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置定朔望加时入交泛日,以日法通之,内余进二位,如三万九千一百二十一而一,为度,不满,退除为分秒,即得定朔望加时月行入交积度;以定朔望加时入转迟疾度迟减疾加之,即为月行入定交积度;如交中度以下,为入阳历积度,以上,去之,为入阴历积度。

(每日夜半准此求之。

求月去黄道度

视月入阴阳历积度及分,交象以下,为少象;以上,覆减交中,余为老象。

置所入老少象度于上位,列交象度于下,相减,相乘,倍之,退位为分,分满百为度,用减所入老少象度及分;余,又与交中度相减、相乘,八因之,以一百一十除之,为分,分满百为度,即得月去黄道度及分。

求朔望加时入交常日及定日

置朔望入交泛日,以入气朓朒定数朓减朒加,为入交常日。

又置入转朓朒定数,进一位,以一百二十七而一,所得,朓减朒加交常日,为入交定日及余秒。

求入交阴阳历交前后分

视入交定日,如交中以下,为阳历;以上,去之,为阴历。

如一日上下,以日法通日内分,内余为交后分;十三日上下,覆减交中日,余为交前分。

求日月食甚定余

置朔望入气入转朓朒定数,同名相从,异名相消,以一千三百三十七乘之,以定朔望加时入转算外转定分除之,所得,以朓减朒加中朔望小余,为泛余。

日食,视泛余,如半法以下,为中前,半法以上,去之,为中后。

置中前后分,与半法相减、相乘,倍之,万约为分,曰时差。

中前以时差减泛余,为定余;覆减半法,余为午前分;中后以时差加泛余,为定余;减去半法,余为午后分。

月食,视泛余,在日入后夜半前,如日法四分之三以下,减去半法,为酉前分;四分之三以上,覆减日法,余为酉后分。

又视泛余,在夜半后日出前者,如日法四分之一以下,为卯前分;四分之一以上,覆减半法,余为卯后分。

其卯酉前后分,自相乘,四因,退位,万约为分,以加泛余,为定余。

各置定余,以发敛加时法求之,即得日月食甚辰刻及分秒。

求日月食甚日行积度

置定朔望食甚大小余,与中朔望大小余相减之,余以加减中朔望入气日余,(以中朔望少加多减。

)即为食甚入气;以加其气中积,为食甚中积。

又置食甚入气余,以所入气日损益率(盈缩之损益。

)乘之,如日法而一,以损益其日盈缩积,盈加缩减食甚中积,即为食甚日行积度及分。

先以食甚中积经分为约分,然后加减之,余类此者,依而求之。

求气差

置日食食甚日行积度及分,满中限去之,余在象限以下,为初限;以上,覆减中限,为末限;皆自相乘,进二位,以四百七十八而一,所得,用减一千七百四十四,余为气差恒数;以午前后分乘之,半昼分除之,所得,以减恒数,为定数。

(如不及减者,覆减为定数,应加者减之,应减者加之。

)春分后,阳历减阴历加;秋分后,阳历加阴历减。

(春分前秋分后,各二日二千一百分为定气,于此宜加减之。

求刻差

置日食食甚日行积度及分,满中限去之,余与中限相减、相乘,进二位,如四百七十八而一,所得,为刻差恒数;以午前后分乘之,日法四分之一除,所得,为定数。

(若在恒数以上者,倍恒数,以所得之数减之,为定数,依其加减。

)冬至后,午前阳加阴减,午后阳减阴加;夏至后,午前阳减阴加,午后阳加阴减。

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