第三部·第三十五至三十六则　世界上的平行与地平下的太阳

CANON XXXV.

第三十五则。

To direct any Significator whatever to the Parallels.

任何征象星向平行的推运。

I call a parallel in the world, that distance which two stars have in an equal proportion from the same angle, the one remaining beyond, the other within; as if one possesses the cusp of the 11th, and the other the 9th, then they are equally distant from the medium cœli, or meridian; and if one is found in 12, the other in the second, they are equally distant from the ascendant, or horizon.

我所称的世界上的平行，是两颗星离同一个角在相等比例上的距离，一颗在角之外，一颗在角之内；例如一颗占据第十一宫宫头，另一颗占据第九宫宫头，它们离中天即子午线就同样远；若一颗在第十二宫，另一颗在第二宫，它们离上升即地平就同样远。

But it is to be observed, that in this aspect, it not only happens that an equal proportionate distance is formed from one of the angles, but likewise in some manner from every one of them; as a star in the ninth is equi-distant from the medium cœli, as another star in the 11th; and these two stars are at an equal distance from the imum cœli, and [Mundane Proportion.] from the east and west horizon.

但要注意，在这种相位中，不仅离其中一个角形成相等的比例距离，而且在某种程度上离每一个角都是如此；例如第九宫的一颗星与第十一宫的另一颗星离中天同样远；这两颗星离天底，［世界上的比例。］离东、西地平也同样远。

This will be evident from the calculation, and should be taken as a proof of the virtue and efficacy of this aspect, and likewise for the ease of calculation; and from hence it is inferred, that the calculation of this aspect may be made several ways, of which the easiest is by the distance, that is, from the medium cœli, whither these two stars form a parallel to the the meridian or horizon, that is, whither both are found above the Earth, or below it:

这从计算中就会明白，应当视为这种相位的力量与效力的一个证明，也便于计算；由此推知，这种相位的计算可用多种方法，其中最容易的是用距离，即离中天的距离，看这两颗星在哪里对子午线或地平形成平行，也就是两者都在地平以上，还是都在地平以下：

I mean when the direction is finished; for it matters not where they remain in the nativity, if both are found above, When they have this parallel, take the significator, and promittor's right distance, which they have in the nativity from the medium cœli, and this distance I call the primary. Then say, if the horary times, or semi-diurnal arc of the significator give his distance from the medium cœli, what distance will the promitary horary times give? When you have found that, proceed according to Canon XIX.

我是指推运完成之时；因为在本命中它们在哪里无关紧要，若两者都在地平以上，当它们成这种平行时，取征象星与允诺星在本命中离中天的赤经距离，我称这距离为初距。然后说：若征象星的时量或半昼弧得出它离中天的距离，允诺星的时量将得出多少距离？求得之后，照第十九则进行。

But if they form this aspect, while they are both below the Earth, take the distances from the imum cœli, in the same manner, and the distances from the horoscope may be taken by the oblique ascension: if one be above the Earth, and the other posited below, the contrary; take the distance of one from the medium cœli, and the other from the imum cœli, or make use of the opposition. One example follows.

但若它们都在地平以下时形成这个相位，就同样取离天底的距离；离上升点的距离可借斜升来取；若一颗在地平以上，另一颗在地平以下，则相反：取一颗离中天的距离，另一颗离天底的距离，或利用对冲之点。下面举一个例子。

[Rapt Canon] Hitherto in this Canon, mention has been made of the direction to the parallels in the world, with the supposition that the significator remain immoveable in the horary circle of position. But because, in the nativity, the virtue both of the significator and promittor is impressed in the primum mobile, and this agreeable to the opinion of all professors, therefore both their virtues are conveyed, by the primum mobile, from east to west, consequently it may sometimes happen, that the significator and promittor are posited in an equal proportionate distance from the same angle that is in the mundane parallel of your or their species.

