卷一·第十六至十九章　手算月交点、月亮的阶与风、求月之法

XVI. To Find the Ascending Node by Hand.

第十六章　手算升交点

To find the ascending node by hand: take the full years from Augustus and multiply them by 19 1/3, and add 1° 35′ for each Egyptian month and 3′ for each day [corrected: Kroll prints 1 1/5 1/35 of a degree and 1/5 1/3]; having added these together, subtract 360 at a time from the first numbers [text uncertain]. Count off the remaining number in the upward direction from Cancer, giving 30 to each sign; and wherever it ends, there the ascending node will be. For example, year 4 of Hadrian, Phamenoth 19: the full years from Augustus are 148; these multiplied by 19 1/3 make 2862; and from Thoth to Phamenoth 10 degrees are collected; together they make 2872. From these I take out 7 circles of 360 each; 352 remain. These I count in the upward direction from Cancer; the count ends at Leo 8°. There, then, will be the ecliptic place, and the descending node will be in the opposite degree.

用手算求升交点：取从奥古斯都起的满年，乘以十九又三分之一，每个埃及月加一度三十五分，每日加三分〔据算改正：Kroll 本作一又五分之一又三十五分之一度、五分之一又三分之一〕；把这些加在一起后，从最初的数中每次减去三百六十〔原文疑有讹误〕。把剩下的数从巨蟹起向上数去，每个星座给三十；数止于哪里，升交点就在那里。例如，哈德良第四年法梅诺特月十九日：从奥古斯都起的满年是一百四十八；乘以十九又三分之一得二千八百六十二；从托特月到法梅诺特月共积得十度；合计二千八百七十二。我从中去掉七个三百六十度的整圈；余三百五十二。我把这些从巨蟹起向上数去；数止于狮子八度。那么交食之位就在那里，降交点在对面那一度。

It will be necessary, then, to examine whether there are benefics in these places, and above all at the ascending node; for the nativity will be well-off and active, and even if it is found to be middling or in decline, it will be raised up and come into glory. The malefics, however, bring about downfalls and accusations. From the lunar epochs and the daily motions the ascending node and the sign of the latitude are found thus. For example, in the nativity set out above, year 4 of Hadrian, Phamenoth 19, from the epoch to the day of birth there are 204 days. Beside the epoch stand 12°18' of latitude, and beside the 204 days 11°37' of latitude; together 23°55'. These multiplied by 15 make 358°45'. I count off from Leo in the order of the signs; the count ends at Cancer 28°45'.

所以必须查看这些位置上有没有吉星，尤其是在升交点上；因为本命将会富足而有作为，即使它显得中等或在衰落之中，也会被抬举起来，进入荣耀。凶星却带来失势与控告。由月亮的历元与日行表，可这样求得升交点与黄纬星座。例如，在上面列出的本命里，哈德良第四年法梅诺特月十九日，从历元到出生之日有二百零四日。历元旁列着黄纬十二度十八分，二百零四日旁列着黄纬十一度三十七分；合计二十三度五十五分。乘以十五得三百五十八度四十五分。我从狮子起按星座次序数去；数止于巨蟹二十八度四十五分。

XVII. Another, Shorter Way.

第十七章　另一种较短的算法

I count off the 23°55' from Leo, giving 2 to each sign; up to Gemini they make 22, and 1°55' remain. These I multiply by 15: they make Cancer 28°45'. Then I always take 1 degree for each sign from Taurus up to the degree where the count fell out: they make about 89. These I count back from the Moon's degree, which is Scorpio 7°; the ascending node ends at Leo 8°. In this way it will be necessary to examine the other nativities as well. And if I wish to learn the sign of the latitude too, I shall proceed thus. I multiply only the 12°18' of latitude that stand beside the epoch by 15: they make 184°30'. I count off from Leo: the count ends at Aquarius 4°30'. Then I multiply by 15 the 11°37' of latitude that stand in the daily table beside the 204 days: they make 174°15'. Adding to these the 4°30' of Aquarius, I counted off from that sign: the count ended at Cancer 28°45'. In this way we shall find the sign of the latitude for the other epochs as well.

