古代附录（三）　次分配的简算与两小时段

And it has given much proof of itself, being well approved in inceptions and not going astray even slightly regarding persons or affairs. This first method of sub-allotment, which is also found in Valens, is simple and more true, not bringing in fractions of months and days, which they do not take by an exact reckoning either. But if we are to take everything by the same reckoning, we must take 1/5, 1/30, and 1/360 of each one's period of months, and, having found it in agreement with each one's second sub-allotment, convert the 1/5, 1/30, and 1/360 again for multiplication; for multiplying is easier than dividing. For example, in the case of Saturn, a fifth of the 900 days or of the 30 months is 180 days, or six months, which are again 180 days. For whatever fraction the days are of the days, the same are the months of the months; likewise the thirtieth, whether of the 900 days, which is 30 days, or of the 30 months, which is months, again 30 days; for since the number of days of each planet is thirty times the number of months, it is clear that, as 1/30 of each month is one day, so 1/30 of the 30 months is 30 days and of the 12 months 12 days; and in general each planet's days are equal in number to its months, being a thirtieth of each one's months. And since the fifth too is the same both for each one's days and for its months (for example, of Jupiter's 360 days 72 days, and of his 12 months 2 1/3 1/15, which is again 72 days; and of Mars's 450 days 90 days, and of his 15 months a fifth is 3 months, which is again 90 days; and also of the Sun's 570 a fifth is 114, and of his 19 months, months 3 2/3 1/10 1/30, which is again 114 days [corrected: Kroll prints 48]; and of Mercury likewise, of the 600 days or 20 months, a fifth is 120 days or 4 months, again 120 days; and likewise for the Moon, of the 750 days or 25 months a fifth is 150 days or 5 months), since, then, the fifth of the days is the same as the fifth of the months, and the fifth of the number of months contains the fifth of each month, which is 6 days, and the 6 days are six times the one day, it is clear that however many months each has, multiplied by six, will make as many days as the fifth made. So that we may take it more easily, then, multiplying each one's months by six we shall have each one's days. For example, Saturn's 30 six times make again the same 180 days, Jupiter's 12 six times 72, Mars's 15 six times make 90, the Sun's 19 six times make 114, Venus's 8 six times make 48; Mercury's 20 six times 120, the Moon's 25 six times make 150; and from the 1/30, without multiplication, we shall take the days equal in number to each one's months. For of Saturn's 30 months, say, the 1/30 is 30 days, and of Jupiter's 12 months the 1/30 is 12 days, and likewise for the others.

它也已大大证明了自己，在起事上得到充分认可，在人或事上丝毫不会走错。这第一种次分配的方法，在瓦伦斯那里也能找到，简单而更真实，不带进月与日的分数，那些分数他们也不是按精确的计算来取的。但若我们要按同一种计算来取一切，就必须取每颗星的月的时期的五分之一、三十分之一与三百六十分之一，在发现它与每颗星的第二次次分配相合之后，再把五分之一、三十分之一与三百六十分之一转换回来用于乘法；因为乘比除容易。例如，就土星而言，九百日或三十个月的五分之一是一百八十日，或六个月，又是一百八十日。因为日是日的几分之几，月也就是月的几分之几；三十分之一同样，无论是九百日的，即三十日，还是三十个月的，即若干个月，又是三十日；因为既然每颗行星的日数是月数的三十倍，显然，正如每个月的三十分之一是一日，三十个月的三十分之一是三十日，十二个月的是十二日；总的说来，每颗行星的日数与它的月数在数目上相等，作为每颗星的月的三十分之一。既然五分之一对每颗星的日与月也相同（例如，木星的三百六十日的是七十二日，他的十二个月的是二又三分之一又十五分之一，又是七十二日；火星的四百五十日的是九十日，他的十五个月的五分之一是三个月，又是九十日；太阳的五百七十的五分之一是一百一十四，他的十九个月的是三又三分之二又十分之一又三十分之一个月，又是一百一十四日〔据算改正：Kroll 本作四十八日〕；水星同样，六百日或二十个月的五分之一是一百二十日或四个月，又是一百二十日；月亮同样，七百五十日或二十五个月的五分之一是一百五十日或五个月），所以，既然日的五分之一与月的五分之一相同，而月数的五分之一包含每个月的五分之一，即六日，六日又是一日的六倍，显然，每颗星有多少个月，乘以六，就会得出五分之一所得的那么多日。所以为了取得更容易，把每颗星的月数乘以六，我们就会得到每颗星的日数。例如，土星的三十的六倍又得同样的一百八十日，木星的十二的六倍七十二，火星的十五的六倍得九十，太阳的十九的六倍得一百一十四，金星的八的六倍得四十八；水星的二十的六倍一百二十，月亮的二十五的六倍得一百五十；而从三十分之一，不用乘法，我们就会取得与每颗星的月数相等的日数。因为比如说，土星三十个月的三十分之一是三十日，木星十二个月的三十分之一是十二日，其余也一样。

