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《第一原动天》 · PART I.

第一部·星位数字的读法 第五至九则 赤经、斜升与离宫的距离

第五至九则:查赤经;赤经加减上升差得斜升、斜降;由赤经或斜升反求黄道度;再由上升度或半弧求星离各宫的距离。

CANON V.

Right Ascension.

This you will have from the proper table; and if the given place be in the ecliptic, so as to have no latitude, look for the right ascension under the column 0° 0', and in the common angle you have it, by taking the proportional part for the minute of longitude, if there are any, as in Canon I. In the nativity of Charles V. the Sun is in 14° 30' of ♓, the right ascension of 14 of ♓, is 345 16; for the 30', 28 are due, to be added, and the Sun's right ascension becomes 345° 44'.

If the given place be not in the ecliptic, but has latitude from it, and is in the integral degrees, both according to extent and breadth in the common angle, you will have the right ascension: but if there are likewise minutes, let the proportional part be taken, as in Canon I.

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CANON V.

第五则。

Right Ascension.

赤经。

This you will have from the proper table; and if the given place be in the ecliptic, so as to have no latitude, look for the right ascension under the column 0° 0', and in the common angle you have it, by taking the proportional part for the minute of longitude, if there are any, as in Canon I. In the nativity of Charles V. the Sun is in 14° 30' of ♓, the right ascension of 14 of ♓, is 345 16; for the 30', 28 are due, to be added, and the Sun's right ascension becomes 345° 44'.

这可从专门的表中得到;若给定的位置在黄道上,没有纬度,就在零度零分的栏下找赤经,在共同的格中就得到它,若有黄经的分数,就取比例部分,如第一则。在查理五世的本命中,太阳在双鱼十四度三十分,双鱼十四度的赤经是三百四十五度十六分;为那三十分,应得二十八分,要加上,太阳的赤经成为三百四十五度四十四分。

If the given place be not in the ecliptic, but has latitude from it, and is in the integral degrees, both according to extent and breadth in the common angle, you will have the right ascension: but if there are likewise minutes, let the proportional part be taken, as in Canon I.

若给定的位置不在黄道上,而离黄道有纬度,且黄经与纬度都在整度上,你在共同的格中就得到赤经:但若也带分,就照第一则取比例部分。

大意与图解点开

🔎 大意:赤经查表:无纬度的在零度栏下查,有纬度的在相应纬度栏下查,带分的取比例部分。查理五世的太阳赤经三百四十五度四十四分。

📖 术语

术语英文原词意思
赤经right ascension沿天赤道量的度数
赤经表table of right ascension由黄经纬度查赤经
零度零分的栏column 0° 0′即黄道本身
黄经 / 纬度extent / breadth原文以长宽称之
比例部分proportional part按分数插值所得

🧭 图解与讲解

第五则求赤经(right ascension),即沿天赤道从春分点量起的度数。它与黄经不同,因为黄道斜交赤道;二分点附近赤经比黄经变化慢,二至点附近变化快。原书的赤经表纵列黄经、横列纬度,排法与第一则的赤纬表相同。

原书例:查理五世本命,太阳在双鱼 14°30′,求赤经
步骤算什么用哪个数结果
一纬度 0°0′ 栏下查双鱼 14°赤经表345°16′
二相邻一度的赤经差约 56′,30′ 得多少56′ × 30 ÷ 6028′
三赤经随黄经增大,故加上345°16′ + 28′345°44′

〔图〕双鱼十四度半在春分点之前十五度半,赤经比黄经略大

查理五世的太阳在双鱼十四度三十分(表一):双鱼十四度的赤经三百四十五度十六分;十五度约三百四十六度十二分,相差约五十六分,半度得二十八分,加上得三百四十五度四十四分。这个数后面起盘、算推运都要用(第十则用它定太阳在中天时的时刻)。

有纬度的点(如月亮、行星)要在相应纬度的栏下查;黄经、纬度都带分时,照第一则取两次比例部分。普拉西德斯坚持行星的赤经、斜升都要连纬度一起算,这是他与许多前人的分别,第十三、二十三则还会讲到何时可略去纬度。

CANON VI.

This Canon, consisting of tables, will be given in a future volume.

CANON VII.

Oblique Ascension and Descension,

Will be had by substracting the ascensional difference from the right ascension of the star, if its declination be northern; but if south, by adding the ascensional difference to the right ascension, and the remainder is the oblique ascension. Lastly, if it has no declination, that right ascension becomes oblique ascension; on the contrary, the descension will be found, by adding; if the declination be northern, by substracting; if south, from the right ascension.

