金史 志第二
历上(shang)
昔(xi)者(zhe)圣人因天(tian)道以授(shou)人时,厘百(bai)工以熙(xi)庶政,步推之法,其(qi)来尚矣。自汉太初迄于前宋(song),治历者(zhe)奚啻七十余(yu)家(jia),大概或(huo)百(bai)年或(huo)数十年,率(lv)一易焉。盖日月(yue)五星盈缩进退(tui),与夫天(tian)运(yun),至不齐(qi)也,人方制器以求(qiu)之,以俾其(qi)齐(qi),积寡至多,不能无爽故尔。
金有天下百余年,历(li)(li)(li)(li)惟(wei)一(yi)易(yi)。天会五年,司(si)天杨级绍(shao)造《大明(ming)历(li)(li)(li)(li)》,十五年春正月(yue)(yue)朔,始(shi)颁行(xing)之(zhi)。其法(fa),以(yi)三亿(yi)八千(qian)三百七十六万八千(qian)六百五十七为(wei)历(li)(li)(li)(li)元,五千(qian)二(er)百三十为(wei)日(ri)法(fa)。然其所本,不能详究,或曰因宋(song)《纪(ji)元历(li)(li)(li)(li)》而(er)增(zeng)损(sun)之(zhi)也(ye)。正隆(long)戊寅(yin)三月(yue)(yue)辛(xin)酉朔,司(si)天言(yan)日(ri)当食(shi),而(er)不食(shi)。大定癸(gui)巳五月(yue)(yue)壬辰(chen)朔,日(ri)食(shi),甲午十一(yi)月(yue)(yue)甲申朔,日(ri)食(shi),加时(shi)皆先天。丁酉九月(yue)(yue)丁酉朔,食(shi)乃后天。由是(shi)占候渐(jian)差,乃命司(si)天监赵(zhao)知微(wei)(wei)重修《大明(ming)历(li)(li)(li)(li)》,十一(yi)年历(li)(li)(li)(li)成(cheng)。时(shi)翰林应奉耶律(lv)履亦(yi)造《乙未历(li)(li)(li)(li)》。二(er)十一(yi)年十一(yi)月(yue)(yue)望,太阴亏食(shi),遂(sui)命尚书省(sheng)委礼部(bu)员外郎任(ren)忠杰与(yu)司(si)天历(li)(li)(li)(li)官验(yan)所食(shi)时(shi)刻分秒,比校知微(wei)(wei)、履及见行(xing)历(li)(li)(li)(li)之(zhi)亲疏(shu),以(yi)知微(wei)(wei)历(li)(li)(li)(li)为(wei)亲,遂(sui)用(yong)之(zhi)。明(ming)昌(chang)初(chu),司(si)天又改进新历(li)(li)(li)(li),礼部(bu)郎中张行(xing)简(jian)言(yan):“请俟(si)他日(ri)月(yue)(yue)食(shi),覆校无差,然后用(yong)之(zhi)。”事(shi)遂(sui)寝。是(shi)以(yi)终金之(zhi)世,惟(wei)用(yong)知微(wei)(wei)历(li)(li)(li)(li),我朝初(chu)亦(yi)用(yong)之(zhi),后始(shi)改《授时(shi)历(li)(li)(li)(li)》焉。今其书存乎太史(shi),采(cai)而(er)录之(zhi),以(yi)为(wei)《历(li)(li)(li)(li)志》。
○步气朔第一
演纪(ji):上(shang)元甲子距今大定庚子,八千八百六(liu)十三万九千六(liu)百五十六(liu)年(nian)。
日(ri)法(fa):五(wu)千二(er)百三十分。
岁(sui)实:一(yi)百九十(shi)一(yi)万二百二十(shi)四分。
通余:二万七千四百(bai)二十(shi)四分。
朔实:一十五(wu)万(wan)四千四百四十五(wu)分(fen)。
通闰:五万(wan)六千(qian)八(ba)百八(ba)十四分。
岁(sui)策(ce):三(san)百六十五日,余(yu)一千二百七十四分(fen)。
朔策:二十(shi)九日,余二千七百七十(shi)五分。
气(qi)策:一(yi)十五日,余一(yi)千一(yi)百四(si)十二分,六十秒。
望策:一十四(si)日,余四(si)千(qian)二(er)分,四(si)十五(wu)秒。
象策:七日,余(yu)二千一分,二十二秒半(ban)。
没限:四(si)千(qian)八十七(qi)分(fen),三十秒(miao)。
朔虚分:二(er)千四百五十(shi)五分。
旬周:三十一万三千八百分(fen)。
纪法:六十。
秒母:九十。
求天正冬至
置(zhi)上元甲子(zi)以来(lai)积年(nian),岁实乘(cheng)之,为通积分。满旬周去之,不尽(jin)以日法约之为日,不盈为余,命甲子(zi)算外,即所求天正冬至(zhi)日大(da)小余。
求次气
置天正冬至大(da)小余,以气策累(lei)加之,秒盈秒母从分(fen),分(fen)满(man)日法从日,即(ji)得次气日及余秒。
求天正经朔
以朔实去(qu)通积分(fen),不尽为(wei)闰余,以减(jian)通积分(fen)为(wei)朔积分(fen)。满旬(xun)周(zhou)去(qu)之,不尽如日法(fa)而一(yi)为(wei)日,不盈为(wei)余,即所求天正(zheng)经大小余也。
求弦望及次朔
置天(tian)正经朔(shuo)大小(xiao)余(yu),以象策累加之,即各得(de)弦、望及次朔(shuo)经日及余(yu)秒也。
求没日
置有没(mei)之(zhi)(zhi)恆气(qi)小(xiao)余,如没(mei)限(xian)以(yi)上,为有没(mei)之(zhi)(zhi)气(qi)。以(yi)秒母(mu)乘之(zhi)(zhi),内其(qi)秒,用(yong)减四十七(qi)万七(qi)千五(wu)百(bai)五(wu)十六,余满六千八百(bai)五(wu)十六而一,所得(de)并恆气(qi)大余,命(ming)为没(mei)日。
求灭日
置(zhi)有(you)灭之朔(shuo)小(xiao)余,经(jing)朔(shuo)小(xiao)余不满朔(shuo)虚(xu)分者。六因之,如四百九十一而一,所得并(bing)经(jing)朔(shuo)大余,命为(wei)灭日。
○步卦候第二
候(hou)策:五,余三百八十,秒(miao)八十。
卦策:六(liu),余四(si)百五十七,秒(miao)六(liu)。
贞策:三(san),余二百二十(shi)八,秒四十(shi)六。