我把二十三度五十五分从狮子数起，每个星座给二；到双子共二十二，余一度五十五分。我把它们乘以十五：得巨蟹二十八度四十五分。然后我总是从金牛起，每个星座取一度，直到数落出的那一度：约得八十九。我把这些从月亮的那一度，即天蝎七度，往回数；升交点止于狮子八度。其他本命也必须这样查看。如果我也想得知黄纬星座，就这样做。我只把历元旁列着的黄纬十二度十八分乘以十五：得一百八十四度三十分。我从狮子数起：数止于水瓶四度三十分。然后我把日行表中二百零四日旁列着的黄纬十一度三十七分乘以十五：得一百七十四度十五分。在这上面加上水瓶的四度三十分，我从那个星座数起：数止于巨蟹二十八度四十五分。用这个办法，我们也能求得其他历元的黄纬星座。

XVIII. On Finding the Steps and Winds of the Moon.

第十八章　论求月亮的阶与风

We shall find the step and the wind thus. From Leo to Libra the Moon descends in the north; from Scorpio to Capricorn she descends in the south; from Aquarius to Aries she ascends in the south; and from Taurus to Cancer she ascends in the north. The steps are found thus. Since each step is of 15 degrees, and the sign occupies 30 degrees, each single sign will contain 2 steps. Making the release of the latitude from Leo, then, we shall find the step. Since, then, in the nativity set out above the latitude was found to be 23°55', counting off from Leo 2 degrees for each sign we shall find Cancer 1°55'. We learned that the Moon is ascending in the north at about the sixth step of the wind.

我们这样求得阶与风。月亮从狮子到天秤在北方下降；从天蝎到摩羯在南方下降；从水瓶到白羊在南方上升；从金牛到巨蟹在北方上升。阶这样求得。每一阶是十五度，一个星座占三十度，所以每个星座含两阶。所以我们从狮子起数黄纬，就求得阶。既然在上面列出的本命里黄纬求得二十三度五十五分，从狮子起每个星座数二度，就得巨蟹一度五十五分。我们得知月亮约在风的第六阶上于北方上升。

XIX. The Hipparchian Method for Calculating in Which Sign the Moon Is.

第十九章　希帕克斯推算月亮在哪个星座之法

I found in which sign the Moon is, by hand, thus. Adding the addition of each king to the year in question, divide by 3, not writing down the remainder but keeping the number in mind: if 1 is left over, add 10 to the number; if 2, 20; if 3, nothing, for the number is exact [corrected: Kroll prints 300 for 10]. Then take half of the months from Thoth up to the month of birth, add it and the days to the first number, subtract the thirties if there are any, and count off the remainder from the Sun's sign: if the Sun is at the beginning of the sign, 2½ to each sign; if in its later degrees, the proportionate amount. Wherever the count ends, there the Moon is.

我这样用手算求得月亮在哪个星座。把每位君王的加数加到所求的年份上，除以三，余数不写下，而把那个数记在心里：如果余一，就在这个数上加十〔据算改正：Kroll 本作三百〕；如果余二，加二十；如果是三，就什么也不加，因为这个数是整的。然后取从托特月到出生之月的月数的一半，把它与日数加到最初的数上，如有三十就去掉，把余数从太阳的星座数去：如果太阳在星座之初，每座二又二分之一；如果在星座的后几度，就按比例。数止于哪里，月亮就在那里。

Likewise, in the same way, to find the day when a nativity has been set out: add the addition to the year in question, divide by 3 as set out above, add half of the months, and note the number. Then, estimating the interval from the Sun to the Moon at 2 2/3 for each sign, compare which number is greater. If the interval from the Sun to the Moon is greater, subtract from it the number first collected, and the remainder will show the day. If the degrees of the interval are fewer, add 30 to them and then subtract the number collected before. If both numbers are found to be 30, the Moon is in conjunction with the Sun.

同样，用同样的办法，在一张本命已列出时求出生之日：把加数加到所求的年份上，照上面所说除以三，加上月数的一半，记下这个数。然后按每个星座二又三分之二估算从太阳到月亮的距离，比较哪个数大。如果从太阳到月亮的距离大，就从中减去先积得的那个数，余数就显示日子。如果距离的度数小，就给它加三十，再减去先前积得的数。如果两个数都是三十，月亮就与太阳会合。

For example, year 3 of Hadrian, Hathyr 28. To the 3rd year I added the 2 customarily added for this king: they make 5. I divided by 3; 2 remain, in place of which I add 20: they make 25. And half of the months, 1½, and the 28: they make 54½. I subtract one thirty; 24½ remain: the Moon will be that many days from the conjunction. These I count off from the Sun's sign, Sagittarius, at 2½ for each sign; the Moon ends in Virgo on the day set out.