［携转之则］在本则中到此为止，讲的是向世界上平行的推运，设定征象星在时位圈中保持不动。但因为在本命中，征象星与允诺星的力量都印在第一原动天上，这也合乎所有从业者的意见，所以两者的力量都被第一原动天由东向西带走，因此有时会发生这样的情形：征象星与允诺星被置于离同一个角相等比例的距离上，也就是处在你们或它们这一类的世界上的平行之中。

Of these, in this Canon, we give the calculation; and how great the active virtue of this application is, will be seen in the example following: but it may happen that, by a direction, even the significator and promittor, both may be posited above the Earth, or both below; or the one above, the other below, though in the nativity they are different If both are posited above the Earth, take the semi-diurnal arc, and the significator's distance from the medium cœli, and the semi-diurnal arc of the promittor, with his distance, in right ascension from the significator, then add their semi-diurnal arcs together, and say, as that sum is to the semi-diurnal arc of the promittor, so is the promittor's distance from the significator.

这些情形的计算，我们在本则中给出；这种施用的主动力量有多大，在下面的例子中可以看到：但也可能借推运，征象星与允诺星两者都被置于地平以上，或都在地平以下；或一上一下，尽管它们在本命中所处不同。若两者都在地平以上，就取征象星的半昼弧及其离中天的距离，以及允诺星的半昼弧及它离征象星的赤经距离，然后把两者的半昼弧相加，说：如那个和数之于允诺星的半昼弧，允诺星离征象星的距离亦然。

To the promittor's secondary distance from the medium cœli use this distance, as in Canon XIX. You may likewise make use of the promittor's place, as significator, together with its semi-diurnal arc, right distance, &c. called a converse direction. If both are below the Earth, use the semi-nocturnal arc and distances from the imum cœli, in like manner. Lastly, if one be above, and the other below the Earth, take its opposite place, and use the semi-diurnal arc of that above the Earth, and the other opposite place.

用这个距离作为允诺星离中天的次距，照第十九则进行。你也可以把允诺星的位置当作征象星，连同它的半昼弧、赤经距离等等，这称为逆向推运。若两者都在地平以下，就同样用半夜弧与离天底的距离。最后，若一颗在地平以上，另一颗在地平以下，就取它的对面之点，用在地平以上那一颗的半昼弧，以及另一颗的对面之点。

CANON XXXVI.

第三十六则。

To direct the Sun, when below the Earth, to the Aspects in the World.

位于地下的太阳向世界上诸相位的推运。

As the situation of the immobility, or position of the Sun, constituted below the Earth, is not the horary circle after the manner of others, but either the crepusculine parallel to the horizon, or that which is made in the proportional distances from the obscure arc, as has been mentioned before, then doubtless the Sun receives the promittor's aspect in the world, when the promittor is proportionally distant from a Cardinal, or other house, as the Sun's distance is in the afore-mentioned places after the direction is finished, where his distance is different from his primary one in the nativity, as has been remarked; for the Sun changes successively his secondary distance, wherefore, the calculations of the Sun's direction to the aspects in the world, are attended with somewhat more difficulty.

位于地下的太阳，它不动的处境或位置，不像其他星那样是时圈，而是与地平平行的晨昏圈，或是按黑暗之弧所成的比例距离，如前面已经提到的；那么无疑，太阳在推运完成后，当允诺星离某个角或其他宫的比例距离，与太阳在上述位置中的距离相同时，就接受允诺星在世界上的相位；这时太阳的距离与它在本命中的初距不同，这一点已经指出；因为太阳相继改变它的次距，所以太阳向世界上诸相位的推运计算，要稍微困难一些。

If the Sun is in the crepuscules, first calculate the Sun's direction to the promittor's ray, whether it be sextile, quartile, or trine, in the manner of other significators, that is, from the proportional distances from the angles, and other houses, by the horary times, &c. as hath been said above, the arc of direction may be called a fictious one.

若太阳在晨昏蒙影之中，先像对待其他征象星那样，计算太阳向允诺星光线的推运，无论是六分、四分还是三分，即按离诸角与其他宫的比例距离，借时量等等，如上面所说；这个推运弧可称为虚构的推运弧。

Second, you may know what degree of the Zodiac the Sun at that time hath arrived at, by taking his polar elevation, in the usual manner with the rest, and in the same place the oblique ascension; and by adding thereto the false arc of direction above, taken for this sum of the oblique ascension, will give the degree of the Zodiac, at which the Sun arrives in its revolution; for it is of very little, or no consequence, in case you do not know its true place in this calculation.