秒母:九十。
辰法:二(er)千六百一十五(wu)。
半辰法:一千三百(bai)七半。
刻法:三(san)(san)百一十三(san)(san),秒八十。
辰刻(ke):八,十(shi)百四分(fen),秒六十(shi)。
半辰刻(ke):四,五十(shi)二分,秒三十(shi)。
秒母:一百。
求七十二候
置中(zhong)气大小余,命之为初候,以候策(ce)累(lei)加之,即次(ci)候及(ji)末候也(ye)。
求六十四卦
置中(zhong)气(qi)大(da)小余,命之(zhi)为公卦(gua)(gua);以卦(gua)(gua)策(ce)累加(jia)(jia)之(zhi),得辟卦(gua)(gua);又加(jia)(jia)之(zhi),得侯内卦(gua)(gua)。以贞(zhen)策(ce)加(jia)(jia)之(zhi),得节气(qi)之(zhi)初(chu),为侯外卦(gua)(gua);又以贞(zhen)策(ce)加(jia)(jia)之(zhi),得大(da)夫卦(gua)(gua)。又以卦(gua)(gua)策(ce)加(jia)(jia)之(zhi),为卿卦(gua)(gua)。
求土王用事
以贞策减四季中气大小余(yu),即土王(wang)用事日也。
求发敛
置小余,以六因之,如辰(chen)法而(er)一为辰(chen)。如不尽(jin),以刻法除之为刻。命子下算外,即得加(jia)时所在辰(chen)刻及分。如加(jia)半辰(chen)法,即命子刻初。
表略
○步日躔第三
周天分(fen):一百九(jiu)十一万二百九(jiu)十三分(fen),五百三十秒。
岁(sui)差:六十九(jiu),五(wu)百三十秒。秒母(mu)一(yi)万。
周(zhou)天谌:三(san)百六十(shi)五度,二十(shi)五分,六十(shi)八秒。
象限:九十一,三十一分,九秒(miao)。
二十四气日(ri)积(ji)度及盈缩(suo)
求每日盈缩朓朒
各(ge)(ge)置其气(qi)(qi)损(sun)(sun)益率(lv)(lv),求盈缩(suo)之(zhi)(zhi)损(sun)(sun)益,求朒(nv)磕(ke)用(yong)朒(nv)磕(ke)之(zhi)(zhi)损(sun)(sun)益。六因,如象限而一,为(wei)(wei)气(qi)(qi)中(zhong)(zhong)率(lv)(lv)。与(yu)后气(qi)(qi)中(zhong)(zhong)率(lv)(lv)相(xiang)减(jian)(jian),为(wei)(wei)合差(cha)。半合差(cha)加减(jian)(jian)其气(qi)(qi)中(zhong)(zhong)率(lv)(lv),为(wei)(wei)初(chu)(chu)(chu)末(mo)泛率(lv)(lv)。至后:加初(chu)(chu)(chu),减(jian)(jian)末(mo)。分(fen)(fen)(fen)后:减(jian)(jian)初(chu)(chu)(chu),加末(mo)。又置合差(cha),六因,如象限而一,为(wei)(wei)日(ri),半之(zhi)(zhi),加减(jian)(jian)初(chu)(chu)(chu)未(wei)泛率(lv)(lv),为(wei)(wei)初(chu)(chu)(chu)末(mo)定率(lv)(lv)。至后:减(jian)(jian)初(chu)(chu)(chu),加末(mo)。分(fen)(fen)(fen)后:加初(chu)(chu)(chu),减(jian)(jian)末(mo)。以(yi)日(ri)差(cha)累加减(jian)(jian)其气(qi)(qi)初(chu)(chu)(chu)末(mo)定率(lv)(lv),为(wei)(wei)每(mei)日(ri)损(sun)(sun)益分(fen)(fen)(fen)。至后减(jian)(jian),分(fen)(fen)(fen)后加。各(ge)(ge)以(yi)每(mei)日(ri)损(sun)(sun)益分(fen)(fen)(fen)加减(jian)(jian)气(qi)(qi)下盈缩(suo)、朒(nv)磕(ke),为(wei)(wei)每(mei)日(ri)盈缩(suo)、朒(nv)磕(ke)二分(fen)(fen)(fen)前一气(qi)(qi)元后率(lv)(lv)相(xiang)减(jian)(jian)为(wei)(wei)合差(cha)者,皆用(yong)前气(qi)(qi)合差(cha)。
求经朔弦望入气
置天(tian)正闰余(yu),以(yi)日(ri)(ri)法除为日(ri)(ri),不满为余(yu),如气(qi)(qi)(qi)策(ce)以(yi)下,以(yi)减气(qi)(qi)(qi)策(ce),为入(ru)大雪(xue)气(qi)(qi)(qi)。以(yi)上去(qu)之,余(yu)亦减气(qi)(qi)(qi)策(ce),为入(ru)小雪(xue)气(qi)(qi)(qi)。即得(de)天(tian)正经朔入(ru)气(qi)(qi)(qi)日(ri)(ri)及(ji)余(yu)也。以(yi)象策(ce)累(lei)加之,满气(qi)(qi)(qi)策(ce)去(qu)之,即得(de)弦(xian)、望入(ru)次气(qi)(qi)(qi)日(ri)(ri)及(ji)余(yu)。因(yin)加,后朔入(ru)气(qi)(qi)(qi)日(ri)(ri)及(ji)余(yu)也。
求每日(ri)损益、盈缩、朒(nv)磕(ke)
以日(ri)差益(yi)(yi)加减(jian)(jian)损加减(jian)(jian)其气初(chu)损益(yi)(yi)率,为(wei)每日(ri)损益(yi)(yi)率。驯积(ji)损益(yi)(yi)其气盈缩、肉(rou)磕积(ji),为(wei)每日(ri)盈、朒(nv)磕积(ji)。
求(qiu)经朔(shuo)弦望入气朒磕定数
各以所入恆气小余(yu),以乘(cheng)其日(ri)损(sun)益(yi)率(lv),如日(ri)法而(er)一,以所损(sun)益(yi)其下朒磕积为定数。
赤道宿度
斗二十(shi)五度(du) 牛七(qi)度(du)少(shao) 女(nv)十(shi)一度(du)少(shao) 虚九度(du)少(shao)秒六十(shi)八(ba)危(wei)十(shi)五度(du)半室(shi)十(shi)七(qi)度(du)壁八(ba)度(du)太
右北方(fang)七宿九十四(si)度秒六十八
