卷一·第二十章　手算太阳与五星

XX. On Calculating the Sun and the Five Planets.

第二十章　论推算太阳与五星

You will learn the Sun's position to the degree thus. Always add to the day of birth 8 degrees from Thoth to Phamenoth, and at that many degrees you will find the Sun; in Pharmouthi 7, in Pachon 6, in Payni 5, in Epiphi 4, in Mesori 3. For example, on Phaophi 6 I added 8: they make 14; at that many degrees the Sun is in Libra. Pachon 6, and 6: it makes 12; at that many degrees the Sun is in Taurus.

太阳的位置可这样求到度数。从托特月到法梅诺特月，总是在出生之日上加八度，太阳就在这么多度；法尔穆提月加七，帕雄月加六，帕尼月加五，埃皮菲月加四，梅索里月加三。例如，法奥菲月六日我加八：得十四；太阳就在天秤这么多度。帕雄月六日，加六：得十二；太阳就在金牛这么多度。

Since some lovers of learning become more eager about the handling of numbers, it is necessary to set out for them the remaining planets as well, reckoned by hand, so that, having taken up through such practice a pleasant and exact teaching to the degree, they may in this way also make the distinction of the greater systems with all eagerness.

既然有些好学之人对数的运用更加热心，就有必要也为他们列出其余诸星的手算，好让他们借这样的练习，得到一种愉快而精确到度的教导，也由此满怀热忱地去分辨那些更大的体系。

Saturn, then, is to be calculated thus. Take the full years from Augustus and cast out 30 as many times as you can, and multiply the remainder by 12; and for as many times as you have cast out thirties, take 5 for each circle, and from Thoth 1 for each month and 1/32 for each day; and having summed these, count off from Cancer in the order of the signs, 30 to each; and wherever it ends, there the planet will be.

土星这样推算。取从奥古斯都起的满年，尽可能多次地去掉三十，把余数乘以十二；去掉了几个三十，就每一圈取五，再从托特月起每月取一，每日取三十二分之一；把这些加起来后，从巨蟹起按星座次序数去，每座三十；数止于哪里，这颗行星就在那里。

Jupiter thus. Divide the full years from Caesar by 12, and multiply the remainder by 12; and add to these, for as many times as you have cast out twelves, 1 for each circle, 1 for each month, and 1/5 1/9 for each day [probably: 1/30, since 1 a month makes 1/30 a day] [text uncertain]; and having summed these, count off from Taurus, 12 to each sign.

木星这样推算。把从凯撒起的满年除以十二，把余数乘以十二；去掉了几个十二，就在这上面每一圈加一，每月加一，每日加五分之一又九分之一〔或当作三十分之一，因每月加一，每日当为其三十分之一〕〔原文疑有讹误〕；把这些加起来后，从金牛数去，每座十二。

Mars thus. Take the years from Augustus up to the year you are seeking and cast out 30 as many times as you can, and determine whether the remaining number is even or odd, so that if you find it even you make the release from Aries, and if odd, from Libra. After learning the number, then, double it, and add 2½ for each month; if it comes to more than 60, count off the rest from Libra or Aries, giving 5 degrees to each sign [text uncertain]. Wherever it ends, note the sign and look in which sign the Sun is: if the Sun is found higher, the planet will go back from the sign found; if lower, it will go forward; that is, always place him nearer to the Sun than the sign found. The other planets too have the same property, since they move about the mean motion of the Sun, and above all Venus.

火星这样推算。取从奥古斯都到所求那一年的年数，尽可能多次地去掉三十，确定余下的数是偶数还是奇数，以便若是偶数就从白羊起数，若是奇数就从天秤起数。得知这个数以后，把它加倍，再每月加二又二分之一；如果超过六十，就把其余的从天秤或白羊数去，每座给五度〔原文疑有讹误〕。数止于哪里，记下那个星座，再看太阳在哪个星座：如果太阳在更高处，这颗行星就从所得的星座退回；如果在更低处，就往前移；也就是说，总是把他放得比所得的星座更靠近太阳。其他行星也有同样的性质，因为它们都围绕太阳的平均运动而行，金星尤其如此。

