卷三·第 191–196 问　天球进退、诸星纬度与伊历四二〇年的远地点交点

§191. What is the motion of the orb?

第一百九十一问　何谓天球的运动？

This is the view that Theon of Alexandria attributes to the makers of talismans, who are the practitioners of judgements among the ancient people of Babylon. They hold that the orb has a forward motion in the order of the signs, reaching at most 8 degrees, and then a backward motion of the same amount against the order, the period of this motion being 80 solar years for each degree of it. When it moves forward, the planets go faster and this motion must be added to them; and when it moves back, they go slower and the motion must be subtracted from them. As to whether this is true or false, no one has yet had observations extending over a period sufficient to ascertain it.

这是亚历山大里亚的塞翁归于护符制作者的见解，他们是古代巴比伦人中从事判断之术的人。他们认为天球有一种顺星座次序的前进运动，最多达到八度，然后有一种同样大小、逆次序的后退运动，这一运动的周期是每一度八十个太阳年。天球前进时，行星走得较快，必须把这一运动加给它们；天球后退时，行星走得较慢，必须从它们中减去这一运动。至于这是真是假，至今还没有人拥有延续足够长时间的观测来加以确定。

§192. What is the latitude of the Moon like?

第一百九十二问　月亮的纬度是怎样的？

Its inclined orb has a fixed inclination of a single amount, its greatest being 5 parts towards the north and the same towards the south, and that is the extreme latitude of the Moon. Its epicycle has no effect on it, for it lies in the plane of the orb. Because the two nodes of its jawzahr move against the order, its greatest latitude, and any latitude of it of whatever amount, never stays at one place in the zodiac, as the declination of the Sun stays at one place in it.

它的斜圈有固定不变的倾角，只有一个量，最大向北五份，向南也是同样，那就是月亮的最大纬度。它的本轮对此没有影响，因为本轮在斜圈的平面上。由于它的焦扎赫尔的两个交点逆次序移动，它的最大纬度，以及它任何大小的纬度，都不会停在黄道的某一处，不像太阳的赤纬停在黄道上的某一处那样。

§193. What are the latitudes of the upper planets like?

第一百九十三问　上行星的纬度是怎样的？

Each of them has an inclined orb of fixed inclination, of a single amount, and their apogees lie in the northern halves of the inclined orbs. The planes of their epicycles are not in the planes of the inclined orbs, as is the case with the Moon; rather, the plane of the epicycle of each of the upper planets is inclined to the plane of the inclined orb by an inclination through which the perigee of the epicycle always stands out from the inclined orb on the side towards which the inclined orb deviates from the zodiac. That is, if the place of the inclined orb where the centre of the epicycle is lies north of the zodiac, the inclination of the perigee of the epicycle from the inclined orb is also northern, and if it is southern, southern; so the inclination of the summit from the inclined orb is in the direction opposite to that of the inclined orb from the zodiac. This inclination of the epicycle belongs to the diameter passing through its summit and perigee, which is called the first diameter, while the other diameter, perpendicular to it, remains fixed, and this second one is always parallel to the plane of the zodiac. It is evident, then, that when the centre of the epicycle comes to one of the two nodes of the inclined orb, the plane of the epicycle coincides with the plane of the zodiac and the first diameter lies in the plane of the zodiac; when it passes the node, it begins to incline to the other side, and its greatest inclination is at the midpoint between the two nodes, which is also the place of the greatest inclination of the inclined orb. It follows from what we have said that the upper planets have two latitudes: one due to the inclined orb, called the first and the mean, which depends on the places in the zodiac; and the other due to the epicycle, called the second, which depends on the distance from the Sun.