奎(kui)十(shi)六(liu)度(du)半(ban)娄十(shi)二度(du)胃(wei)十(shi)五度(du)昴十(shi)一度(du)少毕十(shi)七(qi)度(du)少觜半(ban)度(du)参十(shi)度(du)半(ban)
右西方七宿八十(shi)(shi)(shi)三(san)度(du)井三(san)十(shi)(shi)(shi)三(san)度(du)少鬼二度(du)半柳十(shi)(shi)(shi)三(san)度(du)太(tai)(tai)星六度(du)太(tai)(tai)张十(shi)(shi)(shi)七度(du)少翼十(shi)(shi)(shi)八度(du)太(tai)(tai) 轸十(shi)(shi)(shi)七度(du)
右(you)南方(fang)七宿一百九度少(shao)(shao)角十二度亢九度少(shao)(shao)氐(di)一十六(liu)度房五度太心六(liu)度少(shao)(shao)尾十九度少(shao)(shao)箕十度半
右东方七宿七十九度
求冬至赤道日度
置通(tong)积(ji)分,以周天分去(qu)之(zhi),余(yu)日(ri)法(fa)而一为(wei)度(du)(du),不满退除(chu)为(wei)分秒。以百为(wei)母。命起赤道(dao)虚宿七度(du)(du)外去(qu)之(zhi),至不满宿,即所(suo)求年(nian)天正(zheng)冬至加时日(ri)躔赤道(dao)度(du)(du)及分秒。
求春分夏至(zhi)秋分赤道日(ri)度
置天正(zheng)冬至(zhi)加时赤(chi)道(dao)(dao)日度,累加象限(xian),满赤(chi)道(dao)(dao)宿次去之,即各得春分(fen)、夏至(zhi)、秋分(fen)加时日在宿度及分(fen)秒。
求四正赤道宿积度
置四正赤道宿全度,以(yi)四正赤道日度及(ji)分减之(zhi)(zhi),余为距后(hou)度。以(yi)赤道宿度累加之(zhi)(zhi),各得(de)四正后(hou)赤道宿积度及(ji)分。
求赤道宿(su)积度入(ru)初(chu)末限
视四正(zheng)后赤道(dao)宿积度(du)及(ji)分(fen),在四十五度(du)六十五分(fen)秒五十四半(ban)以下为入初限,以上者用减象限,余(yu)为入末(mo)限。
求二十宿黄道度
以(yi)四正(zheng)后赤道(dao)宿(su)(su)入初末限度(du)(du)(du)(du)及(ji)分(fen)(fen)(fen),减(jian)一百一度(du)(du)(du)(du),余以(yi)初末限度(du)(du)(du)(du)及(ji)分(fen)(fen)(fen)乘之,进位(wei),满百为分(fen)(fen)(fen),分(fen)(fen)(fen)满百为度(du)(du)(du)(du)。至(zhi)后以(yi)减(jian)、分(fen)(fen)(fen)后以(yi)加(jia)赤道(dao)宿(su)(su)积(ji)(ji)度(du)(du)(du)(du),为其(qi)宿(su)(su)黄道(dao)积(ji)(ji)度(du)(du)(du)(du)。以(yi)前(qian)宿(su)(su)黄道(dao)积(ji)(ji)度(du)(du)(du)(du)减(jian)之其(qi)四正(zheng)之宿(su)(su),先加(jia)象限,然后前(qian)宿(su)(su)减(jian)之。为其(qi)宿(su)(su)黄道(dao)度(du)(du)(du)(du)及(ji)分(fen)(fen)(fen)。其(qi)分(fen)(fen)(fen)就约为太、半、少(shao)。
黄道宿度
斗(dou)二十(shi)(shi)(shi)三度(du)(du)(du)牛七度(du)(du)(du)女十(shi)(shi)(shi)一度(du)(du)(du)虚九度(du)(du)(du)少(shao)秒六十(shi)(shi)(shi)八(ba)危十(shi)(shi)(shi)六度(du)(du)(du)室十(shi)(shi)(shi)八(ba)度(du)(du)(du)少(shao)壁九度(du)(du)(du)半
右北方(fang)七宿(su)九十四度六十八秒
奎(kui)十七(qi)度(du)(du)(du)(du)太(tai)(tai)娄(lou)十二度(du)(du)(du)(du)太(tai)(tai)胃(wei)十五(wu)度(du)(du)(du)(du)半(ban)昴十一(yi)度(du)(du)(du)(du)毕十六度(du)(du)(du)(du)半(ban)觜半(ban)度(du)(du)(du)(du)参九(jiu)度(du)(du)(du)(du)太(tai)(tai)
右西方(fang)七(qi)(qi)宿八十(shi)三(san)度太一百七(qi)(qi)十(shi)七(qi)(qi)、七(qi)(qi)十(shi)五、六(liu)十(shi)八
井(jing)三(san)十度(du)半(ban)鬼(gui)二(er)度(du)半(ban)柳(liu)十三(san)度(du)少星(xing)六度(du)太(tai)张十七(qi)度(du)太(tai)翼二(er)十度(du)轸十八度(du)半(ban)
右南方七宿一百九度少二(er)百八(ba)十(shi)七、六十(shi)八(ba)
角十(shi)二度(du)(du)太亢九度(du)(du)太氐十(shi)六(liu)度(du)(du)少房五度(du)(du)太心六(liu)度(du)(du)尾十(shi)八(ba)度(du)(du)少箕九度(du)(du)半
右东(dong)方七宿七十八(ba)度少三百六(liu)十五(wu)、二十五(wu)、六(liu)十八(ba)
前黄道宿度,依今历岁(sui)(sui)差所在(zai)算定。如上考往古,下(xia)验将(jiang)来,当据(ju)岁(sui)(sui)差,每移(yi)一度,依术推变(bian)当时(shi)宿度,然后可(ke)步七曜(yao),知其所在(zai)。
求天正(zheng)冬至加(jia)时黄(huang)道日度
以冬(dong)至(zhi)加时赤(chi)道日度及(ji)(ji)分(fen)秒(miao),减一(yi)百(bai)一(yi)度,余以冬(dong)至(zhi)赤(chi)度及(ji)(ji)分(fen)秒(miao)乘之,进(jin)位,满百(bai)为(wei)分(fen),分(fen)满百(bai)为(wei)度。命曰(yue)黄(huang)赤(chi)道差(cha)。用减冬(dong)至(zhi)加时赤(chi)道日度及(ji)(ji)分(fen)秒(miao),即(ji)所求年天正冬(dong)至(zhi)加时黄(huang)道日度及(ji)(ji)分(fen)秒(miao)。
