(zhong)(zhong)，昴(mao)(mao)距(ju)星(xing)直午(wu)正(zheng)(zheng)(zheng)(zheng)(zheng)之(zhi)(zhi)(zhi)(zhi)(zhi)东(dong)(dong)(dong)(dong)十(shi)二(er)(er)度(du)(du)(du)(du)(du)；夏(xia)(xia)(xia)至(zhi)尾(wei)十(shi)一(yi)度(du)(du)(du)(du)(du)中(zhong)(zhong)(zhong)(zhong)(zhong)，心(xin)(xin)后星(xing)直午(wu)正(zheng)(zheng)(zheng)(zheng)(zheng)之(zhi)(zhi)(zhi)(zhi)(zhi)西(xi)十(shi)二(er)(er)度(du)(du)(du)(du)(du)。四(si)(si)序进退(tui)，不(bu)(bu)逾午(wu)正(zheng)(zheng)(zheng)(zheng)(zheng)间。而(er)(er)淳风以(yi)(yi)为不(bu)(bu)叶，非也(ye)。又(you)王孝通云：“如(ru)岁(sui)差(cha)自昴(mao)(mao)至(zhi)壁(bi)，则(ze)(ze)尧前(qian)七千(qian)余载，冬至(zhi)，日(ri)(ri)应在(zai)东(dong)(dong)(dong)(dong)井。井极(ji)(ji)北，故(gu)暑；斗极(ji)(ji)南(nan)，故(gu)寒。寒暑易位，必不(bu)(bu)然矣(yi)。”所谓岁(sui)差(cha)者，日(ri)(ri)与黄(huang)道(dao)俱差(cha)也(ye)。假(jia)冬至(zhi)日(ri)(ri)躔(chan)大(da)(da)火(huo)之(zhi)(zhi)(zhi)(zhi)(zhi)中(zhong)(zhong)(zhong)(zhong)(zhong)，则(ze)(ze)春(chun)(chun)分黄(huang)道(dao)交于虚(xu)(xu)九(jiu)，而(er)(er)南(nan)至(zhi)之(zhi)(zhi)(zhi)(zhi)(zhi)轨更出(chu)房(fang)、心(xin)(xin)外(wai)，距(ju)赤道(dao)亦二(er)(er)十(shi)四(si)(si)度(du)(du)(du)(du)(du)。设在(zai)东(dong)(dong)(dong)(dong)井，差(cha)亦如(ru)之(zhi)(zhi)(zhi)(zhi)(zhi)。若(ruo)日(ri)(ri)在(zai)东(dong)(dong)(dong)(dong)井，犹去(qu)极(ji)(ji)最(zui)(zui)近(jin)，表景(jing)最(zui)(zui)短，则(ze)(ze)是(shi)(shi)分、至(zhi)常(chang)居(ju)其所。黄(huang)道(dao)不(bu)(bu)迁，日(ri)(ri)行(xing)不(bu)(bu)退(tui)，又(you)安得谓之(zhi)(zhi)(zhi)(zhi)(zhi)岁(sui)差(cha)乎？孝通及淳风以(yi)(yi)为冬至(zhi)日(ri)(ri)在(zai)斗十(shi)三度(du)(du)(du)(du)(du)，昏(hun)东(dong)(dong)(dong)(dong)壁(bi)中(zhong)(zhong)(zhong)(zhong)(zhong)，昴(mao)(mao)在(zai)巽(xun)维之(zhi)(zhi)(zhi)(zhi)(zhi)左，向(xiang)明之(zhi)(zhi)(zhi)(zhi)(zhi)位，非无星(xing)也(ye)。水星(xing)昏(hun)正(zheng)(zheng)(zheng)(zheng)(zheng)可以(yi)(yi)为仲之(zhi)(zhi)(zhi)(zhi)(zhi)候，何必援昴(mao)(mao)于始(shi)觌(di)之(zhi)(zhi)(zhi)(zhi)(zhi)际(ji)，以(yi)(yi)惑(huo)民之(zhi)(zhi)(zhi)(zhi)(zhi)视听哉！
夏后氏四百(bai)三十(shi)(shi)(shi)二(er)年，日(ri)却差五度。太康十(shi)(shi)(shi)二(er)年戊子岁冬至，应在女十(shi)(shi)(shi)一(yi)度。
《书》曰：“乃(nai)季秋月朔(shuo)，辰(chen)弗集(ji)于(yu)房。”刘炫曰：“房，所舍(she)之次也(ye)。集(ji)，会(hui)也(ye)。会(hui)，合(he)(he)也(ye)。不(bu)合(he)(he)则日(ri)蚀可(ke)知。或(huo)以(yi)(yi)(yi)房为房星(xing)，知不(bu)然者(zhe)，且(qie)日(ri)之所在(zai)正可(ke)推而知之。君(jun)子(zi)慎(shen)疑，宁当以(yi)(yi)(yi)日(ri)在(zai)之宿为文(wen)？近代善历者(zhe)，推仲康(kang)时九(jiu)月合(he)(he)朔(shuo)，已在(zai)房星(xing)北矣。”按，古(gu)文(wen)“集(ji)”与“辑(ji)”义同。日(ri)月嘉会(hui)，而阴(yin)阳辑(ji)睦(mu)，则阳不(bu)疚(jiu)乎位(wei)，以(yi)(yi)(yi)常(chang)其(qi)(qi)明，阴(yin)亦含章示冲，以(yi)(yi)(yi)隐(yin)其(qi)(qi)形(xing)。若变而相伤，则不(bu)辑(ji)矣。房者(zhe)辰(chen)之所次，星(xing)者(zhe)所次之名，其(qi)(qi)揆一也(ye)。又《春秋传》“辰(chen)在(zai)斗柄”、“天策(ce)焞焞”、“降娄之初”、“辰(chen)尾之末”，君(jun)子(zi)言(yan)之，不(bu)以(yi)(yi)(yi)为缪，何独慎(shen)疑于(yu)房星(xing)哉？新历仲康(kang)五年癸巳(si)岁九(jiu)月庚戌朔(shuo)，日(ri)蚀在(zai)房二度。炫以(yi)(yi)(yi)《五子(zi)之歌》，仲康(kang)当是其(qi)(qi)一，肇位(wei)四海(hai)，复(fu)脩(xiu)大(da)禹之典，其(qi)(qi)五年，羲、和失职，则王(wang)命徂征。虞广刂以(yi)(yi)(yi)为仲康(kang)元年，非(fei)也(ye)。
《国语》单子(zi)曰：“辰角见(jian)(jian)(jian)而(er)(er)雨毕，天根(gen)见(jian)(jian)(jian)而(er)(er)水涸，本见(jian)(jian)(jian)而(er)(er)草(cao)木节(jie)解，驷见(jian)(jian)(jian)而(er)(er)陨(yun)霜(shuang)，火见(jian)(jian)(jian)而(er)(er)清风戒寒(han)。”韦(wei)昭以为夏后(hou)氏(shi)之令，周人所因。推夏后(hou)氏(shi)之初，秋(qiu)(qiu)分后(hou)五(wu)日(ri)，日(ri)在氏(shi)十三(san)度(du)，龙角尽见(jian)(jian)(jian)，时(shi)雨可以毕矣。又(you)先寒(han)露三(san)日(ri)，天根(gen)朝觌，《时(shi)训》“爰始(shi)(shi)收潦”，而(er)(er)《月令》亦云(yun)“水涸”。后(hou)寒(han)露十日(ri)，日(ri)在尾(wei)八度(du)而(er)(er)本见(jian)(jian)(jian)，又(you)五(wu)日(ri)而(er)(er)驷见(jian)(jian)(jian)。故(gu)(gu)陨(yun)霜(shuang)则(ze)蛰虫墐户(hu)。郑康成据当时(shi)所见(jian)(jian)(jian)，谓天根(gen)朝见(jian)(jian)(jian)，在季秋(qiu)(qiu)之末，以《月令》为谬。韦(wei)昭以仲秋(qiu)(qiu)水始(shi)(shi)涸，天根(gen)见(jian)(jian)(jian)乃(nai)竭(jie)。皆非是。霜(shuang)降六(liu)日(ri)，日(ri)在尾(wei)末，火星初见(jian)(jian)(jian)，营室昏(hun)中(zhong)(zhong)，于(yu)是始(shi)(shi)脩(xiu)城郭、宫(gong)室。故(gu)(gu)《时(shi)儆》曰：“营室之中(zhong)(zhong)，土功其始(shi)(shi)。火之初见(jian)(jian)(jian)，期于(yu)司理。”《麟德历》霜(shuang)降后(hou)五(wu)日(ri)，火伏。小雪(xue)后(hou)十日(ri)，晨见(jian)(jian)(jian)。至(zhi)大雪(xue)而(er)(er)后(hou)定星中(zhong)(zhong)，日(ri)旦南至(zhi)，冰壮地(di)坼。又(you)非土功之始(shi)(shi)也。
《夏历》十(shi)二次，立(li)春，日在东壁(bi)三度(du)，于《太初》星距壁(bi)一度(du)太也。
《颛(zhuan)顼历(li)(li)(li)》上元(yuan)甲(jia)寅岁正月(yue)(yue)甲(jia)寅晨初合朔(shuo)立(li)春，七曜(yao)皆直艮(gen)维之(zhi)(zhi)首。盖重黎(li)受职于颛(zhuan)顼，九黎(li)乱德，二(er)官(guan)咸(xian)废，帝尧复(fu)其子(zi)孙，命掌天地四时，以及虞、夏(xia)。故(gu)本(ben)其所(suo)由生，命曰《颛(zhuan)顼》，其实《夏(xia)历(li)(li)(li)》也(ye)。汤作(zuo)《殷历(li)(li)(li)》，更以十一月(yue)(yue)甲(jia)子(zi)合朔(shuo)冬至为(wei)上元(yuan)。周人因之(zhi)(zhi)，距(ju)羲、和千祀，昏明(ming)中(zhong)星率(lv)差(cha)半(ban)次(ci)。夏(xia)时直月(yue)(yue)节者，皆当十有二(er)中(zhong)，故(gu)因循夏(xia)令。其后吕不(bu)韦得之(zhi)(zhi)，以为(wei)秦法，更考(kao)中(zhong)星，断(duan)取近距(ju)，以乙卯(mao)岁正月(yue)(yue)己(ji)巳(si)合朔(shuo)立(li)春为(wei)上元(yuan)。《洪范(fan)传》曰：“历(li)(li)(li)记(ji)始(shi)于颛(zhuan)顼上元(yuan)太始(shi)阏蒙摄(she)提格之(zhi)(zhi)岁，毕陬之(zhi)(zhi)月(yue)(yue)，朔(shuo)日(ri)己(ji)巳(si)立(li)春，七曜(yao)俱(ju)在营室五度(du)。”是也(ye)。秦《颛(zhuan)顼历(li)(li)(li)》元(yuan)起乙卯(mao)，汉《太初历(li)(li)(li)》元(yuan)起丁丑，推而(er)上之(zhi)(zhi)，皆不(bu)值甲(jia)寅，犹(you)以日(ri)月(yue)(yue)五纬(wei)复(fu)得上元(yuan)本(ben)星度(du)，故(gu)命曰阏蒙摄(she)提格之(zhi)(zhi)岁，而(er)实非甲(jia)寅。
《夏历》章蔀纪首，皆在立春，故其(qi)(qi)课中星、揆斗建与闰余之所(suo)盈缩，皆以(yi)十有二节为(wei)损益(yi)之中。而《殷》、《周》、《汉历》，章蔀纪首皆直冬至，故其(qi)(qi)名察发(fa)敛，亦以(yi)中气为(wei)主。此(ci)其(qi)(qi)异也。
