第三部·世界上的推运　第二十六至二十七则　四角向诸星与光线

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 III.

第三部。

To CALCULATE the DIRECTIONS to the ASPECTS in the WORLD.

计算向世界上诸相位的推运。

ASPECTS in the world are proportional distances acquired by motion round the world; for every star after leaving the east, when its distance is the third part of its diurnal arc, is in the ⚹ to the east, when the half part is in the quadrate; when two of the parts are in the △, then the whole diurnal arc is in the ☍, for it is in the west; therefore the first house has the ⚹ with the eleventh and third houses, quadrate with the tenth and fourth, △ with the ninth and fifth.

世界上的相位，是绕世界运动所得的按比例的距离；因为每颗星离开东方之后，当它的距离是其昼弧的三分之一时，就与东方成六分；是一半时，成四分；是三分之二时，成三分；走完整个昼弧时，成对冲，因为这时它在西方；所以第一宫与第十一宫、第三宫成六分，与第十宫、第四宫成四分，与第九宫、第五宫成三分。

The second house has its ⚹ with the twelfth and fourth, its quadrate with the eleventh and fifth, its △ with the tenth and sixth. The third house hath its ⚹ with the first and fifth, its quadrate with the twelfth and sixth, its trine with the eleventh and seventh.

第二宫与第十二宫、第四宫成六分，与第十一宫、第五宫成四分，与第十宫、第六宫成三分。第三宫与第一宫、第五宫成六分，与第十二宫、第六宫成四分，与第十一宫、第七宫成三分。

And thus the other houses always in the same manner, through the diurnal and nocturnal arcs, differ naturally. The stars also have their mutual aspects alternately from those houses, which, with such rays as are taken in the world, whatever may be their latitude or declination.

其余诸宫也总是照同样的方式，经由昼弧与夜弧，按其本性而有不同。星辰也从这些宫彼此交互成相位，所成的是在世界上所取的光线，无论它们的纬度或赤纬如何。

Farther, as those houses have no real existence, and no distinction, or are proper by nature, force, or limits, but from the stars; so that if they had no existence, and did not move round the world, there could be no place in the heavens for the houses or their partitions, as I have fully demonstrated in the Philosophy of the Heavens.

再者，这些宫并没有真实的存在，也没有区别，其本性、力量或界限也不是本来固有的，而是来自星辰；所以假如星辰不存在、不绕世界运动，天上就不会有宫或宫的划分之处，这一点我在《天的哲学》中已充分证明。

Now, the houses are not alternately aspected, with respect to one another; but if the stars that aspect, constitute, and are the measure of the houses; and for this reason they mutually and alternately aspect each other from those houses; and to these and the cardinal signs they direct their aspects.

诸宫本身并不彼此交互成相位；而是成相位的星辰构成诸宫，并且是诸宫的量度；因此星辰从这些宫彼此交互成相位；它们也向这些宫和四角投射相位。

But in the partition of the houses by the duplicate horary times; or according to Ptolemy, by the two temporal hours, no aspect is had to the ecliptic, just as if there was no ecliptic in the heavens; but every aspect must be confined to the diurnal and nocturnal arc of the stars; and it follows, that even the aspects of the stars to the houses, and vice versa, from the houses, which I thought fit to call mundane, have no aspect to the ecliptic, but to their diurnal and nocturnal arc of every single star, or to their motion round the world. All this, if rightly understood, will render every calculation in this third part perfectly easy.

但在用双倍的时量划分诸宫时，或照托勒密的说法，用两个季节时划分时，完全不涉及黄道，就好像天上没有黄道一样；每个相位都必须限于星辰的昼弧与夜弧之内；由此可知，即使星辰对诸宫的相位，以及反过来诸宫对星辰的相位——我认为宜称之为世界上的相位——也不涉及黄道，而只涉及每一颗星各自的昼弧与夜弧，即它绕世界的运动。这一切若理解正确，会使第三部的每一项计算都十分容易。

CANON XXVI.

第二十六则。

To direct the Cardinal Signs to the Conjunctions and Opposition.

四角向会合与对冲的推运。

If you direct the right cardinal sign, take its right ascension from that of the occurrent star, preserving its latitude, and the remainder is the arc of direction required. In like manner to the opposition, keeping to the contrary latitude. If you direct the cardinal sign of the ascendant, take its oblique ascension from that of the occurrent star, carrying the oblique ascension of both to the latitude of the country, but always preserving the latitude of the opposite star, the remainder will be the arc of direction required. To the ☍ use the ascensions of the opposite places.

