卷三·第十章 论寿数
寿数先定:从五个释放之位选出释放星,看它推进到哪颗杀星,按赤道时度一度一年换算。这是二世纪的古代学说。
The consideration of the length of life takes the leading place among inquiries about events following birth, for, as the ancient says, it is ridiculous to attach particular predictions to one who, by the constitution of the years of his life, will never attain at all to the time of the predicted events. This doctrine is no simple matter, nor unrelated to others, but in complex fashion derived from the domination of the places of greatest authority. The method most pleasing to us and, besides, in harmony with nature is the following. For it depends entirely upon the determination of the prorogative places and the stars that rule the prorogation, and upon the determination of the destructive places or stars. Each of these is determined in the following fashion:
In the first place we must consider those places prorogative in which by all means the planet must be that is to receive the lordship of the prorogation; namely, the twelfth part of the zodiac surrounding the horoscope, from 5° above the actual horizon up to the 25° that remains, which is rising in succession to the horizon; the part sextile dexter to these thirty degrees, called the House of the Good Daemon; the part in quartile, the mid‑heaven; the part in trine, called the House of the God; and the part opposite, the Occident.
Among these there are to be preferred, with reference to power of domination, first those which are in the mid‑heaven, then those in the orient, then those in the sign succedent to the mid‑heaven, then those in the occident, then those in the sign rising before mid‑heaven; for the whole region below the earth must, as is reasonable, be disregarded when a domination of such importance is concerned, except only those parts which in the ascendant itself are coming into the light.
Of the part above the earth it is not fitting to consider either the sign that is disjunct from the ascendant, nor that which rose before it, called the House of the Evil Daemon, because it injures the emanation from the stars in it to the earth and is also declining, and the thick, misty exhalation from the moisture of the earth creates such a turbidity and, as it were, obscurity, that the stars do not appear in either their true colours or magnitudes.

翻译点开
The consideration of the length of life takes the leading place among inquiries about events following birth, for, as the ancient says, it is ridiculous to attach particular predictions to one who, by the constitution of the years of his life, will never attain at all to the time of the predicted events. This doctrine is no simple matter, nor unrelated to others, but in complex fashion derived from the domination of the places of greatest authority. The method most pleasing to us and, besides, in harmony with nature is the following. For it depends entirely upon the determination of the prorogative places and the stars that rule the prorogation, and upon the determination of the destructive places or stars. Each of these is determined in the following fashion:
在探讨降生之后诸事的各种问题中,寿数的考察居于首位;因为正如那位古人所说,一个人按他寿年的构成根本活不到所预言之事发生的时候,却给他附上种种具体的预言,那是可笑的。这一学说并不简单,也不与其他学说无关,而是以复杂的方式,从最有权力之诸位的主宰中推导出来的。我们最喜欢、而且合于自然的方法如下。因为它完全取决于释放之位与主管释放之星的确定,以及杀位或杀星的确定。其中每一项按下面的方式确定:
In the first place we must consider those places prorogative in which by all means the planet must be that is to receive the lordship of the prorogation; namely, the twelfth part of the zodiac surrounding the horoscope, from 5° above the actual horizon up to the 25° that remains, which is rising in succession to the horizon; the part sextile dexter to these thirty degrees, called the House of the Good Daemon; the part in quartile, the mid‑heaven; the part in trine, called the House of the God; and the part opposite, the Occident.
首先,我们必须考察那些释放之位,将要领受释放之主权的那颗行星,无论如何都必须在这些位置上;即:环绕上升点的黄道十二分之一,从实际地平之上五度起,直到其余那二十五度,也就是随后从地平升起的部分;与这三十度成右方六分的部分,称为善灵之位;成四分的部分,即中天;成三分的部分,称为神之位;以及与之对冲的部分,即下降点。
Among these there are to be preferred, with reference to power of domination, first those which are in the mid‑heaven, then those in the orient, then those in the sign succedent to the mid‑heaven, then those in the occident, then those in the sign rising before mid‑heaven; for the whole region below the earth must, as is reasonable, be disregarded when a domination of such importance is concerned, except only those parts which in the ascendant itself are coming into the light.
在这些位置之中,论主宰之力,应当优先取的:首先是在中天的,其次是在东方的,再次是在紧随中天的那一座的,再次是在西方的,再次是在中天之前升起的那一座的;因为涉及如此重大的主宰时,整个地平以下的区域理应一概不计,唯有上升本身之中正升入光明的那些部分除外。
Of the part above the earth it is not fitting to consider either the sign that is disjunct from the ascendant, nor that which rose before it, called the House of the Evil Daemon, because it injures the emanation from the stars in it to the earth and is also declining, and the thick, misty exhalation from the moisture of the earth creates such a turbidity and, as it were, obscurity, that the stars do not appear in either their true colours or magnitudes.
在地平以上的部分里,与上升不相接的那一座不宜考虑,在上升之前升起、称为恶灵之位的那一座也不宜考虑;因为它损害了其中诸星向大地的流溢,而且它也在下坠之中,再加上大地水汽升起的浓重雾气造成一片浑浊,仿佛幽暗,使诸星既显不出真实的颜色,也显不出真实的大小。
大意与图解点开
🔎 大意:寿数居降生后诸事之首。释放星须在五个释放之位:上升、善灵之位、中天、神之位、下降,以中天最强。
📖 术语
| 术语 | 英译原词 | 意思 |
|---|---|---|
| 寿数 | length of life | 一生的年数 |
| 释放之位 | prorogative places | 释放星必须所在的五处 |
| 善灵之位 | House of the Good Daemon | 第十一位 |
| 神之位 | House of the God | 第九位 |
| 恶灵之位 | House of the Evil Daemon | 第十二位,不取 |
🧭 图解与讲解
卷三第三章把本命之学按时间分类,降生之后的诸事里,第一项就是寿数(length of life)。上一章(卷三第九章)说,寿数之问针对能活过太阳一周、即一年以上的人。托勒密引「那位古人」的话(Robbins 注:大概指佩托西里斯)说:一个人若按寿数根本活不到某事发生之时,却给他预言那件事,岂不可笑。所以寿数要最先定。下面讲的是二世纪的古代学说,本页只讲解书中的方法,不据此推断任何人的寿命。
〔图〕五个释放之位:中天最强,其次上升、善灵之位、下降、神之位;地平以下与第八、第十二位不取
| 位 | 本图星座 | 古名(Robbins 注) | 本章取舍 |
|---|---|---|---|
| 第一位 | 白羊 | 上升 | 取,居第二:地平上五度、地平下二十五度 |
| 第二至六位 | 金牛至处女 | 冥府之门、女神(月)、地底中天、好运、厄运 | 不取:在地平以下 |
| 第七位 | 天秤 | 下降 | 取,居第四:与上升对冲 |
| 第八位 | 天蝎 | 死亡之始 | 不取:与上升不相接 |
| 第九位 | 射手 | 神(日) | 取,居第五:与上升三分 |
| 第十位 | 摩羯 | 中天 | 取,居第一:与上升四分 |
| 第十一位 | 水瓶 | 善灵 | 取,居第三:与上升六分 |
| 第十二位 | 双鱼 | 恶灵 | 不取:损害星光,又在下坠;近地平处地气浑浊 |
整个方法由三样东西组成:释放之位、释放星(prorogator,后世阿拉伯占星称「海勒格」,见 Robbins 注)、杀位或杀星(anaeretic)。Robbins 注引布谢-勒克莱尔(Bouché-Leclercq)的概括:黄道好比一条跑道,生命从某个出发点被「释放」出去,走到某处障碍便被截住,或险些被截住;走过的度数换算成赤道上的度数,就是年数。本单元先讲释放星必须落在哪里。
图一以上升点在白羊五度为例。第一位是环绕上升点的三十度:地平之上五度、之下二十五度(正在升起的部分),恰好是白羊整座。由此按相位逆着黄道顺序往前数:右方六分是第十一位,即善灵之位;四分是第十位,即中天;三分是第九位,即神之位;对冲是第七位,即下降点。「右方」(dexter)指在黄道次序上居前的一侧。上升点若不在某座五度,各位就会跨两座,须按度数量。动画按托勒密排的优先次序轮流点亮:中天、上升、善灵之位、下降、神之位。
其余七位为什么不取?地平以下的第二到第六位整片不计,因为如此重大的主宰,必须在光明之中;唯一的例外是上升点下方那二十五度,它们正升入光明。地平以上也去掉两位(表二):第八位与上升「不相接」(卷一第十六章),Robbins 注说这里的「座」指本命的位,不是黄道星座;第十二位恶灵之位,托勒密说它损害星光向地面的流溢,又在下坠(属果宫),加上近地平处地气浓雾,星辰显不出真实的颜色与大小。
表二的「古名」取自 Robbins 注,是当时星占家对十二位的通称,如第二位「冥府之门」、第八位「死亡之始」。托勒密本人很少用这套「位」的体系,本章只点到其中五个。这五个释放之位,正是上升点本身与它的六分、四分、三分、对冲,和卷一第十三章讲的相位一一相合:既在地平以上、又与上升点成相位的位置,才有资格主管寿数。
📖 术语
| 术语 | 英译原词 | 意思 |
|---|---|---|
| 寿数 | length of life | 一生的年数 |
| 释放之位 | prorogative places | 释放星必须所在的五处 |
| 善灵之位 | House of the Good Daemon | 第十一位 |
| 神之位 | House of the God | 第九位 |
| 恶灵之位 | House of the Evil Daemon | 第十二位,不取 |
🧭 图解与讲解
卷三第三章把本命之学按时间分类,降生之后的诸事里,第一项就是寿数(length of life)。上一章(卷三第九章)说,寿数之问针对能活过太阳一周、即一年以上的人。托勒密引「那位古人」的话(Robbins 注:大概指佩托西里斯)说:一个人若按寿数根本活不到某事发生之时,却给他预言那件事,岂不可笑。所以寿数要最先定。下面讲的是二世纪的古代学说,本页只讲解书中的方法,不据此推断任何人的寿命。
| 位 | 本图星座 | 古名(Robbins 注) | 本章取舍 |
|---|---|---|---|
| 第一位 | 白羊 | 上升 | 取,居第二:地平上五度、地平下二十五度 |
| 第二至六位 | 金牛至处女 | 冥府之门、女神(月)、地底中天、好运、厄运 | 不取:在地平以下 |
| 第七位 | 天秤 | 下降 | 取,居第四:与上升对冲 |
| 第八位 | 天蝎 | 死亡之始 | 不取:与上升不相接 |
| 第九位 | 射手 | 神(日) | 取,居第五:与上升三分 |
| 第十位 | 摩羯 | 中天 | 取,居第一:与上升四分 |
| 第十一位 | 水瓶 | 善灵 | 取,居第三:与上升六分 |
| 第十二位 | 双鱼 | 恶灵 | 不取:损害星光,又在下坠;近地平处地气浑浊 |
整个方法由三样东西组成:释放之位、释放星(prorogator,后世阿拉伯占星称「海勒格」,见 Robbins 注)、杀位或杀星(anaeretic)。Robbins 注引布谢-勒克莱尔(Bouché-Leclercq)的概括:黄道好比一条跑道,生命从某个出发点被「释放」出去,走到某处障碍便被截住,或险些被截住;走过的度数换算成赤道上的度数,就是年数。本单元先讲释放星必须落在哪里。
图一以上升点在白羊五度为例。第一位是环绕上升点的三十度:地平之上五度、之下二十五度(正在升起的部分),恰好是白羊整座。由此按相位逆着黄道顺序往前数:右方六分是第十一位,即善灵之位;四分是第十位,即中天;三分是第九位,即神之位;对冲是第七位,即下降点。「右方」(dexter)指在黄道次序上居前的一侧。上升点若不在某座五度,各位就会跨两座,须按度数量。动画按托勒密排的优先次序轮流点亮:中天、上升、善灵之位、下降、神之位。
其余七位为什么不取?地平以下的第二到第六位整片不计,因为如此重大的主宰,必须在光明之中;唯一的例外是上升点下方那二十五度,它们正升入光明。地平以上也去掉两位(表二):第八位与上升「不相接」(卷一第十六章),Robbins 注说这里的「座」指本命的位,不是黄道星座;第十二位恶灵之位,托勒密说它损害星光向地面的流溢,又在下坠(属果宫),加上近地平处地气浓雾,星辰显不出真实的颜色与大小。
表二的「古名」取自 Robbins 注,是当时星占家对十二位的通称,如第二位「冥府之门」、第八位「死亡之始」。托勒密本人很少用这套「位」的体系,本章只点到其中五个。这五个释放之位,正是上升点本身与它的六分、四分、三分、对冲,和卷一第十三章讲的相位一一相合:既在地平以上、又与上升点成相位的位置,才有资格主管寿数。
After this again we must take as prorogatives the four regions of greatest authority, sun, moon, horoscope, the Lot of Fortune, and the rulers of these regions.