它们每一颗都有一个倾角固定、只有一个量的斜圈，它们的远地点位于斜圈的北半。它们本轮的平面不像月亮那样在斜圈的平面上；每颗上行星本轮的平面都以一定倾角倾斜于斜圈的平面，凭借这一倾斜，本轮的近地点总是从斜圈突出到斜圈偏离黄道的那一侧。也就是说，如果本轮中心所在的斜圈之处位于黄道之北，本轮近地点离斜圈的倾斜也向北；如果在南，就向南；因此顶点离斜圈的倾斜，与斜圈离黄道的方向相反。本轮的这一倾斜属于穿过它的顶点与近地点的那条直径，这条称为第一直径；而与之垂直的另一条直径保持固定，这第二条始终与黄道的平面平行。于是显然，当本轮中心来到斜圈的两个交点之一时，本轮的平面与黄道的平面重合，第一直径落在黄道的平面上；越过交点之后，它就开始向另一侧倾斜，最大的倾斜在两个交点的正中，那也是斜圈最大倾斜之处。由我们所说可知，上行星有两种纬度：一种出于斜圈，称为第一纬度和平均纬度，取决于在黄道上的位置；另一种出于本轮，称为第二纬度，取决于与太阳的距离。

§194. What is the latitude of the two lower planets like?

第一百九十四问　两颗下行星的纬度是怎样的？

Each of Venus and Mercury has an inclined orb whose inclination is not fixed; it moves from an extreme in the north to an equal extreme in the south, and its oscillation between them takes a solar year; what results from it is called the latitude of the eccentric. Then each of them has, in its epicycle, two kinds of latitude: one due to the motion of the first diameter, called the latitude of the epicycle, and the other due to the motion of the second diameter, called the slant latitude (warāb) and the latitude of twisting (iltiwāʾ). As for the latitude of the eccentric: when the centre of the epicycle is at the place of one of the two nodes of the inclined orb, the plane of the inclined orb coincides with the plane of the zodiac; when it leaves the node for one of the two halves of the inclined orb, that half of the inclined orb begins to move, for Venus towards the north and for Mercury towards the south, and it reaches its extreme when the centre of the epicycle arrives at the midpoint between the two nodes, which is the place either of their apogee or of their perigee. At that time the latitude of the epicycle belonging to the first diameter begins: if its centre is at the apogee, the summit begins to incline, in Venus towards the north and in Mercury towards the south; and if its centre is at the perigee of the apogee orb, the summit begins to incline, in Venus towards the south and in Mercury towards the north. As for the latitude of twisting, belonging to the second diameter, it begins when the centre of the epicycle arrives at one of the two nodes of the inclined orb; for when it leaves it for the half in which the apogee of the eccentric lies, its eastern end begins to incline, in Venus towards the north and in Mercury towards the south, and the western end the opposite way; and when the centre of the epicycle leaves the node for the half in which the perigee of the eccentric lies, its eastern end begins to incline, in Venus towards the south and in Mercury towards the north. It keeps increasing until it reaches its extreme when the centre of the epicycle arrives at the apogee or the perigee of the eccentric. So the two latitudes, of the epicycle and of twisting, alternate in their beginning and their end. It follows from what we have mentioned that the centre of the epicycle of Venus is always north of the zodiac, and the centre of the epicycle of Mercury always south of it.

金星和水星各有一个倾角不固定的斜圈；它从北方的极限移动到南方相等的极限，在两者之间的摆动需要一个太阳年；由此产生的称为偏心圈纬度。然后，它们各自在本轮中又有两种纬度：一种出于第一直径的运动，称为本轮纬度；另一种出于第二直径的运动，称为斜偏纬度和扭转纬度。至于偏心圈纬度：当本轮中心位于斜圈两个交点之一的地方时，斜圈的平面与黄道的平面重合；当它离开交点进入斜圈两半之一时，斜圈的那一半就开始移动，金星向北，水星向南，到本轮中心抵达两交点之间的正中时达到极限，那正中之处或是它们的远地点、或是它们的近地点。那时属于第一直径的本轮纬度开始：如果本轮中心在远地点，顶点开始倾斜，金星向北，水星向南；如果本轮中心在远地点圈的近地点，顶点开始倾斜，金星向南，水星向北。至于属于第二直径的扭转纬度，它在本轮中心抵达斜圈两个交点之一时开始；当本轮中心离开交点进入偏心圈远地点所在的那一半时，它的东端开始倾斜，金星向北，水星向南，西端则相反；当本轮中心离开交点进入偏心圈近地点所在的那一半时，它的东端开始倾斜，金星向南，水星向北。它不断增大，直到本轮中心抵达偏心圈的远地点或近地点时达到极限。所以本轮纬度与扭转纬度两者，在开始与终结上互相交替。由我们所说可知，金星的本轮中心总在黄道之北，水星的本轮中心总在黄道之南。

§195. Where are the apogees of the planets?