Example: 1° 23' of ♉, the declination is 12°; its ascensional difference at the Pole's elevation 42°, we have mentioned in Canon II. which is 11° 2'; the right ascension is 29° 13'; but when the declination is northern, substract the ascensional difference 11° 2' from the right ascension, and there remains the oblique ascension 18° 11'.

Now 1° 23' of ♏, has the same declination and ascensional difference, which is to be added to the right ascension 209° 13', because the declination is southern, and the oblique ascension 220° 15'; besides, there are extant many tables of oblique ascensions by which they may be gained.

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CANON VI.

第六则。

This Canon, consisting of tables, will be given in a future volume.

这一则由表组成,将在以后的一卷中给出。

CANON VII.

第七则。

Oblique Ascension and Descension,

斜升与斜降,

Will be had by substracting the ascensional difference from the right ascension of the star, if its declination be northern; but if south, by adding the ascensional difference to the right ascension, and the remainder is the oblique ascension. Lastly, if it has no declination, that right ascension becomes oblique ascension; on the contrary, the descension will be found, by adding; if the declination be northern, by substracting; if south, from the right ascension.

求法如下:星的赤纬若为北,就从它的赤经中减去上升差;若为南,就把上升差加到赤经上,所得之数就是斜升。最后,若它没有赤纬,那赤经就成为斜升;反之,斜降的求法是:赤纬为北时,加到赤经上;为南时,从赤经中减去。

Example: 1° 23' of ♉, the declination is 12°; its ascensional difference at the Pole's elevation 42°, we have mentioned in Canon II. which is 11° 2'; the right ascension is 29° 13'; but when the declination is northern, substract the ascensional difference 11° 2' from the right ascension, and there remains the oblique ascension 18° 11'.

例:金牛一度二十三分,赤纬十二度;它在极高四十二度下的上升差,我们在第二则已提过,是十一度二分;赤经是二十九度十三分;赤纬既是北的,就从赤经中减去上升差十一度二分,剩下斜升十八度十一分。

Now 1° 23' of ♏, has the same declination and ascensional difference, which is to be added to the right ascension 209° 13', because the declination is southern, and the oblique ascension 220° 15'; besides, there are extant many tables of oblique ascensions by which they may be gained.

而天蝎一度二十三分有相同的赤纬与上升差,要加到赤经二百零九度十三分上,因为赤纬是南的,斜升为二百二十度十五分;此外,现有许多斜升表,也可借以求得。

大意与图解点开

🔎 大意:斜升:北赤纬以赤经减上升差,南赤纬加上;斜降相反。金牛一度二十三分斜升十八度十一分,天蝎一度二十三分为二百二十度十五分。

📖 术语

术语英文原词意思
斜升oblique ascension某纬度下与星同升的赤道度
斜降oblique descension某纬度下与星同落的赤道度
斜升表tables of oblique ascensions按极高列各度斜升
上升差ascensional difference赤经与斜升之差
以后的一卷a future volume原书预告的表卷

🧭 图解与讲解

第六则原是一组表,原书说留待以后一卷,这里只有一句话。第七则求斜升(oblique ascension):在本地纬度上,一颗星升出东方地平时,与它同时升起的天赤道度数。赤纬为北的星在北半球升得早,所以斜升比赤经小一个上升差;赤纬为南的升得晚,斜升比赤经大一个上升差。斜降(oblique descension)是星落入西方地平时同落的赤道度,加减正好相反。

原书例:两点赤纬相等、南北相反;斜降一行为本站按第七则算出
金牛 1°23′(北赤纬 12°)天蝎 1°23′(南赤纬 12°)
赤经29°13′209°13′
极高 42° 的上升差(第二则)11°2′11°2′
斜升的算法北赤纬:赤经 − 上升差南赤纬:赤经 + 上升差
斜升18°11′220°15′
斜降(照同理反过来)40°15′198°11′

〔图〕金牛一度与天蝎一度相对,赤纬相等而南北相反,上升差相同而加减相反

原书举一对相对的点(图二):金牛一度二十三分赤纬北十二度,天蝎一度二十三分赤纬南十二度,在极高四十二度下上升差都是第二则算过的十一度二分。前者赤经二十九度十三分,减去得斜升十八度十一分;后者赤经二百零九度十三分,加上得二百二十度十五分(表一)。

斜升与斜降是推运计算的主角:第十八则推运上升点附近的太阳,就用斜升相减;第九则量星离宫头的距离,也可用斜升、斜降。普拉西德斯说当时已有许多现成的斜升表,按极高排列,查表即得,不必每次计算。

CANON VIII.