Take as the Lot of Fortune always the amount of the number of degrees, both by night and by day, which is the distance from the sun to the moon, and which extends to an equal distance from the horoscope in the order of the following signs, in order that, whatever relation and aspect the sun bears to the horoscope, the moon also may bear to the Lot of Fortune, and that it may be as it were a lunar horoscope.
Of these, by day we must give first place to the sun, if it is in the prorogative places; if not, to the moon; and if the moon is not so placed, to the planet that has most relations of domination to the sun, to the preceding conjunction, and to the horoscope; that is, when, of the five methods of domination that exist, it has three to one, or even more; but if this cannot be, then finally we give preference to the horoscope.
By night prefer the moon first, next the sun, next the planets having the greater number of relations of domination to the moon, to the preceding full moon, and to the Lot of Fortune; otherwise, finally, if the preceding syzygy was a new moon, the horoscope, but if it was a full moon the Lot of Fortune. But if both the luminaries or the ruler of the proper sect should be in the prorogative places, we must take the one of the luminaries that is in the place of greatest authority.
And we should prefer the ruling planet to both of the luminaries only when it both occupies a position of greater authority and bears a relation of domination to both the sects.
翻译点开
After this again we must take as prorogatives the four regions of greatest authority, sun, moon, horoscope, the Lot of Fortune, and the rulers of these regions.
此后,我们又必须把最有权力的四处,即太阳、月亮、上升点、福点,以及这几处的主星,当作释放者。
Take as the Lot of Fortune always the amount of the number of degrees, both by night and by day, which is the distance from the sun to the moon, and which extends to an equal distance from the horoscope in the order of the following signs, in order that, whatever relation and aspect the sun bears to the horoscope, the moon also may bear to the Lot of Fortune, and that it may be as it were a lunar horoscope.
福点总是这样取:无论夜生还是昼生,都取从太阳到月亮的度数,从上升点起顺着后随星座的次序量出同样的距离;这样,太阳对上升点有什么关系与相位,月亮对福点也有同样的关系与相位,福点就好比是月亮的上升点。
Of these, by day we must give first place to the sun, if it is in the prorogative places; if not, to the moon; and if the moon is not so placed, to the planet that has most relations of domination to the sun, to the preceding conjunction, and to the horoscope; that is, when, of the five methods of domination that exist, it has three to one, or even more; but if this cannot be, then finally we give preference to the horoscope.
这些之中,白天应当首推太阳,如果它在释放之位上;否则推月亮;如果月亮也不在这样的位置,就推对太阳、对前一次的朔、对上升点主宰关系最多的那颗行星,也就是说,在现有的五种主宰方式中,它对一处占有三种,甚至更多;但如果这也不能成立,最后就取上升点。
By night prefer the moon first, next the sun, next the planets having the greater number of relations of domination to the moon, to the preceding full moon, and to the Lot of Fortune; otherwise, finally, if the preceding syzygy was a new moon, the horoscope, but if it was a full moon the Lot of Fortune. But if both the luminaries or the ruler of the proper sect should be in the prorogative places, we must take the one of the luminaries that is in the place of greatest authority.
夜里则先推月亮,其次推太阳,再次推对月亮、对前一次的望、对福点主宰关系较多的行星;否则,最后,若前一次朔望是朔,就取上升点,若是望,就取福点。但若两光,或本命所属之分的主星,都在释放之位上,就应取两光之中居于最有权力之位的那一个。
And we should prefer the ruling planet to both of the luminaries only when it both occupies a position of greater authority and bears a relation of domination to both the sects.
只有当那颗主星既占据更有权力的位置,又对昼夜两分都有主宰关系时,我们才应把它置于两光之前。
大意与图解点开
🔎 大意:候选为日、月、上升、福点及其主星。昼生先日后月,夜生先月后日,再看主宰最多之星,最后取上升或福点。
📖 术语
| 术语 | 英译原词 | 意思 |
|---|---|---|
| 福点 | Lot of Fortune | 好比月亮的上升点 |
| 释放星 | prorogator | 释放生命的起点之星 |
| 主宰关系 | relations of domination | 三方庙旺界相五种 |
| 朔望 | syzygy | 日月相会或相对 |
| 本命所属之分 | proper sect | 昼生属昼,夜生属夜 |
🧭 图解与讲解
第二步是选出释放星。候选有四处「最有权力」的地方——太阳、月亮、上升点、福点(Lot of Fortune)——以及它们的主星。太阳、月亮、上升点都是现成的,福点要算:从太阳顺着黄道顺序量到月亮有多少度,就从上升点起顺着黄道顺序量出同样的度数,落点就是福点。「后随星座的次序」就是黄道的顺序,白羊、金牛、双子依次往后。
〔图〕福点:从上升点量出日到月的距离,福点之于月亮,正如上升点之于太阳
〔图〕选释放星的次序:昼生以太阳为首,夜生以月亮为首,都要在释放之位上
这样算出的福点,对月亮的关系正如上升点对太阳的关系,所以说它「好比月亮的上升点」。图一是一个昼生的示意:太阳在射手十度,月亮在双鱼二十五度,相距一百零五度;上升点在白羊初度,往后数一百零五度,福点落在巨蟹十五度。动画里两条半径同时扫过一百零五度。托勒密强调「无论昼夜」都这样算;有的抄本此处多出一段,主张看日月谁先谁后来改变量法、夜生由月量到日;Robbins 注认为它与托勒密的指示不合,是后人的批注混入了正文。
选的次序分昼夜(图二)。白天以太阳为首,它须在上一单元所说的释放之位上;不在,就看月亮;月亮也不在,就找一颗对太阳、对前一次的朔、对上升点主宰关系最多的行星;再没有,就用上升点本身。夜里以月亮为首,其次太阳,再找一颗对月亮、对前一次的望、对福点主宰关系最多的行星;都不成,前一次朔望若是朔就用上升点,若是望就用福点。可以看出一种对称:昼生配太阳、朔与上升点,夜生配月亮、望与福点,而福点正是「月亮的上升点」。
「主宰关系」指卷三第二章列的五种:三方、庙、旺、界、相(与太阳的相对位置)或相位。「对一处占有三种,甚至更多」,即这颗星至少以三种身份主宰其中一处,才算主宰关系最多。最后两条是补充:两光都在释放之位时,取所居之位更有权力的一个(按上一单元的优先次序);主星要排在两光之前,须两条兼备:所居之位比两光更有权力,又对昼、夜两分都有主宰关系。Robbins 注:「本命所属之分」,昼生属昼,夜生属夜。
📖 术语
| 术语 | 英译原词 | 意思 |
|---|---|---|
| 福点 | Lot of Fortune | 好比月亮的上升点 |
| 释放星 | prorogator | 释放生命的起点之星 |
| 主宰关系 | relations of domination | 三方庙旺界相五种 |
| 朔望 | syzygy | 日月相会或相对 |
| 本命所属之分 | proper sect | 昼生属昼,夜生属夜 |
🧭 图解与讲解
第二步是选出释放星。候选有四处「最有权力」的地方——太阳、月亮、上升点、福点(Lot of Fortune)——以及它们的主星。太阳、月亮、上升点都是现成的,福点要算:从太阳顺着黄道顺序量到月亮有多少度,就从上升点起顺着黄道顺序量出同样的度数,落点就是福点。「后随星座的次序」就是黄道的顺序,白羊、金牛、双子依次往后。
这样算出的福点,对月亮的关系正如上升点对太阳的关系,所以说它「好比月亮的上升点」。图一是一个昼生的示意:太阳在射手十度,月亮在双鱼二十五度,相距一百零五度;上升点在白羊初度,往后数一百零五度,福点落在巨蟹十五度。动画里两条半径同时扫过一百零五度。托勒密强调「无论昼夜」都这样算;有的抄本此处多出一段,主张看日月谁先谁后来改变量法、夜生由月量到日;Robbins 注认为它与托勒密的指示不合,是后人的批注混入了正文。
选的次序分昼夜(图二)。白天以太阳为首,它须在上一单元所说的释放之位上;不在,就看月亮;月亮也不在,就找一颗对太阳、对前一次的朔、对上升点主宰关系最多的行星;再没有,就用上升点本身。夜里以月亮为首,其次太阳,再找一颗对月亮、对前一次的望、对福点主宰关系最多的行星;都不成,前一次朔望若是朔就用上升点,若是望就用福点。可以看出一种对称:昼生配太阳、朔与上升点,夜生配月亮、望与福点,而福点正是「月亮的上升点」。
「主宰关系」指卷三第二章列的五种:三方、庙、旺、界、相(与太阳的相对位置)或相位。「对一处占有三种,甚至更多」,即这颗星至少以三种身份主宰其中一处,才算主宰关系最多。最后两条是补充:两光都在释放之位时,取所居之位更有权力的一个(按上一单元的优先次序);主星要排在两光之前,须两条兼备:所居之位比两光更有权力,又对昼、夜两分都有主宰关系。Robbins 注:「本命所属之分」,昼生属昼,夜生属夜。
When the prorogator has been distinguished, we must still further adopt two methods of prorogation. The one, that which follows the order of the following signs, must be used only in the case of what is called the projection of rays, when the prorogator is in the orient, that is, between mid‑heaven and the horoscope. We must use not only the method that follows the order of following signs, but also that which follows the order of leading signs, in the so‑called horimaea, when the prorogator is in places that decline from mid‑heaven.
This being the case, the destructive degrees in the prorogation that follows the order of leading signs are only the degree of the western horizon, because it causes the lord of life to vanish; and the degrees of the planets that thus approach or bear witness merely take away and add years to the sum of those as far as the setting of the prorogator, and they do not destroy because they do not move toward the prorogative place, but it moves toward them. The beneficent stars add and the maleficent subtract.
Mercury, again, is reckoned with the group to which he bears an aspect. The number of the addition or subtraction is calculated by means of the location in degrees in each case. For the entire number of years is the same as the number of hourly periods of each degree, hours of the day when it is day and hours of the night when it is night; this must be our reckoning when they are in the orient, and subtraction must be made in proportion to their departure therefrom, until at their setting it becomes zero.