求(qiu)二十四气加时黄道日度
置所求(qiu)(qiu)年(nian)冬至日躔黄赤(chi)道(dao)(dao)差(cha),以次年(nian)黄赤(chi)道(dao)(dao)差(cha)减(jian)之(zhi),余(yu)以所求(qiu)(qiu)气(qi)数乘之(zhi),二十四而一(yi),所得以加(jia)其(qi)气(qi)中(zhong)积及(ji)约(yue)分(fen),又以其(qi)气(qi)初日盈缩数盈加(jia)缩减(jian)之(zhi),用加(jia)冬至加(jia)时黄道(dao)(dao)日度(du),依宿次去之(zhi),即(ji)(ji)各得其(qi)气(qi)加(jia)时黄道(dao)(dao)日躔宿度(du)及(ji)分(fen)秒。如(ru)其(qi)年(nian)冬至加(jia)时赤(chi)道(dao)(dao)宿度(du)空(kong)分(fen)秒在岁差(cha)以下者(zhe),即(ji)(ji)加(jia)前宿全度(du),然后求(qiu)(qiu)黄赤(chi)道(dao)(dao)差(cha),余(yu)依术算。
求二十四(si)气每(mei)日(ri)晨前夜半(ban)黄(huang)道(dao)日(ri)度(du)
副置(zhi)其(qi)气(qi)(qi)小余(yu),以其(qi)气(qi)(qi)初日(ri)损(sun)(sun)益率(lv)乘之(zhi),盈(ying)缩(suo)之(zhi)损(sun)(sun)益。万约之(zhi)为分,应益者(zhe)(zhe)盈(ying)加(jia)缩(suo)减(jian)(jian),应损(sun)(sun)者(zhe)(zhe)盈(ying)减(jian)(jian)缩(suo)加(jia)其(qi)副,日(ri)法除之(zhi)为度(du),不(bu)满退除为分秒,以减(jian)(jian)其(qi)气(qi)(qi)加(jia)时黄(huang)(huang)道(dao)日(ri)度(du),即各得其(qi)气(qi)(qi)初日(ri)晨前夜半黄(huang)(huang)道(dao)日(ri)度(du)。每日(ri)加(jia)一度(du),以百(bai)约每日(ri)损(sun)(sun)益率(lv),盈(ying)缩(suo)之(zhi)损(sun)(sun)益。应益者(zhe)(zhe)盈(ying)加(jia)缩(suo)减(jian)(jian),应损(sun)(sun)者(zhe)(zhe)盈(ying)减(jian)(jian)缩(suo)加(jia),为每日(ri)晨前夜半黄(huang)(huang)道(dao)日(ri)度(du)及分秒。
求每日午中黄道日度
置一万(wan)分,以(yi)所入气(qi)日(ri)盈缩(suo)(suo)(suo)损(sun)益率(lv),应(ying)益者(zhe)盈加缩(suo)(suo)(suo)减(jian),应(ying)损(sun)者(zhe)盈减(jian)缩(suo)(suo)(suo)加,皆加减(jian)损(sun)益率(lv),余(yu)半之(zhi),满百(bai)为分,不(bu)满为秒,以(yi)加其日(ri)清(qing)晨前夜(ye)半黄道日(ri)度,即其日(ri)午中日(ri)躔(chan)黄道宿度及分秒。
求每日午中黄道积度
以二(er)至加时黄道日度(du),距至所求日午中(zhong)黄道日度(du),为(wei)入二(er)至后黄道积度(du)及分秒(miao)。
每日午中(zhong)黄(huang)道入(ru)初(chu)末(mo)限
视二(er)(er)至(zhi)后黄道积(ji)度,在(zai)四(si)十(shi)三度一十(shi)二(er)(er)分(fen)秒八十(shi)七以下为(wei)初限(xian)(xian),以上用(yong)减象(xiang)限(xian)(xian),余为(wei)入末(mo)限(xian)(xian)。其积(ji)度满象(xiang)限(xian)(xian)去之,为(wei)二(er)(er)分(fen)后黄道积(ji)度,在(zai)四(si)十(shi)八度一十(shi)八分(fen)秒二(er)(er)十(shi)二(er)(er)以下为(wei)初限(xian)(xian),以上用(yong)减象(xiang)限(xian)(xian),余为(wei)入末(mo)限(xian)(xian)。
求每日午中赤道日度
以(yi)所(suo)(suo)求日(ri)(ri)午(wu)(wu)(wu)中黄道(dao)积(ji)度(du),入(ru)至后(hou)(hou)初限(xian)(xian)(xian),分(fen)(fen)(fen)(fen)后(hou)(hou)末(mo)限(xian)(xian)(xian),度(du)及分(fen)(fen)(fen)(fen)秒,进三位(wei),加(jia)二(er)(er)十(shi)万二(er)(er)千(qian)五十(shi)少,开平方除之(zhi),所(suo)(suo)得(de)减(jian)去四百四十(shi)九半,余(yu)(yu)在(zai)(zai)初限(xian)(xian)(xian)者(zhe),直以(yi)二(er)(er)至赤(chi)道(dao)日(ri)(ri)度(du)加(jia)而(er)命(ming)(ming)之(zhi)。在(zai)(zai)末(mo)限(xian)(xian)(xian)者(zhe),以(yi)减(jian)象限(xian)(xian)(xian),余(yu)(yu)以(yi)二(er)(er)分(fen)(fen)(fen)(fen)赤(chi)道(dao)日(ri)(ri)度(du)加(jia)而(er)命(ming)(ming)之(zhi)。即每(mei)日(ri)(ri)午(wu)(wu)(wu)中赤(chi)道(dao)日(ri)(ri)度(du)。