卷四·第 232–238 问　正午影、卯酉圈、晡时影、礼拜朝向与七个气候带

§232. Into how many kinds are the shadows of midday and its altitude divided?

第二百三十二问　正午的影与高度分为几种？

The tip of the shadow at midday is always towards the north in the lands whose latitudes exceed the amount of the greatest declination, and the altitude of midday there is on the side of the south; I mean that its complement is the distance of the Sun from the zenith towards the south. There the Sun has a greatest altitude in summer, whose shadow is the shortest of the shadows, and that is at the beginning of Cancer; a least altitude in winter, whose shadow is the longest of the midday shadows, and that is in Capricorn; and a third altitude midway between them, equal to the complement of the latitude of the town, whose shadow is called the shadow of equality or the shadow of the equinox, because it and that altitude occur when the Sun enters the beginning of Aries or the beginning of Libra. In the lands whose latitude equals the greatest declination, what we have mentioned holds good, except for the greatest of the midday altitudes, which there is 90 degrees exactly, not ascribed to north or to south; and the shadow then vanishes there and comes to nothing. In the lands whose latitudes from the equator fall short of the amount of the greatest declination, the state of the winter altitude and the equinoctial altitude, and of what follows them, is also as described above; but the summer altitude is on the side of the north. That is because when the Sun, in its ascent in the north and in its descent from it, has a declination equal to the latitude of the town, it passes over its zenith, and the shadow vanishes there at midday. Then, when its declination exceeds the latitude of the town, the altitude of midday comes to be on the side of the north, and its complement is the Sun's distance from the zenith on that side; and the altitude of midday does not increase as it used to increase on the side of the south, but decreases, as far as the beginning of Cancer, and there it begins to increase. When the altitude is in the north, the tip of the midday shadow is found there once towards the north and once towards the south of the base of the gnomon; and so those lands are called the lands of two shadows, because the tip of the midday shadow is found there once towards the north and another time towards the south.

在纬度超过最大赤纬的地方，正午的影端总是朝北，那里的正午高度在南方一侧；我是说，它的余弧就是太阳在天顶以南离天顶的距离。在那里，太阳有一个夏季的最大高度，其影是诸影中最短的，那是在巨蟹座起点；有一个冬季的最小高度，其影是正午诸影中最长的，那是在摩羯座；还有第三个高度，居于二者正中，等于城市纬度的余弧，其影称为均等之影或春秋分之影，因为它和那个高度出现在太阳进入白羊座起点或天秤座起点之时。在纬度等于最大赤纬的地方，我们所说的都成立，只有正午的最大高度例外：那里它恰为九十度，不属北也不属南；那时影子在那里消失，化为乌有。在离赤道的纬度不足最大赤纬的地方，冬季高度与春秋分高度以及随之而来的情形，也如上所述；但夏季高度在北方一侧。那是因为太阳在北方上升与下降的途中，当它的赤纬等于城市纬度时，它经过城市的天顶，正午时影子在那里消失。然后，当它的赤纬超过城市纬度时，正午高度就到了北方一侧，它的余弧就是太阳在那一侧离天顶的距离；而且正午高度不再像在南方一侧时那样增加，而是减小，一直到巨蟹座起点，从那里它又开始增加。当高度在北方时，正午影端在那里有时在表基之北，有时在表基之南；所以那些地方称为有两种影的地方，因为正午影端在那里一时朝北、一时朝南。

§233. What are the altitude and the shadow that have no azimuth?

第二百三十三问　何谓没有方位的高度与影？

This is a companion of the altitude of midday. The altitude circle passing through the intersection of the horizon with the equator is called the circle that has no azimuth, and it is also called the circle of the first of the azimuths (the prime vertical). When the Sun is on it, its altitude is the one that has no azimuth, and so is its shadow, because it lies in a straight line with the equinoctial line and so is not distant from it. This is not found for the Sun or anything else except when it has a declination in the north, just as it has no azimuth towards the north from the equinoctial line except together with a northern declination.