《夏(xia)(xia)小(xiao)(xiao)正(zheng)(zheng)(zheng)(zheng)》虽(sui)颇疏简失传(chuan)，乃(nai)羲、和遗迹(ji)。何承天循大戴(dai)之(zhi)(zhi)说，复用夏(xia)(xia)时，更以正(zheng)(zheng)(zheng)(zheng)月甲子(zi)夜半(ban)合朔雨水为(wei)(wei)上元，进(jin)乖《夏(xia)(xia)历》，退非周正(zheng)(zheng)(zheng)(zheng)，故(gu)(gu)近代(dai)推(tui)(tui)《月令》、《小(xiao)(xiao)正(zheng)(zheng)(zheng)(zheng)》者，皆不与(yu)古合。《开元历》推(tui)(tui)夏(xia)(xia)时立春，日在(zai)营室之(zhi)(zhi)末(mo)，昏东井(jing)(jing)二(er)度中(zhong)。古历以参(can)(can)(can)右肩(jian)为(wei)(wei)距(ju)，方当南(nan)正(zheng)(zheng)(zheng)(zheng)。故(gu)(gu)《小(xiao)(xiao)正(zheng)(zheng)(zheng)(zheng)》曰：“正(zheng)(zheng)(zheng)(zheng)月初昏，斗杓悬(xuan)在(zai)下。”魁(kui)枕参(can)(can)(can)首(shou)，所以著参(can)(can)(can)中(zhong)也。季春，在(zai)昴十(shi)一度半(ban)，去参(can)(can)(can)距(ju)星十(shi)八度，故(gu)(gu)曰：“三月，参(can)(can)(can)则(ze)(ze)伏。”立夏(xia)(xia)，日在(zai)井(jing)(jing)四(si)度，昏角(jiao)(jiao)(jiao)中(zhong)。南(nan)门(men)(men)右星入角(jiao)(jiao)(jiao)距(ju)西五度，其左星入角(jiao)(jiao)(jiao)距(ju)东六(liu)度，故(gu)(gu)曰：“四(si)月初昏，南(nan)门(men)(men)正(zheng)(zheng)(zheng)(zheng)。昴则(ze)(ze)见(jian)(jian)。”五月节，日在(zai)舆鬼一度半(ban)。参(can)(can)(can)去日道最远(yuan)，以浑仪度之(zhi)(zhi)，参(can)(can)(can)体始(shi)见(jian)(jian)，其肩(jian)股(gu)犹(you)在(zai)浊中(zhong)。房星正(zheng)(zheng)(zheng)(zheng)中(zhong)。故(gu)(gu)曰：“五月，参(can)(can)(can)则(ze)(ze)见(jian)(jian)。初昏，大火中(zhong)。”“八月，参(can)(can)(can)中(zhong)则(ze)(ze)曙”，失传(chuan)也。辰伏则(ze)(ze)参(can)(can)(can)见(jian)(jian)，非中(zhong)也。“十(shi)月初昏，南(nan)门(men)(men)见(jian)(jian)”，亦失传(chuan)也。定星方中(zhong)，则(ze)(ze)南(nan)门(men)(men)伏，非昏见(jian)(jian)也。
商(shang)六(liu)百二十八年(nian)，日却差八度(du)。太甲二年(nian)壬午岁(sui)冬至，应在女(nv)六(liu)度(du)。
《国(guo)语》曰：“武(wu)(wu)(wu)(wu)王(wang)(wang)(wang)伐(fa)(fa)商(shang)(shang)，岁在(zai)(zai)(zai)(zai)(zai)鹑火，月(yue)(yue)(yue)(yue)在(zai)(zai)(zai)(zai)(zai)天(tian)驷(si)(si)(si)，日(ri)(ri)(ri)在(zai)(zai)(zai)(zai)(zai)析木之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)津，辰(chen)(chen)在(zai)(zai)(zai)(zai)(zai)斗(dou)(dou)柄(bing)，星(xing)在(zai)(zai)(zai)(zai)(zai)天(tian)鼋。”旧说岁在(zai)(zai)(zai)(zai)(zai)己卯，推(tui)其朏(fei)魄，乃文(wen)(wen)王(wang)(wang)(wang)崩，武(wu)(wu)(wu)(wu)王(wang)(wang)(wang)成君之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)岁也(ye)(ye)(ye)。其明(ming)年，武(wu)(wu)(wu)(wu)王(wang)(wang)(wang)即位(wei)，新历孟春定(ding)朔丙(bing)辰(chen)(chen)，于(yu)商(shang)(shang)为(wei)(wei)二(er)月(yue)(yue)(yue)(yue)，故(gu)(gu)《周(zhou)(zhou)(zhou)书》曰：“维(wei)(wei)王(wang)(wang)(wang)元(yuan)(yuan)祀(si)二(er)月(yue)(yue)(yue)(yue)丙(bing)辰(chen)(chen)朔，武(wu)(wu)(wu)(wu)王(wang)(wang)(wang)访于(yu)周(zhou)(zhou)(zhou)公。”《竹书》：“十(shi)一(yi)年庚(geng)寅，周(zhou)(zhou)(zhou)始(shi)(shi)伐(fa)(fa)商(shang)(shang)。”而(er)(er)(er)《管子》及(ji)(ji)《家语》以(yi)(yi)为(wei)(wei)十(shi)二(er)年，盖通成君之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)岁也(ye)(ye)(ye)。先儒以(yi)(yi)文(wen)(wen)王(wang)(wang)(wang)受命九(jiu)年而(er)(er)(er)崩；至(zhi)(zhi)十(shi)年，武(wu)(wu)(wu)(wu)王(wang)(wang)(wang)观(guan)兵盟(meng)津；十(shi)三年，复(fu)伐(fa)(fa)商(shang)(shang)。推(tui)元(yuan)(yuan)祀(si)二(er)月(yue)(yue)(yue)(yue)丙(bing)辰(chen)(chen)朔，距伐(fa)(fa)商(shang)(shang)日(ri)(ri)(ri)月(yue)(yue)(yue)(yue)，不为(wei)(wei)相(xiang)距四年。所(suo)(suo)说非是(shi)。武(wu)(wu)(wu)(wu)王(wang)(wang)(wang)十(shi)年，夏正十(shi)月(yue)(yue)(yue)(yue)戊(wu)子，周(zhou)(zhou)(zhou)师(shi)始(shi)(shi)起。于(yu)岁差日(ri)(ri)(ri)在(zai)(zai)(zai)(zai)(zai)箕十(shi)度(du)，则析木津也(ye)(ye)(ye)。晨初，月(yue)(yue)(yue)(yue)在(zai)(zai)(zai)(zai)(zai)房(fang)(fang)四度(du)。于(yu)《易(yi)》，雷乘乾曰大壮，房(fang)(fang)、心象焉(yan)。心为(wei)(wei)乾精，而(er)(er)(er)房(fang)(fang)，升(sheng)阳(yang)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)驷(si)(si)(si)也(ye)(ye)(ye)。房(fang)(fang)与(yu)岁星(xing)实相(xiang)经纬，以(yi)(yi)属灵威仰(yang)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)神，后(hou)稷感之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)以(yi)(yi)生(sheng)。故(gu)(gu)《国(guo)语》曰：“月(yue)(yue)(yue)(yue)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)所(suo)(suo)在(zai)(zai)(zai)(zai)(zai)，辰(chen)(chen)马农祥，我(wo)(wo)祖后(hou)稷之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)所(suo)(suo)经纬也(ye)(ye)(ye)。”又三日(ri)(ri)(ri)得周(zhou)(zhou)(zhou)正月(yue)(yue)(yue)(yue)庚(geng)寅朔，日(ri)(ri)(ri)月(yue)(yue)(yue)(yue)会南斗(dou)(dou)一(yi)度(du)。故(gu)(gu)曰“辰(chen)(chen)在(zai)(zai)(zai)(zai)(zai)斗(dou)(dou)柄(bing)”。壬(ren)辰(chen)(chen)，辰(chen)(chen)星(xing)夕见，在(zai)(zai)(zai)(zai)(zai)南斗(dou)(dou)二(er)十(shi)度(du)。其明(ming)日(ri)(ri)(ri)，武(wu)(wu)(wu)(wu)王(wang)(wang)(wang)自(zi)宗周(zhou)(zhou)(zhou)次(ci)于(yu)师(shi)所(suo)(suo)。凡月(yue)(yue)(yue)(yue)朔而(er)(er)(er)未(wei)见曰“死魄”，夕而(er)(er)(er)成光则谓(wei)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)“朏(fei)”。朏(fei)或(huo)以(yi)(yi)二(er)日(ri)(ri)(ri)，或(huo)以(yi)(yi)三日(ri)(ri)(ri)，故(gu)(gu)《武(wu)(wu)(wu)(wu)成》曰：“维(wei)(wei)一(yi)月(yue)(yue)(yue)(yue)壬(ren)辰(chen)(chen)，旁(pang)(pang)死魄。翌(yi)日(ri)(ri)(ri)癸巳，王(wang)(wang)(wang)朝步自(zi)周(zhou)(zhou)(zhou)，于(yu)征伐(fa)(fa)商(shang)(shang)。”是(shi)时辰(chen)(chen)星(xing)与(yu)周(zhou)(zhou)(zhou)师(shi)俱(ju)进，由建星(xing)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)末，历牵牛、须(xu)女(nv)，涉颛顼之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)虚。戊(wu)午，师(shi)度(du)盟(meng)津，而(er)(er)(er)辰(chen)(chen)星(xing)伏于(yu)天(tian)鼋。辰(chen)(chen)星(xing)，汁光纪之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)精，所(suo)(suo)以(yi)(yi)告颛顼而(er)(er)(er)终(zhong)水(shui)行之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)运，且(qie)木帝之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)所(suo)(suo)繇生(sheng)也(ye)(ye)(ye)。