翻译点开
When the prorogator has been distinguished, we must still further adopt two methods of prorogation. The one, that which follows the order of the following signs, must be used only in the case of what is called the projection of rays, when the prorogator is in the orient, that is, between mid‑heaven and the horoscope. We must use not only the method that follows the order of following signs, but also that which follows the order of leading signs, in the so‑called horimaea, when the prorogator is in places that decline from mid‑heaven.
释放星辨明之后,还必须采用两种释放法。一种是顺着后随星座次序的,只用于所谓“投射光线”的情形,即释放星在东方、也就是在中天与上升点之间时。而在所谓“霍里迈亚”的情形,即释放星在从中天下坠的诸位时,就不仅要用顺着后随星座次序的方法,也要用顺着前导星座次序的方法。
This being the case, the destructive degrees in the prorogation that follows the order of leading signs are only the degree of the western horizon, because it causes the lord of life to vanish; and the degrees of the planets that thus approach or bear witness merely take away and add years to the sum of those as far as the setting of the prorogator, and they do not destroy because they do not move toward the prorogative place, but it moves toward them. The beneficent stars add and the maleficent subtract.
既然如此,在顺着前导星座次序的释放中,杀度只有西方地平的那一度,因为它使生命之主隐没;至于这样趋近或作见证的诸行星的度数,只是对到释放星沉没为止的年数总和减去或增添若干年,它们并不致死,因为不是它们向释放之位移动,而是释放之位向它们移动。吉星增添,凶星减去。
Mercury, again, is reckoned with the group to which he bears an aspect. The number of the addition or subtraction is calculated by means of the location in degrees in each case. For the entire number of years is the same as the number of hourly periods of each degree, hours of the day when it is day and hours of the night when it is night; this must be our reckoning when they are in the orient, and subtraction must be made in proportion to their departure therefrom, until at their setting it becomes zero.
水星则算入与他成相位的那一组。增添或减去的数目,按各星所在的度数来计算。因为年数的全数,与各度的时量之数相同,白天用昼时,夜里用夜时;当它们在东方时,应这样计算;随着它们离开东方,要按比例递减,直到它们沉没时减为零。
大意与图解点开
🔎 大意:释放分顺序、逆序两法:东方只用顺序;西方兼用逆序。逆序只有下降点致死,途中诸星只增减年数。
📖 术语
| 术语 | 英译原词 | 意思 |
|---|---|---|
| 后随星座的次序 | order of the following signs | 黄道顺序 |
| 前导星座的次序 | order of the leading signs | 周日运动的方向 |
| 投射光线 | projection of rays | 东方所用的释放法 |
| 霍里迈亚 | horimaea | 西方兼用两法 |
| 生命之主 | lord of life | 即释放星 |
🧭 图解与讲解
释放星定了,还要定「怎么走」。托勒密给两种释放法。一种顺着「后随星座」的次序,即黄道顺序:在后的那一点(杀星或它的光线)被周日旋转带到释放星原来的位置。另一种顺着「前导星座」的次序,即周日运动的方向:释放星自己被带向西方地平。Robbins 注引布谢-勒克莱尔:两种方向的量度单位都是周日运动,寿数都等于两点之间赤道上的度数,一度一年。后世把这类以周日旋转推算的方法称为「主限」(primary directions)。
〔图〕东方只用顺序释放,西方兼用逆序:两种方向,同以周日旋转计时
| 顺着后随星座(黄道顺序) | 顺着前导星座(周日方向) | |
|---|---|---|
| 释放星所在 | 东方:中天到上升之间(「投射光线」);西方也用 | 西方:从中天下坠的诸位(「霍里迈亚」),与前法并用 |
| 谁向谁移动 | 杀星或其光线随周日旋转来到释放之位 | 释放星本身随周日旋转移向西方地平 |
| 什么致死 | 土星、火星的本体或光线等(见下一单元) | 只有西方地平那一度 |
| 途中诸星 | 趋近既能致死,也能保全 | 只增减年数:吉星加,凶星减,水星随他成相位的一组 |
| 增减多少 | —— | 该星所在度的时量:在东方取全数,渐远渐减,沉没时为零 |
用哪一种,看释放星在哪个象限(图一)。释放星在东方,即中天与上升点之间,只用顺序释放,这叫「投射光线」(projection of rays):Robbins 注说,诸星的光线像投掷的标枪,须以正式的相位投出才有效,对冲、四分最有攻击力。释放星在从中天下坠的西方诸位,叫「霍里迈亚」(horimaea,Robbins 照希腊文音写),两种都可用。
逆序释放的规则很简单(表二):致死的只有西方地平那一度,因为「生命之主」,也就是释放星,到那里便沉没不见。途中遇到的行星,无论本体相遇还是以相位作证,都不致死,因为不是它们朝释放之位而来,而是释放星朝它们而去;它们只对「到沉没为止」的年数加减:吉星加,凶星减,水星看他与哪一组成相位就算哪一组(水星可吉可凶,见卷一第五章)。
加减多少?按各星所在那一度的「时量」:一个季节时(白昼或黑夜的十二分之一)合多少赤道时度,就加减多少年,昼生用昼时、夜生用夜时(时量的求法见第六单元)。星在东方时取全数,离东方越远按比例递减,到沉没时为零。图一的动画画了两种情形:东方的太阳沿黄道顺序推进到火星;西方的月亮随周日旋转移向下降点,途中经过的木星只为她增添年数。
📖 术语
| 术语 | 英译原词 | 意思 |
|---|---|---|
| 后随星座的次序 | order of the following signs | 黄道顺序 |
| 前导星座的次序 | order of the leading signs | 周日运动的方向 |
| 投射光线 | projection of rays | 东方所用的释放法 |
| 霍里迈亚 | horimaea | 西方兼用两法 |
| 生命之主 | lord of life | 即释放星 |
🧭 图解与讲解
释放星定了,还要定「怎么走」。托勒密给两种释放法。一种顺着「后随星座」的次序,即黄道顺序:在后的那一点(杀星或它的光线)被周日旋转带到释放星原来的位置。另一种顺着「前导星座」的次序,即周日运动的方向:释放星自己被带向西方地平。Robbins 注引布谢-勒克莱尔:两种方向的量度单位都是周日运动,寿数都等于两点之间赤道上的度数,一度一年。后世把这类以周日旋转推算的方法称为「主限」(primary directions)。
| 顺着后随星座(黄道顺序) | 顺着前导星座(周日方向) | |
|---|---|---|
| 释放星所在 | 东方:中天到上升之间(「投射光线」);西方也用 | 西方:从中天下坠的诸位(「霍里迈亚」),与前法并用 |
| 谁向谁移动 | 杀星或其光线随周日旋转来到释放之位 | 释放星本身随周日旋转移向西方地平 |
| 什么致死 | 土星、火星的本体或光线等(见下一单元) | 只有西方地平那一度 |
| 途中诸星 | 趋近既能致死,也能保全 | 只增减年数:吉星加,凶星减,水星随他成相位的一组 |
| 增减多少 | —— | 该星所在度的时量:在东方取全数,渐远渐减,沉没时为零 |
用哪一种,看释放星在哪个象限(图一)。释放星在东方,即中天与上升点之间,只用顺序释放,这叫「投射光线」(projection of rays):Robbins 注说,诸星的光线像投掷的标枪,须以正式的相位投出才有效,对冲、四分最有攻击力。释放星在从中天下坠的西方诸位,叫「霍里迈亚」(horimaea,Robbins 照希腊文音写),两种都可用。
逆序释放的规则很简单(表二):致死的只有西方地平那一度,因为「生命之主」,也就是释放星,到那里便沉没不见。途中遇到的行星,无论本体相遇还是以相位作证,都不致死,因为不是它们朝释放之位而来,而是释放星朝它们而去;它们只对「到沉没为止」的年数加减:吉星加,凶星减,水星看他与哪一组成相位就算哪一组(水星可吉可凶,见卷一第五章)。
加减多少?按各星所在那一度的「时量」:一个季节时(白昼或黑夜的十二分之一)合多少赤道时度,就加减多少年,昼生用昼时、夜生用夜时(时量的求法见第六单元)。星在东方时取全数,离东方越远按比例递减,到沉没时为零。图一的动画画了两种情形:东方的太阳沿黄道顺序推进到火星;西方的月亮随周日旋转移向下降点,途中经过的木星只为她增添年数。
In the prorogation which follows the order of following signs, the places of the maleficent planets, Saturn and Mars, destroy, whether they are approaching bodily, or project their rays from any place whatever in quartile or in opposition, and sometimes too in sextile, upon the signs called "hearing" or "seeing" on grounds of equality of power; and the sign that is quartile to the prorogative sign in the order of following signs likewise destroys.
And sometimes, also, among the signs that ascend slowly the sextile aspect destroys, when it is afflicted, and again among the signs that ascend rapidly the trine. When the moon is the prorogator, the place of the sun also destroys. For in a prorogation of this kind the approaches of planets avail both to destroy and to preserve, since these are in the direction of the prorogative place. However, it must not be thought that these places always inevitably destroy, but only when they are afflicted.
For they are prevented both if they fall within the term of a beneficent planet and if one of the beneficent planets projects its ray from quartile, trine, or opposition either upon the destructive degree itself or upon the parts that follow it, in the case of Jupiter not more than 12°, and in that of Venus not over 8°; also if, when both the prorogator and the approaching planet are present bodily, the latitude of both is not the same.
Thus when there are two or more on each side, assisting and, vice versa, destroying, we must consider which of them prevails, both by the number of those that co‑operate and by power; by number when one group is perceptibly more numerous than the other, and with regard to power when some of the assisting or of the destroying planets are in their own proper places, and some are not, and particularly when some are rising and others setting.
For in general we must not admit any planet, either to destroy or to aid, that is under the rays of the sun, except that when the moon is prorogator the place of the sun itself is destructive, when it is changed about by the presence of a maleficent planet and is not released by any of the beneficent ones.
翻译点开
In the prorogation which follows the order of following signs, the places of the maleficent planets, Saturn and Mars, destroy, whether they are approaching bodily, or project their rays from any place whatever in quartile or in opposition, and sometimes too in sextile, upon the signs called "hearing" or "seeing" on grounds of equality of power; and the sign that is quartile to the prorogative sign in the order of following signs likewise destroys.
在顺着后随星座次序的释放中,凶星土星与火星的位置致死,无论它们是以星体本身趋近,还是从任何地方以四分或对冲投射光线,有时也以六分,投射到因等力而被称为“相听”或“相望”的星座上;顺着后随星座的次序、与释放之座成四分的那一座,同样致死。
And sometimes, also, among the signs that ascend slowly the sextile aspect destroys, when it is afflicted, and again among the signs that ascend rapidly the trine. When the moon is the prorogator, the place of the sun also destroys. For in a prorogation of this kind the approaches of planets avail both to destroy and to preserve, since these are in the direction of the prorogative place. However, it must not be thought that these places always inevitably destroy, but only when they are afflicted.
有时,在升起慢的星座中,六分相若受损也会致死;在升起快的星座中则是三分相。月亮为释放星时,太阳的位置也致死。因为在这种释放中,诸星的趋近既能致死,也能保全,因为它们是朝着释放之位而来的。不过不可认为这些位置总是必然致死,只有在受损时才如此。
For they are prevented both if they fall within the term of a beneficent planet and if one of the beneficent planets projects its ray from quartile, trine, or opposition either upon the destructive degree itself or upon the parts that follow it, in the case of Jupiter not more than 12°, and in that of Venus not over 8°; also if, when both the prorogator and the approaching planet are present bodily, the latitude of both is not the same.