以(yi)所(suo)(suo)求日(ri)(ri)午(wu)(wu)(wu)中黄道(dao)积(ji)度(du),入(ru)至后(hou)(hou)末(mo)限(xian)(xian)(xian),分(fen)(fen)(fen)(fen)后(hou)(hou)初限(xian)(xian)(xian),度(du)及分(fen)(fen)(fen)(fen)秒,进三位(wei),用减(jian)三十(shi)万三千(qian)五十(shi)少,开平方除之(zhi),所(suo)(suo)得(de),以(yi)减(jian)五百五十(shi)半,其在(zai)(zai)初限(xian)(xian)(xian)者(zhe),以(yi)所(suo)(suo)减(jian)之(zhi)余(yu)(yu),直以(yi)二(er)(er)分(fen)(fen)(fen)(fen)赤(chi)道(dao)日(ri)(ri)度(du)加(jia)而(er)命(ming)(ming)之(zhi)。在(zai)(zai)末(mo)限(xian)(xian)(xian)者(zhe),以(yi)减(jian)象限(xian)(xian)(xian),余(yu)(yu)以(yi)二(er)(er)至赤(chi)道(dao)日(ri)(ri)度(du)加(jia)而(er)命(ming)(ming)之(zhi)。即每(mei)日(ri)(ri)午(wu)(wu)(wu)中赤(chi)道(dao)日(ri)(ri)度(du)。
太阳黄道(dao)十(shi)(shi)(shi)(shi)(shi)(shi)(shi)二次(ci)(ci)入(ru)宫(gong)宿度(du)(du)(du),雨(yu)(yu)水,危十(shi)(shi)(shi)(shi)(shi)(shi)(shi)三(san)(san)(san)度(du)(du)(du)三(san)(san)(san)十(shi)(shi)(shi)(shi)(shi)(shi)(shi)九(jiu)(jiu)(jiu)分(fen)(fen)(fen)(fen)(fen)五(wu)(wu)十(shi)(shi)(shi)(shi)(shi)(shi)(shi)秒(miao)(miao)外(wai)(wai)(wai)(wai),入(ru)卫分(fen)(fen)(fen)(fen)(fen),陬訾之(zhi)(zhi)(zhi)(zhi)次(ci)(ci),辰(chen)在(zai)(zai)亥。春分(fen)(fen)(fen)(fen)(fen),奎二度(du)(du)(du)三(san)(san)(san)十(shi)(shi)(shi)(shi)(shi)(shi)(shi)五(wu)(wu)分(fen)(fen)(fen)(fen)(fen)八十(shi)(shi)(shi)(shi)(shi)(shi)(shi)五(wu)(wu)秒(miao)(miao)外(wai)(wai)(wai)(wai),入(ru)鲁分(fen)(fen)(fen)(fen)(fen),降娄之(zhi)(zhi)(zhi)(zhi)次(ci)(ci),辰(chen)在(zai)(zai)戌(xu)。谷(gu)雨(yu)(yu),胃四(si)度(du)(du)(du)二十(shi)(shi)(shi)(shi)(shi)(shi)(shi)四(si)分(fen)(fen)(fen)(fen)(fen)三(san)(san)(san)十(shi)(shi)(shi)(shi)(shi)(shi)(shi)三(san)(san)(san)秒(miao)(miao)外(wai)(wai)(wai)(wai),入(ru)赵(zhao)分(fen)(fen)(fen)(fen)(fen),大(da)(da)梁(liang)之(zhi)(zhi)(zhi)(zhi)次(ci)(ci),辰(chen)在(zai)(zai)酉。小(xiao)满,毕七(qi)(qi)(qi)度(du)(du)(du)九(jiu)(jiu)(jiu)十(shi)(shi)(shi)(shi)(shi)(shi)(shi)六分(fen)(fen)(fen)(fen)(fen)六秒(miao)(miao)外(wai)(wai)(wai)(wai),入(ru)晋分(fen)(fen)(fen)(fen)(fen),实沈之(zhi)(zhi)(zhi)(zhi)次(ci)(ci),辰(chen)在(zai)(zai)申。夏至,井九(jiu)(jiu)(jiu)度(du)(du)(du)四(si)十(shi)(shi)(shi)(shi)(shi)(shi)(shi)七(qi)(qi)(qi)分(fen)(fen)(fen)(fen)(fen)一(yi)十(shi)(shi)(shi)(shi)(shi)(shi)(shi)秒(miao)(miao)外(wai)(wai)(wai)(wai),入(ru)秦分(fen)(fen)(fen)(fen)(fen),鹑首之(zhi)(zhi)(zhi)(zhi)次(ci)(ci),辰(chen)在(zai)(zai)未。大(da)(da)暑,柳四(si)度(du)(du)(du)九(jiu)(jiu)(jiu)十(shi)(shi)(shi)(shi)(shi)(shi)(shi)五(wu)(wu)分(fen)(fen)(fen)(fen)(fen)一(yi)十(shi)(shi)(shi)(shi)(shi)(shi)(shi)六秒(miao)(miao)外(wai)(wai)(wai)(wai),入(ru)周分(fen)(fen)(fen)(fen)(fen),鹑火之(zhi)(zhi)(zhi)(zhi)次(ci)(ci),辰(chen)在(zai)(zai)午。处暑,张(zhang)十(shi)(shi)(shi)(shi)(shi)(shi)(shi)五(wu)(wu)度(du)(du)(du)五(wu)(wu)十(shi)(shi)(shi)(shi)(shi)(shi)(shi)六分(fen)(fen)(fen)(fen)(fen)三(san)(san)(san)十(shi)(shi)(shi)(shi)(shi)(shi)(shi)五(wu)(wu)秒(miao)(miao)外(wai)(wai)(wai)(wai),入(ru)楚分(fen)(fen)(fen)(fen)(fen),鹑尾之(zhi)(zhi)(zhi)(zhi)次(ci)(ci),辰(chen)在(zai)(zai)巳。秋(qiu)分(fen)(fen)(fen)(fen)(fen),轸(zhen)十(shi)(shi)(shi)(shi)(shi)(shi)(shi)度(du)(du)(du)四(si)十(shi)(shi)(shi)(shi)(shi)(shi)(shi)四(si)分(fen)(fen)(fen)(fen)(fen)五(wu)(wu)秒(miao)(miao)外(wai)(wai)(wai)(wai),入(ru)郑分(fen)(fen)(fen)(fen)(fen),寿星(xing)之(zhi)(zhi)(zhi)(zhi)次(ci)(ci),辰(chen)在(zai)(zai)辰(chen)。