故(gu)(gu)《国(guo)语》曰：“星(xing)与(yu)日(ri)(ri)(ri)辰(chen)(chen)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)位(wei)皆在(zai)(zai)(zai)(zai)(zai)北维(wei)(wei)，颛顼之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)所(suo)(suo)建也(ye)(ye)(ye)，帝喾受之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)。我(wo)(wo)周(zhou)(zhou)(zhou)氏出(chu)自(zi)天(tian)鼋；及(ji)(ji)析木，有建星(xing)、牵牛焉(yan)，则我(wo)(wo)皇妣太姜之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)侄(zhi)、伯(bo)陵之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)后(hou)逢(feng)公之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)所(suo)(suo)凭(ping)神也(ye)(ye)(ye)。”是(shi)岁，岁星(xing)始(shi)(shi)及(ji)(ji)鹑火。其明(ming)年，周(zhou)(zhou)(zhou)始(shi)(shi)革命。岁又退行，旅于(yu)鹑首，而(er)(er)(er)后(hou)进及(ji)(ji)鸟帑，所(suo)(suo)以(yi)(yi)反复(fu)其道，经纶周(zhou)(zhou)(zhou)室。鹑火直轩辕之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)虚，以(yi)(yi)爰稼穑，稷星(xing)系焉(yan)，而(er)(er)(er)成周(zhou)(zhou)(zhou)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)大萃也(ye)(ye)(ye)。鹑首当山河之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)右，太王(wang)(wang)(wang)以(yi)(yi)兴，后(hou)稷封焉(yan)，而(er)(er)(er)宗周(zhou)(zhou)(zhou)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)所(suo)(suo)宅也(ye)(ye)(ye)。岁星(xing)与(yu)房(fang)(fang)实相(xiang)经纬，而(er)(er)(er)相(xiang)距七舍(she)；木与(yu)水(shui)代终(zhong)，而(er)(er)(er)相(xiang)及(ji)(ji)七月(yue)(yue)(yue)(yue)。故(gu)(gu)《国(guo)语》曰；“岁之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)所(suo)(suo)在(zai)(zai)(zai)(zai)(zai)，则我(wo)(wo)有周(zhou)(zhou)(zhou)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)分也(ye)(ye)(ye)。自(zi)鹑及(ji)(ji)驷(si)(si)(si)七列(lie)，南北之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)揆七月(yue)(yue)(yue)(yue)。其二(er)月(yue)(yue)(yue)(yue)戊(wu)子朔，哉生(sheng)明(ming)，王(wang)(wang)(wang)自(zi)克商(shang)(shang)还，至(zhi)(zhi)于(yu)酆，于(yu)周(zhou)(zhou)(zhou)为(wei)(wei)四月(yue)(yue)(yue)(yue)。新历推(tui)定(ding)望甲辰(chen)(chen)，而(er)(er)(er)乙巳旁(pang)(pang)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)。故(gu)(gu)《武(wu)(wu)(wu)(wu)成》曰：“维(wei)(wei)四月(yue)(yue)(yue)(yue)，既旁(pang)(pang)生(sheng)魄，粤六月(yue)(yue)(yue)(yue)庚(geng)戌，武(wu)(wu)(wu)(wu)王(wang)(wang)(wang)燎于(yu)周(zhou)(zhou)(zhou)庙。”《麟德历》，周(zhou)(zhou)(zhou)师(shi)始(shi)(shi)起，岁在(zai)(zai)(zai)(zai)(zai)降娄，月(yue)(yue)(yue)(yue)宿天(tian)根，日(ri)(ri)(ri)躔(chan)心而(er)(er)(er)合辰(chen)(chen)在(zai)(zai)(zai)(zai)(zai)尾(wei)，水(shui)星(xing)伏于(yu)星(xing)纪，不及(ji)(ji)天(tian)鼋。又《周(zhou)(zhou)(zhou)书》，革命六年而(er)(er)(er)武(wu)(wu)(wu)(wu)王(wang)(wang)(wang)崩。《管子》、《家语》以(yi)(yi)为(wei)(wei)七年，盖通克商(shang)(shang)之(zhi)(zhi)(zhi)(zhi)(zhi)(zhi)岁也(ye)(ye)(ye)。
周公(gong)(gong)摄政七(qi)年(nian)(nian)二(er)月(yue)(yue)(yue)甲戌朔(shuo)(shuo)，己丑望，后(hou)六日(ri)(ri)乙(yi)未(wei)(wei)。三(san)(san)月(yue)(yue)(yue)定朔(shuo)(shuo)甲辰，三(san)(san)日(ri)(ri)丙午。故《召诰》曰(yue)(yue)(yue)：“惟(wei)(wei)二(er)月(yue)(yue)(yue)既望，越六日(ri)(ri)乙(yi)未(wei)(wei)，王朝(chao)步(bu)自周，至(zhi)于(yu)酆”，“三(san)(san)月(yue)(yue)(yue)，惟(wei)(wei)丙午朏(fei)(fei)，越三(san)(san)日(ri)(ri)戊(wu)申，太(tai)保朝(chao)至(zhi)于(yu)洛(luo)。”其明(ming)年(nian)(nian)，成王正位。三(san)(san)十(shi)年(nian)(nian)四月(yue)(yue)(yue)乙(yi)酉朔(shuo)(shuo)甲子，哉生魄(po)。故《书(shu)》曰(yue)(yue)(yue)：“惟(wei)(wei)四月(yue)(yue)(yue)，才生魄(po)。”甲子，作《顾命》。康王十(shi)二(er)年(nian)(nian)，岁(sui)在乙(yi)酉，六月(yue)(yue)(yue)戊(wu)辰朔(shuo)(shuo)，三(san)(san)日(ri)(ri)庚(geng)午。故《毕命》曰(yue)(yue)(yue)：“惟(wei)(wei)十(shi)有二(er)年(nian)(nian)，六月(yue)(yue)(yue)庚(geng)午朏(fei)(fei)。越三(san)(san)日(ri)(ri)壬申，王以成周之(zhi)众命毕公(gong)(gong)。”自伐纣(zhou)及(ji)此，五十(shi)六年(nian)(nian)，朏(fei)(fei)魄(po)日(ri)(ri)名，上下无不合(he)。而(er)《三(san)(san)统历(li)》以己卯(mao)为(wei)克(ke)商之(zhi)岁(sui)，非也(ye)。夫有效于(yu)古者，宜合(he)于(yu)今。《三(san)(san)统历(li)》自太(tai)初至(zhi)开元，朔(shuo)(shuo)后(hou)天三(san)(san)日(ri)(ri)。推而(er)上之(zhi)，以至(zhi)周初，先天，失之(zhi)盖益甚焉。是(shi)以知合(he)于(yu)歆者，必非克(ke)商之(zhi)岁(sui)。
自宗周讫(qi)春秋(qiu)之季(ji)，日却差八度(du)。康王十一年甲申岁冬(dong)至，应在牵(qian)牛六度(du)。
《周(zhou)历》十二次(ci)，星纪初(chu)，南(nan)斗十四度(du)，于(yu)《太初(chu)》星距斗十七(qi)度(du)少也。
古历(li)分率简易，岁久辄差。达历(li)数者(zhe)随时迁革，以(yi)合其变。故三代(dai)(dai)之兴，皆(jie)揆测天(tian)行，考正(zheng)星次，为一代(dai)(dai)之制(zhi)。正(zheng)朔(shuo)既革，而服色从之。及(ji)继体守(shou)文，畴人代(dai)(dai)嗣(si)，则(ze)谨(jin)循先王旧制(zhi)焉。
《国(guo)语》曰(yue)：“农祥晨(chen)正，日(ri)(ri)月底于(yu)(yu)(yu)天(tian)(tian)庙，土(tu)乃脉发(fa)。先时九(jiu)日(ri)(ri)，太史(shi)告稷曰(yue)，自(zi)今至(zhi)(zhi)于(yu)(yu)(yu)初(chu)吉，阳(yang)气(qi)(qi)俱(ju)蒸(zheng)，土(tu)膏其动(dong)。弗震(zhen)不(bu)渝(yu)，脉其满(man)(man)眚，谷乃不(bu)殖。”周初(chu)，先立春(chun)(chun)九(jiu)日(ri)(ri)，日(ri)(ri)至(zhi)(zhi)营室。古历距中九(jiu)十一度(du)，是日(ri)(ri)晨(chen)初(chu)，大(da)火正中，故曰(yue)“农祥晨(chen)正，日(ri)(ri)月底于(yu)(yu)(yu)天(tian)(tian)庙”也。于(yu)(yu)(yu)《易》象(xiang)，升气(qi)(qi)究而(er)临(lin)受(shou)之(zhi)，自(zi)冬(dong)至(zhi)(zhi)后(hou)(hou)七日(ri)(ri)，乾精始复。及(ji)大(da)寒，地统(tong)之(zhi)中，阳(yang)洽(qia)于(yu)(yu)(yu)万物根柢，而(er)与萌芽俱(ju)升，木在(zai)地中之(zhi)象(xiang)，升气(qi)(qi)已达(da)，则(ze)当推而(er)大(da)之(zhi)，故受(shou)之(zhi)以(yi)临(lin)。于(yu)(yu)(yu)消息(xi)，龙(long)德(de)在(zai)田，得地道之(zhi)和泽，而(er)动(dong)于(yu)(yu)(yu)地中，升阳(yang)愤盈，土(tu)气(qi)(qi)震(zhen)发(fa)，故曰(yue)：“自(zi)今至(zhi)(zhi)于(yu)(yu)(yu)初(chu)吉，阳(yang)气(qi)(qi)俱(ju)蒸(zheng)，土(tu)膏其动(dong)。”又先立春(chun)(chun)三日(ri)(ri)，而(er)小过(guo)用事，阳(yang)好节(jie)止于(yu)(yu)(yu)内，动(dong)作于(yu)(yu)(yu)外，矫而(er)过(guo)正，然后(hou)(hou)返求中焉。是以(yi)及(ji)于(yu)(yu)(yu)艮维，则(ze)山泽通气(qi)(qi)，阳(yang)精辟户，甲坼(che)之(zhi)萌见(jian)，而(er)莩谷之(zhi)际离，故曰(yue)：“不(bu)震(zhen)不(bu)渝(yu)，脉其满(man)(man)眚，谷乃不(bu)殖。”君子之(zhi)道，必拟(ni)之(zhi)而(er)后(hou)(hou)言，岂亻意度(du)而(er)已哉！韦昭以(yi)为日(ri)(ri)及(ji)天(tian)(tian)庙，在(zai)立春(chun)(chun)之(zhi)初(chu)，非也。于(yu)(yu)(yu)《麟(lin)德(de)历》则(ze)又后(hou)(hou)立春(chun)(chun)十五(wu)日(ri)(ri)矣。