因为它们会受到阻止:如果它们落在吉星的界内;如果有一颗吉星以四分、三分或对冲,把光线投射到杀度本身或其后的部分上,木星不超过十二度,金星不超过八度;还有,如果释放星与趋近的行星都以星体本身相会,而两者的黄纬不同。
Thus when there are two or more on each side, assisting and, vice versa, destroying, we must consider which of them prevails, both by the number of those that co‑operate and by power; by number when one group is perceptibly more numerous than the other, and with regard to power when some of the assisting or of the destroying planets are in their own proper places, and some are not, and particularly when some are rising and others setting.
因此,当双方各有两颗或更多,一方相助、一方反过来致死时,我们必须考虑哪一方占上风,既看合作者的数目,也看力量:看数目,是当一组明显多于另一组时;看力量,是当相助或致死的诸星有的在自己的本位、有的不在时,尤其是有的正在升起、有的正在沉没时。
For in general we must not admit any planet, either to destroy or to aid, that is under the rays of the sun, except that when the moon is prorogator the place of the sun itself is destructive, when it is changed about by the presence of a maleficent planet and is not released by any of the beneficent ones.
因为一般而言,凡在太阳光下的行星,无论致死还是相助,我们都不应采纳;唯有月亮为释放星时,太阳本身的位置是致死的,那是当它因一颗凶星的在场而改变了性质、又没有任何吉星予以解救的时候。
大意与图解点开
🔎 大意:顺序释放中,土星火星的本体或四分对冲之光等致死;落吉星界内、吉星投光在十二或八度内、黄纬不同则受阻。
📖 术语
| 术语 | 英译原词 | 意思 |
|---|---|---|
| 杀星 | destructive (anaeretic) planet | 截断释放的凶星 |
| 受损 | afflicted | 受凶星侵害 |
| 相听、相望 | "hearing," "seeing" | 等力的一对星座 |
| 快升、慢升 | ascend rapidly, slowly | 上升时间短或长 |
| 在太阳光下 | under the rays of the sun | 离太阳太近,不计 |
🧭 图解与讲解
顺序释放里,什么能截断生命?托勒密列了几种杀者(表二):凶星土星、火星以本体趋近;它们从任何地方以四分或对冲投来的光线;有时还有六分,条件是投到卷一第十五章所说因等力而「相听」「相望」的星座上;此外,顺着黄道顺序、与释放星所在之座成四分的那一座本身也致死。这些都在释放星前方,会被周日旋转一一带到释放之位。
〔图〕顺序释放的杀与救:凶星之光挡在路上,吉星之光落在其后不远便能解救
| 条目 | 说明 | |
|---|---|---|
| 致死 | 土星、火星以星体本身趋近 | 凶星本身来到释放之位 |
| 致死 | 土星、火星以四分或对冲投射光线 | 从任何地方投来都算 |
| 有时致死 | 以六分投到「相听」「相望」的星座上 | 以等力为据(卷一第十五章) |
| 致死 | 顺着黄道与释放之座成四分的那一座 | 整座论 |
| 有时致死 | 慢升星座中受损的六分;快升星座中的三分 | 快慢见下一单元表二 |
| 致死 | 月亮为释放星时,太阳的位置 | 须太阳被凶星改变、又无吉星解救 |
| 解救 | 杀度落在吉星的界内 | 界见卷一第二十、二十一章 |
| 解救 | 吉星以四分、三分、对冲投光到杀度或其后 | 木星不超过十二度,金星不超过八度 |
| 解救 | 本体相会而黄纬不同 | 光线射不中(Robbins 注) |
| 权衡 | 双方各有两颗以上 | 比数目;比力量:在本位否、正升起或正沉没 |
| 不计 | 在太阳光下的行星 | 既不能杀,也不能救 |
还有两条看星座升起的快慢:在升起慢的星座里,受损的六分有时也致死;在升起快的星座里,三分也会。Robbins 注:白羊、金牛、双子、摩羯、水瓶、双鱼升起快,其余六座升起慢(各座的上升时间见下一单元表二)。月亮为释放星时,太阳的位置也是杀位。托勒密解释:顺序释放中,诸星是朝释放之位而来的,所以它们的趋近既能杀,也能保全。
但杀位并非必杀,只有受损时才杀。有三种情况能挡住:杀度落在吉星的界内(界见卷一第二十、二十一章);有吉星以四分、三分或对冲把光线投到杀度本身或其后,木星以十二度为限,金星以八度为限;释放星与来犯的星本体相会,而两者黄纬不同。Robbins 注说,最后一条只适用于本体相会,意思是纬度不同,光线就射不中。
图一是一个示意,只演示规则,不是任何人的命盘:上升在白羊初度,释放星太阳在摩羯八度,居中天。火星在金牛二十二度,右方四分的光线落在水瓶二十二度;但木星在双子二十八度,右方三分的光线落在水瓶二十八度,在杀度之后六度,未超过十二度,于是受阻。动画中的半径继续推进,到土星本体所在的双鱼二十度,再无吉星相救,那才是杀位。
双方都有两颗以上时,比数目,也比力量:是否在自己的本位、正在升起还是沉没。在太阳光下的行星一概不计,既不能杀,也不能救;例外是月亮为释放星时太阳本身的位置。Robbins 注引古注说,太阳的气质居中,随同处的星而变吉变凶(参卷一第五章),所以凶星在场改变了它、又无吉星「解救」时,它就致死。
📖 术语
| 术语 | 英译原词 | 意思 |
|---|---|---|
| 杀星 | destructive (anaeretic) planet | 截断释放的凶星 |
| 受损 | afflicted | 受凶星侵害 |
| 相听、相望 | "hearing," "seeing" | 等力的一对星座 |
| 快升、慢升 | ascend rapidly, slowly | 上升时间短或长 |
| 在太阳光下 | under the rays of the sun | 离太阳太近,不计 |
🧭 图解与讲解
顺序释放里,什么能截断生命?托勒密列了几种杀者(表二):凶星土星、火星以本体趋近;它们从任何地方以四分或对冲投来的光线;有时还有六分,条件是投到卷一第十五章所说因等力而「相听」「相望」的星座上;此外,顺着黄道顺序、与释放星所在之座成四分的那一座本身也致死。这些都在释放星前方,会被周日旋转一一带到释放之位。
| 条目 | 说明 | |
|---|---|---|
| 致死 | 土星、火星以星体本身趋近 | 凶星本身来到释放之位 |
| 致死 | 土星、火星以四分或对冲投射光线 | 从任何地方投来都算 |
| 有时致死 | 以六分投到「相听」「相望」的星座上 | 以等力为据(卷一第十五章) |
| 致死 | 顺着黄道与释放之座成四分的那一座 | 整座论 |
| 有时致死 | 慢升星座中受损的六分;快升星座中的三分 | 快慢见下一单元表二 |
| 致死 | 月亮为释放星时,太阳的位置 | 须太阳被凶星改变、又无吉星解救 |
| 解救 | 杀度落在吉星的界内 | 界见卷一第二十、二十一章 |
| 解救 | 吉星以四分、三分、对冲投光到杀度或其后 | 木星不超过十二度,金星不超过八度 |
| 解救 | 本体相会而黄纬不同 | 光线射不中(Robbins 注) |
| 权衡 | 双方各有两颗以上 | 比数目;比力量:在本位否、正升起或正沉没 |
| 不计 | 在太阳光下的行星 | 既不能杀,也不能救 |
还有两条看星座升起的快慢:在升起慢的星座里,受损的六分有时也致死;在升起快的星座里,三分也会。Robbins 注:白羊、金牛、双子、摩羯、水瓶、双鱼升起快,其余六座升起慢(各座的上升时间见下一单元表二)。月亮为释放星时,太阳的位置也是杀位。托勒密解释:顺序释放中,诸星是朝释放之位而来的,所以它们的趋近既能杀,也能保全。
但杀位并非必杀,只有受损时才杀。有三种情况能挡住:杀度落在吉星的界内(界见卷一第二十、二十一章);有吉星以四分、三分或对冲把光线投到杀度本身或其后,木星以十二度为限,金星以八度为限;释放星与来犯的星本体相会,而两者黄纬不同。Robbins 注说,最后一条只适用于本体相会,意思是纬度不同,光线就射不中。
图一是一个示意,只演示规则,不是任何人的命盘:上升在白羊初度,释放星太阳在摩羯八度,居中天。火星在金牛二十二度,右方四分的光线落在水瓶二十二度;但木星在双子二十八度,右方三分的光线落在水瓶二十八度,在杀度之后六度,未超过十二度,于是受阻。动画中的半径继续推进,到土星本体所在的双鱼二十度,再无吉星相救,那才是杀位。
双方都有两颗以上时,比数目,也比力量:是否在自己的本位、正在升起还是沉没。在太阳光下的行星一概不计,既不能杀,也不能救;例外是月亮为释放星时太阳本身的位置。Robbins 注引古注说,太阳的气质居中,随同处的星而变吉变凶(参卷一第五章),所以凶星在场改变了它、又无吉星「解救」时,它就致死。
However, the number of years, determined by the distances between the prorogative place and the destructive planet, ought not to be taken simply or offhand, in accordance with the usual traditions, from the times of ascension of each degree, except only when the eastern horizon itself is the prorogator, or some one of the planets that are rising in that region.
For one method alone is available for him who is considering this subject in a natural manner — to calculate after how many equinoctial periods the place of the following body or aspect comes to the place of the one preceding at the actual time of birth, because the equinoctial periods pass evenly through both the horizon and the mid‑heaven, to both of which are referred the proportions of spatial distances, and, as is reasonable, each one of the periods has the value of one solar year.
Whenever the prorogative and preceding place is actually on the eastern horizon, we should take the times of ascension of the degrees up to the meeting-place; for after this number of equinoctial periods the destructive planet comes to the place of the prorogator, that is, to the eastern horizon.
But when it is actually at the mid‑heaven, we should take the ascensions on the right sphere in which the segment in each case passes mid‑heaven; and when it is on the western horizon, the number in which each of the degrees of the interval descends, that is, the number in which those directly opposite them ascend.
But if the precedent place is not on these three limits but in the intervals between them, in that case the times of the aforesaid ascensions, descensions, or culminations will not carry the following places to the places of the preceding, but the periods will be different. For a place is similar and the same if it has the same position in the same direction with reference both to the horizon and to the meridian.
This is most nearly true of those which lie upon one of those semicircles which are described through the sections of the meridian and the horizon, each of which at the same position makes nearly the same temporal hour. Even as, if the revolution is upon the aforesaid arcs, it reaches the same position with reference to both the meridian and horizon, but makes the periods of the passage of the zodiac unequal with respect to either, in the same way also at the positions of the other distances it makes their passages in times unequal to the former.
We shall therefore adopt one method only, as follows, whereby, whether the preceding place occupies the orient, the mid‑heaven, the occident, or any other position, the proportionate number of equinoctial times that bring the following place to it will be apprehended.

翻译点开
However, the number of years, determined by the distances between the prorogative place and the destructive planet, ought not to be taken simply or offhand, in accordance with the usual traditions, from the times of ascension of each degree, except only when the eastern horizon itself is the prorogator, or some one of the planets that are rising in that region.