第二，你可以知道太阳那时到达了黄道的哪一度：照常与其余的一样取它的极高，并在同一处取斜升；在其上加上前面所得的虚假推运弧，这个斜升之和，就会给出太阳在其周行中所到达的黄道度数；因为在这个计算中，即使你不知道它真正的位置，也几乎或完全无关紧要。

Third, with the Sun's primary distance from the horizon, see what crepuscular it possesses, and in the same, take his secondary distance, to which the supposed feigned direction shall come; then say fourth, as the horary times nocturnal of the Sun is to his secondary distance from the horizon, so is the promittor's horary times to his secondary distance from the angle or other house, and you will have the true arc of direction. Let the example be in Cardinal Odoardus Farnese;

第三，用太阳离地平的初距，看它占据哪一条晨昏圈，在同一圈中取它的次距，即那个假设的虚构推运所到之处；然后，第四，说：如太阳的夜时量比它离地平的次距，允诺星的时量就比它离那个角或其他宫的次距，你就得到真正的推运弧。以奥多阿尔多·法尔内塞枢机为例；

I want to direct the ☉ to the △ of ♃ in the world, which he has to the Sun in an equal proportional distance from the cusp of the fifth, as is the Sun distant from the east, the Sun's horary times nocturnal 19.17; his primary distance from the horoscope 20.57, ♃'s horary times, 11.51, the pole of the eleventh house 18°, the oblique ascension of ♃'s, opposition 242.38; by substracting from this the oblique ascension of the eleventh house, there remains ♃ from the fifth house, 34.3.

我要把太阳推向木星在世界上的三分，这是木星以离第五宫宫头相等的比例距离对太阳所成的，与太阳离东方的距离相等；太阳的夜时量十九度十七分；它离上升点的初距二十度五十七分；木星的时量十一度五十一分；第十一宫的极高十八度；木星对冲之点的斜升二百四十二度三十八分；从中减去第十一宫的斜升，余下木星离第五宫三十四度三分。

By the rule of three, you have ♃'s secondary distance 12.50, which, substracted from the primary, as both distances from the preceding house, leaves the arc of direction 28.40, which arc is necessary, in order to know the degree which the Sun may arrive at.

按三率法，得木星的次距十二度五十分，从初距中减去，因两个距离都从前面那一宫起算，余下推运弧二十八度四十分，这个弧是为了知道太阳可能到达的度数所必需的。

I require the Sun's polar elevation, if its duplicate nocturnal times gives the polar difference between the first and second houses 11°; the Sun's primary distance from the horoscope, 20°57', will give 6° nearly, and there remains the Sun's polar elevation 38, to which the Sun's oblique ascension is, 284.35. To this I add the arc of direction 21.40 and I make the sum 305.46, answering from the same table, 15.20 of ♑.

我求太阳的极高：若它的双倍夜时量得出第一宫与第二宫之间的极高差十一度，太阳离上升点的初距二十度五十七分将得出约六度，于是余下太阳的极高三十八度，在这极高下太阳的斜升是二百八十四度三十五分。我在其上加推运弧二十一度四十分，得和数三百零五度四十六分，在同一表中对应摩羯十五度二十分。

In the tables of crepuscules for the pole 44, I look for the Sun's primary distance from the horoscope, under 25.59 of ♐, and I find it 13.28, under 15.20 of ♑, I take the Sun's secondary distance 20.46, always keeping the proportional part; wherefore again, by proportion, I say, as the Sun's horary times 19.17, is to his secondary distance, horoscope 20.46, so is Jupiter's horary times, 11.51. To ♃'s secondary distance, from the fifth, 12.46, which, being substracted from the primary, leaves the true arc of direction, 21.17. To equate this, proceed as directed in Canon XVI.