《春(chun)(chun)秋(qiu)》“桓公五(wu)年，秋(qiu)，大雩”。《传(chuan)》曰(yue)：“书不(bu)(bu)时也(ye)。凡祀，启蛰而(er)(er)(er)郊，龙(long)(long)见(jian)(jian)而(er)(er)(er)雩。”《周历(li)》立(li)(li)夏日(ri)在(zai)觜觿二(er)度(du)。于(yu)轨漏，昏(hun)(hun)角一度(du)中(zhong)(zhong)(zhong)，苍龙(long)(long)毕见(jian)(jian)。然则(ze)(ze)当在(zai)建巳之(zhi)初，周礼(li)也(ye)。至春(chun)(chun)秋(qiu)时，日(ri)已潜退五(wu)度(du)，节前月(yue)(yue)却，犹在(zai)建辰(chen)。《月(yue)(yue)令》以(yi)为(wei)(wei)五(wu)月(yue)(yue)者，《吕氏》以(yi)《颛顼历(li)》芒种(zhong)亢中(zhong)(zhong)(zhong)，则(ze)(ze)龙(long)(long)以(yi)立(li)(li)夏昏(hun)(hun)见(jian)(jian)，不(bu)(bu)知有岁差，故雩祭失(shi)(shi)时。然则(ze)(ze)唐礼(li)当以(yi)建巳之(zhi)初，农祥始见(jian)(jian)而(er)(er)(er)雩。若据(ju)《麟德历(li)》，以(yi)小满后(hou)(hou)十(shi)(shi)(shi)三日(ri)，则(ze)(ze)龙(long)(long)角过(guo)中(zhong)(zhong)(zhong)，为(wei)(wei)不(bu)(bu)时矣。《传(chuan)》曰(yue)：“凡土(tu)功(gong)，龙(long)(long)见(jian)(jian)而(er)(er)(er)毕务，戒事(shi)。火(huo)(huo)见(jian)(jian)而(er)(er)(er)致用，水(shui)(shui)昏(hun)(hun)正(zheng)而(er)(er)(er)栽，日(ri)至而(er)(er)(er)毕。”十(shi)(shi)(shi)六年冬，城(cheng)(cheng)(cheng)向(xiang)(xiang)。十(shi)(shi)(shi)有一月(yue)(yue)，卫(wei)侯朔出奔(ben)齐。“冬，城(cheng)(cheng)(cheng)向(xiang)(xiang)，书时也(ye)。”以(yi)岁差推之(zhi)，周初霜(shuang)降(jiang)，日(ri)在(zai)心五(wu)度(du)，角、亢晨见(jian)(jian)。立(li)(li)冬，火(huo)(huo)见(jian)(jian)营室中(zhong)(zhong)(zhong)。后(hou)(hou)七日(ri)，水(shui)(shui)星昏(hun)(hun)正(zheng)，可以(yi)兴板干(gan)。故祖(zu)冲(chong)之(zhi)以(yi)为(wei)(wei)定之(zhi)方(fang)中(zhong)(zhong)(zhong)，直营室八度(du)。是(shi)岁九月(yue)(yue)六日(ri)霜(shuang)降(jiang)，二(er)十(shi)(shi)(shi)一日(ri)立(li)(li)冬。十(shi)(shi)(shi)月(yue)(yue)之(zhi)前，水(shui)(shui)星昏(hun)(hun)正(zheng)，故《传(chuan)》以(yi)为(wei)(wei)得时。杜氏据(ju)晋(jin)历(li)，小雪后(hou)(hou)定星乃(nai)中(zhong)(zhong)(zhong)，季秋(qiu)城(cheng)(cheng)(cheng)向(xiang)(xiang)，似为(wei)(wei)太早，因(yin)曰(yue)：功(gong)役之(zhi)事(shi)，皆总指天象，不(bu)(bu)与言历(li)数同。引《诗》云“定之(zhi)方(fang)中(zhong)(zhong)(zhong)”，乃(nai)未正(zheng)中(zhong)(zhong)(zhong)之(zhi)辞，非是(shi)。《麟德历(li)》，立(li)(li)冬后(hou)(hou)二(er)十(shi)(shi)(shi)五(wu)日(ri)火(huo)(huo)见(jian)(jian)，至大雪后(hou)(hou)营室乃(nai)中(zhong)(zhong)(zhong)。而(er)(er)(er)《春(chun)(chun)秋(qiu)》九月(yue)(yue)书时，不(bu)(bu)已早乎。大雪，周之(zhi)孟春(chun)(chun)，阳气静复，以(yi)缮城(cheng)(cheng)(cheng)隍(huang)，治(zhi)宫室，是(shi)谓发天地之(zhi)房，方(fang)于(yu)立(li)(li)春(chun)(chun)断狱，所失(shi)(shi)多(duo)矣。然则(ze)(ze)唐制宜以(yi)玄枵中(zhong)(zhong)(zhong)天兴土(tu)功(gong)。
僖公五年(nian)，晋侯(hou)伐虢。卜偃曰：“克之(zhi)。童(tong)谣云：丙(bing)之(zhi)辰(chen)，龙尾(wei)(wei)伏辰(chen)，袀服(fu)振振，取虢之(zhi)旂，鹑(chun)之(zhi)贲(bi)贲(bi)，天策(ce)焞焞，火(huo)(huo)中(zhong)成军。’其九月(yue)(yue)十月(yue)(yue)之(zhi)交乎！丙(bing)子(zi)旦，日在尾(wei)(wei)，月(yue)(yue)在策(ce)，鹑(chun)火(huo)(huo)中(zhong)，必是(shi)时(shi)。”策(ce)，入尾(wei)(wei)十二度(du)。新历是(shi)岁十月(yue)(yue)丙(bing)子(zi)定(ding)朔，日月(yue)(yue)合尾(wei)(wei)十四度(du)于(yu)黄道(dao)。古历日在尾(wei)(wei)，而月(yue)(yue)在策(ce)，故曰“龙尾(wei)(wei)伏辰(chen)”，于(yu)古距张中(zhong)而曙，直鹑(chun)火(huo)(huo)之(zhi)末，始(shi)将西降，故曰“贲(bi)贲(bi)”。
昭(zhao)公(gong)七(qi)年四月(yue)(yue)甲辰(chen)(chen)朔(shuo)，日(ri)(ri)(ri)(ri)(ri)蚀。士文伯曰：“去卫地，如(ru)鲁(lu)地。于(yu)是有(you)(you)灾，鲁(lu)实(shi)受之。”新(xin)历(li)(li)是岁(sui)二(er)(er)月(yue)(yue)甲辰(chen)(chen)朔(shuo)入(ru)常，雨(yu)水(shui)后七(qi)日(ri)(ri)(ri)(ri)(ri)，在(zai)(zai)(zai)(zai)奎十(shi)(shi)度(du)(du)。周度(du)(du)为降(jiang)(jiang)(jiang)娄(lou)之始(shi)，则(ze)(ze)鲁(lu)、卫之交(jiao)也。自周初(chu)至(zhi)是，已(yi)退(tui)七(qi)度(du)(du)，故入(ru)雨(yu)水(shui)。七(qi)日(ri)(ri)(ri)(ri)(ri)方(fang)及降(jiang)(jiang)(jiang)娄(lou)，虽(sui)日(ri)(ri)(ri)(ri)(ri)度(du)(du)潜移，而(er)周礼(li)未改，其(qi)(qi)配神(shen)主祭之宿，宜书于(yu)建(jian)国(guo)之初(chu)。淳风(feng)驳(bo)《戊寅(yin)历(li)(li)》曰：“《汉志》降(jiang)(jiang)(jiang)娄(lou)初(chu)在(zai)(zai)(zai)(zai)奎五度(du)(du)，今历(li)(li)日(ri)(ri)(ri)(ri)(ri)蚀在(zai)(zai)(zai)(zai)降(jiang)(jiang)(jiang)娄(lou)之中(zhong)，依无岁(sui)差法(fa)，食于(yu)两次(ci)之交(jiao)。”是又不(bu)然。议者晓十(shi)(shi)有(you)(you)二(er)(er)次(ci)之所(suo)由生(sheng)，然后可(ke)以明(ming)其(qi)(qi)得(de)失(shi)。且刘歆(xin)等所(suo)定辰(chen)(chen)次(ci)，非能有(you)(you)以睹阴阳之赜，而(er)得(de)于(yu)鬼神(shen)，各(ge)据(ju)当(dang)时中(zhong)节星(xing)度(du)(du)耳。歆(xin)以《太(tai)初(chu)历(li)(li)》冬至(zhi)日(ri)(ri)(ri)(ri)(ri)在(zai)(zai)(zai)(zai)牵(qian)牛(niu)前(qian)五度(du)(du)，故降(jiang)(jiang)(jiang)娄(lou)直东壁八度(du)(du)。李业兴《正光历(li)(li)》，冬至(zhi)在(zai)(zai)(zai)(zai)牵(qian)牛(niu)前(qian)十(shi)(shi)二(er)(er)度(du)(du)，故降(jiang)(jiang)(jiang)娄(lou)退(tui)至(zhi)东壁三(san)(san)度(du)(du)。及祖冲(chong)之后，以为日(ri)(ri)(ri)(ri)(ri)度(du)(du)渐差，则(ze)(ze)当(dang)据(ju)列宿四正之中(zhong)以定辰(chen)(chen)次(ci)，不(bu)复(fu)系于(yu)中(zhong)节。淳风(feng)以冬至(zhi)常在(zai)(zai)(zai)(zai)斗十(shi)(shi)三(san)(san)度(du)(du)，则(ze)(ze)当(dang)以东壁二(er)(er)度(du)(du)为降(jiang)(jiang)(jiang)娄(lou)之初(chu)，安得(de)守汉历(li)(li)以驳(bo)仁(ren)均耶？又《三(san)(san)统历(li)(li)》昭(zhao)公(gong)二(er)(er)十(shi)(shi)年，己丑，日(ri)(ri)(ri)(ri)(ri)南(nan)至(zhi)，与《麟德》及《开(kai)元历(li)(li)》同。然则(ze)(ze)入(ru)雨(yu)水(shui)后七(qi)日(ri)(ri)(ri)(ri)(ri)，亦入(ru)降(jiang)(jiang)(jiang)娄(lou)七(qi)度(du)(du)，非鲁(lu)、卫之交(jiao)也。三(san)(san)十(shi)(shi)一年十(shi)(shi)二(er)(er)月(yue)(yue)辛亥朔(shuo)，日(ri)(ri)(ri)(ri)(ri)蚀。史墨曰：“日(ri)(ri)(ri)(ri)(ri)月(yue)(yue)在(zai)(zai)(zai)(zai)辰(chen)(chen)尾，庚午(wu)之日(ri)(ri)(ri)(ri)(ri)，日(ri)(ri)(ri)(ri)(ri)始(shi)有(you)(you)谪。”《开(kai)元历(li)(li)》是岁(sui)十(shi)(shi)月(yue)(yue)辛亥朔(shuo)，入(ru)常立冬。五日(ri)(ri)(ri)(ri)(ri)，日(ri)(ri)(ri)(ri)(ri)在(zai)(zai)(zai)(zai)尾十(shi)(shi)三(san)(san)度(du)(du)，于(yu)古距辰(chen)(chen)尾之初(chu)。《麟德历(li)(li)》日(ri)(ri)(ri)(ri)(ri)在(zai)(zai)(zai)(zai)心(xin)三(san)(san)度(du)(du)于(yu)黄道(dao)，退(tui)直于(yu)房矣(yi)。
