卷三·第 197–203 问　行星日行、留、四分带与升降增减

§197. What is buht?

第一百九十七问　何谓“布赫特”？

This is an Indian word, bhukti, and it means the course of a planet in a single day. Our people apply it only to the true course for a day, whereas the Indians distinguish in it between the mean and the true. We have mentioned the mean under each planet. The true is not fixed: the planet sometimes goes fast, so that its buht is large, and sometimes slow, so that its buht is small; sometimes it is stationary and has no buht, and sometimes retrograde, so that its buht is retrograde.

这是一个印度词，原作“布克提”，意思是一颗行星在一日之内的行程。我们的人只把它用于一日的真行程，印度人则在其中分出平均的与真实的两种。平均的，我们已在各星之下提到过。真实的则不固定：行星有时走得快，它的布赫特就大；有时走得慢，它的布赫特就小；有时停留不动，就没有布赫特；有时逆行，它的布赫特就是逆向的。

§198. What is the corrected buht?

第一百九十八问　何谓改正的布赫特？

It is the difference between the buhts of the two luminaries, or of two planets, or of any two things moving in one direction with two unequal motions, when the time of their conjunction is wanted; for this is found from the difference between their two motions in one and the same period, since it is by that difference that the distance or the approach between them comes about. The corrected buht is also called the portion of the course (ḥiṣṣat al-masīr), and in Indian bhukty-antara, that is, the difference between the two buhts. Sometimes one needs to use the sum of the two buhts instead of their difference, and this is called in Indian bhukti-yoga; that is in the case of two planets that are not moving in the same direction, one of them being direct and the other retrograde.

它是两个发光体、或两颗行星、或任何两个以不相等的两种运动朝同一方向运行之物的布赫特之差，用于求它们相合的时刻；因为相合的时刻是由二者在同一段时间里两种运动之差求出的，二者之间的拉开或靠近，正是由这个差造成的。改正的布赫特又称“行程之份”，印度语称“布克提安塔拉”，意思是两个布赫特之差。有时需要用两个布赫特之和来代替它们的差，这在印度语里称“布克提瑜伽”；那是两颗行星运行方向不同的情形，其中一颗顺行，另一颗逆行。

§199. What are the stations?

第一百九十九问　何谓留？

They are amounts and numbers laid down for each planet, and for each place in its apogee orb, such that when the true anomaly of the planet equals them, the planet is then standing still and stationary, and no motion of it is seen in the zodiac. If the station is more than six signs [corrected: MS has 'less than six signs'], the planet is called stationary for the second time, and the standing after it is for direct motion. When one of the two stations is subtracted from 360 parts, the other station remains.

留是为每颗行星、并为它在远地点圈上的每一处位置所定的一些数值；当行星的真近点角等于这些数值时，行星便停住不动，处于留的状态，在黄道上看不出它有任何运动。若留的数值多于六个星座〔抄本作“少于六个星座”，据文义改正〕，这颗行星就称为第二次留，留过之后转为顺行。把两个留中的一个从三百六十度中减去，剩下的就是另一个留。

§200. What are the murābaṭāt ('tetherings')?

第二百问　何谓“穆拉巴塔特”（“系缚”）？

They are the stations, except that some of the ancients knew them by received tradition rather than by verification, believing that the planets are tethered to the Sun. So they expressed them in terms of a tether that slackens as the planets come near the Sun, so that their course becomes direct, and is drawn tight as they move away from it, so that at that point they stand still and go back. This is false and deserves no attention, since there is no use in it and nothing to be gained from it.

它们就是留，只是有些古人是凭传承而不是凭验证知道它们的，以为诸行星被系在太阳上。于是他们用一根系绳来表述：行星靠近太阳时，系绳松弛，所以它的行程变为顺行；离开太阳时，系绳被拉紧，所以到了那一点它便停住并往回走。这是错误的，不值得理会，因为它毫无用处，也得不到任何东西。

§201. What are the niṭāqāt ('belts')?