霜降,氐一(yi)度(du)(du)(du)七(qi)(qi)(qi)十(shi)(shi)(shi)(shi)(shi)(shi)(shi)七(qi)(qi)(qi)分(fen)(fen)(fen)(fen)(fen)七(qi)(qi)(qi)十(shi)(shi)(shi)(shi)(shi)(shi)(shi)七(qi)(qi)(qi)秒(miao)(miao)外(wai)(wai)(wai)(wai),入(ru)宋分(fen)(fen)(fen)(fen)(fen),大(da)(da)火之(zhi)(zhi)(zhi)(zhi)次(ci)(ci),辰(chen)在(zai)(zai)卯。小(xiao)雪,尾三(san)(san)(san)度(du)(du)(du)九(jiu)(jiu)(jiu)十(shi)(shi)(shi)(shi)(shi)(shi)(shi)七(qi)(qi)(qi)分(fen)(fen)(fen)(fen)(fen)九(jiu)(jiu)(jiu)十(shi)(shi)(shi)(shi)(shi)(shi)(shi)二秒(miao)(miao)外(wai)(wai)(wai)(wai),入(ru)燕分(fen)(fen)(fen)(fen)(fen),析(xi)木之(zhi)(zhi)(zhi)(zhi)次(ci)(ci),辰(chen)在(zai)(zai)寅。冬至,斗四(si)度(du)(du)(du)三(san)(san)(san)十(shi)(shi)(shi)(shi)(shi)(shi)(shi)六分(fen)(fen)(fen)(fen)(fen)六十(shi)(shi)(shi)(shi)(shi)(shi)(shi)六秒(miao)(miao)外(wai)(wai)(wai)(wai),入(ru)吴越分(fen)(fen)(fen)(fen)(fen),星(xing)纪之(zhi)(zhi)(zhi)(zhi)次(ci)(ci),辰(chen)在(zai)(zai)丑。大(da)(da)寒,女(nv)二度(du)(du)(du)九(jiu)(jiu)(jiu)十(shi)(shi)(shi)(shi)(shi)(shi)(shi)一(yi)分(fen)(fen)(fen)(fen)(fen)九(jiu)(jiu)(jiu)十(shi)(shi)(shi)(shi)(shi)(shi)(shi)一(yi)秒(miao)(miao)外(wai)(wai)(wai)(wai),入(ru)齐分(fen)(fen)(fen)(fen)(fen),玄枵之(zhi)(zhi)(zhi)(zhi)次(ci)(ci),辰(chen)在(zai)(zai)子。
求入宫时刻
各(ge)置入宫宿度及分秒,以(yi)其(qi)日(ri)(ri)晨前(qian)夜半日(ri)(ri)度减之,相近一(yi)度之间者求之。余以(yi)日(ri)(ri)法乘(cheng)其(qi)分,其(qi)秒从于(yu)下,亦通乘(cheng)之,为(wei)实;以(yi)其(qi)日(ri)(ri)太阳行分为(wei)法,实如法而一(yi),所得,依发敛加时求之,即(ji)得其(qi)日(ri)(ri)太阳入宫时刻(ke)及分秒。
○步晷漏第四
中限(xian):一(yi)百八十(shi)(shi)二日,六十(shi)(shi)二分(fen),一(yi)十(shi)(shi)八秒。
冬至(zhi)初(chu)限(xian),夏至(zhi)末(mo)限(xian):六十(shi)二日,二十(shi)分。
夏至(zhi)初限,冬至(zhi)末(mo)限:一百二十日,四十二分。
冬(dong)至地(di)中(zhong)晷影常数:一丈二(er)尺八寸三(san)分(fen)。
夏至(zhi)地中晷影常数:一尺五寸六分。
周法:一千四百二十八。
内外(wai)法:一万八百(bai)九十六。
半(ban)法:二千六百一十五。
日法:四分之三:三千(qian)九(jiu)百二十二半(ban)。
日法:四分之一(yi):一(yi)千三百七(qi)半。
昏明分(fen):一(yi)百(bai)三十分(fen),七十五秒。
昏明刻(ke):二刻(ke),一百五(wu)十六分,九十秒(miao)。
刻法:三百一十三分,八十秒。
秒母:一百。
求午中入气中积
置所(suo)求日(ri)(ri)大余及半(ban)法,以(yi)所(suo)入(ru)之气大小余减之,为其(qi)日(ri)(ri)午(wu)中(zhong)入(ru)气。以(yi)加其(qi)气中(zhong)积,为其(qi)日(ri)(ri)午(wu)中(zhong)中(zhong)积。小余以(yi)日(ri)(ri)法除(chu)为约分。
求二至后午中入初(chu)末(mo)限
置午中(zhong)中(zhong)积(ji)及分(fen),如中(zhong)限以下(xia),为(wei)冬(dong)至(zhi)后(hou)。以上(shang)(shang)去中(zhong)限,为(wei)夏(xia)至(zhi)后(hou)。其二至(zhi)后(hou),如在初(chu)(chu)限以下(xia),为(wei)初(chu)(chu)限。以上(shang)(shang)覆减中(zhong)限,余为(wei)入末限也。
求午中晷影定数