这是正午高度的伴侣。通过地平与天赤道交点的那个高度圈，称为没有方位之圈，也称为诸方位之首圈（即卯酉圈）。太阳在它上面时，它的高度就是没有方位的高度，它的影也是如此，因为影与春秋分线成一直线，所以不离开它。这对太阳或别的东西来说，只在它有北赤纬时才会出现，正如它不会有春秋分线以北的方位，除非同时有北赤纬。

§234. What is the shadow of the afternoon (ʿaṣr)?

第二百三十四问　何谓晡时之影？

This belongs to the chapters of the imams on the end of the times of the noon prayer (ẓuhr) and the beginning and the end of the times of the afternoon prayer (ʿaṣr). When the shadow of midday is known, which they call the shadow at the declining (zawāl), and then the length of the gnomon is added to it once, and one watches until its shadow becomes of that amount, that is the beginning of the time of the afternoon prayer on that day according to the people of the Ḥijāz. It is called the addition of the like, and on instruments 'beginning of the ʿaṣr' is written against it. When the length of the gnomon is added twice to the shadow at the declining, and one then watches until its shadow becomes of that amount, that is the time of the afternoon prayer according to the people of Iraq. It is called the addition of the two likes, and on instruments 'end of the ʿaṣr' is written against it.

这属于伊玛目们论晌礼时间之末与晡礼时间之始末的章节。当正午之影——他们称为偏转之影——已知，再把表长加上一次，然后守候到影长等于这个量，按希贾兹人的说法，那就是那一天晡礼时间的开始。这称为“加一倍”，器物上在它的对应处写着“晡时之始”。若在偏转之影上把表长加两次，再守候到影长等于这个量，按伊拉克人的说法，那就是晡礼的时间。这称为“加两倍”，器物上在它的对应处写着“晡时之末”。

§235. What is the azimuth of the qibla?

第二百三十五问　何谓礼拜朝向的方位？

It is the meeting of the horizon of the town with the circle that passes through the zenith of the people of that town and of the people of Mecca [corrected: MS omits 'and of the people of Mecca']; and its distance from the equinoctial line or from the meridian line is the amount by which the one who prays must turn away from these. This is the figure of it.

它是城市的地平与那个通过该城居民天顶和麦加居民天顶〔抄本脱“和麦加居民”，据文义改正〕的圆的交点；它离春秋分线或离子午线的距离，就是礼拜的人须从这两条线转开的量。这是它的图。

§236. What are the climes?

第二百三十六问　何谓气候带？

The practitioners of this art have divided the habitable part of the inhabited quarter into seven oblong strips, which they have called climes (aqālīm), running from east to west parallel to the equinoctial line, such that the longest summer daytime in their middles differs by half an hour; for the changes come only from latitude, and from longitude there comes nothing but the difference in rising, which is known only by report. The hours of the longest daytime in the middle of the middle one of them, which is the fourth, are 14 1/2 hours; then one goes back from it until the hours of the longest daytime in the middle of the first of them are 13, and one goes beyond it to the middle of the seventh clime, where the hours of its longest daytime are 16. Since their latitudes are found in the books with differing amounts, on account of the disagreement about the amount of the greatest declination, of the different methods of dividing the sines, and of some who reckon them hitting on what is right while others deviate from it in [illegible] their reckoning [text uncertain], I have put them in this table with the utmost accuracy.

本行的从业者把有人居住的四分之一中可以居住的部分分成七条长带，称为气候带，自东向西延伸，与赤道线平行，使各带中线上的夏季最长白昼相差半小时；因为变化只来自纬度，从经度来的只是升起时刻的差别，而那只能凭传闻得知。居中的一带即第四带，其中线上的最长白昼为十四个半小时；然后由它往回退，直到第一带中线上的最长白昼为十三小时；再往前，直到第七带中线，那里的最长白昼为十六小时。由于书中所载各带的纬度数值不一，原因在于对最大赤纬之数有分歧、正弦的分法不同，以及推算的人有的算对了，有的在〔抄本此处字迹难辨〕他们的推算上有偏差〔原文疑有讹误〕，我就以极其精确的方式把它们列在这张表里。

§237. What happens in the climes, and is there habitation beyond them?