哀公(gong)(gong)十(shi)(shi)(shi)(shi)二年(nian)(nian)冬十(shi)(shi)(shi)(shi)有(you)二月(yue)(yue)(yue)(yue)，螽。《开元历》推置闰当(dang)在十(shi)(shi)(shi)(shi)一(yi)(yi)年(nian)(nian)春(chun)，至(zhi)十(shi)(shi)(shi)(shi)二年(nian)(nian)冬，失闰已久。是岁九月(yue)(yue)(yue)(yue)己亥朔(shuo)，先寒露三日，于定气(qi)，日在亢五度，去心近(jin)一(yi)(yi)次。火(huo)(huo)(huo)(huo)星明(ming)(ming)大，尚未(wei)(wei)当(dang)伏(fu)(fu)(fu)(fu)(fu)。至(zhi)霜(shuang)降(jiang)(jiang)五日，始潜日下(xia)。乃(nai)《月(yue)(yue)(yue)(yue)令》“蛰(zhe)虫咸俯(fu)”，则(ze)(ze)火(huo)(huo)(huo)(huo)辰(chen)未(wei)(wei)伏(fu)(fu)(fu)(fu)(fu)，当(dang)在霜(shuang)降(jiang)(jiang)前。虽节气(qi)极晚，不得(de)十(shi)(shi)(shi)(shi)月(yue)(yue)(yue)(yue)昏见(jian)(jian)。故仲(zhong)尼(ni)(ni)曰(yue)：“丘闻之(zhi)(zhi)(zhi)(zhi)，火(huo)(huo)(huo)(huo)伏(fu)(fu)(fu)(fu)(fu)而(er)(er)后(hou)(hou)蛰(zhe)者毕。今(jin)火(huo)(huo)(huo)(huo)犹(you)西流，司(si)历过(guo)也(ye)。”方夏后(hou)(hou)氏之(zhi)(zhi)(zhi)(zhi)初(chu)，八(ba)月(yue)(yue)(yue)(yue)辰(chen)伏(fu)(fu)(fu)(fu)(fu)，九月(yue)(yue)(yue)(yue)内(nei)火(huo)(huo)(huo)(huo)，及(ji)霜(shuang)降(jiang)(jiang)之(zhi)(zhi)(zhi)(zhi)后(hou)(hou)，火(huo)(huo)(huo)(huo)已朝觌东方，距春(chun)秋(qiu)(qiu)之(zhi)(zhi)(zhi)(zhi)季千五百余年(nian)(nian)，乃(nai)云“火(huo)(huo)(huo)(huo)伏(fu)(fu)(fu)(fu)(fu)而(er)(er)后(hou)(hou)蛰(zhe)者毕。”向使冬至(zhi)常居其所，则(ze)(ze)仲(zhong)尼(ni)(ni)不得(de)以(yi)(yi)(yi)西流未(wei)(wei)伏(fu)(fu)(fu)(fu)(fu)，明(ming)(ming)是九月(yue)(yue)(yue)(yue)之(zhi)(zhi)(zhi)(zhi)初(chu)也(ye)。自春(chun)秋(qiu)(qiu)至(zhi)今(jin)又千五百岁，《麟德历》以(yi)(yi)(yi)霜(shuang)降(jiang)(jiang)后(hou)(hou)五日，日在氐(di)八(ba)度，房、心初(chu)伏(fu)(fu)(fu)(fu)(fu)，定增二日，以(yi)(yi)(yi)月(yue)(yue)(yue)(yue)蚀冲(chong)校之(zhi)(zhi)(zhi)(zhi)，犹(you)差三度。闰余稍多，则(ze)(ze)建亥之(zhi)(zhi)(zhi)(zhi)始，火(huo)(huo)(huo)(huo)犹(you)见(jian)(jian)西方。向使宿度不移，则(ze)(ze)仲(zhong)尼(ni)(ni)不得(de)以(yi)(yi)(yi)西流未(wei)(wei)伏(fu)(fu)(fu)(fu)(fu)，明(ming)(ming)非(fei)十(shi)(shi)(shi)(shi)月(yue)(yue)(yue)(yue)之(zhi)(zhi)(zhi)(zhi)候(hou)也(ye)。自羲(xi)、和已来，火(huo)(huo)(huo)(huo)辰(chen)见(jian)(jian)伏(fu)(fu)(fu)(fu)(fu)，三睹厥变。然(ran)则(ze)(ze)丘明(ming)(ming)之(zhi)(zhi)(zhi)(zhi)记(ji)，欲(yu)令后(hou)(hou)之(zhi)(zhi)(zhi)(zhi)作者参求(qiu)微象，以(yi)(yi)(yi)探仲(zhong)尼(ni)(ni)之(zhi)(zhi)(zhi)(zhi)旨。是岁失闰浸久，季秋(qiu)(qiu)中气(qi)后(hou)(hou)天三日，比及(ji)明(ming)(ming)年(nian)(nian)仲(zhong)冬，又得(de)一(yi)(yi)闰。寤仲(zhong)尼(ni)(ni)之(zhi)(zhi)(zhi)(zhi)言(yan)，补正(zheng)时历，而(er)(er)十(shi)(shi)(shi)(shi)二月(yue)(yue)(yue)(yue)犹(you)可以(yi)(yi)(yi)螽。至(zhi)哀公(gong)(gong)十(shi)(shi)(shi)(shi)四年(nian)(nian)五月(yue)(yue)(yue)(yue)庚申朔(shuo)，日蚀。以(yi)(yi)(yi)《开元历》考之(zhi)(zhi)(zhi)(zhi)，则(ze)(ze)日蚀前又增一(yi)(yi)闰，《鲁(lu)历》正(zheng)矣。《长历》自哀公(gong)(gong)十(shi)(shi)(shi)(shi)年(nian)(nian)六(liu)月(yue)(yue)(yue)(yue)，迄十(shi)(shi)(shi)(shi)四年(nian)(nian)二月(yue)(yue)(yue)(yue)，才(cai)置一(yi)(yi)闰，非(fei)是。
战国及秦(qin)，日(ri)却(que)退三度。始皇(huang)十(shi)(shi)七年辛未岁冬至(zhi)，应在斗二(er)十(shi)(shi)二(er)度。秦(qin)历(li)上元正(zheng)(zheng)(zheng)月己(ji)巳朔，晨(chen)初(chu)立(li)春，日(ri)、月、五(wu)星俱(ju)起营室五(wu)度。蔀首日(ri)名皆(jie)(jie)直四(si)孟(meng)。假(jia)朔退十(shi)(shi)五(wu)日(ri)，则闰(run)(run)在正(zheng)(zheng)(zheng)月前。朔进十(shi)(shi)五(wu)日(ri)，则闰(run)(run)在正(zheng)(zheng)(zheng)月后。是以(yi)十(shi)(shi)有二(er)节，皆(jie)(jie)在盈缩(suo)之(zhi)中(zhong)，而(er)(er)晨(chen)昏(hun)(hun)宿(su)(su)(su)度随之(zhi)。以(yi)《颛顼历(li)》依《月令(ling)》自(zi)(zi)十(shi)(shi)有二(er)节推(tui)之(zhi)，与不韦所记合(he)。而(er)(er)颍子严之(zhi)伦谓《月令(ling)》晨(chen)昏(hun)(hun)距宿(su)(su)(su)，当(dang)在中(zhong)气(qi)，致雩祭太晚，自(zi)(zi)乖左氏之(zhi)文(wen)，而(er)(er)杜预又(you)据《春秋》，以(yi)《月令(ling)》为(wei)否。皆(jie)(jie)非是。梁《大同历(li)》夏后氏之(zhi)初(chu)，冬至(zhi)日(ri)在牵(qian)牛初(chu)，以(yi)为(wei)《明堂》、《月令(ling)》乃(nai)夏时之(zhi)记，据中(zhong)气(qi)推(tui)之(zhi)不合(he)，更以(yi)中(zhong)节之(zhi)间为(wei)正(zheng)(zheng)(zheng)，乃(nai)稍相符。不知进在节初(chu)，自(zi)(zi)然契合(he)。自(zi)(zi)秦(qin)初(chu)及今(jin)，又(you)且千岁，节初(chu)之(zhi)宿(su)(su)(su)，皆(jie)(jie)当(dang)中(zhong)气(qi)。淳风因为(wei)说曰：“今(jin)孟(meng)春中(zhong)气(qi)，日(ri)在营室，昏(hun)(hun)明中(zhong)星，与《月令(ling)》不殊。”按秦(qin)历(li)立(li)春，日(ri)在营室五(wu)度。《麟(lin)德历(li)》以(yi)启(qi)蛰之(zhi)日(ri)乃(nai)至(zhi)营室，其昏(hun)(hun)明中(zhong)宿(su)(su)(su)十(shi)(shi)有二(er)建，以(yi)为(wei)不差，妄矣。
古历，冬至昏(hun)明中星去日九十(shi)二度，春分、秋分百度，夏至百一十(shi)八度，率一气差(cha)三(san)度，九日差(cha)一刻。
秦历十二次，立春在营室(shi)五度(du)(du)，于《太(tai)(tai)初》星距危十六度(du)(du)少也(ye)。昏(hun)(hun)，毕八(ba)度(du)(du)中(zhong)(zhong)(zhong)，《月(yue)令(ling)》参中(zhong)(zhong)(zhong)，谓肩股也(ye)。晨，心八(ba)度(du)(du)中(zhong)(zhong)(zhong)，《月(yue)令(ling)》尾中(zhong)(zhong)(zhong)，于《太(tai)(tai)初》星距尾也(ye)。仲(zhong)春昏(hun)(hun)，东(dong)(dong)井(jing)(jing)十四度(du)(du)中(zhong)(zhong)(zhong)，《月(yue)令(ling)》弧(hu)中(zhong)(zhong)(zhong)，弧(hu)星入东(dong)(dong)井(jing)(jing)十八(ba)度(du)(du)。晨，南斗二度(du)(du)中(zhong)(zhong)(zhong)，《月(yue)令(ling)》建(jian)星中(zhong)(zhong)(zhong)，于《太(tai)(tai)初》星距西建(jian)也(ye)。《甄耀(yao)度(du)(du)》及《鲁历》，南方有(you)狼、弧(hu)，无东(dong)(dong)井(jing)(jing)、鬼，北方有(you)建(jian)星，无南斗，井(jing)(jing)、斗度(du)(du)长，弧(hu)、建(jian)度(du)(du)短，故以正昏(hun)(hun)明云。