视(shi)(shi)冬至(zhi)(zhi)(zhi)后(hou)初(chu)限(xian)(xian)(xian)、夏至(zhi)(zhi)(zhi)后(hou)末限(xian)(xian)(xian),百(bai)(bai)通(tong)日(ri)(ri),内分(fen),自(zi)相(xiang)乘,副(fu)置(zhi)之。以一千(qian)四百(bai)(bai)五(wu)十(shi)(shi)除(chu)之,所得加(jia)五(wu)万三百(bai)(bai)八十(shi)(shi),折半(ban)限(xian)(xian)(xian)分(fen)并之;除(chu)其(qi)副(fu)为(wei)(wei)(wei)分(fen)。分(fen)满(man)十(shi)(shi)为(wei)(wei)(wei)寸,寸满(man)十(shi)(shi)为(wei)(wei)(wei)尺(chi),用减(jian)冬至(zhi)(zhi)(zhi)地中晷(gui)影常(chang)数(shu),为(wei)(wei)(wei)所求晷(gui)影定数(shu)。视(shi)(shi)夏至(zhi)(zhi)(zhi)后(hou)初(chu)限(xian)(xian)(xian)、冬至(zhi)(zhi)(zhi)后(hou)末限(xian)(xian)(xian),百(bai)(bai)通(tong)日(ri)(ri),内分(fen),自(zi)相(xiang)乘为(wei)(wei)(wei)上位(wei)(wei)。下置(zhi)入(ru)限(xian)(xian)(xian)分(fen),以二(er)百(bai)(bai)二(er)十(shi)(shi)五(wu)乘,百(bai)(bai)约(yue)之,加(jia)一十(shi)(shi)九万八千(qian)七十(shi)(shi)五(wu)为(wei)(wei)(wei)法(fa)。夏至(zhi)(zhi)(zhi)前(qian)后(hou)半(ban)限(xian)(xian)(xian)以上者,减(jian)去半(ban)限(xian)(xian)(xian),列于上位(wei)(wei)。下位(wei)(wei)置(zhi)半(ban)限(xian)(xian)(xian)。各百(bai)(bai)通(tong)日(ri)(ri),内分(fen),先相(xiang)减(jian),后(hou)相(xiang)乘。以七千(qian)七百(bai)(bai)除(chu)之,所得以加(jia)其(qi)法(fa)反除(chu)上位(wei)(wei),为(wei)(wei)(wei)分(fen),分(fen)满(man)十(shi)(shi)为(wei)(wei)(wei)寸,寸满(man)十(shi)(shi)为(wei)(wei)(wei)尺(chi),用加(jia)夏至(zhi)(zhi)(zhi)地中晷(gui)影常(chang)数(shu),为(wei)(wei)(wei)所求晷(gui)影定数(shu)。
求四方所在晷影
各于(yu)其(qi)(qi)处(chu)测冬(dong)(dong)夏(xia)二(er)(er)至(zhi)(zhi)晷(gui)(gui)(gui)影(ying),乃(nai)相减(jian)(jian)之(zhi)余,为(wei)其(qi)(qi)处(chu)二(er)(er)至(zhi)(zhi)晷(gui)(gui)(gui)差(cha)(cha)。亦(yi)以(yi)(yi)地(di)中(zhong)二(er)(er)至(zhi)(zhi)晷(gui)(gui)(gui)数(shu)相减(jian)(jian),为(wei)地(di)中(zhong)二(er)(er)至(zhi)(zhi)晷(gui)(gui)(gui)差(cha)(cha)。其(qi)(qi)所(suo)(suo)(suo)求日(ri)在(zai)(zai)冬(dong)(dong)至(zhi)(zhi)后初限(xian)、夏(xia)至(zhi)(zhi)后末限(xian)者(zhe),如(ru)在(zai)(zai)半(ban)限(xian)以(yi)(yi)下(xia),倍之(zhi);半(ban)限(xian)以(yi)(yi)上,覆(fu)减(jian)(jian)半(ban)限(xian),余亦(yi)倍之(zhi),并入(ru)限(xian)日(ri),三(san)因(yin)折半(ban),以(yi)(yi)日(ri)为(wei)分,十为(wei)寸,以(yi)(yi)减(jian)(jian)地(di)中(zhong)二(er)(er)至(zhi)(zhi)晷(gui)(gui)(gui)差(cha)(cha)为(wei)法(fa)。置地(di)中(zhong)冬(dong)(dong)至(zhi)(zhi)晷(gui)(gui)(gui)影(ying)常数(shu),以(yi)(yi)所(suo)(suo)(suo)求日(ri)地(di)中(zhong)晷(gui)(gui)(gui)影(ying)定数(shu)减(jian)(jian)之(zhi),余以(yi)(yi)其(qi)(qi)年二(er)(er)至(zhi)(zhi)晷(gui)(gui)(gui)差(cha)(cha)乘(cheng)之(zhi)为(wei)实(shi)(shi)。实(shi)(shi)如(ru)法(fa)而(er)一,所(suo)(suo)(suo)得,以(yi)(yi)减(jian)(jian)其(qi)(qi)处(chu)冬(dong)(dong)至(zhi)(zhi)晷(gui)(gui)(gui)数(shu),即得其(qi)(qi)处(chu)其(qi)(qi)日(ri)晷(gui)(gui)(gui)影(ying)定数(shu)。所(suo)(suo)(suo)求日(ri)在(zai)(zai)夏(xia)至(zhi)(zhi)后初限(xian)、冬(dong)(dong)至(zhi)(zhi)后末限(xian)者(zhe),如(ru)在(zai)(zai)半(ban)限(xian)以(yi)(yi)下(xia),倍之(zhi);半(ban)限(xian)以(yi)(yi)上,覆(fu)减(jian)(jian)半(ban)限(xian),余亦(yi)倍之(zhi),并入(ru)限(xian)日(ri),三(san)因(yin)四除(chu),以(yi)(yi)日(ri)为(wei)分,十为(wei)寸,以(yi)(yi)加地(di)中(zhong)二(er)(er)至(zhi)(zhi)晷(gui)(gui)(gui)差(cha)(cha)为(wei)法(fa)。置所(suo)(suo)(suo)求日(ri)地(di)中(zhong)晷(gui)(gui)(gui)影(ying)定数(shu),以(yi)(yi)地(di)中(zhong)夏(xia)至(zhi)(zhi)晷(gui)(gui)(gui)影(ying)常数(shu)减(jian)(jian)之(zhi),余以(yi)(yi)其(qi)(qi)处(chu)二(er)(er)至(zhi)(zhi)晷(gui)(gui)(gui)差(cha)(cha)乘(cheng)之(zhi)为(wei)实(shi)(shi)。实(shi)(shi)如(ru)法(fa)而(er)一,所(suo)(suo)(suo)得,以(yi)(yi)加其(qi)(qi)处(chu)夏(xia)至(zhi)(zhi)晷(gui)(gui)(gui)数(shu),即得其(qi)(qi)处(chu)其(qi)(qi)日(ri)晷(gui)(gui)(gui)影(ying)定数(shu)。