第二百零一问　何谓“尼塔卡特”（“带”）？

They are of two kinds: one in the eccentric orb and the other in the epicycle. As to the first kind, the apogee orb is divided by these two lines: one of them passes through the apogee and the perigee, and at its two ends the equation vanishes, the mean and the true places of the planet coincide, and the course differs to the utmost, being slowest at the apogee and fastest at the perigee; the other line is the one perpendicular to the first, passing through the centre of the world, and at its two ends the greatest equation and the mean course occur. The first belt runs from the apogee in the order of the signs, the second to the perigee, the third from the perigee, and the fourth to the apogee. This is the figure of it.

带有两类：一类在偏心圈上，另一类在本轮上。先说第一类：远地点圈被这样两条线分开：一条通过远地点与近地点，在它的两端均差消失，行星的平均位置与真位置重合，而行程的差异达到极点，在远地点最慢，在近地点最快；另一条线与第一条垂直，通过世界的中心，在它的两端出现最大均差与平均行程。第一带从远地点起按星座次序而行，第二带到近地点为止，第三带从近地点起，第四带到远地点为止。这是它的图。

As to their amounts: if the reckoning is by the true centre, the beginning of the first is at the apogee, the beginning of the second at 90 degrees beyond the apogee, the beginning of the third at 180 beyond the apogee, and the beginning of the fourth at 270 beyond it. If the reckoning is by the uncorrected centre, their beginnings come when the centre is as given in the following table.

至于它们的数值：若按真的中心计算，第一带始于远地点，第二带始于远地点之后九十度，第三带始于远地点之后一百八十度，第四带始于远地点之后二百七十度。若按未改正的中心计算，它们的起点就在中心达到下表所给的数值之时。

As to the second kind of belts, the epicycle is divided by them along lines, one of which passes through its summit and its perigee, while the other two touch it when drawn from the centre of the deferent; at the points of contact, too, the greatest equation occurs. The first of these belts begins at the summit and goes in the direction of the course: for the Moon against the order of the signs, and for the planets in the order of the signs; then the rest follow in succession.

至于第二类带，本轮被一些线分开：其中一条通过本轮的顶点与近地点，另外两条从均轮的中心引出，与本轮相切；在切点上也出现最大均差。这些带中的第一带始于顶点，朝行程的方向而行：对月亮来说是逆着星座次序，对诸行星来说是顺着星座次序；其余各带依次相继。

As to their amounts: if the two lines tangent to the epicycle are drawn from the centre of the world or from the centre of the equant, they vary; but if they are drawn from the deferent, they do not vary, as given in this table. So the mean anomaly of each planet is to be compared with them.

至于它们的数值：如果与本轮相切的两条线是从世界的中心或从偏心等速圈的中心引出的，数值就会变动；但若从均轮引出，就不变动，如本表所给。所以每颗行星的平均近点角要拿来与它们比较。

The form of the table.

表的样式。

§202. What are ascending and descending?

第二百零二问　何谓上升与下降？

A planet ascends in the north towards its extreme latitude so long as its latitude in the north is increasing; then it descends in the north when its latitude there begins to decrease. When it passes the node into the southern half of its inclined orb, it begins to descend in the south towards its extreme latitude so long as its latitude in the south is increasing; and after that it ascends in the south when its latitude there begins to decrease. There is also a kind of ascent and descent with respect to the earth: by it the planet is descending in the first and second belts and ascending in the third and fourth, though some make it ascending in the first and fourth and descending in the second and third. Another kind is when the planet is in the half from the beginning of Capricorn to the end of Gemini, in which case it is called ascending, and in the other half descending. And another kind again is when it is between the meridian and the orb of midnight: towards the east it is called ascending and towards the west descending.

行星在北方、朝它的极限纬度而行，只要它的北纬在增大，就是在北方上升；当它在北方的纬度开始减小，它就在北方下降。当它越过交点，进入它斜圈的南半，只要它的南纬在增大，就开始在南方朝它的极限纬度下降；此后当它在南方的纬度开始减小，它就在南方上升。还有一种上升与下降是相对于地而言的：按这一种，行星在第一、第二带时是下降，在第三、第四带时是上升；不过也有人把它定为在第一、第四带上升，在第二、第三带下降。另一种是：行星在从摩羯座起点到双子座末尾的那一半时，称为上升，在另一半时称为下降。还有一种是：行星在子午线与午夜之圈之间时，朝东的一侧称为上升，朝西的一侧称为下降。

§203. What are increase and decrease?