It remains that the 1/360 is awkward to grasp; it is, for Saturn's 900, 2½; for Jupiter's 360, 1; for Mars's 450, 1¼; for the Sun's 570, 1½ 1/12; for Venus's 240, ½ 1/6; for Mercury's 600, 1½ 1/6; for the Moon's 750, 2 1/12. We shall therefore convert this fraction 1/360 too into something nearer and easier; for since the number of the months is 1/30 of the number of the days contained in them (for what fraction one is of 30, that 12 is of 360 [corrected: Kroll prints 60] and 3 of 90, and in general their number is of that of the days), conversely, then, the number of the days is thirty times the number of the months; so that even if I take some other fraction of the months instead of the 1/30, thirty times the fraction taken will be a fraction of a day. Since, then, 1/360 of the days is thirty times 1/12 of the months (for thirty times 12 makes 360), if we take 1/12 of each one's months, it will be the same as 1/360 of the days. And 1/12 of Saturn's 30 months is 2½, which is 1/360 of his 900 days; of Jupiter's 12 months it is 1, which again is 1/360 of his 360 days; and of Mars's 15 the 1/12 is 1¼, which is 1/360 of his 450 days; and likewise for the others.

剩下的是三百六十分之一不便把握；它对土星的九百是二又二分之一；对木星的三百六十是一；对火星的四百五十是一又四分之一；对太阳的五百七十是一又二分之一又十二分之一；对金星的二百四十是二分之一又六分之一；对水星的六百是一又二分之一又六分之一；对月亮的七百五十是二又十二分之一。所以我们也要把这个三百六十分之一的分数转换成更近、更容易的东西；因为既然月数是其中所含日数的三十分之一（因为一是三十的几分之几，十二就是三百六十的几分之几〔据算改正：Kroll 本作六十〕，三是九十的几分之几，总之它们的数是日数的几分之几），那么反过来，日数就是月数的三十倍；所以即使我取月的另一个分数代替三十分之一，所取分数的三十倍就是一日的分数。所以，既然日的三百六十分之一是月的十二分之一的三十倍（因为三十乘十二得三百六十），若我们取每颗星月数的十二分之一，它就与日的三百六十分之一相同。土星三十个月的十二分之一是二又二分之一，这是他九百日的三百六十分之一；木星十二个月的是一，这又是他三百六十日的三百六十分之一；火星十五的十二分之一是一又四分之一，这是他四百五十日的三百六十分之一；其余也一样。

Therefore instead of 1/360 of the days we shall take 1/12 of the months; and if one further converts this into the 24 hours of the day and night by multiplying, he will find Saturn's 2½ to be 60 hours, which make 30 two-hour periods, equal in number to his months and his days; Jupiter's 1, 24 hours, and 12 two-hour periods, as many as Jupiter's months and days; Mars's 1¼, 30 hours, and clearly fifteen two-hour periods, as many as Mars's days and months; the Sun's 1½ 1/12, which makes 38 hours, and 19 two-hour periods, equal in number to his days and months; Venus's two-thirds makes 16 hours, 8 two-hour periods, which are equal in number to her 8 days and her months; likewise Mercury's 1½ 1/6 days make 40 hours, and 20 two-hour periods, equal in number to his 20 days and 20 months; and the Moon's 2 1/12 days, being 50 hours, are 25 two-hour periods, as many as her days and her months.

所以我们将取月的十二分之一来代替日的三百六十分之一；若再有人把它乘成昼夜的二十四小时，他就会发现土星的二又二分之一是六十小时，合三十个两小时段，与他的月数与日数相等；木星的一，二十四小时，十二个两小时段，与木星的月数与日数一样多；火星的一又四分之一，三十小时，显然十五个两小时段，与火星的日数与月数一样多；太阳的一又二分之一又十二分之一，合三十八小时，十九个两小时段，与他的日数与月数相等；金星的三分之二合十六小时，八个两小时段，与她的八日与她的月数相等；水星的一又二分之一又六分之一日同样合四十小时，二十个两小时段，与他的二十日与二十个月相等；月亮的二又十二分之一日，是五十小时，二十五个两小时段，与她的日数与月数一样多。