古(gu)历(li)(li)(li)星(xing)(xing)(xing)(xing)(xing)度(du)(du)(du)(du)及汉(han)落下闳(hong)等所测，其星(xing)(xing)(xing)(xing)(xing)距(ju)(ju)远近不同，然二(er)(er)(er)十(shi)(shi)八宿之(zhi)(zhi)(zhi)体不异(yi)。古(gu)以(yi)牵(qian)牛(niu)上星(xing)(xing)(xing)(xing)(xing)为(wei)距(ju)(ju)，《太(tai)初(chu)(chu)》改用(yong)中(zhong)星(xing)(xing)(xing)(xing)(xing)，入古(gu)历(li)(li)(li)牵(qian)牛(niu)太(tai)半(ban)度(du)(du)(du)(du)，于气(qi)法当(dang)三(san)十(shi)(shi)二(er)(er)(er)分(fen)日之(zhi)(zhi)(zhi)二(er)(er)(er)十(shi)(shi)一(yi)。故(gu)《洪(hong)范传》冬(dong)至日在(zai)牵(qian)牛(niu)一(yi)度(du)(du)(du)(du)，减《太(tai)初(chu)(chu)》星(xing)(xing)(xing)(xing)(xing)距(ju)(ju)二(er)(er)(er)十(shi)(shi)一(yi)分(fen)，直南斗二(er)(er)(er)十(shi)(shi)六(liu)度(du)(du)(du)(du)十(shi)(shi)九分(fen)也。《颛顼(xu)历(li)(li)(li)》立春(chun)起(qi)营室(shi)五(wu)(wu)度(du)(du)(du)(du)，冬(dong)至在(zai)牵(qian)年(nian)一(yi)度(du)(du)(du)(du)少。《洪(hong)范传》冬(dong)至所起(qi)无余(yu)分(fen)，故(gu)立春(chun)在(zai)营室(shi)四度(du)(du)(du)(du)太(tai)。祖冲之(zhi)(zhi)(zhi)自(zi)营室(shi)五(wu)(wu)度(du)(du)(du)(du)，以(yi)《太(tai)初(chu)(chu)》星(xing)(xing)(xing)(xing)(xing)距(ju)(ju)命之(zhi)(zhi)(zhi)，因云(yun)(yun)秦(qin)历(li)(li)(li)冬(dong)至，日在(zai)牵(qian)牛(niu)六(liu)度(du)(du)(du)(du)。虞(yu)广(guang)刂(dao)等袭冲之(zhi)(zhi)(zhi)之(zhi)(zhi)(zhi)误，为(wei)之(zhi)(zhi)(zhi)说(shuo)(shuo)云(yun)(yun)：“夏(xia)时冬(dong)至，日在(zai)斗末，以(yi)岁差(cha)考之(zhi)(zhi)(zhi)，牵(qian)牛(niu)六(liu)度(du)(du)(du)(du)乃(nai)《颛顼(xu)》之(zhi)(zhi)(zhi)代。汉(han)时虽(sui)觉(jue)其差(cha)，顿移(yi)五(wu)(wu)度(du)(du)(du)(du)，故(gu)冬(dong)至还在(zai)牛(niu)初(chu)(chu)。”按《洪(hong)范》古(gu)今星(xing)(xing)(xing)(xing)(xing)距(ju)(ju)，仅差(cha)四分(fen)之(zhi)(zhi)(zhi)三(san)，皆起(qi)牵(qian)牛(niu)一(yi)度(du)(du)(du)(du)。广(guang)刂(dao)等所说(shuo)(shuo)，亦(yi)非是。鲁宣公十(shi)(shi)五(wu)(wu)年(nian)，丁卯岁，《颛顼(xu)历(li)(li)(li)》第(di)十(shi)(shi)三(san)蔀首(shou)与(yu)《麟(lin)德历(li)(li)(li)》俱以(yi)丁巳平旦立春(chun)。至始(shi)皇(huang)三(san)十(shi)(shi)三(san)年(nian)丁亥(hai)，凡三(san)百八十(shi)(shi)岁，得《颛顼(xu)历(li)(li)(li)》壬(ren)申蔀首(shou)。是岁，秦(qin)历(li)(li)(li)以(yi)壬(ren)申寅初(chu)(chu)立春(chun)，而《开元历(li)(li)(li)》与(yu)《麟(lin)德历(li)(li)(li)》俱以(yi)庚午平旦，差(cha)二(er)(er)(er)日，日当(dang)在(zai)南斗二(er)(er)(er)十(shi)(shi)二(er)(er)(er)度(du)(du)(du)(du)。古(gu)历(li)(li)(li)后天二(er)(er)(er)日，又增(zeng)二(er)(er)(er)度(du)(du)(du)(du)。然则秦(qin)历(li)(li)(li)冬(dong)至，定在(zai)午前二(er)(er)(er)度(du)(du)(du)(du)。气(qi)后天二(er)(er)(er)日，日不及天二(er)(er)(er)度(du)(du)(du)(du)，微(wei)而难觉(jue)，故(gu)《吕(lv)氏》循用(yong)之(zhi)(zhi)(zhi)。
及汉兴(xing)，张(zhang)苍(cang)等(deng)亦以(yi)《颛顼历》比(bi)五家(jia)疏(shu)阔中(zhong)最(zui)近密(mi)。今(jin)(jin)考(kao)月蚀冲，则开元冬(dong)至(zhi)，上(shang)及牛初(chu)正(zheng)差一次。淳风以(yi)为古术疏(shu)舛，虽(sui)弦望、昏明(ming)差天十(shi)五度(du)而(er)犹不(bu)知。又(you)引(yin)《吕氏春秋》，黄(huang)(huang)帝以(yi)仲(zhong)春乙卯日在(zai)(zai)奎(kui)，始奏(zou)十(shi)二(er)钟，命之曰《咸池》。至(zhi)今(jin)(jin)三千(qian)余(yu)年，而(er)春分亦在(zai)(zai)奎(kui)，反谓秦(qin)历与(yu)今(jin)(jin)不(bu)异。按不(bu)韦所(suo)记(ji)，以(yi)其(qi)《月令》孟春在(zai)(zai)奎(kui)，谓黄(huang)(huang)帝之时(shi)亦在(zai)(zai)奎(kui)，犹淳风历冬(dong)至(zhi)斗十(shi)三度(du)，因谓黄(huang)(huang)帝时(shi)亦在(zai)(zai)建(jian)星耳。经籍所(suo)载(zai)，合于岁(sui)差者，淳风皆不(bu)取，而(er)专(zhuan)取于《吕氏春秋》。若(ruo)谓十(shi)二(er)纪可以(yi)为正(zheng)，则立春在(zai)(zai)营(ying)室五度(du)，固当不(bu)易，安得顿移使当启蛰之节？此又(you)其(qi)所(suo)不(bu)思(si)也。
汉四(si)百二(er)十六年，日却差五度。景帝(di)中元三年甲午岁冬至，应在斗二(er)十一(yi)度。
太初元年(nian)，《三(san)统历(li)(li)(li)(li)(li)(li)(li)(li)》及《周(zhou)(zhou)(zhou)历(li)(li)(li)(li)(li)(li)(li)(li)》皆以(yi)(yi)十(shi)(shi)一(yi)(yi)月(yue)夜(ye)半合(he)(he)朔(shuo)(shuo)(shuo)(shuo)冬至(zhi)(zhi)，日(ri)月(yue)俱起牵牛一(yi)(yi)度。古历(li)(li)(li)(li)(li)(li)(li)(li)与(yu)近代密率相(xiang)较，二(er)(er)百年(nian)气(qi)差(cha)(cha)一(yi)(yi)日(ri)，三(san)百年(nian)朔(shuo)(shuo)(shuo)(shuo)差(cha)(cha)一(yi)(yi)日(ri)。推(tui)而上之(zhi)，久益(yi)(yi)先天(tian)；引而下之(zhi)，久益(yi)(yi)后(hou)天(tian)。僖公五(wu)年(nian)，《周(zhou)(zhou)(zhou)历(li)(li)(li)(li)(li)(li)(li)(li)》正月(yue)辛(xin)亥朔(shuo)(shuo)(shuo)(shuo)，余四(si)分之(zhi)一(yi)(yi)，南至(zhi)(zhi)。以(yi)(yi)岁差(cha)(cha)推(tui)之(zhi)，日(ri)在牵牛初。至(zhi)(zhi)宣公十(shi)(shi)一(yi)(yi)年(nian)癸亥，《周(zhou)(zhou)(zhou)历(li)(li)(li)(li)(li)(li)(li)(li)》与(yu)《麟(lin)(lin)德(de)历(li)(li)(li)(li)(li)(li)(li)(li)》俱以(yi)(yi)庚(geng)戌日(ri)中冬至(zhi)(zhi)，而月(yue)朔(shuo)(shuo)(shuo)(shuo)尚先《麟(lin)(lin)德(de)历(li)(li)(li)(li)(li)(li)(li)(li)》十(shi)(shi)五(wu)辰。至(zhi)(zhi)昭公二(er)(er)十(shi)(shi)年(nian)己(ji)卯，《周(zhou)(zhou)(zhou)历(li)(li)(li)(li)(li)(li)(li)(li)》以(yi)(yi)正月(yue)己(ji)丑朔(shuo)(shuo)(shuo)(shuo)日(ri)中南至(zhi)(zhi)，《麟(lin)(lin)德(de)历(li)(li)(li)(li)(li)(li)(li)(li)》以(yi)(yi)己(ji)丑平(ping)旦冬至(zhi)(zhi)。哀公十(shi)(shi)一(yi)(yi)年(nian)丁(ding)巳，《周(zhou)(zhou)(zhou)历(li)(li)(li)(li)(li)(li)(li)(li)》入己(ji)酉蔀首(shou)，《麟(lin)(lin)德(de)历(li)(li)(li)(li)(li)(li)(li)(li)》以(yi)(yi)戊(wu)申禺(yu)(yu)中冬至(zhi)(zhi)。惠王四(si)十(shi)(shi)三(san)年(nian)己(ji)丑，《周(zhou)(zhou)(zhou)历(li)(li)(li)(li)(li)(li)(li)(li)》入丁(ding)卯蔀首(shou)，《麟(lin)(lin)德(de)历(li)(li)(li)(li)(li)(li)(li)(li)》以(yi)(yi)乙丑日(ri)昳冬至(zhi)(zhi)。吕后(hou)八年(nian)辛(xin)酉，《周(zhou)(zhou)(zhou)历(li)(li)(li)(li)(li)(li)(li)(li)》入乙酉蔀首(shou)，《麟(lin)(lin)德(de)历(li)(li)(li)(li)(li)(li)(li)(li)》以(yi)(yi)壬午黄昏冬至(zhi)(zhi)；其十(shi)(shi)二(er)(er)月(yue)甲申，人定合(he)(he)朔(shuo)(shuo)(shuo)(shuo)。太初元年(nian)，《周(zhou)(zhou)(zhou)历(li)(li)(li)(li)(li)(li)(li)(li)》以(yi)(yi)甲子夜(ye)半合(he)(he)朔(shuo)(shuo)(shuo)(shuo)冬至(zhi)(zhi)，《麟(lin)(lin)德(de)历(li)(li)(li)(li)(li)(li)(li)(li)》以(yi)(yi)辛(xin)酉禺(yu)(yu)中冬至(zhi)(zhi)，十(shi)(shi)二(er)(er)月(yue)癸亥晡时合(he)(he)朔(shuo)(shuo)(shuo)(shuo)。气(qi)差(cha)(cha)三(san)十(shi)(shi)二(er)(er)辰，朔(shuo)(shuo)(shuo)(shuo)差(cha)(cha)四(si)辰。此疏密之(zhi)大较也。