To reduce the Right Ascension, or Oblique, to the Degree of Longitude in the Ecliptic, or to any other Place of Latitude or Longitude.

Look for the given right ascension of the ecliptic in the body of the table of right ascensions under the column of latitude 0° 0', and you will have the places in the ecliptic, corresponding to it, by taking the proportional part for the minutes, if there be any.

But if, when the right ascension of the latitudinal planet is given, you are desirous to know to what longitude in the ecliptic it corresponds, look for that right ascension under the column of the given latitude, and in the column of longitude, you will have the degree of the ecliptic corresponding to it: as for example, the right ascension of 157° 48' in the ecliptic, answers to 6 of ♍; but if the right ascension 157° 48' be, for example, for the Moon, in latitude 5° southern, it answers to 8 of ♍; but with this caution, because the Moon then mediates the heaven with 6° of ♍, but has the rays in the Zodiac to the other planets from 8° of ♍.

In like manner you must reduce the oblique ascension to the ecliptic from the table of the oblique ascensions of the Pole's elevation; as the oblique ascension of the ecliptic 168 9' to the Pole's elevation is 45° reduced to 21 of ♍ in the ecliptic; but if the oblique ascension be of the Moon in south latitude 5°, I say it is reduced to 19° of ♍ with latitude, as is there posited, but with the same distinction; for then the Moon co-ascends in the same circle of position with 21° of ♍, but has the rays to the other planets in 19° of ♍.

This revocation is of service, in order to know what longitude and declination the significator encompasses by the direction, and consequently with what planets it contracts the aspect when in the Zodiac, which is, by adding the arc of direction to its right ascension, if in the right circle it be found in the nativity; or to the oblique ascension, if elsewhere.

黑像陶瓶画:月亮女神与天顶上的一点并立,光线射向别处
与处女六度同中天
翻译点开

CANON VIII.

第八则。

To reduce the Right Ascension, or Oblique, to the Degree of Longitude in the Ecliptic, or to any other Place of Latitude or Longitude.

把赤经或斜升还原为黄道上的黄经度数,或还原为任何其他有纬度或黄经的位置。

Look for the given right ascension of the ecliptic in the body of the table of right ascensions under the column of latitude 0° 0', and you will have the places in the ecliptic, corresponding to it, by taking the proportional part for the minutes, if there be any.

在赤经表的表身中、纬度零度零分的栏下,找给定的黄道赤经,就得到与之对应的黄道位置,若有分数就取比例部分。

But if, when the right ascension of the latitudinal planet is given, you are desirous to know to what longitude in the ecliptic it corresponds, look for that right ascension under the column of the given latitude, and in the column of longitude, you will have the degree of the ecliptic corresponding to it: as for example, the right ascension of 157° 48' in the ecliptic, answers to 6 of ♍; but if the right ascension 157° 48' be, for example, for the Moon, in latitude 5° southern, it answers to 8 of ♍; but with this caution, because the Moon then mediates the heaven with 6° of ♍, but has the rays in the Zodiac to the other planets from 8° of ♍.

但若给定的是有纬度的行星的赤经,而你想知道它对应黄道上的哪个黄经,就在给定纬度的栏下找那个赤经,在黄经栏中就得到与之对应的黄道度数:例如,黄道上的赤经一百五十七度四十八分,对应处女六度;但若赤经一百五十七度四十八分属于,比如说,月亮,在南纬五度,它就对应处女八度;但须注意这一区别:因为那时月亮与处女六度同中天,而在黄道上对其他行星发出光线,却是从处女八度。

In like manner you must reduce the oblique ascension to the ecliptic from the table of the oblique ascensions of the Pole's elevation; as the oblique ascension of the ecliptic 168 9' to the Pole's elevation is 45° reduced to 21 of ♍ in the ecliptic; but if the oblique ascension be of the Moon in south latitude 5°, I say it is reduced to 19° of ♍ with latitude, as is there posited, but with the same distinction; for then the Moon co-ascends in the same circle of position with 21° of ♍, but has the rays to the other planets in 19° of ♍.

