卷七·第 337–343 问　恒星高度、夜间求时、星的升落、均齐十二宫与河宽

§337. How is the altitude of the fixed stars found?

第三百三十七问　怎样求恒星的高度？

Choose one of them that is fixed on the spider and face it, and hang the astrolabe from your right hand, hanging down freely; then the quadrant of altitude will necessarily face the star, provided that its back is toward you. Then raise and lower the alidade, looking with one eye through the hole of the lower 'brick', until you happen to see that star through both holes of the two bricks. When that happens, look at the pointer of the alidade, at how many of the parts of altitude it has fallen: that is the altitude of that star. Then find out its direction with respect to the meridian line, whether it is east of it or west of it.

在蛛网上标定了的恒星中选一颗，面向它，用右手提起星盘，让它自由下垂；只要背面朝着你，高度象限就必然对着那颗星。然后升降照准尺，用一只眼从下面那块“砖”的孔里望去，直到恰好透过两块砖的两个孔看见那颗星。这时看照准尺的指针落在高度的多少份上：那就是那颗星的高度。然后弄清它相对于子午线的方向，是在它以东还是以西。

§338. How do you find the ascendant from it?

第三百三十八问　你怎样由它求上升点？

Put the pointer of that star, which is its sharpened tip on the spider, on the like of the altitude you found for it among the almucantars of the east if the altitude was eastern, and among the almucantars of the west if it was western. Then look at the horizon of the east: what part of the zodiac meets it is the sign of the ascendant with its degrees. And look at the degree of the Sun, where it has fallen among the crooked hours: those are your hours.

把那颗星的星针，也就是它在蛛网上削尖的尖头，放在与你为它测得的高度相同的地平纬圈上：高度若是东方的，就在东方地平纬圈中，若是西方的，就在西方地平纬圈中。然后看东方地平：黄道带与它相遇的部分，就是上升星座及其度数。再看太阳的度数落在曲时之中的哪里：那就是你的时数。

§339. How is what has passed of the night found?

第三百三十九问　怎样求夜间已过了多少？

When the ascendant has been put on the horizon of the east, make a mark at the place of the pointer on the ḥujra. Then turn the spider backwards, toward the left, until the opposite of the degree of the Sun meets the horizon of the east, and see how far the pointer has moved along the ḥujra: that is the revolved part. Then turn it into hours, as was said before.

把上升点放在东方地平上以后，在指针于围垣上的位置作个记号。然后把蛛网向左倒转，直到太阳度数的对冲点与东方地平相遇，看指针沿着围垣移动了多远：那就是已转之度。然后照前面所说，把它化为小时。

§340. How is the time of the rising and the setting of a star found, by night and by day?

第三百四十问　怎样求一颗星在夜里或白天升起与落下的时刻？

Put its sharpened tip on the horizon of the east, then look at the degree of the Sun. If it is above the earth, in the region of the almucantars, the rising of that star will be by day; so make a mark at that moment at the place of the pointer on the ḥujra, then turn the spider backwards until the degree of the Sun meets the horizon of the east. What the pointer has moved of the parts of the ḥujra is the revolved part; turn it into hours, and they are what has passed of the daytime up to the time of the rising of the star. If the degree of the Sun is beneath the horizon, in the region of the hours, the rising of that star will be by night; so make a mark at the place of the pointer on the ḥujra, and turn the spider backwards until the opposite of the degree of the Sun meets the horizon of the east. Then what the pointer has moved is the revolved part; turn it into hours, and they are what has passed of the night up to the rising of the star. If you want the like of this for its setting, use the horizon of the west instead of the horizon of the east, and follow in the rest of the work exactly what we have described, until you obtain the circumstances of its setting.

把它削尖的尖头放在东方地平上，然后看太阳的度数。若太阳在地上，在地平纬圈的区域里，那颗星的升起就在白天；于是在此刻于指针在围垣上的位置作个记号，然后把蛛网倒转，直到太阳度数与东方地平相遇。指针在围垣的刻度上移动了多少，就是已转之度；把它化为小时，就是到那颗星升起时白昼已过的时数。若太阳度数在地平以下，在时辰的区域里，那颗星的升起就在夜里；于是在指针于围垣上的位置作个记号，把蛛网倒转，直到太阳度数的对冲点与东方地平相遇。那么指针移动的就是已转之度；把它化为小时，就是到那颗星升起时夜间已过的时数。若想求它落下时的同样数据，就用西方地平代替东方地平，其余的做法完全照我们所描述的去做，直到得出它落下时的情形。

§341. How are the twelve houses equalized?

