卷三·第 153–157 问　焦伤、月相与恒星的星等

§153. What is combustion?

第一百五十三问　何谓焦伤？

Combustion is the conjunction of the planets with the Sun. It is so called because the Sun is likened to fire, and the disappearance of the planets from sight in its light to burning and vanishing away. This combustion occurs generally to all the wandering planets in the middle of their direct motion, on the circuit of the epicycle; but the upper differs from the lower in the middle of retrogradation, at the perigee of the epicycle, for the lower planet is combust there too, while the upper is not combust there, but is in opposition to the Sun.

焦伤就是诸行星与太阳会合。它之所以这样称呼，是因为太阳被比作火，而诸行星在它的光芒中从视野里隐没，被比作焚烧与消亡。这种焦伤一般地发生在所有游星顺行的中途，在本轮的轮周上；但在逆行的中途、在本轮的近地点上，上行星与下行星就不一样了：下行星在那里也焦伤，上行星在那里却不焦伤，而是与太阳对冲。

§154. How is this in the case of the Moon?

第一百五十四问　月亮的情形又如何？

The new Moon is sighted in the evenings at the beginning of the month, and is seen as a slender crescent in the west. Every night its distance from the Sun keeps increasing and the light in its body grows, until at the beginning of the seventh night of the month it reaches the midpoint between east and west; then the light covers half of what is seen of it, in the shape of a semicircle. After that the light exceeds the darkness in it until the fourteenth night, on which it becomes complete as a full moon and rises at sunset, the distance between them being half the circuit. When the Moon's distance exceeds that, it diminishes on the other side, and the light begins to be notched and to decrease, until light and darkness are again equal in its body on the twenty-second night; after that the darkness exceeds the light, until it returns to the shape of the first thin crescent, in the east in the mornings. In all these states its light is on the side facing the Sun. Then it is concealed by the rays of the Sun, and for this reason the period of its concealment is called sirār (concealment), and also muḥāq (effacement), from the effacement of the light in it, until it returns to the shape of the crescent in the west in the evening. It comes together with the Sun in the middle of this period, and this is called conjunction without qualification; Ptolemy in the book of the Almagest calls it 'joining' (ittiṣāl), just as by custom and convention it is described as conjunction (muqārana) and as combustion. As a matter of reasoning, this coming together is the Moon's conjunction with the Sun and its combustion by it. Likewise its full moon is called opposition without qualification, and 'fullness'.

新月在月初的傍晚被望见，在西方呈一弯细细的月牙。每一夜它离太阳的距离都在增大，它体上的光也随之增长，直到月中第七夜之初，它到达东西之间的正中；这时光覆盖了所见部分的一半，呈半圆形。此后它体上的光胜过暗，直到第十四夜，它圆满成为满月，在日落时升起，两者相距半个圆周。月亮的距离超过这一点后，它就从另一侧减损，光开始缺损、减少，直到第二十二夜它体上的光与暗再次相等；此后暗胜过光，直到它回到最初那弯细月牙的样子，清晨出现在东方。在所有这些状态中，它的光都在朝向太阳的一侧。然后它被太阳的光芒遮掩，因此它隐藏的这段时间被称为“西拉尔”（隐藏），也称为“穆哈格”（抹去），取光在它身上被抹去之意，直到它又回到傍晚西方的月牙之形。它在这段时间的正中与太阳相会，这就是不加限定所说的“会合”；托勒密在《天文学大成》一书中称之为“相接”，正如按习惯与约定，人们也把它说成“相合”与“焦伤”。按道理说，这一相会就是月亮与太阳相合并被它焦伤。同样，它的满月被称为不加限定所说的“对冲”，也称为“满”。

§155. How does the Moon's light increase and decrease?

第一百五十五问　月亮的光怎样增减？

The body of the Moon is spherical in shape and not luminous. The light that is seen in it falls on it only from the Sun, as it is seen on the earth, the mountains, the walls and similar dense things through which sight does not pass. When the Moon is with the Sun, it lies between it and us, because it is below it; the Sun's light falls on the side facing it, which we do not see, and our sight reaches only the other side, which faces us. So we cannot distinguish the Moon from the azure of the sky because of the predominance of the rays, and for this reason it is hidden from us. It remains so until, when it has moved some distance from the Sun, part of the lit side begins to come into the side facing us and to be seen, until it becomes a portion that the light of the twilight may not overpower; it is then seen as a crescent. For the rays falling on it end, because of its sphericity, at the circumference of a circle, and what is seen of it likewise ends at the circumference of a circle; so the part of the lit side that enters into the seen side, and is shared by the two circles, is bounded like a slice of a melon, a segment; and this requires the intersection of circles on the surface of the sphere. Then this shared, entering part increases until it equals the dark part; that time is called the first quarter, because what lies between the Sun and the Moon is a quarter of a circle, and the equality of light and darkness in it is evident. At opposition, when there is half a circle between them, the half on which our sight falls is the very same half on which the light falls: the Sun's rays and sight have met on one and the same part of the Moon's body, and the light is seen in its fullness. This is its figure.