同样,你要从本极高的斜升表中,把斜升还原到黄道上;如黄道的斜升一百六十八度九分,在极高四十五度下,还原为黄道上的处女二十一度;但若这是月亮在南纬五度的斜升,我说它还原为带纬度的处女十九度,如那里所列,但须作同样的区别;因为那时月亮在同一个位置圈中与处女二十一度同升,而对其他行星的光线却在处女十九度。

This revocation is of service, in order to know what longitude and declination the significator encompasses by the direction, and consequently with what planets it contracts the aspect when in the Zodiac, which is, by adding the arc of direction to its right ascension, if in the right circle it be found in the nativity; or to the oblique ascension, if elsewhere.

这种还原的用处,是要知道征象星经推运走到了什么黄经与赤纬,从而在黄道上与哪些行星结成相位;办法是:若它在本命中位于正圈上,就把推运弧加到它的赤经上;若在别处,就加到斜升上。

大意与图解点开

🔎 大意:由赤经或斜升反查黄道度。有纬度的月亮与处女六度同中天,光线却从处女八度发出:同中天、同升之点与它真正的黄经不同。

📖 术语

术语英文原词意思
还原reduce, revocation由赤经斜升求黄道度
同中天mediates the heaven与某度同时到中天
同升co-ascends与某度同时升起
推运弧arc of direction推运所走的赤道度数
正圈right circle指子午圈

🧭 图解与讲解

第八则是第五、七则的反算:已知赤经或斜升,求它对应黄道上哪一度。黄道上的点(无纬度)在零度栏下反查即可,例如赤经一百五十七度四十八分对应处女六度;斜升一百六十八度九分在极高四十五度下对应处女二十一度(表一)。

原书两例:同一个赤经或斜升,有纬度的点对应的黄经不同
给定黄道上(纬度 0°)月亮在南纬 5°
赤经 157°48′处女 6°处女 8°
斜升 168°9′(极高 45°)处女 21°处女 19°

〔图〕月亮的位置要分两层看:随天球运行看同中天、同升之点,发光线看自己的黄经

有纬度的点要分清两件事(图二)。同一个赤经一百五十七度四十八分,若属于南纬五度的月亮,在南纬五度栏下反查得处女八度:这是月亮自己的黄经,她对其他行星的光线从这里发出;可是她到中天时,与她同时到中天的黄道度是处女六度。斜升同理:南纬五度的月亮与处女二十一度同升,光线却在处女十九度。

这个区别是普拉西德斯推运学的要点。推运时,征象星随天球转动,被带到某个赤经或斜升上;要知道它此时在黄道上与哪颗行星成相位,就得把推运后的赤经(在子午圈上的星)或斜升(在别处的星)还原到黄道上,并照它的纬度来还原。推运弧(arc of direction)就是加上去的那段赤道度数,第十七则起详算。

CANON IX.

The distance of any cardinal sign or house from their cusp, will be easily obtained after the ascension of that house or cardinal sign, and likewise the ascension of a star is given; for substracting the lesser of the preceding place from the greater, which, if of the following, the remainder will be the distance of a star from that house or cardinal sign; but if the house or angle be in the descending part of heaven, taking the descensions the house, and in the same place of the star, or the ascensions of the opposite places, and substracting, in like manner, the lesser from the greater, the remainder will be the distance required.

The preceding place is that which is in the lesser degrees; the succeeding in the greater: as the beginning of ♈ precedes, the beginning of ♊ follows; and thus in all. The distances of the stars are taken from the cusps of the houses without the oblique ascensions; but the right ascension is to be known, together with the semi-diurnal and nocturnal arcs, or the temporary hours; for after taking their distance from the primary culminations, the secondary distances are made in the centers of the houses; but the ninth and tenth houses are distant from the culmination, by doubling the horary times, or the third part of the semi-diurnal arc; the eighth and twelfth, by double gemination, &c.

Wherefore the primary and secondary distance of a star from the culmination being given, always substract the lesser from the greater, and you will have the star's distance from the given house by primary distance; I mean that which the planets have in a nativity; but the secondary, that which they acquire by direction. There are several examples in the nativities which are shewn further on.

翻译点开

CANON IX.

