卷四·第 242–243 问　星座的上升时间、星的过中天度与升没度

§242. What are the ascensions of the signs and the degrees of equality?

第二百四十二问　何谓星座的上升时间与等分度？

The degrees of equality are those that divide the zodiac into equal parts, 30 being assigned to each sign. Since the zodiac is drawn about a pole other than the pole of the first motion, the risings of the signs and of the degrees of equality take unequal times, so that the part of the equator that rises with each sign differs from the part that rises with another sign. The ascensions of the signs, or of any assumed degrees of equality, are thus the times of the equator that rise with them. On the equinoctial line they are called the ascensions of the right orb and the ascensions of the upright sphere; there the ascensions of every four signs, each two of which are equally distant from the points of the two equinoxes on both sides, are equal: for example Aries, Pisces, Libra and Virgo, whose ascensions are equal; likewise the ascensions of Taurus, Aquarius, Scorpio and Leo are equal; and the ascensions of the remaining four are equal. On the equinoctial line, too, the ascensions of each sign are equal to its descensions. But in places that have latitudes, only the ascensions of each two signs equally distant from one particular point of the two equinoctial points are equal: for example the ascensions of Aries and Pisces, which are equal; and likewise the ascensions of Libra and Virgo, which, though equal to each other, are not equal to the ascensions of Aries and Pisces. Further, if the ascensions of each sign and the ascensions of the seventh sign from it, which is its opposite, are added together, the sum of their ascensions is equal to the sum in the right orb; and the descensions of each sign are equal to the ascensions of its opposite. In this table are the ascensions of the signs in the right orb and in the middles of the seven climes.

等分度是把黄道分为相等部分的度，每个星座分得三十度。由于黄道是绕着与第一运动之极不同的极而画的，星座与等分度升起所用的时间便不相等，所以与一个星座一同升起的那段天赤道，和与另一个星座一同升起的那段不同。星座或任何所设等分度的上升时间，就是与它们一同升起的天赤道的时度。在赤道线上，它们称为正球的上升时间、直立之球的上升时间；在那里，每四个星座的上升时间相等，这四个中每两个在两分点的两侧，离分点的距离相等：例如白羊、双鱼、天秤与处女，它们的上升时间相等；同样金牛、宝瓶、天蝎与狮子的上升时间相等；其余四个的上升时间也相等。在赤道线上，每个星座的上升时间又等于它的沉没时间。但在有纬度的地方，只有离两分点中某一个特定分点距离相等的每两个星座，上升时间才相等：例如白羊与双鱼的上升时间相等；同样天秤与处女的上升时间彼此相等，但不等于白羊与双鱼的上升时间。再者，若把每个星座的上升时间与从它数起第七个、即与它相对的星座的上升时间相加，二者之和等于正球中的和；每个星座的沉没时间等于其对宫的上升时间。这张表里是正球与七个气候带中线上诸星座的上升时间。

This is the figure of it.

这是它的图。

§243. What are the degree of a star, the degree of its passage, of its rising and of its setting?

第二百四十三问　何谓星的度、它的过中天度、升起度与落下度？

If the star has no latitude, its degree is the one of the zodiac on which it stands; it rises with it and passes with it through the middle of the sky. But if it has latitude, its degree is the one at which its circle of latitude ends, I mean the great circle that passes through it and through the pole of the zodiac. If its latitude is northern, it rises before its degree rises and sets after it sets; and if its latitude is southern, it rises after its degree rises and sets before it sets. It is clear that the degree that rises with the rising of a star having latitude is other than its degree, and that is the one called the degree of its rising; likewise the degree that sets with the setting of the star is the degree of its setting. As for when it reaches the middle of the sky and meets the meridian: if it is at one of the two solstices, it arrives there together with its degree and there is no difference between them, whether its latitude is northern or southern. But if its degree is other than one of the two solstices, then, if its latitude is northern and its degree is in the ascending half, which is from the beginning of Capricorn to the end of Gemini, it arrives at the middle of the sky before its degree; and if its degree is in the descending half, it arrives there after its degree arrives [corrected: MS has 'after' and 'before' the other way round]. If its latitude is southern, the matter is the reverse: I mean, if its degree is in the ascending half, it arrives at the meridian after its degree arrives, and in the descending half before it [corrected: MS has 'before' and 'after' the other way round]. It is known that when it arrives at the middle of the sky, a degree other than its own is with it; that is the one that passes with it over the meridian, and it is called the degree of passage. The situation at the orb of midnight is exactly what has been said for the meridian.

若星没有纬度，它的度就是它所在的黄道之度；它与这一度一同升起，一同经过天的中央。若它有纬度，它的度就是它的纬度圈所终止的那一度，我是说，通过它和黄道之极的那个大圆所终止之处。若它的纬度在北，它在它的度升起之前升起，在它的度落下之后落下；若它的纬度在南，它在它的度升起之后升起，在它的度落下之前落下。显然，与有纬度之星一同升起的那一度不是它的度，那一度称为它的升起度；同样，与星一同落下的那一度是它的落下度。至于它到达天的中央、与子午圈相遇的时候：若它在两至之一，它就与它的度一同到达，二者没有差别，无论它的纬度在北还是在南。但若它的度不在两至之一，那么，若它的纬度在北，而它的度在上升的一半，即从摩羯座起点到双子座末尾，它就先于它的度到达天的中央；若它的度在下降的一半，它就在它的度到达之后到达〔抄本“之后”与“之前”互倒，据算改正〕。若它的纬度在南，情形相反：我是说，若它的度在上升的一半，它在它的度到达之后到达子午圈，在下降的一半则在它之前〔抄本“之前”与“之后”互倒，据算改正〕。可知它到达天的中央时，与它同在的是另一个度，不是它自己的度；那就是与它一同经过子午圈的度，称为过中天度。在午夜之圈上的情形，与对子午圈所说的完全一样。