第二百三十七问　诸气候带中会发生什么？气候带之外还有人居住吗？

As for habitation, Ptolemy has asserted that its farthest end is found in the island of Thule (Tūlī), whose latitude is close to the complement of the greatest declination, which is approximately 66 parts. But the nations between the end of the seventh clime and that limit are more like wild beasts than men in their way of living and their eating. With all that, the differences we have mentioned, and the difference in the ascensions of the signs, keep increasing as one goes farther into the north. The risings of the two solstices widen and come nearer to their settings, until they coincide at the latitude equal to the complement of the greatest declination. Then the whole orbit of the beginning of Cancer is visible, and the longest daytime is 24 hours, since the Sun stays visible. It happens at this place that the north pole of the zodiac passes over the zenith once each day, and the zodiac then coincides with the horizon; then six signs of it appear all at once. From this place on, the summer shadows begin to go round the gnomons on all sides.

至于居住，托勒密断言它的最远之处在图勒岛，其纬度接近最大赤纬的余弧，约为六十六度。但从第七带的末尾到那个界限之间的民族，在生活方式和饮食上，更像野兽而不像人。尽管如此，我们所说的那些差别，以及星座上升时间的差别，越往北深入就越增大。两至的日出处越来越向两旁展开，越来越靠近它们的日落处，直到在纬度等于最大赤纬之余弧的地方两者重合。那时巨蟹座起点的日周圈全都可见，最长白昼为二十四小时，因为太阳一直可见。在这个地方，黄道的北极每天经过天顶一次，那时黄道与地平重合；于是它的六个星座一下子同时出现。从这个地方起，夏季的影子开始绕着表四面转。

§238. What happens beyond this place?

第二百三十八问　过了这个地方又会怎样？

Together with the orbit of the beginning of Cancer other orbits appear, on which the Sun stays visible as long as it goes round with them, so that the longest daytime grows from a single day to several days, then months. Opposite it, together with the orbit of the beginning of Capricorn, orbits are hidden on which the Sun stays hidden as long as it is on them, and the amount of the longest night goes beyond a day to days and months, according to how far one penetrates towards the north. It happens in these places at certain times that the signs rise in reverse of their order: I mean Taurus, then Aries, then Pisces, then Aquarius. Just as the daily orbits stand upright on the horizon of the equinoctial line, which is why the orb there is called the right orb and its revolution an upright one, and then incline on the horizons of the towns that have latitudes, so that the revolution of the orb there is called ḥamāʾilī ('like a sword-belt'), so at the extreme of latitude, where the north pole is at the zenith, the equator always coincides with the horizon, all the northern orbits are visible there and the southern ones hidden, and the revolution of the orb is raḥawī ('like a millstone'). As long as the Sun is north of the equator it is visible there, and as long as it is south it is hidden; so the year there becomes a single day, of which about 6 months are daytime and the rest night.

与巨蟹座起点的日周圈一起，又有别的日周圈显现出来，太阳随它们运转期间一直可见，所以最长白昼从一日增到好几日，再到几个月。与之相对，与摩羯座起点的日周圈一起，有些日周圈隐没，太阳在它们上面时一直隐没，最长黑夜的长度超过一日，到几日、几个月，视人向北深入多远而定。在这些地方，某些时候星座会逆着次序升起：我是说，先金牛，再白羊，再双鱼，再宝瓶。正如日周圈在赤道线的地平上直立，所以那里的天球称为正球，它的运转称为直立的运转；在有纬度的城市的地平上则倾斜，所以那里天球的运转称为“佩带式”；同样，在纬度的极端，北极在天顶，天赤道总与地平重合，北方的诸日周圈在那里全都可见，南方的全都隐没，天球的运转是“磨盘式”。太阳在天赤道以北时，在那里可见；在以南时，就隐没；所以那里的一年成为一日，其中约六个月是白昼，其余是黑夜。