第九则。

The distance of any cardinal sign or house from their cusp, will be easily obtained after the ascension of that house or cardinal sign, and likewise the ascension of a star is given; for substracting the lesser of the preceding place from the greater, which, if of the following, the remainder will be the distance of a star from that house or cardinal sign; but if the house or angle be in the descending part of heaven, taking the descensions the house, and in the same place of the star, or the ascensions of the opposite places, and substracting, in like manner, the lesser from the greater, the remainder will be the distance required.

离任一角或任一宫宫头的距离,在得知那宫或那角的上升度、也得知星的上升度之后,很容易求得;以前导位置的较小数,从后随位置的较大数中减去,余数就是星离那宫或那角的距离;但若那宫或角在天空下降的一边,就取那宫的斜降与星在同一处的斜降,或取对宫之点的斜升,同样以大减小,余数就是所求的距离。

The preceding place is that which is in the lesser degrees; the succeeding in the greater: as the beginning of ♈ precedes, the beginning of ♊ follows; and thus in all. The distances of the stars are taken from the cusps of the houses without the oblique ascensions; but the right ascension is to be known, together with the semi-diurnal and nocturnal arcs, or the temporary hours; for after taking their distance from the primary culminations, the secondary distances are made in the centers of the houses; but the ninth and tenth houses are distant from the culmination, by doubling the horary times, or the third part of the semi-diurnal arc; the eighth and twelfth, by double gemination, &c.

前导的位置是度数较小的,后随的是度数较大的:如白羊之始在前,双子之始在后;其余皆然。星离宫头的距离,不用斜升也可求得;但须知道赤经,连同半昼弧与半夜弧,或季节时;因为先取得它们离上下中天的第一距离之后,第二距离便在诸宫的中心构成;第九宫与第十一宫离中天的距离,是时量的两倍,即半昼弧的三分之一;第八宫与第十二宫,是两倍再加倍,等等。

Wherefore the primary and secondary distance of a star from the culmination being given, always substract the lesser from the greater, and you will have the star's distance from the given house by primary distance; I mean that which the planets have in a nativity; but the secondary, that which they acquire by direction. There are several examples in the nativities which are shewn further on.

因此,已知星离中天的第一距离与第二距离,总是以小减大,就得到星离给定之宫的第一距离;第一距离,我指的是行星在本命中所有的;第二距离,是它们经推运所获得的。后面所列的本命中有好几个例子。

大意与图解点开

🔎 大意:星离宫头的距离,可用上升度或下降度相减;也可用赤经离中天的距离,比照半弧的三分之一、三分之二求得。

📖 术语

术语英文原词意思
宫头cusp宫的起点
前导 / 后随preceding / following度数较小 / 较大
第一距离primary distance本命中的距离
第二距离secondary distance推运后应有的距离
赤经距离right distance以赤经量离子午线

🧭 图解与讲解

第九则讲怎样量星离某一宫头的距离。第一种办法用上升度:宫在天空东升的一半,取宫头的斜升与星的斜升,以大减小;宫在西降的一半,改取斜降,或取对宫之点的斜升。普拉西德斯顺便定义「前导」与「后随」:度数小的在前,度数大的在后,如白羊之始在双子之始前面。

地平以上的宫头离中天的距离;地平以下照半夜弧同理,从天底量起
宫头离中天(以昼时量计)合半昼弧的
第十宫(中天)00
第十一宫、第九宫2 个时量三分之一
第十二宫、第八宫4 个时量三分之二
第一宫(上升)、第七宫(下降)6 个时量整个半昼弧

〔图〕用赤经与半弧量星离宫头的距离

第二种办法不用斜升,只用赤经与半弧(表一)。普拉西德斯的宫制按半弧三等分:第十一宫、第九宫的宫头离中天是半昼弧的三分之一,即两个时量;第十二宫、第八宫是三分之二,即四个时量;上升、下降点离中天是整个半昼弧。所以只要知道星离子午线的赤经距离和它的半弧,就能算出它离任一宫头多远。原书此处印作「第九宫与第十宫」,第十宫就是中天本身,当是「第十一宫」之误(扫描本上已有后人手改),本站按第十一宫译。

末段引入两个贯穿全书的名词(图二):第一距离(primary distance)是行星在本命中实际的距离,第二距离(secondary distance)是它经推运后应有的距离。两者之差就是推运弧;这正是第十九则太阳远离四角时的算法。普拉西德斯说后面的本命例子里有许多算例。

原文为公有领域古籍;翻译、印象画与图文解读由 AI 辅助生成,鲲侯审校。