Since, then, when each one's number of months is resolved into days, the fifth was shown to be six times the number of the months, and the thirtieth equal to the number of the months, clearly the fifth and the thirtieth of each together will be seven times the same number; for example, for Saturn the fifth of the 900 is 180, which is six times the 30, and the 1/30 is 30; the 210, then, are seven times the 30, which is the number of Saturn's months; and for Jupiter the 72 and the 12, which make 84, are seven times the 12; and likewise for the others. Since, then, each is lord not only of his months of return but also of days seven times the number of the months, it is clear that, when these must be assigned to the 7 planets, giving to each of the others as much as he grants himself, he will leave nothing but the 1/60 [text uncertain], which has itself been shown to consist of two-hour periods equal in number to each one's months. Let it be, then, that by this procedure too we find which planets hold the given period. Let there be 18 years, 4 months, and 13 days [corrected: Kroll prints 88 years]; and let the Moon, as was said before, take the first decennial, of 129 months out of the 220; there remain 91 of the 2nd decennial; next to the Moon let Mars lie, lord of the 2nd decennial. Since, then, it is not complete, he will give himself 15 months; after him to Mercury 20 months; after him to Jupiter 12 months; after him to Venus 8; after her to Saturn 30 months; after him the Sun will have the remaining 6 months and 13 days, so that there are 193 days; for since the Sun does not have complete months on account of the given period, the incomplete ones must be resolved into the 193 days; of these the Sun gives himself, by this method, 163 days; after him the Moon, since she cannot take her complete days, the 175, takes the 30 as incomplete and will resolve them into 720 hours, of 360 two-hour periods; of these she gives herself 25, then to Mars 15, to Mercury 20, to Jupiter 12, to Venus 8, to Saturn 30, to the Sun 19. Then, after 129 two-hour periods, beginning again from herself she gives another 129 two-hour periods, and the remaining 102; again beginning from herself she gives to those in order, and 22 will be left, of which Saturn is master, since he is master of up to 30 two-hour periods. Of the second decennial, then, Mars will be lord, of the months the Sun, of the days the Moon, and of the hours Saturn, of the 44; for the 22 two-hour periods must be resolved into hours. And the division is of months, the sub-division of days, and the sub-division of hours. The changes of each day are clearly signified by the planet that is in transit and governs. One must examine what entries and configurations the lords of the decennials, months, and days have; for if regarded harmoniously by beneficent places or planets they will show the planets accordingly, and if by opposing ones, in the opposite way.

所以，既然当每颗星的月数化成日时，已表明五分之一是月数的六倍，三十分之一与月数相等，显然每颗星的五分之一与三十分之一合起来就是同一个数的七倍；例如对土星，九百的五分之一是一百八十，这是三十的六倍，三十分之一是三十；所以二百一十是三十的七倍，三十是土星的月数；对木星，七十二与十二，合八十四，是十二的七倍；其余也一样。所以，既然每颗星不仅是他回归的月数之主，也是月数七倍的日数之主，显然，当这些必须分给七颗行星时，给其他每一颗与他给自己一样多，他除了六十分之一〔原文疑有讹误〕之外就什么也不剩，而这已表明本身由与每颗星月数相等的两小时段组成。那么就让我们也用这个程序找出哪些行星掌管所给的时期。设为十八年四个月十三日〔据算改正：Kroll 本作八十八年〕；让月亮如前所说取第一个十年期，即二百二十个月中的一百二十九个月；余下第二个十年期的九十一个；设火星排在月亮之后，是第二个十年期之主。既然它没有满，他就会给自己十五个月；在他之后给水星二十个月；在他之后给木星十二个月；在他之后给金星八个；在她之后给土星三十个月；在他之后太阳将有余下的六个月十三日，所以有一百九十三日；因为既然由于所给的时期，太阳没有完整的月，不完整的就必须化成一百九十三日；其中太阳按这个方法给自己一百六十三日；在他之后月亮，既然她取不到她完整的日数一百七十五，就取那三十作为不完整的，并将把它们化成七百二十小时，即三百六十个两小时段；其中她给自己二十五，然后给火星十五，给水星二十，给木星十二，给金星八，给土星三十，给太阳十九。然后，在一百二十九个两小时段之后，她又从自己开始，给出另外一百二十九个两小时段，与余下的一百零二个；她又从自己开始，依次给出，将剩下二十二个，土星是它们的主人，因为他是到三十个两小时段为止的主人。所以第二个十年期的主将是火星，诸月之主是太阳，诸日之主是月亮，诸时之主是土星，四十四小时的；因为二十二个两小时段必须化成小时。这划分是月的，次划分是日的，再次划分是时的。每一天的变化，由正在行运并主管的那颗行星清楚地表示。必须查看十年期、诸月与诸日之主有什么样的进入与格局；因为若它们受吉祥的位置或行星和谐地照看，就会相应地显示诸行星，若受对立的照看，就以相反的方式显示。