僖(xi)(xi)公(gong)五年(nian)(nian)(nian)，《周(zhou)历(li)(li)》、汉历(li)(li)、唐(tang)(tang)(tang)历(li)(li)皆(jie)(jie)以(yi)(yi)(yi)辛(xin)亥南至(zhi)(zhi)。后五百五十余岁(sui)，至(zhi)(zhi)太初(chu)(chu)元年(nian)(nian)(nian)，《周(zhou)历(li)(li)》、汉历(li)(li)皆(jie)(jie)得甲(jia)子(zi)(zi)夜半冬(dong)至(zhi)(zhi)，唐(tang)(tang)(tang)历(li)(li)皆(jie)(jie)以(yi)(yi)(yi)辛(xin)酉，则(ze)汉历(li)(li)后天三日矣(yi)。祖冲(chong)之(zhi)、张胄玄(xuan)促(cu)上章岁(sui)至(zhi)(zhi)太初(chu)(chu)元年(nian)(nian)(nian)，冲(chong)之(zhi)以(yi)(yi)(yi)癸(gui)亥鸡鸣冬(dong)至(zhi)(zhi)，而(er)胄玄(xuan)以(yi)(yi)(yi)癸(gui)亥日出(chu)。欲令(ling)合于(yu)甲(jia)子(zi)(zi)，而(er)适与《鲁历(li)(li)》相会(hui)。自(zi)此(ci)推僖(xi)(xi)公(gong)五年(nian)(nian)(nian)，《鲁历(li)(li)》以(yi)(yi)(yi)庚(geng)戌(xu)冬(dong)至(zhi)(zhi)，而(er)二家皆(jie)(jie)以(yi)(yi)(yi)甲(jia)寅。且僖(xi)(xi)公(gong)登(deng)观台(tai)以(yi)(yi)(yi)望(wang)而(er)书云物，出(chu)于(yu)表晷(gui)天验，非时史亻意度。乖(guai)丘明正时之(zhi)意，以(yi)(yi)(yi)就(jiu)刘歆之(zhi)失。今考麟德元年(nian)(nian)(nian)甲(jia)子(zi)(zi)，唐(tang)(tang)(tang)历(li)(li)皆(jie)(jie)以(yi)(yi)(yi)甲(jia)子(zi)(zi)冬(dong)至(zhi)(zhi)，而(er)《周(zhou)历(li)(li)》、汉历(li)(li)皆(jie)(jie)以(yi)(yi)(yi)庚(geng)午。然则(ze)自(zi)太初(chu)(chu)下至(zhi)(zhi)麟德差四日，自(zi)太初(chu)(chu)上及僖(xi)(xi)公(gong)差三日，不足疑(yi)也。
以岁差(cha)考太(tai)(tai)初(chu)元年辛酉(you)冬(dong)至(zhi)加时(shi)，日(ri)在斗二十三(san)度(du)。汉(han)历，气(qi)后天三(san)日(ri)，而日(ri)先天三(san)度(du)，所差(cha)尚少。故落下闳等虽候昏(hun)明中(zhong)(zhong)星，步(bu)日(ri)所在，犹未觉其(qi)差(cha)。然《洪范》、《太(tai)(tai)初(chu)》所揆，冬(dong)至(zhi)昏(hun)奎(kui)八(ba)度(du)中(zhong)(zhong)，夏(xia)至(zhi)昏(hun)氐十三(san)度(du)中(zhong)(zhong)，依汉(han)历，冬(dong)至(zhi)日(ri)在牵(qian)牛初(chu)太(tai)(tai)半度(du)，以昏(hun)距(ju)中(zhong)(zhong)命之，奎(kui)十一度(du)中(zhong)(zhong)；夏(xia)至(zhi)，房一度(du)中(zhong)(zhong)。此皆闳等所测，自差(cha)三(san)度(du)，则刘向(xiang)等殆(dai)已(yi)知《太(tai)(tai)初(chu)》冬(dong)至(zhi)不及天三(san)度(du)矣。
及永平(ping)中，治历(li)(li)者(zhe)考(kao)行事，史官注日(ri)，常不及《太(tai)初(chu)历(li)(li)》五度(du)。然诸儒守谶纬，以(yi)为(wei)(wei)(wei)当在(zai)(zai)牛(niu)(niu)(niu)初(chu)，故贾逵等议：“石氏星(xing)距，黄道(dao)规牵牛(niu)(niu)(niu)初(chu)直斗(dou)(dou)(dou)二(er)(er)十度(du)，于(yu)赤道(dao)二(er)(er)十一(yi)(yi)度(du)也。《尚书》《考(kao)灵耀》斗(dou)(dou)(dou)二(er)(er)十二(er)(er)度(du)，无(wu)余分(fen)。冬至，日(ri)在(zai)(zai)牵牛(niu)(niu)(niu)初(chu)，无(wu)牵年所起文。编䜣等据今日(ri)所去牵牛(niu)(niu)(niu)中星(xing)五度(du)，于(yu)斗(dou)(dou)(dou)二(er)(er)十一(yi)(yi)度(du)四(si)分(fen)一(yi)(yi)，与(yu)《考(kao)灵耀》相近。”遂更历(li)(li)从斗(dou)(dou)(dou)二(er)(er)十一(yi)(yi)度(du)起。然古历(li)(li)以(yi)斗(dou)(dou)(dou)魁首为(wei)(wei)(wei)距，至牵牛(niu)(niu)(niu)为(wei)(wei)(wei)二(er)(er)十二(er)(er)度(du)，未闻移牵牛(niu)(niu)(niu)六度(du)以(yi)就《太(tai)初(chu)》星(xing)距也。逵等以(yi)末学(xue)僻于(yu)所传，而(er)昧天象，故以(yi)权诬之，而(er)后听从他术，以(yi)为(wei)(wei)(wei)日(ri)在(zai)(zai)牛(niu)(niu)(niu)初(chu)者(zhe)，由此(ci)遂黜。
今岁差，引(yin)而(er)(er)退之(zhi)，则(ze)辛酉冬(dong)至，日(ri)(ri)在(zai)斗(dou)(dou)二十度(du)，合于(yu)(yu)密(mi)率，而(er)(er)有验于(yu)(yu)今；推而(er)(er)进之(zhi)，则(ze)甲子冬(dong)至，日(ri)(ri)在(zai)斗(dou)(dou)二十四度(du)，昏奎八度(du)中，而(er)(er)有证于(yu)(yu)古。其(qi)虚(xu)退之(zhi)度(du)，又适及牵牛(niu)之(zhi)初。而(er)(er)冲之(zhi)虽促(cu)减(jian)气分，冀符汉历(li)(li)，犹差六度(du)，未及于(yu)(yu)天。而(er)(er)《麟(lin)德历(li)(li)》冬(dong)至不移，则(ze)昏中向差半(ban)次。淳风以(yi)为太初元年得本星(xing)度(du)，日(ri)(ri)月合璧(bi)，俱起(qi)建星(xing)。贾逵考历(li)(li)，亦(yi)云古历(li)(li)冬(dong)至皆起(qi)建星(xing)。两汉冬(dong)至，日(ri)(ri)皆后天，故(gu)其(qi)宿(su)度(du)多在(zai)斗(dou)(dou)末。今以(yi)仪测，建星(xing)在(zai)斗(dou)(dou)十三四度(du)间，自古冬(dong)至无差，审矣。
按古之六(liu)术(shu)，并(bing)同《四分(fen)(fen)》。《四分(fen)(fen)》之法(fa)，久则(ze)后(hou)天(tian)(tian)。推古历(li)之作(zuo)，皆在汉初，却较《春秋(qiu)》，朔并(bing)先天(tian)(tian)，则(ze)非三(san)代之前明矣(yi)。
古历(li)，南斗(dou)(dou)(dou)至(zhi)牵(qian)牛(niu)上(shang)星(xing)(xing)(xing)二十(shi)(shi)一度(du)(du)，入《太(tai)初》星(xing)(xing)(xing)距四(si)度(du)(du)，上(shang)直(zhi)西建(jian)之(zhi)初。故(gu)六家或以南斗(dou)(dou)(dou)命(ming)度(du)(du)，或以建(jian)星(xing)(xing)(xing)命(ming)度(du)(du)。方周、汉之(zhi)交，日已潜(qian)退，其(qi)袭《春秋》旧(jiu)历(li)者，则(ze)以为(wei)在(zai)(zai)牵(qian)牛(niu)之(zhi)首；其(qi)考当时(shi)之(zhi)验者，则(ze)以为(wei)入建(jian)星(xing)(xing)(xing)度(du)(du)中(zhong)。然气朔(shuo)前后(hou)不逾一日，故(gu)汉历(li)冬至(zhi)，当在(zai)(zai)斗(dou)(dou)(dou)末。以为(wei)建(jian)星(xing)(xing)(xing)上(shang)得(de)《太(tai)初》本星(xing)(xing)(xing)度(du)(du)，此其(qi)明据也(ye)。《四(si)分》法虽疏(shu)，而(er)先贤谨(jin)于天(tian)事，其(qi)迁(qian)革之(zhi)意，俱(ju)有效于当时(shi)，故(gu)太(tai)史公等观二十(shi)(shi)八(ba)宿疏(shu)密，立晷仪，下(xia)漏刻，以稽晦朔(shuo)、分至(zhi)、躔离、弦(xian)望，其(qi)赤(chi)道(dao)遗法，后(hou)世无以非之(zhi)。故(gu)杂候(hou)清台(tai)，《太(tai)初》最密。若(ruo)当时(shi)日在(zai)(zai)建(jian)星(xing)(xing)(xing)，已直(zhi)斗(dou)(dou)(dou)十(shi)(shi)三度(du)(du)，则(ze)寿王(wang)《调历(li)》宜允得(de)其(qi)中(zhong)，岂容(rong)顿(dun)差一气而(er)未知其(qi)谬？不能观乎时(shi)变，而(er)欲厚诬古人也(ye)。
后(hou)百(bai)余岁(sui)，至永平十(shi)一(yi)(yi)年(nian)，以《麟德历(li)》较之(zhi)，气(qi)当(dang)后(hou)天二日(ri)(ri)(ri)(ri)(ri)半，朔当(dang)后(hou)天半日(ri)(ri)(ri)(ri)(ri)。是岁(sui)《四分(fen)历(li)》得辛酉蔀首，已减《太(tai)(tai)初历(li)》四分(fen)日(ri)(ri)(ri)(ri)(ri)之(zhi)三，定后(hou)天二日(ri)(ri)(ri)(ri)(ri)太(tai)(tai)半。《开元(yuan)历(li)》以戊(wu)午禺中冬至，日(ri)(ri)(ri)(ri)(ri)在(zai)斗十(shi)八(ba)度半弱，潜退至牛前八(ba)度。进至辛酉夜半，日(ri)(ri)(ri)(ri)(ri)在(zai)斗二十(shi)一(yi)(yi)度半弱。《续汉志》云(yun)：“元(yuan)和二年(nian)冬至，日(ri)(ri)(ri)(ri)(ri)在(zai)斗二十(shi)一(yi)(yi)度四分(fen)之(zhi)一(yi)(yi)。”是也。
祖冲之曰：“《四(si)分历》立冬(dong)景长一丈，立春九(jiu)尺六寸(cun)(cun)，冬(dong)至(zhi)(zhi)南(nan)极日(ri)(ri)晷最长。二(er)气去至(zhi)(zhi)日(ri)(ri)数既同，则中(zhong)景应等。而相(xiang)差(cha)四(si)寸(cun)(cun)，此(ci)冬(dong)至(zhi)(zhi)后天(tian)之验也(ye)。二(er)气中(zhong)景，日(ri)(ri)差(cha)九(jiu)分半弱，进退调(diao)均，略(lve)无盈缩。各退二(er)日(ri)(ri)十(shi)(shi)(shi)二(er)刻，则景皆九(jiu)尺八寸(cun)(cun)。以(yi)此(ci)推冬(dong)至(zhi)(zhi)后天(tian)亦二(er)日(ri)(ri)十(shi)(shi)(shi)二(er)刻矣。”东汉晷漏定于永元十(shi)(shi)(shi)四(si)年(nian)，则《四(si)分》法施行后十(shi)(shi)(shi)五岁也(ye)。
