卷三·第 184–190 问　真位置、月亮与五星诸轮、水星与各星周期

§184a. What is the equation of the second portion?

第一百八十四问之二　何谓第二份的均差？

It is the amount of the angle enclosed by the two lines drawn from the centre of the world, one to the centre of the epicycle and the other to the body of the planet.

它是从世界中心引出的两条线——一条到本轮中心，另一条到行星本体——所夹之角的大小。

§185. What is the true position of a planet?

第一百八十五问　何谓行星的真位置？

It is the point of the parecliptic orb at which the line drawn from the centre of the world to the body of the planet ends; and that is its place, in which it is seen in the zodiac. This is the figure of it.

它是拟黄道圈上的一点，从世界中心引向行星本体的线终止于此；那就是行星所在之处，行星就在黄道上这一处被看见。这是它的图。

§186. What are the orbs of the Moon like?

第一百八十六问　月亮的诸圈是怎样的？

It has a parecliptic orb, an orb inclined to it, and an apogee orb carrying its epicycle, on which its body revolves.

它有一个拟黄道圈、一个倾斜于拟黄道圈的圈，以及一个载着本轮的远地点圈，月亮本体就在本轮上运转。

§187. What are the motions in its sphere like, and what are their amounts?

第一百八十七问　月亮天球中的诸运动是怎样的，大小如何？

The two poles of its inclined orb revolve round the two poles of the parecliptic against the order of the signs, and so carry the Head and the Tail 3 minutes each day in the reverse direction of the signs. The Moon itself moves on its epicycle from the summit towards the west, that is, against the order of the signs, 13;4 degrees. The centre of the epicycle moves on the circumference of the deferent in the order of the signs 24;23 degrees a day, which is equal to twice the distance by which the Moon moves away from the Sun in a day, that is, the difference between their two courses; and for this reason it is called the double elongation. The centre of the deferent moves against the order, and so carries its apogee in that direction 11;9 degrees a day. But the visible summit of the epicycle always faces a point whose distance from the centre of the world, towards the perigee of the deferent, is equal to the distance of the centre of the deferent from the centre of the world; the amount of this distance is 12½ parts in the measure in which the radius of the deferent is 60 parts, and in this measure the radius of the epicycle is 5¼ parts. This is the figure of it.

它的斜圈的两极绕着拟黄道圈的两极逆星座次序旋转，于是带着“龙头”与“龙尾”每天逆着星座的方向移动三分。月亮本身在本轮上从顶点向西、即逆星座次序运行，每天十三度四分。本轮中心在均轮圆周上顺星座次序每天运行二十四度二十三分，这等于月亮一天之内离开太阳的距离的两倍，即两者行程之差的两倍，因此称为“双倍距角”。均轮圆心逆星座次序运行，于是带着它的远地点向那个方向每天移动十一度九分。但本轮的可见顶点始终正对一点，这一点在世界中心朝均轮近地点的方向上，到世界中心的距离等于均轮圆心到世界中心的距离；按均轮半径为六十份的量度，这段距离是十二份半，在这一量度下本轮半径是五份又四分之一。这是它的图。

§188. How are these states and amounts in the planets?

第一百八十八问　这些状态与数量在诸行星中是怎样的？

The planets move on the circumferences of their epicycles from the summit towards the east and in the order of the signs, contrary to the motion of the Moon on its epicycle towards the west. Their motions in a day are: Saturn, 57 minutes; Jupiter, 54 minutes; Mars, 28 minutes; Venus, 37 minutes; and Mercury, 3;6 degrees. The centres of their epicycles move towards the east and in the order of the signs with the mean motion, which is reckoned by the centre of the equant orb: the centre of the epicycle of Saturn moves 2 minutes a day, that of Jupiter 5 minutes, that of Mars 31 minutes, that of Venus, like the motion of the Sun, 59 minutes, and that of Mercury, equal to twice the motion of the Sun, 1;58 degrees.

诸行星在本轮圆周上从顶点向东、顺星座次序运行，与月亮在本轮上向西的运动相反。它们每天的运动是：土星五十七分，木星五十四分，火星二十八分，金星三十七分，水星三度六分。它们的本轮中心以平均运动向东、顺星座次序运行，这一平均运动是按偏心等速圈的圆心来计算的：土星的本轮中心每天运行二分，木星五分，火星三十一分，金星与太阳的运动相同，为五十九分，水星等于太阳运动的两倍，为一度五十八分。

As for the amount by which the centre of the equant is removed from the centre of the world, in the measure in which the radius of the deferent is 60 parts: in Saturn it is 6;45 parts, in Jupiter 5½ parts, in Mars 12 parts and in Venus 2;5 parts; and the centre of the deferent lies at the midpoint of this distance. The radii of their epicycles in this measure are: in Saturn 6½ parts, in Jupiter 11½ parts, in Mars 39½ parts, in Venus 43;10 parts and in Mercury 22½ parts.