例如，哈德良第三年哈蒂尔月二十八日。我在第三年上加上这位君王惯常所加的二：得五。我除以三；余二，代替它我加二十：得二十五。再加上月数的一半一又二分之一，以及二十八：得五十四又二分之一。我减去一个三十；余二十四又二分之一：月亮离合朔就有这么多日。我把这些从太阳的星座射手数起，每座二又二分之一；月亮在所列的那一日止于处女。

The day thus: again I added the 2 to the 3rd year and divided by 3; 2 remain. In place of these I added 20, and half of the months, 1½; it makes 26½. Then I estimated the interval from the Sun to the Moon, that is, from Sagittarius to Virgo, as 24½ days. Since, then, the 26½ collected before cannot be subtracted from these, I added 30 to them: it makes 54½. From these I took away 26½; 28 remain, which showed the day of birth.

日子这样求：我又在第三年上加二，除以三；余二。代替它们我加二十，再加月数的一半一又二分之一；得二十六又二分之一。然后我估算从太阳到月亮，即从射手到处女的距离，为二十四又二分之一日。既然先前积得的二十六又二分之一不能从中减去，我给它加三十：得五十四又二分之一。从中去掉二十六又二分之一；余二十八，这就显示了出生之日。

⟦The number customarily added for each king, set out below, is derived by the following reckoning.

⟦下面列出的每位君王惯常所加之数，是由以下的推算得出的。

For Augustus 1, and he reigned 43 years: it makes 44. I subtract 30; 14 remain. These I add for Tiberius, together with the 22 of Tiberius's reign: it makes 36. I subtract 30; six remain. These I add for Gaius, and he ruled 4: it makes 10. I added them for Claudius, and he reigned 14: it makes 24. From these I subtract a nineteen-year cycle; 5 remain. These for Nero; and he reigned 14: it makes 19; the nineteen-year cycle, then, is complete. And this holds good; if, then, one puts 11 for Vespasian to complete the 30 [text uncertain], and he reigned 10: it makes 21. I took away a nineteen-year cycle; 2 remain. These for Titus; and the years of his rule, 3: it makes 5. These for Domitian; and the years of his rule, 15: it makes 20. From these I subtract a nineteen-year cycle; 1 remains: this is Nerva's addition, and the year he ruled, 1: it makes 2. These for Trajan, and the 19 he ruled: it makes 21. When the nineteen-year cycle is taken away, 2 are left over, which are Hadrian's; and the twenty-one years of his reign that he ruled: it makes 23. From these I subtract a nineteen-year cycle; 4 remain, Antoninus's. Likewise I add the 23 years he ruled: it makes 27. From these I subtract 19; 8 remain. These will be added for Antoninus and Lucius Commodus, and the 32 they reigned: it makes 40. From these I subtract 30; 10 remain, for Severus and Antoninus. And they reigned 25: it makes 35. From these I subtract 30; 5 remain, for Antoninus; and he reigned 4: it makes 9, for Alexander; and the 13 he reigned: it makes 22. From these I subtract a nineteen-year cycle; 4 remain [sic], the addition of Maximinus, and the 3 he ruled: it makes 7. And 6 of Gordian and 6 of Philip: together it makes 19; the nineteen-year cycle is complete.⟧

奥古斯都为一，他在位四十三年：得四十四。我减去三十；余十四。我把这些加给提比略，连同提比略在位的二十二年：得三十六。我减去三十；余六。我把这些加给盖乌斯，他统治了四年：得十。我把它们加给克劳狄，他在位十四年：得二十四。我从中减去一个十九年周期；余五。这些给尼禄；他在位十四年：得十九；于是十九年周期满了。这是成立的；那么，如果给韦斯巴芗定为十一以补足三十〔原文疑有讹误〕，他在位十年：得二十一。我去掉一个十九年周期；余二。这些给提图斯；加上他统治的年数三：得五。这些给图密善；加上他统治的年数十五：得二十。我从中减去一个十九年周期；余一：这是涅尔瓦的加数，加上他统治的一年：得二。这些给图拉真，加上他统治的十九年：得二十一。去掉十九年周期，余二，这是哈德良的；加上他在位统治的二十一年：得二十三。我从中减去一个十九年周期；余四，是安敦宁的。同样我加上他统治的二十三年：得二十七。我从中减去十九；余八。这些将加给安敦宁与卢基乌斯·康茂德，以及他们在位的三十二年：得四十。我从中减去三十；余十，给塞维鲁与安敦宁。他们在位二十五年：得三十五。我从中减去三十；余五，给安敦宁；他在位四年：得九，给亚历山大；加上他在位的十三年：得二十二。我从中减去一个十九年周期；余四〔原书如此〕，是马克西米努斯的加数，加上他统治的三年：得七。再加戈尔迪安的六年与菲利普的六年：合计十九；十九年周期满了。⟧