第二部·第十七至十九则　黄道上的推运：太阳近四角与远离四角

ASTRONOMY AND ELEMENTARY PHILOSOPHY, TRANSLATED FROM THE LATIN OF PLACIDUS DE TITUS.

天文学与元素哲学，译自普拉西德斯·德·提图斯的拉丁文。

PART II.

第二部。

To CALCULATE the DIRECTIONS to the ASPECTS in the ZODIAC.

计算黄道上相位的推运。

I Have divided the Canons into four parts, for greater distinction and perspicuity, that I might not always repeat the same thing, under any other title than of Canons, that is, either in the Zodiac, or in the world; wherefore, in this SECOND PART, know, that I treat of the Directions in the Aspects in the Zodiac; or, in other words, in the primum mobile, and of no other.

为了更加分明清楚，我把诸则分为四部分，免得总要在「则」以外的标题下重复同样的事，即或在黄道上，或在世界上；所以，要知道在这第二部里，我讲的是黄道上相位的推运，换句话说，是在第一原动天中的推运，不及其他。

But what the aspects in the primum mobile are, and what in the world, together with the cause of this true distinction, I have very plainly demonstrated, from natural principles in the Philosophy of the Heavens; for the aspects in the primum mobile are mutually independent of the horizon of the country, by reason of their motions in the same primum mobile; under which, they are so situate, in all countries and cities of the world, with the difference only of time, or polar elevation.

但第一原动天中的相位是什么，世界上的相位又是什么，以及这种真实区分的原因，我已在《天的哲学》中从自然的原理很明白地论证过；因为第一原动天中的相位彼此之间与本地的地平无关，原因在于它们在同一个第一原动天中的运动；在第一原动天之下，它们在世界上所有国家与城市里都处于同样的位置，只有时间或极高的不同。

The aspects in the world are made dependent on the horizon of every country, because of the motion of the stars towards the world, and cardinal houses: But as it is a dispute whether it is proper to say, that the significator is directed to the promittors, and their rays, or the promittors and rays to the significator, know, there is a double motion of directions.

世界上的相位则取决于每个国家的地平，因为星辰朝着世界与四角运动：但既然有人争论，究竟应该说征象星被推运到允诺星及其光线，还是允诺星与光线被推运到征象星，要知道，推运的运动有两重。

I say, that the significator remains immoveable in the mundane situation, always under the same Pole's elevation, but advances under the primum mobile from its more western parts, to the more eastern; the erratics, however, remain immoveable under the primum mobile, but are moved with a rapid and universal motion from the eastern quarter of the world to the more western, or the place of the significators.

我说，征象星在世界上的位置保持不动，始终在同一个极高之下，但在第一原动天之下从较西的部分前进到较东的部分；而游星在第一原动天之下保持不动，却被一种迅速而普遍的运动从世界的东方象限带到较西之处，即征象星所在之处。

Again, I say, in the converse motion of the direction, that the significator remains immoveable under the primum mobile, but is hurried on by an universal motion from the eastern quarter of the world to the more western, towards the place of the promittors in the world; but the occurrent remain altogether immoveable in their mundane situation, or polar elevation. It follows, then, that both may have a name, but with a difference; and, I will say, indifferently, according as I should have occasion to mention them.

再者，我说，在逆向的推运运动中，征象星在第一原动天之下保持不动，却被普遍的运动从世界的东方象限匆匆带往较西之处，朝向允诺星在世界上的位置；而相遇之星在它们世界上的位置，即极高上，完全保持不动。由此可知，两种说法都可以用，但有分别；我会随时视需要而不加区别地使用。

Finally, as experience in every place ever convinces us, that besides the reason I have advanced in the Philosophy of the Heavens, the aspects of the star to the luminaries and cardinal houses, which happen every day after the nativity, have a very strong influence, viz. from every day to every year, whence, above the rest, are derived the climactrical years, as I shall shew afterwards; and it is likely that Ptolemy, in the last Chapter of Book IV. under the name of Annual Places, means the places of those motions.