至于偏心等速圈圆心离开世界中心的距离，按均轮半径为六十份的量度：土星是六份四十五分，木星五份半，火星十二份，金星二份五分；均轮圆心位于这段距离的中点。在这一量度下，它们本轮的半径是：土星六份半，木星十一份半，火星三十九份半，金星四十三份十分，水星二十二份半。

§189. How does Mercury differ from them?

第一百八十九问　水星与它们有何不同？

The centre of its deferent orb moves towards the west on a small circle whose centre lies on a straight line with the centre of the equant and the centre of the world, the centre of the equant lying at the midpoint between the centre of the world and the centre of the said circle. Therefore the centre of the deferent has varying distances from the centre of the world, the greatest being 9½ parts and the least 3 1/6 parts. Because of this motion the apogee of the deferent moves against the order by the amount of the mean course of the Sun, and it follows that the centre of the epicycle meets the apogee of the deferent twice every year, just as for the Moon the centre of its epicycle and the apogee of its deferent meet twice in the month. It follows for each of Venus and Mercury that the centre of their epicycle is always in line with the body of the Sun, and for this reason they are combust both at the summit and at the perigee, that is, in the middle of direct motion and in the middle of retrogradation; while the upper planets are combust only at the summit, because the centres of their epicycles do not keep in line with the Sun always, but come into line with it only when the planet is at the summit of the epicycle. This is the figure of the orbs of Mercury.

它的均轮圆心在一个小圆上向西运行；这个小圆的圆心与偏心等速圈圆心、世界中心在一条直线上，偏心等速圈的圆心位于世界中心与该圆圆心之间的正中。因此均轮圆心到世界中心的距离有变化，最大为九份半，最小为三份又六分之一。由于这一运动，均轮的远地点按太阳平均行程的量逆次序移动，结果本轮中心每年两次与均轮远地点相遇，正如月亮的本轮中心与均轮远地点每月相遇两次。由此可知，金星与水星各自的本轮中心总是与太阳本体在一条直线上，因此它们在顶点和近地点都会焦伤，即在顺行的正中与逆行的正中；而上行星只在顶点焦伤，因为它们的本轮中心并不总与太阳成一直线，只有当行星在本轮顶点时才与太阳成一直线。这是水星诸圈的图。

§190. In what periods are the revolutions of these motions completed?

第一百九十问　这些运动的周转在多少时间内完成？

We have said that the revolution of the Sun in the zodiac is completed in 365 days and a quarter of a day, less one part of 111 parts of a day; that is its year, which is the standard of the years. As for the other planets, since their simple motions are of two kinds, one on the circumference of the epicycle and the other on the circumference of the deferent, their revolutions on the circumferences of the epicycles are completed: for Saturn in one solar year and approximately 12 days; for Jupiter in one year, one month and 3 days; for Mars in two years, one month and 18 days; for Venus in one year, seven months and 5 days; for Mercury in three months and 26 days [corrected: MS has 14 days]; and for the Moon in 27 days, 13 hours and 18 minutes.

我们说过，太阳在黄道上的周转在三百六十五日又四分之一日、减去一日的一百一十一分之一内完成；那就是它的年，是诸年的标准。至于其他行星，由于它们的简单运动有两种，一种在本轮圆周上，另一种在均轮圆周上，它们在本轮圆周上的周转完成于：土星一个太阳年又约十二日；木星一年又一个月零三日；火星两年又一个月零十八日；金星一年又七个月零五日；水星三个月零二十六日〔抄本作“十四日”，据算改正〕；月亮二十七日十三小时十八分。

As for the revolutions of the centres of their epicycles until they have gone through all the signs: for Saturn, 29 years, 4 months and 15 days; for Jupiter, 11 years, 10 months and 4 days; for Mars, one year, 10 months and 17 days; for each of Venus and Mercury, one solar year; for the Moon, 27 days, 7 hours and 43 minutes; for the jawzahr of the Moon, 18 years, 7 months and 9 days; and for each of the fixed stars and the apogees of the planets, according to the findings of the ancients, 36000 years, and according to the findings of the moderns 23760 years.

至于它们的本轮中心走遍所有星座的周转：土星二十九年四个月零十五日；木星十一年十个月零四日；火星一年十个月零十七日；金星与水星各为一个太阳年；月亮二十七日七小时四十三分；月亮的焦扎赫尔十八年七个月零九日；至于每颗恒星以及诸行星的远地点，照古人的测定是三万六千年，照近人的测定是二万三千七百六十年。