卷七·第 332–336 问　由太阳高度求上升、已过昼时、曲时与夜间诸法

§332. Finding the ascendant from the altitude of the Sun.

第三百三十二问　由太阳的高度求上升点。

Turn the astrolabe over to its face, and put the face of the plate whose latitude either agrees with the latitude of your town or is nearer to it than the other latitudes above all the plates, visible to the eye. Then look among the almucantars for an almucantar whose number is the same as the altitude of the Sun that you have: if it is eastern, among the eastern almucantars, and if western, among the western almucantars; and mark it. Do not doubt of finding it if the astrolabe is complete. If it is not complete, one may not find that very altitude among its almucantars, but it falls between two of the almucantars drawn on it. Say, for example, the altitude was 20 degrees and the astrolabe a sixth; the altitude then lies between the almucantars 18 and 24. But between 18 and the altitude are 2 degrees, which are a third of what lies between the two almucantars; so a third of the gap between the almucantars 18 and 24 is kept, from the almucantar 18, estimated by the judgement of the eye, and marked there, for that is the place of the almucantar 20. If the astrolabe were, say, a third, the altitude we have would lie between the almucantars 18 and 21, and between 18 and this altitude are 2 degrees, which are two thirds of what lies between the two almucantars; so two thirds of the distance are taken from 18, and where it ends is marked, for that is the place of the almucantar 20. Then find the place of the Sun at that time from the almanac of the year, and look for its degree on the zodiac of the spider, in the sign in which it is. If the astrolabe is not complete and the degree of the Sun does not coincide with one of the lines by which the signs are divided, we follow in that what we have taught in looking for the altitude between two almucantars. When we have got the degree of the Sun, we put a mark on it; then we put it on the almucantar of its altitude that we had marked on its side, east or west, and look at what part of the zodiac meets the horizon of the east: that is the ascending sign with its degrees. If it does not happen that the horizon of the east is at one of the lines dividing the sign, but is between two of them, we find the number of the first line, which is the one nearer to the head of the sign, and keep it; then we estimate what lies between the first line and the horizon of the east, and how much it is of the whole of what lies between the two lines, and add it to what we kept; the sum is what has risen of the degrees of that ascending sign. For example, we looked, and what was on the horizon of the east was the sign of Pisces, and the horizon fell between the third and the fourth of the dividing lines on an astrolabe that is a sixth. The number of the third line, which is the first of the two, is 18, and that is what is kept. We estimated what lay between the first line and the horizon, and it was a third of what lies between that line and the second; but what lies between them is 6 degrees, so a third of it is 2 degrees. We added that to the 18 kept, and the sum was 20, which is the degrees of the sign of Pisces rising at that time. So one works in everything of that kind in all the chapters, for to repeat the account of it would be long and wearisome.

把星盘翻到正面，把纬度与你所在城市的纬度相合、或比其他纬度更接近它的那块盘片的那一面，放在所有盘片的最上面，使它显露在眼前。然后在地平纬圈中找一条编号与你所测得的太阳高度相同的地平纬圈：高度若是东方的，就在东方地平纬圈中找；若是西方的，就在西方地平纬圈中找；并作上记号。星盘若是全盘，就不必怀疑找不到它。若不是全盘，就可能在它的地平纬圈中找不到那个高度本身，而它落在盘上所画的两条地平纬圈之间。比如说，高度是二十度，星盘是六分盘；那么这个高度就在十八与二十四两条地平纬圈之间。但从十八到这个高度是两度，是两条地平纬圈之间的三分之一；所以从十八这条地平纬圈起，凭眼力估量，取十八与二十四两条地平纬圈间隔的三分之一，在那里作记号，因为那就是二十这条地平纬圈的位置。若星盘比如是三分盘，我们所测的高度就在十八与二十一两条地平纬圈之间，从十八到这个高度是两度，是两条地平纬圈之间的三分之二；所以从十八起取这段距离的三分之二，在终点作记号，因为那就是二十这条地平纬圈的位置。然后从当年的年历中查出此时太阳的位置，在蛛网的黄道带上、太阳所在的星座里找到它的度数。若星盘不是全盘，太阳的度数又不恰好落在划分星座的某条线上，我们就照教过的在两条地平纬圈之间找高度的办法去做。得到太阳的度数后，在上面作个记号；然后把它放到我们在其所属一侧（东或西）记下的那条高度地平纬圈上，看黄道带的哪一部分与东方地平相遇：那就是上升星座及其度数。若东方地平不恰好在划分星座的某条线上，而在两条线之间，我们就找出第一条线，也就是离星座起点较近的那条线的编号，把它记住；然后估量第一条线与东方地平之间的距离，是两条线之间全部距离的几分之几，加到记住的数上；其和就是那个上升星座已升起的度数。例如，我们看到，在东方地平上的是双鱼座，地平落在一块六分盘上划分线的第三与第四条之间。第三条线，也就是两条中的第一条，编号是十八，这就是要记住的数。我们估量第一条线与地平之间的距离，是那条线到第二条线之间距离的三分之一；而两线之间是六度，其三分之一是两度。我们把它加到记住的十八上，和是二十，这就是此时双鱼座升起的度数。一切同类的事，在所有各章里都这样做，因为重复讲述就冗长而令人厌倦了。

§333. How is what has passed of the daytime known?