Venus thus. Take the years from Caesar up to the year you are seeking and divide by 8; and look whether the number left within the 8 has an epoch of a station, and using that epoch take the number of days up to the day sought, if it admits of it. If not, use the one above it, as in the case of the Moon: if this epoch is found before the nativity, it is to be used; if after the nativity, use the one above. Having collected the total and subtracted the epoch of the sign, count off 120 degrees for each sign, that is, for the station; count off the rest from the sign following the epoch, giving 25 to each sign [text uncertain]. Wherever the number ends, there Venus will be. The epochs of the stations will be evident from the years left over: if there remain, for example, 1, 3, 4, 6, or 7, she is stationary; if 2 or 5, she is moving. The first epoch, then, will hold Phamenoth 10 in Taurus; the 3rd, Phaophi 10 in Sagittarius; the 4th, Payni 22 in Leo; the 6th, Tybi 8 in Pisces; the 7th, Mesori 14 in Libra; she holds the station into the 8th year.

金星这样推算。取从凯撒到所求那一年的年数，除以八；看留在八以内的那个数有没有留的历元，如果容许，就用那个历元，取到所求那一日的天数。如果没有，就用它上面的那一个，就像月亮的情形：如果这个历元落在本命之前，就用它；如果在本命之后，就用上面的那一个。把总数积起来，减去那个星座的历元后，为每个星座，也就是为留，数去一百二十度；其余的从历元之后的那个星座数去，每座给二十五〔原文疑有讹误〕。数止于哪里，金星就在那里。留的历元由余下的年数显示：例如余一、三、四、六或七，她就是留；余二或五，她就在行进中。于是第一个历元是法梅诺特月十日在金牛；第三个是法奥菲月十日在射手；第四个是帕尼月二十二日在狮子；第六个是提比月八日在双鱼；第七个是梅索里月十四日在天秤；她把留一直保持到第八年。

Mercury is to be calculated thus. Take the days up to the day of birth, always add to them 162 from outside, and sum them; if the total is over 360, subtract a circle and count off the rest from Aries, giving 30 to each sign; and wherever it ends, there the planet is. Always place him very near the Sun. For example, if the Sun was at the beginning of the sign, he can be found in the sign behind; if at the end, in the following sign.

水星这样推算。取到出生之日的天数，总是从外面加上一百六十二，把它们加起来；如果总数超过三百六十，就减去一圈，把其余的从白羊数去，每座给三十；数止于哪里，这颗行星就在那里。总是把他放得很靠近太阳。例如，如果太阳在星座之初，他可能在身后的那个星座里被找到；如果在星座之末，就在下一个星座里。

Let there be as an example year 13 of Trajan, Phamenoth 18. The full years from Augustus are 138. From these I took away 4 thirties, in place of which I take 5 for each circle: they make 20. The remaining 18 I multiply by 12: they make 216. And from Thoth to Phamenoth 1 for each month: they make 7. All together, 243. Then I count these off from Cancer, 30 to each; the count ends in Pisces: there is Saturn. — Again, I divided 138 by 12: 11, and 6 remain. These twelve times make 72; and 1 for each circle cast out: they make 11; and of the months 7: they make 90. These from Taurus, 12 to each; the count ends in Sagittarius: there is Jupiter. — Then Mars thus. From Caesar to the year in question there are 139; from these I took away 30 four times; 11 remain [sic]. Since, then, the number left over was found to be odd, I knew that I must make the release from Libra. I doubled these, then: they make 22; and for each month up to Phamenoth: they make 17; all together, 39. I divided these: I count off from Libra, giving 5 to each sign; the count ends in Taurus: there is Mars. — Venus thus. I divided 139 by 8; 3 remain, which signify a station, with the epoch Phaophi 10 in Sagittarius. I take the remaining 20 of Phaophi, and from Hathyr to Mechir 120, and the 18 of Phamenoth: together they make 158. From these I subtract the 120 of the station and of Sagittarius; 38 remain, which I count off from Capricorn, 25 to each; the count ends in Aquarius: there is Venus.