然而,由释放之位与杀星之间的距离所定的年数,不应照通常的传统,简单随便地从各度的上升时间来取;唯有东方地平本身就是释放者,或者是正在那一带升起的某颗行星时,才可以这样做。
For one method alone is available for him who is considering this subject in a natural manner — to calculate after how many equinoctial periods the place of the following body or aspect comes to the place of the one preceding at the actual time of birth, because the equinoctial periods pass evenly through both the horizon and the mid‑heaven, to both of which are referred the proportions of spatial distances, and, as is reasonable, each one of the periods has the value of one solar year.
因为对按自然之理考察此事的人来说,只有一种方法可用:计算经过多少赤道时度,在后之星或相位的位置,会来到降生那一刻在前者所在的位置;因为赤道时度均匀地经过地平与中天,而空间距离的比例都以这两者为准;并且,理所当然,每一个时度值一个太阳年。
Whenever the prorogative and preceding place is actually on the eastern horizon, we should take the times of ascension of the degrees up to the meeting-place; for after this number of equinoctial periods the destructive planet comes to the place of the prorogator, that is, to the eastern horizon.
每当释放之位、即在前之位正好在东方地平上时,就应取到会合之处为止各度的上升时间;因为经过这么多赤道时度,杀星就来到释放星的位置,也就是东方地平。
But when it is actually at the mid‑heaven, we should take the ascensions on the right sphere in which the segment in each case passes mid‑heaven; and when it is on the western horizon, the number in which each of the degrees of the interval descends, that is, the number in which those directly opposite them ascend.
当它正好在中天时,就应取正球上的上升时间,即这一段各自经过中天所需的时间;当它在西方地平时,就取这段间隔各度沉没所需的时间数,也就是与它们正相对的各度升起所需的时间数。
But if the precedent place is not on these three limits but in the intervals between them, in that case the times of the aforesaid ascensions, descensions, or culminations will not carry the following places to the places of the preceding, but the periods will be different. For a place is similar and the same if it has the same position in the same direction with reference both to the horizon and to the meridian.
但如果在前之位不在这三个界限上,而在它们之间的间隔里,那么上述的上升、沉没或过中天的时间,就不会把在后之位带到在前之位上,所需的时段会有所不同。因为一个位置,若在同一方向上,相对于地平与子午线都有同样的位置,才算是相似、相同的位置。
This is most nearly true of those which lie upon one of those semicircles which are described through the sections of the meridian and the horizon, each of which at the same position makes nearly the same temporal hour. Even as, if the revolution is upon the aforesaid arcs, it reaches the same position with reference to both the meridian and horizon, but makes the periods of the passage of the zodiac unequal with respect to either, in the same way also at the positions of the other distances it makes their passages in times unequal to the former.
这一点,对位于经过子午线与地平之交点所作的那些半圆中同一个半圆上的诸点,最为接近成立;这些半圆每一个在同一位置上都构成几乎相同的季节时。正如旋转若在上述那些弧上进行,它会到达相对于子午线与地平都相同的位置,却使黄道经过两者所需的时段并不相等;同样,在其他距离的位置上,它使黄道经过所需的时间也与前者不等。
We shall therefore adopt one method only, as follows, whereby, whether the preceding place occupies the orient, the mid‑heaven, the occident, or any other position, the proportionate number of equinoctial times that bring the following place to it will be apprehended.
因此我们只采用下面这一种方法:无论在前之位占据东方、中天、西方还是任何其他位置,都能借此求得把在后之位带到它那里的、合乎比例的赤道时度之数。
大意与图解点开
🔎 大意:年数不可一律取上升时间:应算后位经几赤道时度到达前位的相似之位,一时度一年;前位不在三角时另算。
📖 术语
| 术语 | 英译原词 | 意思 |
|---|---|---|
| 赤道时度 | equinoctial periods | 赤道一度转过所需时间 |
| 上升时间 | times of ascension | 一段黄道升起所需时度 |
| 正球 | right sphere | 赤道上所见的天球 |
| 相似之位 | similar place | 对地平子午位置相同 |
| 季节时 | temporal hour | 昼或夜的十二分之一 |
🧭 图解与讲解
杀位找到了,下一步是把距离换成年数。托勒密先批评通常的做法:不管释放之位在哪里,一律拿黄道各度的「上升时间」来算。他说这只在释放者就是东方地平、或是正在东方升起的行星时才对。按自然之理只有一种算法:算出要经过多少「赤道时度」,在后的那颗星(或那道相位光线)才来到降生那一刻在前者所在的位置;每一时度当一个太阳年。
〔图〕前位在哪一角,就用哪一种时间:上升用上升时间,中天用正球时间,下降用沉没时间
| 星座 | 正球上升时间(前位在中天用) | 下埃及上升时间(前位在上升用) | 下埃及沉没时间(前位在下降用) | 升起 |
|---|---|---|---|---|
| 白羊 | 27°50′ | 20°53′ | 34°47′ | 快 |
| 金牛 | 29°54′ | 24°12′ | 35°37′ | 快 |
| 双子 | 32°16′ | 29°54′ | 34°37′ | 快 |
| 巨蟹 | 32°16′ | 34°37′ | 29°54′ | 慢 |
| 狮子 | 29°54′ | 35°37′ | 24°12′ | 慢 |
| 处女 | 27°50′ | 34°47′ | 20°53′ | 慢 |
| 天秤 | 27°50′ | 34°47′ | 20°53′ | 慢 |
| 天蝎 | 29°54′ | 35°37′ | 24°12′ | 慢 |
| 射手 | 32°16′ | 34°37′ | 29°54′ | 慢 |
| 摩羯 | 32°16′ | 29°54′ | 34°37′ | 快 |
| 水瓶 | 29°54′ | 24°12′ | 35°37′ | 快 |
| 双鱼 | 27°50′ | 20°53′ | 34°47′ | 快 |
| 白羊+金牛 | 57°44′ | 45°05′ | 70°24′ | 第七单元算例的 58、46、70 |
「赤道时度」(equinoctial periods)据 Robbins 注,是天赤道上一度转过一个固定点所需的时间,即一昼夜的三百六十分之一,约合今天的四分钟;十五时度为一个「赤道时」(equinoctial hour),即今天的一小时。为什么用赤道?天球绕天轴均匀旋转,赤道上的度数均匀地经过地平与中天;黄道是斜的,各段经过的快慢不一。用赤道量,就是用天球旋转本身来计时,再以一时度折一年,这正是第三单元所说「主限」的根本。
于是看前位在哪里(图一):在东方地平上,用这段黄道的上升时间;在中天,用「正球」上的上升时间,正球指赤道上所见的天球,地平通过两极,其上升时间就是今天说的赤经差,也是这段黄道经过子午线所需的时间;在西方地平,用沉没时间,它等于与之相对各度的上升时间。表二列出下埃及(最长白昼十四小时)的这三种时间,可以看出同一座在三处所需的时度相差很大。
但前位若在这三处之间,三种时间都不对。托勒密因此给「相似之位」下定义:在同一方向上,相对于地平与子午线位置相同。他说,最接近这一要求的,是落在同一个「经过子午线与地平之交点所作的半圆」上的诸点,它们离子午线的季节时数几乎相同。十七世纪的普拉西德斯(Placidus)自称据这一章发展出以季节时划分宫位与推运的方法,后世称为普拉西德斯制。下一单元就是托勒密自己的通用算法。
📖 术语
| 术语 | 英译原词 | 意思 |
|---|---|---|
| 赤道时度 | equinoctial periods | 赤道一度转过所需时间 |
| 上升时间 | times of ascension | 一段黄道升起所需时度 |
| 正球 | right sphere | 赤道上所见的天球 |
| 相似之位 | similar place | 对地平子午位置相同 |
| 季节时 | temporal hour | 昼或夜的十二分之一 |
🧭 图解与讲解
杀位找到了,下一步是把距离换成年数。托勒密先批评通常的做法:不管释放之位在哪里,一律拿黄道各度的「上升时间」来算。他说这只在释放者就是东方地平、或是正在东方升起的行星时才对。按自然之理只有一种算法:算出要经过多少「赤道时度」,在后的那颗星(或那道相位光线)才来到降生那一刻在前者所在的位置;每一时度当一个太阳年。
| 星座 | 正球上升时间(前位在中天用) | 下埃及上升时间(前位在上升用) | 下埃及沉没时间(前位在下降用) | 升起 |
|---|---|---|---|---|
| 白羊 | 27°50′ | 20°53′ | 34°47′ | 快 |
| 金牛 | 29°54′ | 24°12′ | 35°37′ | 快 |
| 双子 | 32°16′ | 29°54′ | 34°37′ | 快 |
| 巨蟹 | 32°16′ | 34°37′ | 29°54′ | 慢 |
| 狮子 | 29°54′ | 35°37′ | 24°12′ | 慢 |
| 处女 | 27°50′ | 34°47′ | 20°53′ | 慢 |
| 天秤 | 27°50′ | 34°47′ | 20°53′ | 慢 |
| 天蝎 | 29°54′ | 35°37′ | 24°12′ | 慢 |
| 射手 | 32°16′ | 34°37′ | 29°54′ | 慢 |
| 摩羯 | 32°16′ | 29°54′ | 34°37′ | 快 |
| 水瓶 | 29°54′ | 24°12′ | 35°37′ | 快 |
| 双鱼 | 27°50′ | 20°53′ | 34°47′ | 快 |
| 白羊+金牛 | 57°44′ | 45°05′ | 70°24′ | 第七单元算例的 58、46、70 |
「赤道时度」(equinoctial periods)据 Robbins 注,是天赤道上一度转过一个固定点所需的时间,即一昼夜的三百六十分之一,约合今天的四分钟;十五时度为一个「赤道时」(equinoctial hour),即今天的一小时。为什么用赤道?天球绕天轴均匀旋转,赤道上的度数均匀地经过地平与中天;黄道是斜的,各段经过的快慢不一。用赤道量,就是用天球旋转本身来计时,再以一时度折一年,这正是第三单元所说「主限」的根本。
于是看前位在哪里(图一):在东方地平上,用这段黄道的上升时间;在中天,用「正球」上的上升时间,正球指赤道上所见的天球,地平通过两极,其上升时间就是今天说的赤经差,也是这段黄道经过子午线所需的时间;在西方地平,用沉没时间,它等于与之相对各度的上升时间。表二列出下埃及(最长白昼十四小时)的这三种时间,可以看出同一座在三处所需的时度相差很大。
但前位若在这三处之间,三种时间都不对。托勒密因此给「相似之位」下定义:在同一方向上,相对于地平与子午线位置相同。他说,最接近这一要求的,是落在同一个「经过子午线与地平之交点所作的半圆」上的诸点,它们离子午线的季节时数几乎相同。十七世纪的普拉西德斯(Placidus)自称据这一章发展出以季节时划分宫位与推运的方法,后世称为普拉西德斯制。下一单元就是托勒密自己的通用算法。
For after we have first determined the culminating degree of the zodiac and furthermore the degree of the precedent and that of the subsequent, in the first place we shall investigate the position of the precedent, how many ordinary hours it is removed from the meridian, counting the ascensions that properly intervene up to the very degree of mid‑heaven, whether over or under the earth, on the right sphere, and dividing them by the amount of the horary periods of the precedent degree, diurnal if it is above the earth and nocturnal if it is below.
But since the sections of the zodiac which are an equal number of ordinary hours removed from the meridian lie upon one and the same of the aforesaid semicircles, it will also be necessary to find after how many equinoctial periods the subsequent section will be removed from the same meridian by the same number of ordinary hours as the precedent.