第一百九十五问　诸行星的远地点在哪里？

They move in the order of the signs, so their places cannot be fixed except for a definite time. But since their motion is slow, 1 degree in every 66 years, their places in our time, which is the year 420 of the Hijra, according to the findings of Muḥammad ibn Jābir al-Battānī in his zīj, are: the apogee of the Sun in Gemini 24;30, the apogee of Saturn in Sagittarius 6;48, the apogee of Jupiter in Virgo 16;48, the apogee of Mars in Leo 28, the apogee of Venus in Gemini 24;39, and the apogee of Mercury in Libra 23;48.

它们顺星座次序移动，所以它们的位置只能就某一确定的时间来定。但由于它们的运动缓慢，每六十六年一度，照穆罕默德·本·贾比尔·巴塔尼在他的历表中的测定，它们在我们这个时代，即伊历四百二十年的位置是：太阳的远地点在双子二十四度三十分，土星的远地点在射手六度四十八分，木星的远地点在处女十六度四十八分，火星的远地点在狮子二十八度，金星的远地点在双子二十四度三十九分，水星的远地点在天秤二十三度四十八分。

§196. Where are the jawzahrs of the planets?

第一百九十六问　诸行星的焦扎赫尔在哪里？

According to the observations of the people of the West, they move in the order of the signs with a motion equal to that of the apogees and the fixed stars, because the motion of the zodiac is towards the east and is common to all the orbs. The Head of the jawzahr of Saturn is 80;0 from its apogee, so that in our said time it is in Aquarius 26;48; the Head of the jawzahr of Jupiter is 70;0 from its apogee, so that in our time it is in Scorpio 26;48; the Head of the jawzahr of Mars is 90;0 from its apogee, so that it is in Virgo 24;29 [sic]; and the Head of the jawzahr of Mercury is 90;0 from its apogee, so that it is in Capricorn 23;48. Among the Indians, however, their motion is not uniform, and it is reversed, against the order of the signs, like that of the jawzahr of the Moon, about which they do not disagree. In our time the Head of the jawzahr of Saturn is in Gemini 28;8, the Head of the jawzahr of Jupiter in Cancer 11, the Head of the jawzahr of Mars in Aries 21;55, the Head of the jawzahr of Venus in Taurus 29;48, and the Head of the jawzahr of Mercury in Aries 21;41. As for the Head of the jawzahr of the Moon, since its motion is faster than theirs, its place cannot be fixed without calculation.

照西方人的观测，它们顺星座次序移动，其运动与远地点和恒星的运动相等，因为黄道的运动是向东的，为一切天球所共有。土星焦扎赫尔的“龙头”距它的远地点八十度整，所以在我们所说的时代它在水瓶二十六度四十八分；木星焦扎赫尔的“龙头”距它的远地点七十度整，所以在我们的时代它在天蝎二十六度四十八分；火星焦扎赫尔的“龙头”距它的远地点九十度整，所以它在处女二十四度二十九分〔原书如此〕；水星焦扎赫尔的“龙头”距它的远地点九十度整，所以它在摩羯二十三度四十八分。然而在印度人那里，它们的运动并不均匀，而且是反向的，逆星座次序，就像月亮的焦扎赫尔那样，对此他们没有分歧。在我们的时代，土星焦扎赫尔的“龙头”在双子二十八度八分，木星焦扎赫尔的“龙头”在巨蟹十一度，火星焦扎赫尔的“龙头”在白羊二十一度五十五分，金星焦扎赫尔的“龙头”在金牛二十九度四十八分，水星焦扎赫尔的“龙头”在白羊二十一度四十一分。至于月亮焦扎赫尔的“龙头”，由于它的运动比它们快，不经计算就无法确定它的位置。