二(er)十四(si)气陟(zhi)降及日出分
表略
二分前后陟降率
春(chun)分前三(san)(san)日(ri)太阳入赤(chi)道内(nei),秋分后三(san)(san)日(ri)太阳出(chu)赤(chi)道外,故其陟(zhi)降(jiang)与(yu)他日(ri)不伦(lun),今各别立数而用之。
惊(jing)蛰,十二日,陟四(si)(si)六十七,一(yi)十六此为(wei)末(mo)率(lv),于(yu)(yu)此用(yong)毕。其减差亦(yi)止于(yu)(yu)此。十三日,陟四(si)(si)四(si)(si)十一(yi),六。十四(si)(si)日,陟四(si)(si)三十六,九十。十五日,陟四(si)(si)一(yi)。
秋分,初(chu)日,降(jiang)四(si)(si)(si)三(san)十(shi)八(ba)。一日,降(jiang)四(si)(si)(si)三(san)十(shi)九。二日,降(jiang)四(si)(si)(si)五十(shi)七。三(san)日降(jiang)四(si)(si)(si)六十(shi)八(ba)。此(ci)(ci)为初(chu)率,始用之(zhi)。其加差亦始于此(ci)(ci)。
求每(mei)日出入晨昏半昼分
各以(yi)陟(zhi)降初(chu)率,陟(zhi)减(jian)(jian)降加(jia)其气初(chu)日(ri)日(ri)出(chu)分(fen),为(wei)(wei)(wei)一(yi)日(ri)下日(ri)出(chu)分(fen)。以(yi)增损(sun)差,仍加(jia)减(jian)(jian)加(jia)减(jian)(jian)差。增损(sun)陟(zhi)降率,驯(xun)积而加(jia)减(jian)(jian)之(zhi),即为(wei)(wei)(wei)每日(ri)日(ri)出(chu)分(fen)。覆减(jian)(jian)日(ri)法,余为(wei)(wei)(wei)日(ri)入(ru)分(fen)。以(yi)日(ri)出(chu)分(fen)日(ri)入(ru)分(fen)而半之(zhi),为(wei)(wei)(wei)半昼分(fen)。以(yi)昏(hun)明分(fen)减(jian)(jian)日(ri)出(chu)分(fen)为(wei)(wei)(wei)晨(chen)分(fen),加(jia)日(ri)入(ru)分(fen)为(wei)(wei)(wei)昏(hun)分(fen)。
求日出入辰刻
置日出(chu)入分,以六因(yin)之,满(man)辰(chen)法(fa)而一,为辰(chen)数(shu),不尽,刻(ke)法(fa)除之为刻(ke)数(shu),不满(man)为分,命子正(zheng)算外,即(ji)得所求(qiu)。
求昼夜刻
置日出分(fen),十二(er)乘(cheng)之,刻法而(er)一,为(wei)刻,不满为(wei)分(fen),即(ji)为(wei)夜刻。覆减百刻,余为(wei)昼(zhou)刻。
求更点率
置晨(chen)分,四因,退(tui)位为更率。二因更率,退(tui)位为点率。
求更点所在辰刻
置(zhi)更点率,以所(suo)求更点数因(yin)之,又(you)六因(yin),内加(jia)昏明分(fen),满(man)辰法而一,为(wei)辰数。不尽,满(man)刻法除之为(wei)刻数,不满(man)为(wei)分(fen),命(ming)其辰刻算外(wai),即(ji)得所(suo)求。
求四方所在漏刻
各于(yu)所(suo)在下水漏(lou),以(yi)定其(qi)处冬至(zhi)或(huo)夏至(zhi)夜刻(ke)(ke)(ke),乃与五十(shi)(shi)刻(ke)(ke)(ke)相(xiang)减,余为(wei)至(zhi)差刻(ke)(ke)(ke)。置(zhi)所(suo)求(qiu)日黄道(dao)去赤道(dao)内外度(du)及分,以(yi)至(zhi)差刻(ke)(ke)(ke)乘之,进一位(wei),如二百(bai)三(san)十(shi)(shi)九(jiu)而(er)一,为(wei)刻(ke)(ke)(ke),不尽以(yi)刻(ke)(ke)(ke)法(fa)乘之,退除为(wei)分,内减外加(jia)五十(shi)(shi)刻(ke)(ke)(ke),即(ji)所(suo)求(qiu)日夜刻(ke)(ke)(ke),以(yi)减百(bai)刻(ke)(ke)(ke),余为(wei)昼(zhou)刻(ke)(ke)(ke)。其(qi)日出入辰(chen)刻(ke)(ke)(ke)及更点差率算等,并(bing)依术求(qiu)之。
求黄道内外度
置日(ri)出分(fen),如日(ri)法四分(fen)之(zhi)(zhi)一(yi)以上,去(qu)(qu)之(zhi)(zhi),余为(wei)外分(fen)。如日(ri)法四分(fen)之(zhi)(zhi)一(yi)以下,覆减(jian)之(zhi)(zhi),余为(wei)内(nei)分(fen)。置内(nei)外分(fen),千(qian)乘(cheng)之(zhi)(zhi),如内(nei)外法而一(yi),为(wei)度(du),不(bu)满退除为(wei)分(fen),即为(wei)黄(huang)道(dao)(dao)去(qu)(qu)赤(chi)道(dao)(dao)内(nei)外度(du)。内(nei)减(jian)外加象限,即得内(nei)道(dao)(dao)去(qu)(qu)极(ji)度(du)。
求距中度及更差度
置半法,以(yi)晨分(fen)减之,余为距中分(fen),百乘(cheng)之,如(ru)周法而一(yi),为距中度(du)。用(yong)减一(yi)百八十(shi)三度(du)一(yi)十(shi)二分(fen)八十(shi)四秒,余四因退位,为每更(geng)差度(du)。
求昏明五更中星
置距中度,以其(qi)日午中赤(chi)道(dao)日度加而命(ming)之,即昏中星(xing)所格宿(su)次,因(yin)为(wei)初(chu)更中星(xing)。以更差度累加之,命(ming)赤(chi)道(dao)宿(su)次去之,即得逐更及明(ming)中星(xing)。
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