第三百四十一问　怎样均齐十二宫？

Put the degree of the ascendant on the horizon of the east; then its opposite, which is the degree of the seventh, meets the horizon of the west. Then look at the meridian line: whatever sign and degrees meet it are those of mid-heaven. By count, the sign of mid-heaven ought to be the tenth from the sign of the ascendant. If what you have found is indeed the tenth from the ascendant, write down its degrees with it, for the angles are upright. When they are inclining, what comes out with the astrolabe is the eleventh sign; so begin the writing for mid-heaven with the tenth by count, say for example Aquarius, then follow it with what was found together with its degrees, so that it becomes 'Aquarius, of Pisces so many degrees'. When the angles are declining, what comes out with the astrolabe is the ninth sign; so begin with the count and say 'Aquarius, of Capricorn so many degrees'. The degrees of the fourth are equal to the degrees of the tenth, and likewise every house and its opposite, and the signs are opposite one another: I mean that if the tenth is Aquarius, the fourth is Leo; if the tenth is 'Aquarius of Pisces', the fourth is 'Leo of Virgo'; and if the tenth is 'Aquarius of Capricorn', the fourth is 'Leo of Cancer'. This is a rule that holds for all the houses once one of them is known. Then turn the spider backwards until the degree of the ascendant goes down beneath the horizon by two crooked hours and comes onto the line of the beginning of the eleventh hour; then look at the meridian line: whatever sign and degree meet it are the sign of the ninth house and its degrees, and its opposite is the sign of the third and its degrees. Then turn it backwards further, until the degree of the ascendant goes down two more crooked hours and comes onto the beginning of the ninth hour; then what meets the meridian line is the sign of the eighth house and its degree, and its opposite is the sign of the second house and its degree. Then put the opposite of the degree of the ascendant on the line of the beginning of the third hour beneath the horizon of the west; then what is on the meridian line is the sign of the eleventh house and its degree, and its opposite is the sign of the fifth house and its degree. Then turn the spider in the direct direction, toward the right, until the opposite of the degree of the ascendant goes down and comes onto the line of the beginning of the fifth hour; then the sign of the twelfth house and its degree meet the meridian line, and the houses are complete and equalized.

把上升点的度数放在东方地平上；它的对冲点，即第七宫的度数，就与西方地平相遇。然后看子午线：与它相遇的星座与度数，就是中天的星座与度数。按数，中天的星座应当是从上升星座起的第十个。若你所得到的确实是从上升起的第十个，就把它的度数连同它写下，因为这时诸角是直立的。当诸角倾斜时，用星盘得出的是第十一个星座；那就以按数的第十个，比如说水瓶座，开头来写中天，再接着写所得到的星座及其度数，成为“水瓶座、双鱼座若干度”。当诸角偏离时，用星盘得出的是第九个星座；那就以按数的开头，说“水瓶座、摩羯座若干度”。第四宫的度数等于第十宫的度数，每一宫与其对宫都是如此，星座也彼此相对：我是说，若第十宫是水瓶座，第四宫就是狮子座；若第十宫是“水瓶座、双鱼座”，第四宫就是“狮子座、处女座”；若第十宫是“水瓶座、摩羯座”，第四宫就是“狮子座、巨蟹座”。这是一条规则，只要知道其中一宫，就适用于所有各宫。然后把蛛网倒转，直到上升点的度数沉到地平以下两个曲时，到达第十一时起点的那条线上；然后看子午线：与它相遇的星座与度数，就是第九宫的星座及其度数，它的对冲点就是第三宫的星座及其度数。然后再往回转，直到上升点的度数再沉下两个曲时，到达第九时的起点；这时与子午线相遇的，就是第八宫的星座及其度数，它的对冲点就是第二宫的星座及其度数。然后把上升点度数的对冲点放在西方地平以下第三时起点的那条线上；这时子午线上的就是第十一宫的星座及其度数，它的对冲点就是第五宫的星座及其度数。然后把蛛网顺着方向向右转，直到上升点度数的对冲点沉下去，到达第五时起点的那条线上；这时第十二宫的星座及其度数就与子午线相遇，诸宫就齐全而均齐了。

§342. How is the ascendant found from another angle?

第三百四十二问　怎样由另一个角求上升点？

If what is known is the angle of the setting, put its degree within its sign on the horizon of the west; if it is the angle of mid-heaven, put it on the line of mid-heaven toward the throne (kursī); and if it is the angle of the earth, put it on the line beneath the horizon. Then in all of these look at what meets the east: that is the sign of the ascendant and its degree.

若已知的是下降之角，就把它在其星座中的度数放在西方地平上；若是中天之角，就把它放在朝向宝座的中天线上；若是地之角，就把它放在地平以下的那条线上。然后在所有这些情形下看与东方相遇的是什么：那就是上升星座及其度数。

§343. Finding the breadth of a river, or a distance on the ground, when something intervenes between the measurer and the measuring of it

第三百四十三问　求一条河的宽度，或测量者与所量之物之间有阻隔时求地面上的一段距离

Stand on its bank and hang the astrolabe from your right hand; look with one of your eyes through the hole of the sight next to you, and lower and raise the alidade until you see through both holes of the two sights what faces you on the other bank. Then turn round on yourself where you stand until you face the dry land, the alidade remaining as it was, and look through the holes of the two sights with one of your eyes until your sight falls through them on the ground. Make a mark at the place where your sight ended, and measure what is between where you stand and that mark: whatever it is, that is the breadth of the river. Likewise, if the place whose measure is sought is on the surface of the earth and its open space cannot be reached, put it in the place of the river and its far boundary in the place of the other bank, and do what was said before, until you find its like in distance on the ground, which can be measured.

站在河岸上，用右手提起星盘；用一只眼从靠近你的那块觇板的孔里望去，降低、升高照准尺，直到透过两块觇板的两个孔看见对岸正对你的东西。然后在你所站之处原地转身，直到面对旱地，照准尺保持原样，用一只眼透过两块觇板的孔看去，直到你的视线穿过它们落在地上。在你视线所止之处作个记号，量你所站之处与那个记号之间的距离：不论是多少，那就是河的宽度。同样，若所求量的地方在地面上，而它的空旷处无法走到，就把它放在河的位置上，把它的远端放在对岸的位置上，照前面所说的去做，直到在地面上找到一段与它距离相等、可以量的距离。