最后，因为各地的经验总使我们确信，除了我在《天的哲学》中提出的理由之外，出生后每一天所发生的星对两光与四角的相位，有很强的影响，即从每一天对应到每一年，由此，胜过其他一切，得出关口之年，我以后会说明；托勒密在第四卷最后一章以「年度之位」之名所指的，很可能就是这些运动的位置。

I thought proper to give these motions the name of Secondary Directions; but the others, which we are going to mention, to characterize under that of Primary Directions.

我认为宜把这些运动称为次限推运；而我们将要讲的其他推运，则冠以主限推运之名。

CANON XVII.

第十七则。

To direct the Sun, being near the Mid-heaven, to the Conjunctions, and all Rays.

推运靠近中天的太阳到会合与一切光线。

The Sun is accounted near the cusp of the house when he is not more than 3° distant. First, take the Sun's right ascension, then the places of the aspect, whether it be the conjunction or opposition, or any other intermediate ray, by always taking the right ascensions, and omitting the latitude in this case, even in the conjunction and opposition, if, however, the promittor hath not greater latitude than the orb of his light: for this is the difference between the zodiacal and mundane aspects; the former being caused by a greater proximity to the greater distance of the stars between each other, and above their real ways in the Zodiac, the greater proximity happening in the same partile longitude, though their distance and difference be according to latitude, if the distance of latitude in the conjunction and opposition, as I have said, be not greater than the sphere of activity of light of the stars; for if it be greater, the conjunction is not powerful; nor the opposition in the Zodiac, as I have demonstrated in the Celestial Philosophy.

太阳离宫头不超过三度时，就算在宫头附近。首先，取太阳的赤经，再取相位的位置，不论是会合、对冲还是其他居间的光线，一律取赤经，在这种情形下略去纬度，即使在会合与对冲中也是如此，只要允诺星的纬度不大于它光的容许度：因为这正是黄道相位与世界相位的分别；前者是由星辰彼此之间较大距离中的较大接近、在它们于黄道上的真实道路之上所造成的，较大的接近发生在精确的同一黄经上，虽然它们的距离与差别是按纬度的，只要会合与对冲中的纬度距离，如我所说，不大于星辰光的作用范围；因为若更大，会合就没有力量；黄道上的对冲也没有，如我在《天的哲学》中所论证的。

Lastly, substract the Sun's right ascension from that of the aspects, and the remainder is the arc of direction. In the nativity of George Aldobrandinus, the right ascension is 215° 58', but the right ascension of Venus, taken in the ecliptic, is 262° 8', from which, substracting the Sun's right ascension, there remains the arc of direction, 46° 9'.

最后，从相位的赤经中减去太阳的赤经，余数就是推运弧。在乔治·阿尔多布兰迪尼的本命中，〔太阳的〕赤经是二百一十五度五十八分，而在黄道上所取的金星的赤经是二百六十二度八分，从中减去太阳的赤经，剩下推运弧四十六度九分。

CANON XVIII.

第十八则。

To direct the Sun, where found near the Cusp of the Horoscope, or Seventh House, to the Conjunctions, and all the Rays.

推运位于上升点或第七宫宫头附近的太阳到会合与一切光线。

I take the Sun's oblique ascension, if in the ascendant, under the latitude of the country, or the descension; if in the seventh, or oblique ascension of the opposite place; then the ascension or descension of the place of the aspect under the same Pole, leaving out the latitude in this case, provided that, in conjunction and opposition, the latitude of the planet does not exceed its orbs, and take the Sun's oblique ascension from that of the ray, and the remainder is the arc of direction required.

太阳若在上升点，我就取它在本地纬度下的斜升；若在第七宫，取它的斜降，或对面之点的斜升；然后取相位之处在同一极高下的斜升或斜降，这种情形下略去纬度，只要在会合与对冲中，行星的纬度不超过它的容许度；从光线的斜升中减去太阳的斜升，余数就是所求的推运弧。

CANON XIX.

第十九则。

To direct the Sun, when found above the Earth, far distant from the Cardinal Houses, to the Conjunction, and all the Rays.

