卷四·第 222–231 问　昼弧、恒显恒隐之星、高度、表影与方位

§222. What are the arc of daytime, its excess and its equation?

第二百二十二问　何谓昼弧、昼之余与昼之均差？

The arc of daytime is the part of the daily orbit that is above the horizon, and the arc of night the part of it that is below the horizon; it is expressed as the amount of its times. The excess of daytime is its increase over the equal daytime, which is 12 hours or 180 times, or its shortfall from it. The equation of daytime is half the excess of daytime. This is the figure of it.

昼弧是日周圈在地平以上的部分，夜弧是它在地平以下的部分；昼弧以它所含时度的多少来表示。昼之余是白昼比等昼——即十二小时，或一百八十时度——多出的部分，或比它短少的部分。昼之均差是昼之余的一半。这是它的图。

§223. What are the stars that are always visible and always hidden?

第二百二十三问　何谓恒显之星与恒隐之星？

If you imagine a circle drawn about the north pole at the distance of its altitude, it is the greatest of the circles visible in the town whose latitude is the altitude of the pole, by touching the horizon. The circles drawn about the pole inside it do not reach the horizon, and the stars that revolve on them are the ones always visible, because they complete their circuits above the horizon and do not cut it so as to appear by rising and be hidden by setting, since rising and setting come about through the intersection of the daily orbit with the horizon; they are only concealed from sight by the brightness of daytime and appear to it in the darkness of night. An example of this is the Greater Banāt Naʿsh, all of which do not set in the lands of Transoxiana (mā warāʾ al-nahr), while some of the Daughters set at Mecca and in al-Yaman. The same is the case with the stars that revolve inside the circle drawn about the south pole at the amount of its depression: they are always hidden in that town. An example of this is Suhayl, which is seen above the horizon but is never seen at all in the lands of Transoxiana.

若你设想绕北极、以北极高度为距离画一个圆，它就是在纬度等于北极高度的那座城市里可见诸圆中最大的一个，因为它与地平相切。绕北极画在它里面的诸圆碰不到地平，在这些圆上运转的星就是恒显之星，因为它们在地平以上走完一周，不与地平相交，不会因升起而出现、因落下而隐没——升起与落下，是由日周圈与地平相交而来的；它们只是被白昼的光亮遮住，看不见，到夜晚的黑暗中又显现出来。例子是大棺架之女，它们在河中地区全都不落，而其中“女儿”的一部分在麦加和也门会落下。绕南极、以南极低落的度数为距离所画之圆以内运转的星，也是同样的情形：它们在那座城市里永远隐没。例子是苏海勒：它［在别处］见于地平之上，在河中地区却全然看不见。

§224. Is this permanence in visibility and hiddenness real or not?

第二百二十四问　这种恒显与恒隐是真实的吗？

It is not, because the motion of the fixed stars is about the pole of the zodiac, so that their distances from it do not change; only their distances from the pole of the universe change. So a star may come inside one of the two circles touching the horizon that we have mentioned, after not having been in it, and become always visible or always hidden after it used to rise and set; or it may go out of the two circles and come to have rising and setting after its visibility or hiddenness had been permanent. But that happens over long stretches of time, because of the length of the periods of that motion. The rule for it is that any star that is visible and is not hidden, or hidden and does not appear: if its latitude is subtracted from 90 and the remainder is more than the difference between the latitude of the town and the greatest declination, then it is one that may come to have rising and setting there; but if the remainder is less, its passing out of that state is impossible.

不是。因为恒星的运动是绕黄道之极的，所以它们与黄道之极的距离不变，变的只是它们与宇宙之极的距离。于是一颗星可能在不曾进入我们所说的那两个与地平相切的圆之后，进入其中一个，原先有升有落，变成恒显或恒隐；也可能出了这两个圆，原先恒显或恒隐，变成有升有落。但这要经过很长的时间才会发生，因为那种运动的周期很长。它的法则是：任何一颗显而不隐、或隐而不显的星，若从九十中减去它的纬度，余数大于城市纬度与最大赤纬之差，它就是在那里可能变成有升有落的星；若余数较小，它就不可能脱离那种状态。

§225. What are altitude and depression and their complements?

第二百二十五问　何谓高度、低落及其余弧？

If the Sun, or a star, or any assumed point of the orb whatever, happens to be above the horizon, and a great circle passing through the pole of the horizon is turned round to pass over it, then the part of it falling between the thing and the horizon is the altitude of that thing, and it stands perpendicular; and what lies between that thing and the zenith, which is one of the two poles of the horizon, is the complement of that altitude. If the assumed thing is below the horizon and what we have mentioned is done, then the part of that circle falling between it and the horizon is its depression, and what lies between it and the nadir, which is the other pole of the horizon, is the complement of that depression.

