卷七·第 344–346 问　井深、可达与不可达之塔高，转入占星

§344. Finding the depth of a well

第三百四十四问　求井的深度

Stand on the brink of the well and take the astrolabe in your left hand, so that the quadrant of altitude is toward you and the quadrant of the shadow toward the well. Turn the alidade until you see with one of your eyes, through both holes, the edge of the water or of the bottom on the side that faces where you stand. Find out the amount of the shadow from the place of the pointer of the alidade, [then set the pointer] on the like of what you have, [with one more] of the fingers [text uncertain]. Then go up from where you stand, straight, until you come to where you see through the two holes the edge of the water that you saw at first, without moving the alidade from its second setting. Measure in cubits what is between the two standing-places, and multiply whatever it is by the fingers of the shadow kept in memory: what results is the depth of the well in cubits. And if you multiply the cubits between the two standing-places by 12, the breadth of the well results, I mean the width of its diameter [sic].

站在井沿上，用左手拿着星盘，使高度象限朝着你，影象限朝着井。转动照准尺，直到你用一只眼透过两个孔看见水面的边缘或井底的边缘，就在正对你所站之处的那一侧。从照准尺指针的位置求出影的数量，［然后把指针放］在与你所得相同的数上，［再多一］指〔原文疑有讹误〕。然后从你所站之处笔直向上，直到你来到透过两个孔又看见你起初所见的那个水面边缘之处，照准尺不离开它的第二个位置。用肘尺量两个站立处之间的距离，不论是多少，用记住的影指去乘它：所得就是以肘尺计的井深。若用十二去乘两站之间的肘尺数，就得出井的宽度，我是说它的直径的宽〔原书如此〕。

§345. Finding the height of a minaret or a wall that can be reached

第三百四十五问　求能走到其脚下的宣礼塔或墙的高度

Watch the altitude of the Sun until it becomes 45 parts; then measure at that moment the shadow of that minaret or wall from its tip to its foot: whatever it is, that is its height that is sought. If the Sun does not reach this amount of altitude on that day, and you want it at that time without waiting, put the pointer of the alidade on 45 of the parts of altitude, then go forward or back, looking with one of your eyes through both holes of the two sights at the top of the minaret or the wall, until you see it through both together, the alidade remaining in its setting. Then measure from where you stand to its foot, and whatever it is, add to it the height of your stature: what results is the height of the minaret.

守候太阳的高度，直到它成为四十五份；就在那一刻量那座宣礼塔或那堵墙的影，从影端量到它的脚下：不论是多少，那就是所求的高度。若那一天太阳达不到这个高度，或者你想当时就求而不愿等待，就把照准尺的指针放在高度的四十五份上，然后前进或后退，用一只眼透过两块觇板的两个孔望宣礼塔或墙的顶端，直到同时透过两孔看见它，照准尺保持原样。然后从你所站之处量到它的脚下，不论是多少，再加上你身体的高度：所得就是宣礼塔的高度。

§346. Finding the height of a minaret or a wall that cannot be reached

第三百四十六问　求走不到其脚下的宣礼塔或墙的高度

Stand in some place and lower and raise the alidade, looking with one eye through the holes of the two sights at the top that is sought, until you see it, just as the altitude of the stars is taken. Then see on how many of the fingers of the shadow the pointer of the alidade has fallen: that is the first shadow. Then go forward or back, so long as the ground is truly level in that direction. If you go forward toward the mountain or the minaret, subtract one finger from the first shadow and put the pointer of the alidade on that setting; if you go back from the mountain or the minaret, add one finger to the first shadow and put the pointer of the alidade on the sum, and keep going back until you see the top again through the two holes. Then measure what is between the two standing-places and multiply it by 12: the height of the perpendicular sought results. And if you multiply what is between the two standing-places by the first shadow, what is between the first standing-place and the foot of the body whose perpendicular you wanted results. If there were in the air something, a cloud or a bird, and it could stay still and not move until you measured it from two places in which its altitude differs, it would be possible to know its distance from the earth and what is between your place and the fall of its stone (masqaṭ al-ḥajar) on the earth. Now that we have reached this point, and have finished, after indicating the conventions in the sciences of number and geometry, informing about the configuration of the world, and indicating the knowledge of calculating the positions of the stars (taqwīm) and the use of the astrolabe, the time has come for us to mention the conventions in the art of the judgements of the stars; for the answer to the questioner's question is confined to these, and because for most people it is the fruit of the mathematical sciences, even though our own belief about this fruit and this art is like the belief of the fewest of them. So let us begin first with mentioning what of this belongs specifically to the signs by themselves.

站在某处，降低、升高照准尺，用一只眼透过两块觇板的孔望所求的顶端，直到看见它，正如测星的高度那样。然后看照准尺的指针落在影指的多少上：那就是第一影。然后前进或后退，只要那个方向上的地面确实平坦。若你朝山或宣礼塔前进，就从第一影减去一指，把照准尺的指针放在这个位置上；若你从山或宣礼塔后退，就在第一影上加一指，把照准尺的指针放在和数上，一直后退，直到又透过两孔看见顶端。然后量两个站立处之间的距离，用十二去乘：就得出所求的垂直高度。若用第一影去乘两站之间的距离，就得出第一站与你要求其垂直高度的那个物体脚下之间的距离。若空中有某物，一片云或一只鸟，而它能静止不动，直到你从两处测它，两处所得的高度不同，那就能知道它离地面的距离，以及你所在之处与它在地面上的“落石点”之间的距离。我们既已到达此处，而且已经完成了：指出数与几何诸学的规矩，讲述世界的构形，指出推算诸星位置之学与星盘的用法，现在是时候讲述星的判断这门技艺的规矩了；因为对提问者问题的回答就限于这些，又因为在大多数人看来，它是数理诸学的果实，尽管我们自己对这果实与这门技艺的看法，与他们当中最少数人的看法一样。那么让我们先从专属于星座本身的东西讲起。