推运在地平之上、远离四角的太阳到会合与一切光线。

If the Sun's distance from the cardinal houses is more than 3° from the cusp, first take the Sun's right distance from the meridian; and from the same, the right distance of the aspect the Sun is to be directed to, which we call the primary, the semi-diurnal arc, and that of the aspect; and by the Golden rule say, if the Sun's semi-diurnal arc, and that of the aspects, give the right distance of the same, what distance will the semi-diurnal arc of the promittor, or opposite place give, which is the secondary distance of the aspect?

太阳若离四角宫头超过三度，首先取太阳离子午线的赤经距离，同样取太阳要推运到的那个相位离子午线的赤经距离，这我们称为第一距离；再取太阳的半昼弧与相位的半昼弧；按黄金法则说：若太阳的半昼弧给出它的赤经距离，那么允诺星或对面之点的半昼弧给出多少距离？这就是相位的第二距离。

Now, if both the primary and secondary distance of the aspect be from the same cardinal house, and in the same hemisphere of Heaven, ascendant or descendant, substract the lesser from the greater, and the remainder is the arc of direction; but if one is in the ascendant, and the other in the descendant, add both distances together, and the sum is the arc of direction. You may take the semi-diurnal arc, both of the Sun and the aspect, either in hours or minutes, or degrees and minutes; or, instead of the semi-diurnal arc, you may use the temporary hours.

现在，如果相位的第一距离与第二距离都是离同一个角，又在天空的同一半球，上升的一半或下降的一半，就以小减大，余数就是推运弧；但若一个在上升的一半，另一个在下降的一半，就把两个距离相加，和数就是推运弧。太阳与相位的半昼弧，可以用时和分，也可以用度和分；或者不用半昼弧，改用季节时。

In the nativity of Cardinal Fachenetti, I have a mind to direct the Sun to the quintile of Jupiter in the Zodiac, which happens in 19.41 ♈, the right ascension medium cœli being 326.26.

在法凯内蒂枢机主教的本命中，我要推运太阳到木星在黄道上的五分，它落在白羊十九度四十一分，中天的赤经是三百二十六度二十六分。

Now, if the Sun's semi-diurnal arc, viz. 6h, give its distance from the medium cœli 33.42, what will the semi-diurnal arc of ♈, 19.41, viz. 6h 30' give? Answer, 36.30, which is the secondary distance of the aspect's place. But because both the primary and secondary distances are produced in the ascending part of heaven, I substract the secondary distance from the primary, and the remainder is the arc of direction. Thus,

那么，若太阳的半昼弧，即六时，给出它离中天的距离三十三度四十二分，白羊十九度四十一分的半昼弧，即六时三十分，给出多少？答：三十六度三十分，这就是相位之处的第二距离。但因为第一距离与第二距离都出在天空上升的一半，我从第一距离中减去第二距离，余数就是推运弧。如下：

For the equation, I add the arc of direction to the Sun's right ascension; and I make the Sun 15.21, which answer to 16.40 ♈, at which the Sun, from the day and hour of the nativity, arrives in 16 days, with some hours, which are the compass of so many years.

为了均化，我把推运弧加到太阳的赤经上，得太阳十五度二十一分，对应白羊十六度四十分，太阳从出生的日子与时刻起，十六天又几小时到达那里，这就包含了同样多的年数。

Another way.—To direct the Sun by the oblique ascension, under his Pole of position, take the Pole's elevation, in the manner explained in Canon XII. and the oblique ascension of the Sun, and the aspects, by substracting the Sun's right ascension, the one from the other, &c. of which more examples will be given, we having laid down a table of the Pole's elevation of the eleventh, twelfth, second, and third houses, for the latitude of the country, to 60°: in these tables of the houses, there is placed, above every house, its polar elevation.

另一法。——要在太阳自己的位置极高下用斜升推运太阳，就照第十二则所说的方法取极高，再取太阳与诸相位的斜升，以太阳的赤经与之相减，等等，更多例子以后给出；我们已附有本地纬度直到六十度的第十一、第十二、第二、第三宫的极高表：在这些宫位表中，每宫之上都列有它的极高。