若太阳、或一颗星、或天球上任意假设的一点恰在地平以上，让一个通过地平之极的大圆转过来经过它，那么这圆上落在该物与地平之间的部分，就是该物的高度，它是垂直立着的；该物与天顶——地平的两极之一——之间的部分，就是这高度的余弧。若所设之物在地平以下，照我们所说的去做，那么那圆上落在它与地平之间的部分就是它的低落，它与天底——地平的另一极——之间的部分就是这低落的余弧。

§226. What is the mean altitude?

第二百二十六问　何谓中高度？

It is the part of the altitude circle of the thing that falls between the equator and the horizon, and its complement is what lies between the equator and the zenith on this circle.

它是该物的高度圈上落在天赤道与地平之间的部分；它的余弧是这个圈上天赤道与天顶之间的部分。

§227. What are the gnomon and the shadow?

第二百二十七问　何谓表与影？

The gnomon is an upright body of wood or some other substance, straight, with a sharp head shaped like a cone, set up like a peg perpendicular to the surface on which it is set. The shadow is the shadow of that gnomon, measured in the parts of its length so that it is known how much it is of it. The line joining the tips of the gnomon and of the shadow is called the hypotenuse of the shadow.

表是一根直立的物体，用木头或别种材料做成，挺直，顶端尖锐，作圆锥之形，像木桩一样垂直立在所安放的面上。影就是这根表的影子，用表长的份数来量，以便知道它是表长的多少。连接表端与影端的线，称为影的斜边。

§228. How many are the parts of the gnomon?

第二百二十八问　表分为几份？

When they are 12 equal parts they are called parts [sic]; when they are 60 they are called parts; and when they are 6 1/2 they are called feet. In this there is disagreement, for some of them divide the body for feet into 7 equal parts.

分成十二等份时，称为“份”〔原书如此〕；分成六十份时，称为“份”；分成六又二分之一份时，称为“足”。这一点有分歧：有些人按足来分时，把表身分成七等份。

§229. How many are the kinds of shadow?

第二百二十九问　影有几种？

They are two. One is called spread out and level: that is when the gnomon is set up on the plane of the horizon after levelling and correction, and its shadow spreads out on the ground. The other kind is called reversed and upright: that is when the gnomon is set up on a surface facing the Sun, such as a wall or something else, the gnomon being on it like a peg, and its shadow stands upright on the ground, with its head downward; and so it is called reversed.

有两种。一种称为铺开的、平的影：那是把表在整平、校正之后立在地平的平面上，它的影子铺在地上。另一种称为倒的、竖的影：那是把表安在朝向太阳的面上，例如墙壁之类，表像木桩一样钉在上面，它的影子竖着向地面伸去，头朝下；所以称为倒影。

§230. What is the azimuth?

第二百三十问　何谓方位？

The meeting of the circle of altitude of the elevated thing, whether Sun, star or anything else, when it passes through the two poles of the horizon, with the horizon, is its azimuth. Then its distance is found either from the equinoctial line, in which case its distance from the meridian line is the complement of the azimuth, or from the meridian line, in which case its distance from the equinoctial line is the complement of the azimuth. If a line is drawn on the plane of the level shadow, in a straight line with it, until it reaches the circumference of the Indian circle, its end is at the tip of the azimuth, and the amount of its distance is equal to that of the azimuth but on the opposite side: I mean, if the shadow is towards the west, the azimuth is towards the east, and the reverse; and if it is towards the north, the azimuth is towards the south, and the reverse. This is the figure of it.

高起之物——太阳、星或别的什么——的高度圈通过地平两极，它与地平相交之处，就是该物的方位。然后求它的距离：或从春秋分线量起，这时它离子午线的距离就是方位的余弧；或从子午线量起，这时它离春秋分线的距离就是方位的余弧。若在平影的平面上，沿着影子画一条与它成一直线的线，一直画到印度圆的圆周，它的端点就对着方位的端点，距离的大小与方位相等，但在相反的一侧：我是说，影在西，方位就在东，反之亦然；影在北，方位就在南，反之亦然。这是它的图。

§231. What is all this at midday?

第二百三十一问　这一切在正午时如何？

The circles passing through the two poles of the horizon, when altitude is meant by them, are named after it; and the meridian is one of them, the one of them that passes through the centre and the two poles of the equator. When the altitude is taken on it, it is called the altitude of midday; and since the shadow goes according to the altitude, its shadow is called the shadow of midday, which, on the plane of the horizon, is the shortest of the shadows of the gnomon on that day. Since the meridian circle cuts the horizon at the very points of north and south, the azimuth of midday is one of these two points, and no distance from anything is mentioned with it.

通过地平两极的诸圆，用来量高度时，就以高度为名；子午圈是其中之一，就是其中通过天赤道中心与两极的那一个。在它上面取的高度称为正午高度；又因为影随高度而变，它的影称为正午之影，在地平面上，它是那一天表影中最短的。又因为子午圈恰在正北、正南两点切过地平，正午的方位就是这两点之一，不必说它离什么有多少距离。