在极高四十四度的晨昏蒙影表中，我在射手二十五度五十九分下查太阳离上升点的初距，得十三度二十八分；在摩羯十五度二十分下，取太阳的次距二十度四十六分，始终取比例部分；所以再按比例说：如太阳的时量十九度十七分比它离上升点的次距二十度四十六分，木星的时量十一度五十一分就比木星离第五宫的次距十二度四十六分，从初距中减去它，余下真正的推运弧二十一度十七分。要换算它，照第十六则所说进行。

Book III. If the Sun is found in the obscure nocturnal place, first calculate the false direction, whether it be to the sextile, quartile, or trine ray, as we said in the first part of this chapter; secondly, find the degree of the ecliptic, which the Sun arrives at, by this direction; thirdly, let it be required, if the Sun's obscure arc gives his primary distance, what secondary distance of the same will that degree of the ecliptic give, at which the Sun arrives by the aforesaid direction; and when this secondary distance from the imum cœli is known, if it be in the third or fourth house, use this distance; but if it be in the second or fifth house, substract the Sun's duplicate horary times nocturnal from this distance, and the remainder will be the Sun's secondary distance from the third or fifth house; that is, when the direction is finished, then again say, as the Sun's horary times nocturnal is to his secondary distance from the determinate house, so is the promittor's horary times from that house from which it projects its proposed ray, to that other house, from which you have received the Sun's secondary distance, &c. you must finish as usual.

第三卷。若太阳在夜间的黑暗之处，先计算虚假的推运，无论是向六分、四分还是三分光线，如本章第一部分所说；第二，求太阳借这个推运所到达的黄道度数；第三，要问：若太阳的黑暗之弧得出它的初距，太阳借上述推运所到达的那个黄道度数的黑暗之弧，将得出同一太阳的多少次距；知道了这个离天底的次距后，若它在第三宫或第四宫，就用这个距离；但若它在第二宫或第五宫，就从这个距离中减去太阳的双倍夜时量，余数就是太阳离第三宫或第五宫的次距；即推运完成之时；然后再说：如太阳的夜时量比它离那个确定之宫的次距，允诺星离它投射所提光线的那一宫的时量，就比你求得太阳次距的那另一宫，等等；你要照常完成。

Let the example be in Cardinal Zacohia: in this I want to calculate the Sun's direction to the ⚹ of ☿, in the world, which ☿ has to the ☉, in a proportional distance from the third house, as the Sun is from the fifth; the Sun's horary times nocturnal 14 26, the oblique ascension of the opposite is under the pole 18, the eleventh house is 189.7, from which substract the oblique ascension of the eleventh, 175.22, there remains the Sun's distance from the fifth house, 13.45, Mercury's horary times nocturnal 16, his oblique ascension, under the pole of the third house, is 354.13, wherefore there remains his primary distance from the third 58.51.

以扎基亚枢机为例：在这个例子中，我要计算太阳向水星在世界上的六分的推运，水星以离第三宫的比例距离对太阳成此光线，与太阳离第五宫的距离相同；太阳的夜时量十四度二十六分，对面之点在极高十八度下，即第十一宫的斜升是一百八十九度七分，从中减去第十一宫的斜升一百七十五度二十二分，余下太阳离第五宫的距离十三度四十五分；水星的夜时量十六度，他在第三宫极高下的斜升是三百五十四度十三分，所以余下他离第三宫的初距五十八度五十一分。

I therefore say, if the Sun's horary times, 14.26, give his distance from the fifth house, viz. 13.45, what distance will ☿'s horary times give from third, viz. 16.0? Answer, the secondary distance of ☿, 15.5, which, substracted from the primary, leaves the false arc of direction 43.36, which is necessary to know the degree of the ecliptic, at which the Sun may arrive in its revolution.

所以我说：若太阳的时量十四度二十六分得出它离第五宫的距离十三度四十五分，水星的时量十六度零分将得出他离第三宫多少距离？答：水星的次距十五度五分，从初距中减去，余下虚假推运弧四十三度三十六分，这是为了知道太阳在其周行中可能到达的黄道度数所必需的。

The Sun's pole, taken as usual is 25; the oblique ascension in the same place of his opposite, is 189.35; by adding to this the feigned arc of direction, the sum is 233.1〔?〕, answering in the same table to the 17.30, of ♏, so that the Sun must remain in 17.30 of ♉. Now it remains to know what is the Sun's distance from the imum cœli, or fifth house under 17.30 of ♉, according to the proportional parts of the Sun's obscure arc, and also 17.30 of ♉. The semi-nocturnal arc is 5.46, the arc of the whole crepusculine 1.44; the Sun's obscure arc is, by substraction, 4h 2'.