例如设为图拉真第十三年法梅诺特月十八日。从奥古斯都起的满年是一百三十八。我从中去掉四个三十，代替它们，我每一圈取五：得二十。余下的十八我乘以十二：得二百一十六。从托特月到法梅诺特月每月一：得七。合计二百四十三。然后我把这些从巨蟹数去，每座三十；数止于双鱼：土星就在那里。——又，我把一百三十八除以十二：十一，余六。这六乘十二得七十二；每去掉一圈加一：得十一；加上月数七：得九十。这些从金牛数去，每座十二；数止于射手：木星就在那里。——然后火星这样求。从凯撒到所求的那一年是一百三十九；从中我去掉四次三十；余十一〔原书如此〕。既然余下的数是奇数，我知道必须从天秤起数。于是我把它们加倍：得二十二；再每月加到法梅诺特月：得十七；合计三十九。我把这些分开：从天秤数去，每座给五；数止于金牛：火星就在那里。——金星这样求。我把一百三十九除以八；余三，表示留，历元是法奥菲月十日在射手。我取法奥菲月余下的二十日，从哈蒂尔月到梅希尔月的一百二十日，以及法梅诺特月的十八日：合计一百五十八。从中我减去留与射手的一百二十；余三十八，我从摩羯数去，每座二十五；数止于水瓶：金星就在那里。

Since there seems to be much [lacuna] about the nativity, I shall set it out for another nativity as well. Year 4 of Hadrian, Hathyr 30: the years from Augustus are 148. These I divided by 8; 4 remain, which signify the epoch Payni 22 in Leo. Since, then, this epoch is not valid, because it is found to fall after the nativity, I go back to the one above, which is the third, Phaophi 10 in Sagittarius. I take the remaining 20 of Phaophi, and from Hathyr to Mesori 300, and the 5 epagomenal days: they make 325 of the previous year; and of the current year itself, from Thoth to Hathyr 30, 90: altogether they make 415. From these I subtract the 120 of the station and of the sign Sagittarius; 295 remain. These from Capricorn, 25 to each; the count ends at Sagittarius 20: there is the planet. —

既然关于这张本命似乎有许多〔此处原文有缺〕，我再为另一张本命列出。哈德良第四年哈蒂尔月三十日：从奥古斯都起的年数是一百四十八。我把它们除以八；余四，表示历元帕尼月二十二日在狮子。既然这个历元不可用，因为它落在本命之后，我就退回到上面的那一个，即第三个，法奥菲月十日在射手。我取法奥菲月余下的二十日，从哈蒂尔月到梅索里月的三百日，以及五个附加日：得前一年的三百二十五；本年从托特月到哈蒂尔月三十日，九十：总共四百一十五。从中我减去留与射手星座的一百二十；余二百九十五。这些从摩羯数去，每座二十五；数止于射手二十度：这颗行星就在那里。——

Another way. Year 4 of Hadrian, Mechir 13: from Augustus, 149 [sic]. Divided by 8, 5 remain, which signify neither an epoch nor a station. I go back to the epoch above, which is Payni 22 in Leo. I take the remaining 8 of Payni, and Epiphi and Mesori, and the 5 epagomenal days: they make 73; and of the current year, from Thoth to Mechir 13: they make 163; together 236. From these I subtract the 120 of the station and of the sign Leo; 116 remain. These from Virgo, 25 to each; they end at Capricorn 16°. There is Venus.

另一法。哈德良第四年梅希尔月十三日：从奥古斯都起，一百四十九〔原书如此〕。除以八，余五，既不表示历元，也不表示留。我退回到上面的历元，即帕尼月二十二日在狮子。我取帕尼月余下的八日，埃皮菲月与梅索里月，以及五个附加日：得七十三；本年从托特月到梅希尔月十三日：得一百六十三；合计二百三十六。从中我减去留与狮子星座的一百二十；余一百一十六。这些从处女数去，每座二十五；止于摩羯十六度。金星就在那里。

Likewise, for the same nativity, I calculated Mercury thus. I took the 163 days from Thoth to the 13th of Mechir and added 162 from outside: together 325. These I counted off from Aries, 30 to each; the count ended at Aquarius 25°: there is the planet.

同样，对同一张本命，我这样推算水星。我取从托特月到梅希尔月十三日的一百六十三日，从外面加上一百六十二：合计三百二十五。我把这些从白羊数去，每座三十；数止于水瓶二十五度：这颗行星就在那里。