第三百三十三问　怎样知道白昼已过了多少？

When the ascendant with its degrees is set on the horizon of the east, look where the pointer, which is the head of Capricorn, is among the parts of the ḥujra, and put a mark where it falls. Then turn the spider backwards, against the order of the signs [sic], I mean from the west to mid-heaven to the east, until the degree of the Sun that you marked meets the horizon of the east, and look where the pointer has reached on the ḥujra. Count from the first mark up to it: what it comes to is the times of the equator that have revolved from the rising of the Sun to the time when the altitude was measured. Take from them an hour for every 15 times, and for what does not make up 15, take for each time 4 minutes of an hour. What is gathered from that is what has passed of the daytime, in equal hours and their fractions.

把上升点连同其度数放在东方地平上以后，看指针，也就是摩羯座的起点，落在围垣的哪一份上，在它所落之处作个记号。然后把蛛网倒转，逆着星座的次序〔原书如此〕，我是说从西方转到中天、再转到东方，直到你记下的太阳度数与东方地平相遇，看指针在围垣上到了哪里。从第一个记号数到它：所得之数，就是从太阳升起到测高之时天赤道所转过的时度。每十五时度取一小时，不满十五的，每一时度取一小时的四分钟。由此合起来的，就是白昼已过的等时及其零头。

§334. How are the ascendant and the altitude of the Sun known from what has passed of the daytime?

第三百三十四问　怎样由白昼已过的时数知道上升点与太阳的高度？

When you are given hours that have been observed by water or sand or the like, take for every hour 15 times, and for the fractions of the hour one time for every 4 minutes; the times gathered are the revolved part. Then put the degree of the Sun on the horizon of the east, mark where the pointer falls on the ḥujra, and count from it in the direct direction, from left to right, I mean from the east to mid-heaven to the west, as much as the revolved part that you have, and mark where it ends. Then turn the spider until the pointer reaches this last mark at which you ended, and look at the horizon of the east, what sign and degree meet it: that is the ascendant. And look at the degree of the Sun, what almucantar it meets: its number is the altitude of the Sun at that time, on the side of the almucantar, east or west.

若给了你用水、沙或类似之物观测到的时数，就每一小时取十五时度，小时的零头每四分钟取一时度；合起来的时度就是已转之度。然后把太阳的度数放在东方地平上，在指针落在围垣上的地方作记号，从那里顺着方向，即从左到右，我是说从东方到中天再到西方，数出你所有的已转之度，在数完之处作记号。然后转动蛛网，直到指针到达你最后数完的这个记号，看东方地平，与它相遇的是哪个星座、哪一度：那就是上升点。再看太阳的度数与哪条地平纬圈相遇：它的编号就是此时太阳的高度，在那条地平纬圈所在的一侧，东或西。

§335. How are the crooked hours known?

第三百三十五问　怎样知道曲时？

When the ascendant is set on the horizon of the east, look at the opposite of the Sun's degree, which is the seventh sign from it at the same degree, and where it falls among the crooked hours, between their lines drawn beneath the horizon: that hour is the one sought. Only its name is needed; how much of it has passed is not needed.

把上升点放在东方地平上以后，看太阳度数的对冲点，即从太阳起第七个星座的同一度，落在曲时之中、地平以下所画诸线之间的哪里：那一时就是所求的。只需要知道它的名称；它已过了多少，则不需要。

§336. How are these things known from the hours of the night?

第三百三十六问　怎样由夜间的时数知道这些事？

The altitude of the Sun at night is non-existent, because it is hidden. So when you are given hours of the night that have been observed, make them the revolved part. Then put the opposite of the Sun's degree on the horizon of the east, for this opposite stands at night in the place of the Sun's degree by day; count from where the pointer falls on the ḥujra, in the direct direction, as much as the revolved part you have, and turn the spider until the pointer reaches where the count ended. Look at the horizon of the east, what part of the zodiac meets it: that is the ascendant with its degrees. And look at the degree of the Sun, where it falls among the crooked hours: those are the crooked hours that have passed of the night.

夜间太阳的高度是不存在的，因为它隐没了。所以给了你观测到的夜间时数时，就把它们当作已转之度。然后把太阳度数的对冲点放在东方地平上，因为这个对冲点在夜里所处的位置，正如白天太阳度数所处的位置；从指针落在围垣上的地方，顺着方向数出你所有的已转之度，再转动蛛网，直到指针到达数完之处。看东方地平，黄道带的哪一部分与它相遇：那就是上升点及其度数。再看太阳的度数落在曲时之中的哪里：那就是夜间已过的曲时。