照常求得太阳的极高是二十五度；在同一处它对面之点的斜升是一百八十九度三十五分；加上这个虚构的推运弧，和数是二百三十三度一〔？〕分，在同一表中对应天蝎十七度三十分，所以太阳必在金牛十七度三十分。现在还要知道在金牛十七度三十分下，按太阳黑暗之弧的比例部分，太阳离天底即第五宫的距离是多少，也按金牛十七度三十分的比例部分。太阳的半夜弧是五小时四十六分，整个晨昏弧一小时四十四分；相减得太阳的黑暗之弧四小时二分。

The Sun's right ascension 8°, from which substract right ascension of imum cœli, gives the primary distance therefrom 42.38. If the Sun's obscure arc 4.2, gives his primary distance from the imum cœli 42.38, what will be the distance of the obscure arc of ♉ 17.30, which is 2.46? But the secondary distance is 29.15; from which I substract the ☉'s duplicate horary times 28.52, for the fourth house, and there remains the ☉'s distance from the fifth 0.23.

太阳的赤经八度，从中减去天底的赤经，得离天底的初距四十二度三十八分。若太阳的黑暗之弧四小时二分得出它离天底的初距四十二度三十八分，金牛十七度三十分的黑暗之弧二小时四十六分将得出多少距离？次距是二十九度十五分；我从中减去太阳的双倍时量二十八度五十二分，即第四宫，余下太阳离第五宫的距离零度二十三分。

Lastly, I demand, if the ☉'s horary times 14.26, give his distance from the 5th, 0.23, what will the horary times of ☿ give 16.0? Answer, ☿ secondary distance from the third, 0.26; which being substracted from the primary distance of the same, there remains the true arc of direction 58.25, of this and others; in the example, you will see afterwards in its place so the other rays, quintile, sesqui-quadrate, and biquintile, After you have calculated the false arc of direction to the sextile, quar-. tile, or trine, add or substract the proportional parts, as we have said above, then see what degree the Sun has arrived at, and in that, his secondary distance from the angles and houses: the promittor always should be at this distance.

最后我问：若太阳的时量十四度二十六分得出它离第五宫的距离零度二十三分，水星的时量十六度零分将得出多少？答：水星离第三宫的次距零度二十六分；从同一星的初距中减去，余下真正的推运弧五十八度二十五分，这一个和其他的；在例子中，你以后会在适当之处看到，其他光线，五分、倍半四分与倍五分也是如此。在你算出向六分、四分或三分的虚假推运弧之后，如我们上面所说，加上或减去比例部分，然后看太阳到达了哪一度，并在那一度求它离诸角与诸宫的次距：允诺星总要在这个距离上。

See also, what I have said elsewhere in an example given for illustration, This Canon serves to shew the ways to direct the Sun to the proper rays in the world, for his place it taken under the primum mobile, as if it was another promittor different from the Sun, always remaining immoveable under the same polar elevation; wherefore let all be done as has been said, for the Sun's virtue is impressed on the primum mobile, under the determinate degree of elevation, and on either side, their virtue continues immoveable; but that which is impressed in the primum mobile, is moved round the world with the same primum mobile, and is separated from the mundane impressing; and this remaining immoveable, under its polar elevation, is moved to the more eastern parts under the primum mobile, and so arrives at the rays of the other virtue impressed under the primum mobile; this in a direct motion is the same as the promittor; in a converse, as a significator; on the contrary, the other, &c.

另请看我在别处为说明而举的一个例子。本则也用来说明怎样把太阳推向它在世界上本身的光线，因为它的位置是在第一原动天之下取的，仿佛是不同于太阳的另一颗允诺星，始终在同一极高下保持不动；所以一切都照所说的去做，因为太阳的力量印在第一原动天上确定的极高度数之下，而在两边，它们的力量保持不动；但印在第一原动天中的那个，随同一第一原动天绕世界运动，与世界上的印记分离；而这个保持不动的，在它的极高之下，被移向第一原动天之下更东的部分，于是到达印在第一原动天之下的另一力量的光线；这在顺向运动中与允诺星相同；在逆向运动中与征象星相同；反之，另一个，等等。