二十(shi)四气加(jia)时(shi)，进(jin)退不等，其去午正(zheng)极(ji)远者，四十(shi)九刻有余(yu)。日(ri)中之晷，颇有盈缩，故(gu)治历者皆(jie)就其中率(lv)，以午正(zheng)言(yan)之。而《开元历》所推气及(ji)日(ri)度，皆(jie)直子半(ban)之始。其未及(ji)日(ri)中，尚五十(shi)刻。因加(jia)二日(ri)十(shi)二刻，正(zheng)得二日(ri)太半(ban)。与冲之所算及(ji)破章(zhang)二百年间辄(zhe)差一日(ri)之数，皆(jie)合。
自汉(han)时辛酉冬至(zhi)，以后(hou)(hou)天(tian)(tian)之(zhi)数(shu)减(jian)之(zhi)，则合于今(jin)历(li)岁差斗(dou)十(shi)八度(du)(du)。自今(jin)历(li)戊午冬至(zhi)，以后(hou)(hou)天(tian)(tian)之(zhi)数(shu)加之(zhi)，则合于贾(jia)逵(kui)所测斗(dou)二十(shi)一度(du)(du)。反(fan)复佥同。而淳(chun)风冬至(zhi)常(chang)在斗(dou)十(shi)三度(du)(du)，岂当时知不及(ji)牵(qian)牛五度(du)(du)，而不知过建星八度(du)(du)耶？
晋武帝太(tai)始三(san)年(nian)丁亥(hai)岁(sui)冬至(zhi)，日(ri)当在(zai)斗十六(liu)度(du)。晋用魏《景初历》，其(qi)冬至(zhi)亦(yi)在(zai)斗二十一度(du)少。太(tai)元九(jiu)年(nian)，姜岌(ji)更造《三(san)纪(ji)术》，退在(zai)斗十七度(du)。曰(yue)：“古(gu)历斗分强，故不(bu)可(ke)施于(yu)今(jin)；《乾象》斗分细，故不(bu)可(ke)通于(yu)古(gu)。《景初》虽得其(qi)中，而日(ri)之所在(zai)，乃差四度(du)，合朔亏盈，皆不(bu)及其(qi)次。假月在(zai)东井一度(du)蚀，以日(ri)检之，乃在(zai)参六(liu)度(du)。”岌(ji)以月蚀冲知日(ri)度(du)，由是躔次遂正，为后代治历者宗。
宋文帝时，何承(cheng)天上《元(yuan)(yuan)嘉历》，曰：“《四(si)分(fen)》、《景初(chu)历》，冬(dong)至(zhi)同在(zai)斗(dou)(dou)二十(shi)一度(du)，臣以月蚀(shi)检之，则(ze)(ze)今应在(zai)斗(dou)(dou)十(shi)七度(du)。又(you)土圭测(ce)二至(zhi)，晷差三日有余，则(ze)(ze)天之南(nan)至(zhi)，日在(zai)斗(dou)(dou)十(shi)三四(si)度(du)矣。”事下(xia)太史考验，如(ru)承(cheng)天所上。以《开(kai)元(yuan)(yuan)历》考元(yuan)(yuan)嘉十(shi)年冬(dong)至(zhi)，日在(zai)斗(dou)(dou)十(shi)四(si)度(du)，与承(cheng)天所测(ce)合。
大(da)明八年(nian)(nian)，祖(zu)冲之(zhi)上(shang)《大(da)明历(li)(li)》，冬(dong)至在斗(dou)十一(yi)度(du)，《开元历(li)(li)》应在斗(dou)十三度(du)。梁天监八年(nian)(nian)，冲之(zhi)子员外(wai)散骑侍郎(lang)恒之(zhi)上(shang)其家术(shu)。诏太(tai)史令(ling)将作大(da)匠道(dao)秀等(deng)较之(zhi)，上(shang)距大(da)明又五十年(nian)(nian)，日(ri)度(du)益差。其明年(nian)(nian)，闰月(yue)十六日(ri)，月(yue)蚀(shi)，在虚十度(du)，日(ri)应在张四度(du)。承天历(li)(li)在张六度(du)，冲之(zhi)历(li)(li)在张二(er)度(du)。
大(da)同九年，虞广刂等议(yi)：“姜岌(ji)、何承天(tian)(tian)(tian)俱以月(yue)蚀冲(chong)步日(ri)(ri)(ri)所在(zai)(zai)(zai)。承天(tian)(tian)(tian)虽(sui)移岌(ji)三(san)度(du)，然其冬(dong)(dong)(dong)至(zhi)(zhi)亦上岌(ji)三(san)日(ri)(ri)(ri)。承天(tian)(tian)(tian)在(zai)(zai)(zai)斗(dou)(dou)(dou)十(shi)(shi)(shi)三(san)四(si)度(du)，而(er)岌(ji)在(zai)(zai)(zai)斗(dou)(dou)(dou)十(shi)(shi)(shi)七度(du)。其实非(fei)移。祖(zu)冲(chong)之谓为(wei)实差，以推(tui)今冬(dong)(dong)(dong)至(zhi)(zhi)，日(ri)(ri)(ri)在(zai)(zai)(zai)斗(dou)(dou)(dou)九度(du)，用求(qiu)中(zhong)(zhong)星不合。自岌(ji)至(zhi)(zhi)今，将二(er)百(bai)年，而(er)冬(dong)(dong)(dong)至(zhi)(zhi)在(zai)(zai)(zai)斗(dou)(dou)(dou)十(shi)(shi)(shi)二(er)度(du)。然日(ri)(ri)(ri)之所在(zai)(zai)(zai)难知，验以中(zhong)(zhong)星，则漏(lou)(lou)刻(ke)不定。汉世课昏明中(zhong)(zhong)星，为(wei)法已(yi)浅(qian)。今候夜(ye)半中(zhong)(zhong)星，以求(qiu)日(ri)(ri)(ri)冲(chong)，近于得密(mi)。而(er)水(shui)有清浊，壶有增(zeng)减，或积尘所拥(yong)，故漏(lou)(lou)有迟疾。臣等频夜(ye)候中(zhong)(zhong)星，而(er)前后(hou)相差或至(zhi)(zhi)三(san)度(du)。大(da)略冬(dong)(dong)(dong)至(zhi)(zhi)远不过斗(dou)(dou)(dou)十(shi)(shi)(shi)四(si)度(du)，近不出十(shi)(shi)(shi)度(du)。”又以九年三(san)月(yue)十(shi)(shi)(shi)五日(ri)(ri)(ri)夜(ye)半，月(yue)在(zai)(zai)(zai)房四(si)度(du)蚀。九月(yue)十(shi)(shi)(shi)五日(ri)(ri)(ri)夜(ye)半，月(yue)在(zai)(zai)(zai)昴三(san)度(du)蚀。以其冲(chong)计，冬(dong)(dong)(dong)至(zhi)(zhi)皆(jie)在(zai)(zai)(zai)斗(dou)(dou)(dou)十(shi)(shi)(shi)二(er)度(du)。自姜岌(ji)、何承天(tian)(tian)(tian)所测，下及大(da)同，日(ri)(ri)(ri)已(yi)却(que)差二(er)度(du)。而(er)淳(chun)风(feng)以为(wei)晋、宋以来三(san)百(bai)余岁(sui)，以月(yue)蚀冲(chong)考之，固在(zai)(zai)(zai)斗(dou)(dou)(dou)十(shi)(shi)(shi)三(san)四(si)度(du)间，非(fei)矣。
刘孝孙(sun)(sun)(sun)《甲子元(yuan)(yuan)历》，推(tui)太初(chu)冬(dong)至在(zai)牵牛(niu)初(chu)，下及晋太元(yuan)(yuan)、宋元(yuan)(yuan)嘉(jia)皆在(zai)斗(dou)十(shi)(shi)(shi)七(qi)度(du)(du)(du)。开皇(huang)十(shi)(shi)(shi)四年，在(zai)斗(dou)十(shi)(shi)(shi)三(san)(san)(san)度(du)(du)(du)。而(er)刘焯历仁(ren)寿四年冬(dong)至，日(ri)(ri)在(zai)黄道斗(dou)十(shi)(shi)(shi)度(du)(du)(du)，于赤道斗(dou)十(shi)(shi)(shi)一度(du)(du)(du)也。其(qi)后孝孙(sun)(sun)(sun)改从(cong)焯法(fa)，而(er)仁(ren)寿四年冬(dong)至，日(ri)(ri)亦(yi)在(zai)斗(dou)十(shi)(shi)(shi)度(du)(du)(du)。焯卒后，胄玄(xuan)以其(qi)前(qian)历上(shang)元(yuan)(yuan)起(qi)虚五度(du)(du)(du)，推(tui)汉太初(chu)，犹不(bu)及牵牛(niu)，乃更起(qi)虚七(qi)度(du)(du)(du)，故(gu)太初(chu)在(zai)斗(dou)二十(shi)(shi)(shi)三(san)(san)(san)度(du)(du)(du)，永平在(zai)斗(dou)二十(shi)(shi)(shi)一度(du)(du)(du)，并与今历合(he)。而(er)仁(ren)寿四年，冬(dong)至在(zai)斗(dou)十(shi)(shi)(shi)三(san)(san)(san)度(du)(du)(du)，以验近事，又不(bu)逮其(qi)前(qian)历矣。《戊(wu)寅历》，太初(chu)元(yuan)(yuan)年辛酉(you)(you)冬(dong)至，进及甲子，日(ri)(ri)在(zai)牵牛(niu)三(san)(san)(san)度(du)(du)(du)。永平十(shi)(shi)(shi)一年，得戊(wu)午冬(dong)至，进及辛酉(you)(you)，在(zai)斗(dou)二十(shi)(shi)(shi)六度(du)(du)(du)。至元(yuan)(yuan)嘉(jia)，中气上(shang)景初(chu)三(san)(san)(san)日(ri)(ri)，而(er)冬(dong)至犹在(zai)斗(dou)十(shi)(shi)(shi)七(qi)度(du)(du)(du)。欲(yu)以求合(he)，反更失(shi)之(zhi)。又曲循(xun)孝孙(sun)(sun)(sun)之(zhi)论，而(er)不(bu)知孝孙(sun)(sun)(sun)已(yi)变从(cong)《皇(huang)极》，故(gu)为淳风(feng)等所驳。岁差之(zhi)术，由此不(bu)行。
以太史注记月(yue)蚀冲考日(ri)度(du)，麟(lin)德元(yuan)年(nian)九月(yue)庚(geng)(geng)申，月(yue)蚀在娄十度(du)。至开(kai)元(yuan)四年(nian)六月(yue)庚(geng)(geng)申，月(yue)蚀在牛六度(du)。较《麟(lin)德历》率差(cha)三度(du)，则今(jin)冬至定在赤道(dao)斗(dou)十度(du)。
又(you)《皇极历》，岁(sui)差皆自(zi)黄道(dao)(dao)命之，其每岁(sui)周分，常当南(nan)至之轨，与赤(chi)道(dao)(dao)相较，所减尤多。计黄道(dao)(dao)差三十(shi)六度，赤(chi)道(dao)(dao)差四十(shi)余度，虽(sui)每岁(sui)遁之，不足为过。然立法之体，宜尽其原，是(shi)以《开元历》皆自(zi)赤(chi)道(dao)(dao)推之，乃以今有(you)术从变黄道(dao)(dao)。
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