第二部·第二十则　太阳在晨昏蒙影中的推运

CANON XX.

第二十则。

To direct the Sun, when found below the Earth, in the Space of the Crepuscule, to the Conjunctions and Rays.

推运位于地平之下、在晨昏蒙影范围内的太阳到会合与光线。

The reason why the Sun, when found in the crepuscular space, should be directed above the circles parallel to the horizon, and not above horary circles, as when the Sun is above the Earth, has been given in the Thesis, and demonstrated in the clearest manner, in the Philosophy of the Heavens; but now attend to what pertains to the practice of calculating.

太阳在晨昏蒙影的范围中时，为什么要在与地平平行的圈上推运，而不像太阳在地平之上时那样在时圈上推运，其理由已在论点中给出，并在《天的哲学》中以最清楚的方式论证过；现在请注意计算的实际做法。

If the Sun is found in the morning crepuscule, first direct the Sun to the degree of the aspects, under the latitude of the country, that is, to the elevation of your pole, though indeed the Sun does not remain there, but below, and in a separate place.

若太阳在晨间蒙影中，首先在本地纬度下，即在你的极高下，把太阳推运到相位的度数，虽然太阳实际上并不在那里，而是在地平之下，在另外的地方。

You must observe the arc of direction, then take the Sun's distance from the horoscope, by its oblique ascension, which I call the Sun's primary distance, and take care, that if this distance be greater than the whole quantity of the crepusculine to the parallel of depression, 18°, the Sun is not the cause of twilight; and in this case you are to calculate by the following Canon.

你要记下这推运弧，然后用太阳的斜升取它离上升点的距离，我称之为太阳的第一距离；并且要注意，若这个距离大于直到十八度下沉平行圈的整个晨昏蒙影之量，太阳就不是曙暮光的成因；这时你要按下一则来计算。

But if the Sun is in the space of the crepuscules, with the Sun's distance from the horoscope, above taken, enter the table of crepuscules at your Pole's elevation, placed in your first column; and with the Sun's sign, and degree, according as they are placed, in the beginning or end; and when, in the body of the table, you have found this distance from the Sun's rising on the back of the same opposite to it, you are to observe what degree of the crepusculine parallels the Sun possesses, viz. in the second column, by taking the part proportionate only to the Sun's degree of longitude, as I shall mention afterwards; and under the same parallel see what the distance of the place or opposite degree is, by the direction; that is, what the Sun's distance is from the horoscope, in the same crepusculine parallel, after the direction is finished; and this distance I call secondary; but if the primary and secondary distances are equal, the true arc is that which you have calculated above, viz. the Sun's arc in the horoscope; if they are unequal, substract the lesser from the greater, and the remainder I call the eastern difference.

但若太阳在晨昏蒙影的范围内，就以上面所取的太阳离上升点的距离，查你的极高下的晨昏蒙影表，那极高列在你的第一栏中；并按太阳的星座与度数在表的开头或末尾的排列来查；当你在表身中找到这个离太阳升起的距离时，在它背面与之相对之处，你要看太阳占着晨昏圈的哪一度，即在第二栏中，只按太阳的黄经度数取比例部分，如我以后要说的；在同一平行圈下，看推运所到的那个位置或对面度数的距离是多少；也就是说，推运完成之后，在同一个晨昏圈中太阳离上升点的距离是多少；这个距离我称为第二距离；若第一距离与第二距离相等，真正的弧就是你上面算出的那个，即太阳在上升点的弧；若不相等，就以小减大，余数我称为东方差。

Lastly, if the secondary distance be less, and the primary greater, add that remainder, or eastern difference, to the Sun's arc of direction, calculated in the horoscope; but if the secondary distance be greater, and the primary less, substract the eastern distance from the arc of direction, and you will have in the remainder the true arc of direction calculated in the crepusculine circle, which is to be equated the usual way, as in Canon XVI.

最后，若第二距离较小，第一距离较大，就把那余数即东方差加到在上升点算出的太阳推运弧上；但若第二距离较大，第一距离较小，就从推运弧中减去东方差，你就在余数中得到在晨昏圈中算出的真正推运弧，再照通常的方法均化，如第十六则。

And observe, that in seeking for the Sun's primary distance from the horoscope in the tables of the crepusculine, it is sufficient to take the part proportionally to the degree of the crepusculines or paralell's depression; opposite to which, you will find the distance which you have taken, with the proportional part near it, omitting that primary one of the natural Sun; for it is of no consequence to take the degree and minute of the crepusculine depression; but it is enough if you take the integral degree nearest the Sun's longitude distance, taken with the proportional part. For example;

还要注意，在晨昏表中求太阳离上升点的第一距离时，按晨昏圈即平行圈的下沉度取比例就够了；与之相对，你会找到你所取的距离，旁边附有比例部分，略去本命太阳的那个第一距离；因为取晨昏下沉的度与分无关紧要；只要取最接近太阳黄经距离的整度，连同比例部分就够了。例如：

John Duke Rainutius Farnese, the Sun's distance from the horoscope is 18° 56', to the latitude of the country 44; opposite to 13 of the depression, under 10° of ♈, the distance is 29, from which, for the 6° (for the Sun in 16° of ♈) 17 are due, which, when added together, the distance is 18° 49', but the Sun's distance, 18° 56'; yet this is nothing to the purpose, as the distance is but small, therefore make use of the former 18° 49', without any regard to that of the Sun, 18° 56'; to the same depression of the crepuscule 13.