When we have determined these, we shall inquire how many equinoctial hours at its original position the degree of the subsequent was removed from the degree at mid‑heaven, again by means of ascensions in the right sphere, and how many when it made the same number of ordinary hours as the precedent, multiplying these into the number of the horary periods of the degree of the subsequent; if again the comparison of the ordinary hours relates to the mid‑heaven above the earth, multiplying into the number of diurnal hours, but if it relates to that below the earth, the number of nocturnal hours. And taking the results from the difference of the two distances, we shall have the number of years for which the inquiry was made.
翻译点开
For after we have first determined the culminating degree of the zodiac and furthermore the degree of the precedent and that of the subsequent, in the first place we shall investigate the position of the precedent, how many ordinary hours it is removed from the meridian, counting the ascensions that properly intervene up to the very degree of mid‑heaven, whether over or under the earth, on the right sphere, and dividing them by the amount of the horary periods of the precedent degree, diurnal if it is above the earth and nocturnal if it is below.
我们先定出黄道上正过中天的那一度,再定出在前者与在后者的度数,然后首先考察在前者的位置:它离子午线有几个季节时;办法是数出到中天那一度为止、其间应有的正球上升时间,无论是地上的中天还是地下的中天,再除以在前那一度的时量,在地平以上用昼时的时量,在地平以下用夜时的时量。
But since the sections of the zodiac which are an equal number of ordinary hours removed from the meridian lie upon one and the same of the aforesaid semicircles, it will also be necessary to find after how many equinoctial periods the subsequent section will be removed from the same meridian by the same number of ordinary hours as the precedent.
既然黄道上离子午线季节时数相等的各段,都位于上述半圆中的同一个上,那么还必须求出:经过多少赤道时度,在后的那一段会与在前者一样,离同一条子午线相同数目的季节时。
When we have determined these, we shall inquire how many equinoctial hours at its original position the degree of the subsequent was removed from the degree at mid‑heaven, again by means of ascensions in the right sphere, and how many when it made the same number of ordinary hours as the precedent, multiplying these into the number of the horary periods of the degree of the subsequent; if again the comparison of the ordinary hours relates to the mid‑heaven above the earth, multiplying into the number of diurnal hours, but if it relates to that below the earth, the number of nocturnal hours. And taking the results from the difference of the two distances, we shall have the number of years for which the inquiry was made.
定出这些之后,我们要再借正球上的上升时间,求在后那一度在原来位置时离中天那一度有多少赤道时;又求它达到与在前者相同的季节时数时离中天多少,办法是把这些季节时数乘以在后那一度的时量;比较季节时若以地上的中天为准,就乘以昼时的时量,若以地下的中天为准,就乘以夜时的时量。取两段距离之差,就得到所要求的年数。
大意与图解点开
🔎 大意:通用算法:先求前位离子午线几个季节时,再求后位到同样季节时位置所需的赤道时度,两距之差即年数。
📖 术语
| 术语 | 英译原词 | 意思 |
|---|---|---|
| 季节时 | ordinary hours | 昼或夜的十二分之一 |
| 时量 | horary periods | 某度一季节时合几时度 |
| 在前者、在后者 | precedent, subsequent | 释放之位与杀位 |
| 中天之度 | culminating degree | 正过子午线的黄道度 |
| 子午线 | meridian | 过天顶的南北大圆 |
🧭 图解与讲解
本单元给出通用算法,前位无论在哪里都适用(图一)。第一步,定出正过中天的黄道度,以及前位、后位各自的度数。第二步,求前位离子午线几个季节时:数出它到中天那一度之间的正球上升时间(今天说的赤经差),除以前位那一度的「时量」。季节时(ordinary hours)是古人的计时法:把白昼、黑夜各分成十二等分,夏天的昼时长,冬天的昼时短;时量(horary periods)就是某一度上一个季节时合多少赤道时度。
〔图〕通用算法:以季节时定「相似之位」,以赤道时度量要走多远
〔图〕同是六个季节时到中天,两点的昼弧长短不同:相似之位要按各自的时量去量
时量怎么求?Robbins 注据《天文学大成》卷二第八、九章说明:查出该度在正球与本地的上升时间累计,取两者之差的六分之一;该度在赤道以北,就加到十五上,在赤道以南,就从十五中减去。所以在北方的纬度上,赤道以北诸度的时量大于十五,以南诸度小于十五,两分点恰为十五。前位在地平以上用昼时的时量,在地平以下用夜时的时量。
第三步,离子午线季节时数相同的点,落在同一个半圆上,也就是处在「相似之位」;所以要求后位到达与前位同样的季节时数时,离子午线多少赤道时度,即季节时数乘以后位的时量。第四步,用正球上升时间求后位原来离中天多少。两段距离一比,就是后位走过的赤道时度,也就是所求的年数;若两段分处子午线两侧,「差」实际是两者相加(见下一单元的第四例)。
图二把这个道理画成两条「昼弧」。前位白羊之首在天赤道上,每个季节时恰是十五时度,从升起到中天九十时度;后位双子之首在赤道以北,每个季节时约十七时度,半弧一百零二时度。同是「偏西三个季节时」,前位在中天以西四十五时度,后位却要到五十一时度。两点在钟面上并不对齐,这正是不能直接拿赤经差或上升时间来算的缘故。
📖 术语
| 术语 | 英译原词 | 意思 |
|---|---|---|
| 季节时 | ordinary hours | 昼或夜的十二分之一 |
| 时量 | horary periods | 某度一季节时合几时度 |
| 在前者、在后者 | precedent, subsequent | 释放之位与杀位 |
| 中天之度 | culminating degree | 正过子午线的黄道度 |
| 子午线 | meridian | 过天顶的南北大圆 |
🧭 图解与讲解
本单元给出通用算法,前位无论在哪里都适用(图一)。第一步,定出正过中天的黄道度,以及前位、后位各自的度数。第二步,求前位离子午线几个季节时:数出它到中天那一度之间的正球上升时间(今天说的赤经差),除以前位那一度的「时量」。季节时(ordinary hours)是古人的计时法:把白昼、黑夜各分成十二等分,夏天的昼时长,冬天的昼时短;时量(horary periods)就是某一度上一个季节时合多少赤道时度。
时量怎么求?Robbins 注据《天文学大成》卷二第八、九章说明:查出该度在正球与本地的上升时间累计,取两者之差的六分之一;该度在赤道以北,就加到十五上,在赤道以南,就从十五中减去。所以在北方的纬度上,赤道以北诸度的时量大于十五,以南诸度小于十五,两分点恰为十五。前位在地平以上用昼时的时量,在地平以下用夜时的时量。
第三步,离子午线季节时数相同的点,落在同一个半圆上,也就是处在「相似之位」;所以要求后位到达与前位同样的季节时数时,离子午线多少赤道时度,即季节时数乘以后位的时量。第四步,用正球上升时间求后位原来离中天多少。两段距离一比,就是后位走过的赤道时度,也就是所求的年数;若两段分处子午线两侧,「差」实际是两者相加(见下一单元的第四例)。
图二把这个道理画成两条「昼弧」。前位白羊之首在天赤道上,每个季节时恰是十五时度,从升起到中天九十时度;后位双子之首在赤道以北,每个季节时约十七时度,半弧一百零二时度。同是「偏西三个季节时」,前位在中天以西四十五时度,后位却要到五十一时度。两点在钟面上并不对齐,这正是不能直接拿赤经差或上升时间来算的缘故。
To make this clearer, suppose that the precedent place is the beginning of Aries, for example, and the subsequent the beginning of Gemini, and the latitude that where the longest day is fourteen hours long, and the horary magnitude of the beginning of Gemini is approximately 17 equinoctial times. Assume first that the beginning of Aries is rising, so that the beginning of Capricorn is at mid‑heaven, and let the beginning of Gemini be removed from the mid‑heaven above the earth 148 equinoctial times.
Now since the beginning of Aries is six ordinary hours removed from the diurnal mid‑heaven, multiplying these into the 17 equinoctial times, which are the times of the horary magnitude of the beginning of Gemini, since the distance of 148 times relates to the mid‑heaven above the earth, we shall have for this interval also 102 times. Hence, after 46 times, which is the difference, the subsequent place will pass to the position of the precedent.
These are very nearly the equinoctial times of the ascension of Aries and Taurus, since it is assumed that the prorogative sign is the horoscope.
Similarly, let the beginning of Aries be at mid‑heaven, so that at its original position the beginning of Gemini may be 58 equinoctial times removed from the mid‑heaven above the earth. Therefore, since at its second position the beginning of Gemini should be at mid‑heaven, we shall have for the difference of the distances precisely this amount of 58 times, in which again, because the prorogative sign is at mid‑heaven, Aries and Taurus pass through the meridian.
In the same way let the beginning of Aries be setting, so that the beginning of Cancer may be at mid‑heaven and the beginning of Gemini may be removed from the mid‑heaven above the earth in the direction of the leading signs by 32 equinoctial periods. Since, then, again the beginning of Aries is six ordinary hours removed from the meridian in the direction of the occident, if we multiply this by 17 we shall have 102 times, which will be the distance of the beginning of Gemini from the meridian when it sets.
At its first position also it was distant from the same point 32 times; hence it moved to the occident in the 70 times of the difference, in which period also Aries and Taurus descend and the opposite signs Libra and Scorpio ascend.
Now let it be assumed that the beginning of Aries is not on any of the angles, but removed, for example, three ordinary hours from the meridian in the direction of the leading signs, so that the 18th degree of Taurus is at mid‑heaven, and in its first position the beginning of Gemini is 13 equinoctial times removed from the mid‑heaven above the earth in the order of the following signs.
If, then, again we multiply 17 equinoctial times into the three hours, the beginning of Gemini will at its second position be distant from mid‑heaven in the direction of the leading signs 51 equinoctial times, and it will make in all 64 times. But it made 46 times by the same procedure when the prorogative place was rising, 58 when it was in mid‑heaven, and 70 when it was setting. Hence the number of equinoctial times at the position between mid‑heaven and the occident differs from each of the others.
For it is 64, and the difference is proportional to the excess of three hours, since this was 12 equinoctial times in the case of the other quadrants at the centres, but 6 equinoctial times in the case of the distance of three hours. And inasmuch as in all cases approximately the same proportion is observed, it will be possible to use the method in this simpler way.
翻译点开
To make this clearer, suppose that the precedent place is the beginning of Aries, for example, and the subsequent the beginning of Gemini, and the latitude that where the longest day is fourteen hours long, and the horary magnitude of the beginning of Gemini is approximately 17 equinoctial times. Assume first that the beginning of Aries is rising, so that the beginning of Capricorn is at mid‑heaven, and let the beginning of Gemini be removed from the mid‑heaven above the earth 148 equinoctial times.
为了说得更清楚,举例来说,假设在前之位是白羊之首,在后之位是双子之首,纬度是最长白昼为十四小时之处,双子之首的时量约为十七赤道时度。先假定白羊之首正在升起,于是摩羯之首在中天,而双子之首离地上的中天一百四十八赤道时度。
Now since the beginning of Aries is six ordinary hours removed from the diurnal mid‑heaven, multiplying these into the 17 equinoctial times, which are the times of the horary magnitude of the beginning of Gemini, since the distance of 148 times relates to the mid‑heaven above the earth, we shall have for this interval also 102 times. Hence, after 46 times, which is the difference, the subsequent place will pass to the position of the precedent.