第二百零三问　何谓增与减？

This notion divides into two kinds: one according to the place in the apogee orb and the epicycle, and the other according to the place relative to the horizon. The first kind takes several forms. One is increase in course: that is, when the planet goes more in a day than its mean course in it; and when it goes less than that, it is decreasing in course. Another is increase in number: the equations of the planets are laid down against numbers in two columns, one of which goes down as far as 6 signs and the other goes up to complete 12 signs; if the argument with which one enters falls in the first column, the planet is called increasing in number, and in the second, decreasing in it. Another is increase in equation: that is, when its equation grows as the portion by which the equation is taken grows, and it is then called increasing in equation; this belongs to the first and third of the belts, and decrease in it belongs to the other two. Another is increase in calculation: that is, when the last equation is added to it, it is called increasing in calculation, and when it is subtracted, decreasing in it; increase belongs, in the apogee orb, to the third and fourth belts, and in the epicycle to the first and second. Another is increase in light and size through coming near the earth. Some have made the planet increasing in light and size from the summit to the perigee, because it keeps coming nearer to the earth, and from the perigee to the summit decreasing in both, because it keeps getting farther from the earth. Others have put the increase in both on either side of the perigee as far as the two mean distances, and the decrease in both on either side of the apogee as far as them; their rule is that the planet's mean size occurs at the mean distance, so that when it rises above it its size decreases, and when it sinks below it its size increases. Reasoning based on what the eye sees requires that the epicycle be given an ample share of these two, but the custom of the practitioners of the art is to attribute them to the belts of the apogee orb. The increase of the Moon's light is not reckoned by the apogee orb but by the distance from the Sun: some make it increasing from the beginning of the month to its middle, and some make it increasing whenever its light is more than half its body. As for increase according to the place relative to the horizon: the eastern quarter between the meridian and the eastern horizon, and the quarter opposite them, are the two increasing ones, because the daytime and the night in them are on the increase; the remaining two quarters are decreasing.

这一概念分为两类：一类按在远地点圈和本轮上的位置而言，另一类按相对于地平的位置而言。第一类有好几种形式。一种是行程之增：行星一日所行多于它这一日的平均行程时就是增；少于平均行程时，它就是行程之减。另一种是数之增：诸行星的均差是对着数列在两栏里的，其中一栏往下一直到六个星座，另一栏往上补足十二个星座；若用来查表的引数落在第一栏，行星就称为数之增，落在第二栏则称为数之减。另一种是均差之增：随着用来求均差的那一份增大，它的均差也增大，这时就称为均差之增；这属于诸带中的第一带和第三带，均差之减属于另外两带。另一种是计算之增：最后一项均差要加上去时，称为计算之增，要减去时称为计算之减；计算之增在远地点圈上属于第三、第四带，在本轮上属于第一、第二带。另一种是因靠近地而来的光与大小之增。有些人把行星从顶点到近地点定为光与大小都在增，因为它一直在靠近地；从近地点到顶点则二者都在减，因为它一直在远离地。另一些人则把二者之增放在近地点两侧、直到两个平均距离为止，把二者之减放在远地点两侧、也直到它们为止；他们的法则是：行星的平均大小出现在平均距离上，所以它升到其上时大小就减，降到其下时大小就增。按肉眼所见来推理，就要求给本轮在这二者中分得一份充足的份额，但本行从业者的习惯是把它们归于远地点圈的诸带。月亮光之增不按远地点圈计，而按与太阳的距离计：有人把它定为从月初到月中为增，有人则定为只要它的光多于其体之半就是增。至于按相对于地平的位置而言的增：子午线与东地平之间的东方象限，以及与它们相对的那个象限，是两个增的象限，因为在其中白昼与黑夜都在增长；其余两个象限是减的。