约翰公爵拉努奇奥·法尔内塞，太阳离上升点的距离是十八度五十六分，在本地纬度四十四度下；对着下沉十三度，在白羊十度之下，距离是二十九，从中为六度（因为太阳在白羊十六度）应得十七，相加之后，距离是十八度四十九分，而太阳的距离是十八度五十六分；但这无关紧要，因为差很小，所以就用前者十八度四十九分，不管太阳的十八度五十六分；对应同一晨昏下沉十三〔度〕。

Under 0° 0' of ♋, of the place of the quartile of Mars, I take the secondary distance, 24° 45', from which I substract the Sun's distance, which I obtained after taking the proportional, which is 18° 49'; and I suppose, that the Sun in the nativity, might have this distance from the horoscope, that I may place it under the crepusculine circle 13 exactly.

在巨蟹零度零分之下，即火星四分之处，我取第二距离二十四度四十五分，从中减去太阳的距离，即我取比例部分后所得的十八度四十九分；我假定本命中的太阳离上升点就是这个距离，以便把它恰好放在十三〔度〕的晨昏圈下。

But if you are desirous to have the crepusculine circle in minutes, take the proportional part; but it would be attended with greater trouble than advantage; for you will find the difference in the ascensions almost imperceptible, and not greater than that which arises from the difference of some minutes of the pole's elevation of the circle of position, in which all professors entirely omit minutes.

但若你想要晨昏圈精确到分，就取比例部分；但那样麻烦多于好处；因为你会发现上升度中的差别几乎察觉不到，不比位置圈的极高差几分所生的差别更大，而所有的从业者都完全略去这几分。

Wherefore, when you have occasion to use the eastern difference, do as already mentioned, &c. of which the examples follow in Gustavus King of Sweden, Odoardus Cardinal Farnese, Rainutius, of whom we have just now spoken, and John Columna, which are given by Argol. I meet with more examples of authors relating to this point. I would have undertaken to give you a thorough examination.

所以，当你需要用东方差时，就照上面所说的做，等等；其例子见于后面瑞典国王古斯塔夫、枢机主教奥多阿尔多·法尔内塞、刚才说过的拉努奇奥，以及约翰·科隆纳，都是阿尔戈利所给的。我遇到更多作者关于这一点的例子。我本可以着手给你一个彻底的考察。

I alledge nothing of my own observations, lest they should be rejected as spurious and false; but from these four, and all examples that Argol gives of this nature, I think, that to any one diligent in searching into the truth of things, my opinion on this subject, will appear highly satisfactory. But if again the Sun possesses the evening twilight, the same method entirely is to be preserved, except only changing the manner.

我不举我自己的观察，免得它们被当作伪造虚假而遭拒绝；但从这四例，以及阿尔戈利所给的这类的所有例子，我想，对任何勤于探求事物真相的人来说，我在这一问题上的意见都会显得十分令人满意。但若太阳在黄昏的蒙影中，完全要保持同样的方法，只是改变做法。

Let the Sun's direction be to the place of the aspect, by the oblique descension or oblique ascension of the places opposite to the Pole of the country; then let the Sun's distance be taken from the west, through the same descensions or opposite ascensions; let this distance be required in the table of twilight, which, if it be greater then the whole quantity of the crepusculine to the inferior parallels, 18°, the Sun is no longer in the crepusculine; and then we must make use of the following Canon.

让太阳在本地极高下，按斜降或对面之点的斜升，推运到相位之处；再按同样的斜降或对面之点的斜升，取太阳离西方的距离；在曙暮光表中求这距离，若它大于直到下方平行圈十八度的整个晨昏蒙影之量，太阳就不再在晨昏蒙影中；那时我们须用下一则。

Lastly, let the secondary distance under the same crepusculine circle be taken, I mean, of the opposite place, and let the lesser be substracted from the greater, and the remainder added to the arc of direction found above, if the secondary distance be greater than the primary; let it be substracted, if less; that is, in a manner different from that we spoke of above, and the sum or remainder is the true arc of the direction.

最后，在同一晨昏圈下取第二距离，我指对面之点的；以小减大，若第二距离大于第一距离，就把余数加到上面求得的推运弧上；若较小，就减去；也就是说，做法与上面所说的相反；所得的和数或余数就是真正的推运弧。