既然白羊之首离白天的中天六个季节时,把这六时乘以十七赤道时度,也就是双子之首时量的时度数,因为一百四十八时度的距离是相对于地上的中天而言,这段间隔也就得一百零二时度。因此,经过两者之差四十六时度,在后之位就会移到在前之位的位置上。
These are very nearly the equinoctial times of the ascension of Aries and Taurus, since it is assumed that the prorogative sign is the horoscope.
这差不多正是白羊与金牛上升的赤道时度,因为已假定释放之座就是上升点。
Similarly, let the beginning of Aries be at mid‑heaven, so that at its original position the beginning of Gemini may be 58 equinoctial times removed from the mid‑heaven above the earth. Therefore, since at its second position the beginning of Gemini should be at mid‑heaven, we shall have for the difference of the distances precisely this amount of 58 times, in which again, because the prorogative sign is at mid‑heaven, Aries and Taurus pass through the meridian.
同样,设白羊之首在中天,于是双子之首在原来的位置上离地上的中天五十八赤道时度。既然双子之首在第二个位置上应当在中天,两段距离之差就恰好是这五十八时度;因为释放之座在中天,白羊与金牛也正是在这段时间里经过子午线。
In the same way let the beginning of Aries be setting, so that the beginning of Cancer may be at mid‑heaven and the beginning of Gemini may be removed from the mid‑heaven above the earth in the direction of the leading signs by 32 equinoctial periods. Since, then, again the beginning of Aries is six ordinary hours removed from the meridian in the direction of the occident, if we multiply this by 17 we shall have 102 times, which will be the distance of the beginning of Gemini from the meridian when it sets.
同理,设白羊之首正在沉没,于是巨蟹之首在中天,双子之首朝前导星座的方向离地上的中天三十二赤道时度。既然白羊之首又是朝西方离子午线六个季节时,把六乘以十七,便得一百零二时度,这就是双子之首沉没时离子午线的距离。
At its first position also it was distant from the same point 32 times; hence it moved to the occident in the 70 times of the difference, in which period also Aries and Taurus descend and the opposite signs Libra and Scorpio ascend.
它在第一个位置上离同一点三十二时度;所以它经过两者之差七十时度移到西方,在这段时间里,白羊与金牛也正好沉没,而与之相对的天秤与天蝎正好升起。
Now let it be assumed that the beginning of Aries is not on any of the angles, but removed, for example, three ordinary hours from the meridian in the direction of the leading signs, so that the 18th degree of Taurus is at mid‑heaven, and in its first position the beginning of Gemini is 13 equinoctial times removed from the mid‑heaven above the earth in the order of the following signs.
现在假定白羊之首不在任何一个角上,而是比如朝前导星座的方向离子午线三个季节时,于是金牛第十八度在中天,而双子之首在第一个位置上,顺着后随星座的次序离地上的中天十三赤道时度。
If, then, again we multiply 17 equinoctial times into the three hours, the beginning of Gemini will at its second position be distant from mid‑heaven in the direction of the leading signs 51 equinoctial times, and it will make in all 64 times. But it made 46 times by the same procedure when the prorogative place was rising, 58 when it was in mid‑heaven, and 70 when it was setting. Hence the number of equinoctial times at the position between mid‑heaven and the occident differs from each of the others.
那么,再把十七赤道时度乘以三时,双子之首在第二个位置上就朝前导星座的方向离中天五十一赤道时度,合计为六十四时度。而用同样的步骤,释放之位在升起时得四十六时度,在中天时得五十八,在沉没时得七十。可见在中天与西方之间的位置上,赤道时度之数与其余各处都不相同。
For it is 64, and the difference is proportional to the excess of three hours, since this was 12 equinoctial times in the case of the other quadrants at the centres, but 6 equinoctial times in the case of the distance of three hours. And inasmuch as in all cases approximately the same proportion is observed, it will be possible to use the method in this simpler way.
因为它是六十四,而这个差额与多出的三时成比例:在其他象限中,就各角而论,这差额是十二赤道时度,而在相距三时的情形中则是六赤道时度。既然在所有情形中大致都保持同样的比例,就可以用下面这种较简单的办法。
大意与图解点开
🔎 大意:算例:前位白羊之首、后位双子之首。前位在上升得四十六,在中天五十八,在下降七十,偏西三时得六十四。
📖 术语
| 术语 | 英译原词 | 意思 |
|---|---|---|
| 白羊之首 | beginning of Aries | 春分点,在赤道上 |
| 时量 | horary magnitude | 一季节时合几时度 |
| 最长白昼十四小时 | longest day fourteen hours | 下埃及的纬度 |
| 沉没 | setting | 在西方地平落下 |
| 角 | angles | 上升、中天、下降、天底 |
🧭 图解与讲解
托勒密用一个例子把算法走一遍(表二)。前位取白羊之首,即春分点,它正在天赤道上,每个季节时恰为十五时度;后位取双子之首;地点取最长白昼十四小时之处,Robbins 注说即下埃及的纬度;那里双子之首的时量约为十七赤道时度,照《天文学大成》的表算是十七又六分半。下面让前位依次处在上升、中天、下降、中天与下降之间,看后位到达相似之位要走多少时度。
〔图〕前位在上升:白羊之首推进到双子之首,黄道六十度,只合约四十六赤道时度
| 前位白羊之首在 | 中天之度 | 后位原离中天 | 后位到相似之位时离中天 | 后位走过(时度) | 恰好等于 |
|---|---|---|---|---|---|
| 上升 | 摩羯之首 | 东 148 | 东 6×17=102 | 148-102=46 | 白羊、金牛的上升时间(表:45°05′) |
| 中天 | 白羊之首 | 东 58 | 0(正在中天) | 58 | 白羊、金牛的正球上升时间(57°44′) |
| 下降 | 巨蟹之首 | 西 32 | 西 6×17=102 | 102-32=70 | 白羊、金牛的沉没时间(表:70°23′) |
| 中天以西三个季节时 | 金牛十八度 | 东 13 | 西 3×17=51 | 13+51=64 | 介于 58 与 70 正中 |
前位在上升:摩羯之首在中天,双子之首在中天以东一百四十八时度,尚未过中天。白羊之首离白天的中天六个季节时,所以双子之首到达同样的位置,也就是正在上升时,离中天六乘十七,即一百零二时度。两数之差四十六,就是所求。图一的动画画的就是这一段:从白羊之首推进到双子之首,黄道上六十度,折成时间只有四十六时度左右,正是白羊、金牛两座的上升时间,Robbins 注引《天文学大成》的表为四十五时度又五分。
前位在中天:双子之首在中天以东五十八时度,到中天时距离为零,差五十八,正是白羊、金牛的正球上升时间。前位在下降:巨蟹之首在中天,双子之首在中天以西三十二时度;它沉没时在中天以西一百零二时度,差七十,正是白羊、金牛的沉没时间,也就是天秤、天蝎的上升时间。在三个角上,通用算法与上一单元所说的三种现成时间完全相符。
关键是第四种情形:前位在中天以西三个季节时,金牛十八度在中天。双子之首原在中天以东十三时度,到达「偏西三个季节时」的相似之位时,在中天以西三乘十七,即五十一时度,合计六十四。六十四既不是五十八,也不是七十,恰在两者正中。托勒密指出,这个差与多出的三时成比例:相邻两角相差十二时度,三时是象限的一半,就差六时度。这就引出下一单元的简便法。
📖 术语
| 术语 | 英译原词 | 意思 |
|---|---|---|
| 白羊之首 | beginning of Aries | 春分点,在赤道上 |
| 时量 | horary magnitude | 一季节时合几时度 |
| 最长白昼十四小时 | longest day fourteen hours | 下埃及的纬度 |
| 沉没 | setting | 在西方地平落下 |
| 角 | angles | 上升、中天、下降、天底 |
🧭 图解与讲解
托勒密用一个例子把算法走一遍(表二)。前位取白羊之首,即春分点,它正在天赤道上,每个季节时恰为十五时度;后位取双子之首;地点取最长白昼十四小时之处,Robbins 注说即下埃及的纬度;那里双子之首的时量约为十七赤道时度,照《天文学大成》的表算是十七又六分半。下面让前位依次处在上升、中天、下降、中天与下降之间,看后位到达相似之位要走多少时度。
| 前位白羊之首在 | 中天之度 | 后位原离中天 | 后位到相似之位时离中天 | 后位走过(时度) | 恰好等于 |
|---|---|---|---|---|---|
| 上升 | 摩羯之首 | 东 148 | 东 6×17=102 | 148-102=46 | 白羊、金牛的上升时间(表:45°05′) |
| 中天 | 白羊之首 | 东 58 | 0(正在中天) | 58 | 白羊、金牛的正球上升时间(57°44′) |
| 下降 | 巨蟹之首 | 西 32 | 西 6×17=102 | 102-32=70 | 白羊、金牛的沉没时间(表:70°23′) |
| 中天以西三个季节时 | 金牛十八度 | 东 13 | 西 3×17=51 | 13+51=64 | 介于 58 与 70 正中 |
前位在上升:摩羯之首在中天,双子之首在中天以东一百四十八时度,尚未过中天。白羊之首离白天的中天六个季节时,所以双子之首到达同样的位置,也就是正在上升时,离中天六乘十七,即一百零二时度。两数之差四十六,就是所求。图一的动画画的就是这一段:从白羊之首推进到双子之首,黄道上六十度,折成时间只有四十六时度左右,正是白羊、金牛两座的上升时间,Robbins 注引《天文学大成》的表为四十五时度又五分。
前位在中天:双子之首在中天以东五十八时度,到中天时距离为零,差五十八,正是白羊、金牛的正球上升时间。前位在下降:巨蟹之首在中天,双子之首在中天以西三十二时度;它沉没时在中天以西一百零二时度,差七十,正是白羊、金牛的沉没时间,也就是天秤、天蝎的上升时间。在三个角上,通用算法与上一单元所说的三种现成时间完全相符。
关键是第四种情形:前位在中天以西三个季节时,金牛十八度在中天。双子之首原在中天以东十三时度,到达「偏西三个季节时」的相似之位时,在中天以西三乘十七,即五十一时度,合计六十四。六十四既不是五十八,也不是七十,恰在两者正中。托勒密指出,这个差与多出的三时成比例:相邻两角相差十二时度,三时是象限的一半,就差六时度。这就引出下一单元的简便法。
For again, when the precedent degree is at rising, we shall employ the ascensions up to the subsequent; if it is at mid‑heaven, the degrees on the right sphere; and if it is setting, the descensions. But when it is between these points, for example, at the aforesaid interval from Aries, we shall take first the equinoctial times corresponding to each of the surrounding angles, and we shall find, since the beginning of Aries was assumed to be beyond the mid‑heaven above the earth, between mid‑heaven and the occident, that the corresponding equinoctial times up to the first of Gemini from mid‑heaven are 58 and from the occident 70.
Next let us ascertain, as was set forth above, how many ordinary hours the precedent section is removed from either of the angles, and whatever fraction they may be of the six ordinary hours of the quadrant, that fraction of the difference between both sums we shall add to or subtract from the angle with which comparison is made.
For example, since the difference between the above mentioned 70 and 58 is 12 times, and it was assumed that the precedent place was removed by an equal number of ordinary hours, three, from each of the angles, which are one half of the six hours, then taking also one-half of the 12 equinoctial times and either adding them to the 58 or subtracting them from the 70, we shall find the result to be 64 times.