月亮的体是球形的，本身不发光。在它身上看到的光，全是从太阳落到它上面的，就像在大地、山岭、墙壁以及类似的、视线穿不过去的密实之物上看到的那样。月亮与太阳在一起时，它位于太阳与我们之间，因为它在太阳之下；太阳的光落在朝向太阳的那一面，那一面我们看不见，我们的视线只到达朝向我们的另一面。所以由于光芒的压倒之势，我们无法把月亮从天空的蔚蓝中分辨出来，它因此对我们隐而不见。它一直这样，直到离开太阳一段距离，受光那一面的一部分开始进入朝向我们的那一面而被看见，直到成为暮光压不住的一份；这时它就被看成月牙。因为落在它上面的光芒，由于它是球形，止于一个圆的圆周；它被看见的部分，同样止于一个圆的圆周；所以受光面进入可见面、为两个圆所共有的那一部分，边界像甜瓜的一瓣，是一个弧形的片；而这需要球面上的圆彼此相交。然后这共有的、进入的部分逐渐增大，直到等于暗的部分；这时称为上弦，因为太阳与月亮之间相隔四分之一圆，月中光与暗的相等也显而易见。到了对冲，两者相隔半个圆，我们的视线所落的那一半，正是光所落的那一半：太阳的光芒与视线在月体的同一部分上相遇，于是光被看得圆满。这是它的图。

§156. Why, among the planets, is the Moon alone characterized by the increase and decrease of its light?

第一百五十六问　诸星之中，为何唯独月亮有光的增减？

Those who study nature have disagreed about the lights of the stars, whether they are their own or acquired from the Sun by the falling of its rays. Some held that the Sun alone has light and that all the stars are not luminous, reasoning from the dependence of the motions of the planets on the motions of the Sun, and so they made their lights follow it too. Others held that all the stars are luminous except the Moon, which alone is dull and without light. This is the nearer of the two views to the truth, even though it is not so compelling as to remove the disagreement. That is because the stars are luminous in their existence, and their disappearance under the rays is like their disappearance in the daytime, when the light dazzles our eyes and they are thereby too weary to perceive them. For one who looks from the bottom of a deep well, when a star happens to pass over his zenith in the daytime, sees it, because the darkness preserves his sight and strengthens it; for black gathers sight and strengthens it, while white disperses it and weakens it. Now the upper planets, whether luminous or not luminous in themselves, are in any case always seen in one and the same state, just as the Moon, if it were above the Sun, would escape the notching of its light and would always be seen full. The question lies with Venus and Mercury: if they were not luminous, a difference in the amount of light would be seen between their state at their greatest elongation from the Sun and their state when they are near disappearing, since they are below the Sun; and this is not perceptible in them. So the reason why the Moon alone shows varying shapes of light is the dullness of its colour and its lack of light, together with its being below the Sun.

研究自然的人对诸星的光有过争论：它们的光是自身的，还是由太阳的光芒落在上面而从太阳得来的。有些人认为只有太阳有光，所有的星都不发光，他们的理由是诸行星的运动依从太阳的运动，于是让诸星的光也依从于它。另一些人则认为所有的星都发光，只有月亮例外，唯独它暗淡无光。这是两种说法中较接近真相的一种，尽管它还没有有力到足以消除争论的地步。这是因为诸星在其存在上就是发光的，它们在日光下隐没，就像它们在白天隐没一样：那时光使我们的眼睛目眩，眼睛因此疲乏而察觉不到它们。凡从一口深井的井底仰望的人，当白天有一颗星恰好经过他的天顶时，他就能看见它，因为黑暗护住他的视力、使之增强；因为黑色聚拢视力、使之增强，而白色则使视力分散、变弱。至于上行星，不论它们本身发光与否，在任何情形下总是以同一种状态被看见，正如月亮若在太阳之上，就能免于光的缺损，总被看成满月一样。问题在于金星与水星：如果它们不发光，那么它们离太阳最远时的状态与它们将要隐没时的状态之间，就会看出光量的差别，因为它们在太阳之下；而在它们身上察觉不到这种差别。所以，唯独月亮呈现出光的不同形状，原因在于它颜色暗淡、不发光，再加上它在太阳之下。

§157. How many fixed stars are there?

第一百五十七问　恒星有多少颗？

The fixed stars in the sky are so many that they defeat the counter. But those who took pains to determine their positions in longitude in the signs, and the amounts of their latitudes north and south of the zodiac, finding them of different sizes to view and to the eye, ranked them in successive grades which they called magnitudes and greatnesses. The greatest are 15 stars, counted as of the first greatness or magnitude; the practitioners of judgements sometimes express this by 'honour' (sharaf), saying 'of the first honour' instead of what others say, 'of the first magnitude'. Then those somewhat smaller than these, in the second magnitude, are 45 stars; in the third magnitude 208 stars; in the fourth magnitude 474 stars; in the fifth magnitude 217 stars; and in the sixth magnitude 58 stars. In this magnitude are those which Ptolemy called obscure, which are nine, besides three not counted, which together are called the Lock and the Braid. What is smaller than the sixth magnitude is what sight can hardly fix on by itself; and if it perceives it, fixing and observing it is difficult. Beyond that there are in the sky five stars of the kind of the Milky Way, nebulous, like pieces of cloud and smudges; and with these the number of the observed stars is completed at 1022 stars.

天上的恒星多到让计数的人无能为力。但那些费心确定它们在诸星座中的经度位置、以及它们在黄道以北和以南的纬度大小的人，看到它们在视觉上、在眼中大小各异，就把它们排成相继的等级，称为“星等”与“大小”。最大的有十五颗，算作第一等大或第一星等；断事之家有时用“尊位”来表达这一点，说“第一尊位”，代替别人所说的“第一星等”。其次是比这些稍小的，在第二等的有四十五颗；第三等的有二百零八颗；第四等的有四百七十四颗；第五等的有二百一十七颗；第六等的有五十八颗。在这一等里，有托勒密称为“暗星”的，共九颗，此外还有不计入的三颗，合起来称为“发绺”与“发辫”。比第六等更小的，是视力几乎无法单独看定的；即便察觉到了，要看定它、观测它也很困难。此外天上还有五颗属于银河一类的星，是云状的，像一片片云和污斑；连同这些，观测到的星数就凑足一千零二十二颗。