But if it was removed two ordinary hours from either one of the angles, which are one-third of the six hours, again we shall take one-third of the 12 times of the excess, that is, 4, and if the removal by two hours had been assumed to be from the mid‑heaven, we would have added them to the 58 times, but if it was measured from the occident we would have subtracted them from 70.
The method of ascertaining the amount of the temporal intervals ought in this way consistently to be followed. For the rest, we shall determine in each of the aforesaid cases of approach or setting, in the order of those that ascend more rapidly, those which are destructive, climacteric, or otherwise transitional, according as the meeting is afflicted or assisted in the way we have already explained, and by means of the particular significance of the predictions made from the temporal ingresses of the meeting.
For when at the same time the places are afflicted and the transit of the stars relative to the ingress of the years of life afflicts the governing places, we must understand that death is definitely signified; if one of them is benignant, great and dangerous crises; if both are benignant, only sluggishness, injuries, or transitory disasters. In these matters the special quality is ascertained from the familiarity of the occurrent places with the circumstances of the nativity.
Sometimes, when it is doubtful which ought to take over the destroying power, there is nothing to prevent our calculating the occourses of each and then either following, in predicting the future, the occourses which most agree with past events, or observing them all, as having equal power, determining as before the question of their degree.
翻译点开
For again, when the precedent degree is at rising, we shall employ the ascensions up to the subsequent; if it is at mid‑heaven, the degrees on the right sphere; and if it is setting, the descensions. But when it is between these points, for example, at the aforesaid interval from Aries, we shall take first the equinoctial times corresponding to each of the surrounding angles, and we shall find, since the beginning of Aries was assumed to be beyond the mid‑heaven above the earth, between mid‑heaven and the occident, that the corresponding equinoctial times up to the first of Gemini from mid‑heaven are 58 and from the occident 70.
也就是说,在前那一度在升起时,我们用到在后者为止的上升时间;在中天时,用正球上的度数;在沉没时,用沉没时间。而当它在这些点之间时,比如在上面所说那个离白羊的间隔上,我们先取相邻两角各自对应的赤道时度;由于已假定白羊之首过了地上的中天、在中天与西方之间,我们会发现到双子第一度为止的对应赤道时度,从中天算是五十八,从西方算是七十。
Next let us ascertain, as was set forth above, how many ordinary hours the precedent section is removed from either of the angles, and whatever fraction they may be of the six ordinary hours of the quadrant, that fraction of the difference between both sums we shall add to or subtract from the angle with which comparison is made.
接着,照上面所说,查明在前的那一段离两角各有几个季节时;它们占象限六个季节时的几分之几,我们就取两个总数之差的几分之几,加到或减去作比较的那一角的数上。
For example, since the difference between the above mentioned 70 and 58 is 12 times, and it was assumed that the precedent place was removed by an equal number of ordinary hours, three, from each of the angles, which are one half of the six hours, then taking also one-half of the 12 equinoctial times and either adding them to the 58 or subtracting them from the 70, we shall find the result to be 64 times.
例如,上面所说的七十与五十八之差是十二时度,又假定在前之位离两角各有相等的季节时数,即三时,是六时的一半;那么也取十二赤道时度的一半,或加到五十八上,或从七十减去,都会得到六十四时度。
But if it was removed two ordinary hours from either one of the angles, which are one-third of the six hours, again we shall take one-third of the 12 times of the excess, that is, 4, and if the removal by two hours had been assumed to be from the mid‑heaven, we would have added them to the 58 times, but if it was measured from the occident we would have subtracted them from 70.
但如果它离其中一角两个季节时,即六时的三分之一,我们就同样取差额十二时度的三分之一,即四;若假定这两时是从中天算起的,就把四加到五十八时度上;若是从西方量起的,就从七十中减去。
The method of ascertaining the amount of the temporal intervals ought in this way consistently to be followed. For the rest, we shall determine in each of the aforesaid cases of approach or setting, in the order of those that ascend more rapidly, those which are destructive, climacteric, or otherwise transitional, according as the meeting is afflicted or assisted in the way we have already explained, and by means of the particular significance of the predictions made from the temporal ingresses of the meeting.
求时间间隔长短的方法,应当始终照此进行。其余的,在上述每一种趋近或沉没的情形中,我们要按升起较快者的次序,判定哪些是致死的、哪些是关口、哪些是其他的转折,依据是会合按我们已经讲过的方式受损还是得助,以及由会合在时间上的进入所作预言的特定含义。
For when at the same time the places are afflicted and the transit of the stars relative to the ingress of the years of life afflicts the governing places, we must understand that death is definitely signified; if one of them is benignant, great and dangerous crises; if both are benignant, only sluggishness, injuries, or transitory disasters. In these matters the special quality is ascertained from the familiarity of the occurrent places with the circumstances of the nativity.
因为当诸位同时受损,而诸星相对于寿年之进入的行经又伤害主管之位时,就应理解为明确预示死亡;若其中一方是吉的,就是重大而危险的危机;若两方都是吉的,就只是迟滞、损伤或短暂的灾祸。在这些事情上,具体的性质要从所遇诸位与本命情形的亲缘来判定。
Sometimes, when it is doubtful which ought to take over the destroying power, there is nothing to prevent our calculating the occourses of each and then either following, in predicting the future, the occourses which most agree with past events, or observing them all, as having equal power, determining as before the question of their degree.
有时,当难以确定该由哪一个承担致死之力时,不妨把每一个的会遇都算出来,然后在预言未来时,要么依从与过去之事最相符的那些会遇,要么把它们都当作同等有力而一并观察,照前面的方法判定它们的程度。
大意与图解点开
🔎 大意:简便法按离角的季节时数比例插值;再看会合与行经:皆凶主死,一吉为大险,皆吉只是小灾;拿不准时以往事校验。
📖 术语
| 术语 | 英译原词 | 意思 |
|---|---|---|
| 关口 | climacteric | 危险的转折之年 |
| 行经 | transit | 诸星后来经过 |
| 会遇 | occourses | 后位与前位相遇 |
| 主管之位 | governing places | 主管寿数的诸位 |
🧭 图解与讲解
由此托勒密给出简便法(图一):前位在上升,用到后位为止的上升时间;在中天,用正球上的度数;在下降,用沉没时间;在两角之间,先求出相邻两角各自对应的时度,再看前位离其中一角几个季节时,占象限六个季节时的几分之几,就把两角之差取同样的几分之几,加到或减去作比较的那一角上。这就是线性插值。
〔图〕两角之间按季节时比例插值:离中天每多一时,加十二时度的六分之一
| 会合本身 | 到那一年时诸星的行经 | 书中所断 |
|---|---|---|
| 受损(凶) | 伤害主管之位(凶) | 明确预示死亡 |
| 得助(吉) | 伤害主管之位(凶) | 重大而危险的危机 |
| 受损(凶) | 不伤害(吉) | 重大而危险的危机 |
| 得助(吉) | 不伤害(吉) | 只是迟滞、损伤或短暂的灾祸 |
例子仍是双子之首:前位在中天与西方之间,中天对应五十八,西方对应七十,差十二。离两角各三时,是一半,取十二的一半即六,五十八加六或七十减六,都得六十四,与上一单元用通用算法算出的完全一样。离中天二时,是三分之一,取四,五十八加四得六十二;离西方二时,七十减四得六十六。托勒密说各处大致保持同样的比例,所以这样插值就够了。
时间算出之后,还要判断每一次会合的性质(表二)。对上述每一种趋近(顺序释放)或沉没(逆序释放),按到达的先后次序,分出致死的、「关口」(climacteric,危险的转折之年)、其他的转折。依据有两样:会合本身是否按前面讲的方式受损或得助;到那一年时,诸星的行经(transit)是否又伤害主管之位。两者都凶,明确预示死亡;一方为吉,是重大而危险的危机;两方皆吉,只是迟滞、损伤或短暂的灾祸。具体是什么事,要看所遇诸位与本命的亲缘。
最后一句很见托勒密的态度:拿不准该由哪一个当杀者时,不妨把每一个的会遇都算出来,预言时依从与过去之事最相符的那些,或者把它们都当作同样有力,一并观察。也就是说,这套方法要拿当事人已经发生的事来校验。Robbins 注指出,按年份推算行经与时主的细节,见卷四第十章;死亡的方式则另见卷四第九章。
全章到此结束。需要再说一遍:这是二世纪亚历山大里亚的古代学说,记录古人如何把天球的旋转换算成人生的年数;本站只讲解书中的方法与推理,不据此对任何人作寿命断语。从学术史看,本章的价值在于托勒密坚持用天球旋转的实际时间来量度,不肯沿用通行的粗略算法,后世的「主限」推运即由此而来。
📖 术语
| 术语 | 英译原词 | 意思 |
|---|---|---|
| 关口 | climacteric | 危险的转折之年 |
| 行经 | transit | 诸星后来经过 |
| 会遇 | occourses | 后位与前位相遇 |
| 主管之位 | governing places | 主管寿数的诸位 |
🧭 图解与讲解
由此托勒密给出简便法(图一):前位在上升,用到后位为止的上升时间;在中天,用正球上的度数;在下降,用沉没时间;在两角之间,先求出相邻两角各自对应的时度,再看前位离其中一角几个季节时,占象限六个季节时的几分之几,就把两角之差取同样的几分之几,加到或减去作比较的那一角上。这就是线性插值。
| 会合本身 | 到那一年时诸星的行经 | 书中所断 |
|---|---|---|
| 受损(凶) | 伤害主管之位(凶) | 明确预示死亡 |
| 得助(吉) | 伤害主管之位(凶) | 重大而危险的危机 |
| 受损(凶) | 不伤害(吉) | 重大而危险的危机 |
| 得助(吉) | 不伤害(吉) | 只是迟滞、损伤或短暂的灾祸 |
例子仍是双子之首:前位在中天与西方之间,中天对应五十八,西方对应七十,差十二。离两角各三时,是一半,取十二的一半即六,五十八加六或七十减六,都得六十四,与上一单元用通用算法算出的完全一样。离中天二时,是三分之一,取四,五十八加四得六十二;离西方二时,七十减四得六十六。托勒密说各处大致保持同样的比例,所以这样插值就够了。
时间算出之后,还要判断每一次会合的性质(表二)。对上述每一种趋近(顺序释放)或沉没(逆序释放),按到达的先后次序,分出致死的、「关口」(climacteric,危险的转折之年)、其他的转折。依据有两样:会合本身是否按前面讲的方式受损或得助;到那一年时,诸星的行经(transit)是否又伤害主管之位。两者都凶,明确预示死亡;一方为吉,是重大而危险的危机;两方皆吉,只是迟滞、损伤或短暂的灾祸。具体是什么事,要看所遇诸位与本命的亲缘。
最后一句很见托勒密的态度:拿不准该由哪一个当杀者时,不妨把每一个的会遇都算出来,预言时依从与过去之事最相符的那些,或者把它们都当作同样有力,一并观察。也就是说,这套方法要拿当事人已经发生的事来校验。Robbins 注指出,按年份推算行经与时主的细节,见卷四第十章;死亡的方式则另见卷四第九章。
全章到此结束。需要再说一遍:这是二世纪亚历山大里亚的古代学说,记录古人如何把天球的旋转换算成人生的年数;本站只讲解书中的方法与推理,不据此对任何人作寿命断语。从学术史看,本章的价值在于托勒密坚持用天球旋转的实际时间来量度,不肯沿用通行的粗略算法,后世的「主限」推运即由此而来。
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。