若推运正的角，就从来会之星的赤经中减去它的赤经，保留该星的纬度，余数就是所求的推运弧。向对冲也一样，保留相反的纬度。若推运上升这个角，就从来会之星的斜升中减去它的斜升，两者的斜升都按本地的纬度来取，但始终保留对面那颗星的纬度，余数就是所求的推运弧。向对冲则用对面之点的上升。

The ascendant may be directed to the stars without the oblique ascension; for if you substract the semi-diurnal arc, from the star's right ascension and from the remainder, take the right ascension of the medium cœli, what remains, is the arc of direction required. Or, if you substract the stars primary distance, that is, betwixt it and the imum cœli, from its semi-nocturnal arc, the remainder is the arc of direction.

上升也可以不用斜升而推向诸星；因为若从该星的赤经中减去它的半昼弧，再从余数中减去中天的赤经，所剩就是所求的推运弧。或者，若从该星的半夜弧中减去它的初距，即它与天底之间的距离，余数就是推运弧。

But if the star has not reached the imum cœli, add its primary distance from the imum cœli to its semi-nocturnal arc, and the sum will be the arc of direction.

但若该星尚未到达天底，就把它离天底的初距加到它的半夜弧上，和数就是推运弧。

These calculations are easy, and need no example; and from what will be said afterwards, they will still be easier. To the fixed, in like manner, by the ascensions, &c. by taking their oblique ascension, with the help of the ascensional difference, if their latitude be extensive.

这些计算很容易，不需要例子；从后面要说的看来，还会更容易。向恒星也同样借上升等来算，取它们的斜升，若它们的纬度很大，就借助上升差。

CANON XXVII.

第二十七则。

To direct the Medium Cœli to the Sextile, Quartile, and Trine.

中天向六分、四分与三分的推运。

Now, it is plain from what has been said, that the intermediate rays to the rays to the angles, are taken by dividing the semi-nocturnal or semi-diurnal arc into three equal parts; or, which is the same, by doubling the horary times of the aspecting stars. by which is known the space of the houses, as to longitude, what the measure is, and degree of those stars in their motions round the world.

由前面所说已很明白：向四角的居间光线，是把半夜弧或半昼弧分成三等分来取的；或者，同样地，把成相位之星的时量加倍；由此可知诸宫在经度上的空间，其量度是多少，以及那些星在绕世界运动中的度数。

When this is known, it is very easy to calculate the directions of the angles to the intermediate rays of the stars; for the sextile is the distance of two houses, the quardrate three, the trine four; these are called secondary distances. So if you want the ⚹ to the medium cœli, which begins from the eighth house, add the two diurnal houses, that is, the stars diurnal horary times twice doubled to the ascension.

知道这一点后，计算四角向诸星居间光线的推运就很容易了；因为六分是两宫的距离，四分是三宫，三分是四宫；这些称为次距。所以，若你要求中天的六分，它从第八宫开始，就把两个昼宫，即该星的昼时量两次加倍，加到上升度上。

If you want the other Sextile, which is produced by the twelve〔?〕 houses, substract in the same manner the two diurnal houses from the right ascension, from the remainder take the right ascension of the medium cœli, and it will give the arc of direction.

若你要求另一个六分，它由第十二宫产生，就同样从赤经中减去两个昼宫，再从余数中减去中天的赤经，就得出推运弧。

But if you seek for the Trine which originates from the sixth house, substract the two nocturnal houses from the stars right ascension: if you seek for the other Trine, which comes from the second house, add the two nocturnal houses to the stars right ascension, and from the remainder or sum, substract the right ascension of the imum cœli, the remainder will be the arc of direction of the medium cœli to the △ of the star.

但若你求的是由第六宫发出的三分，就从该星的赤经中减去两个夜宫；若求另一个由第二宫发出的三分，就把两个夜宫加到该星的赤经上，再从余数或和数中减去天底的赤经，余数就是中天向该星三分的推运弧。

Lastly, if you want the arc of direction to the quadrate, direct the star to the horizon, as above mentioned; but if you have already the primary distance of the stars from the medium cœli of the star, in the ascendant part of heaven, substract the secondary of the sextile from the primary of the star from the medium cœli, and you will have the sextile arc of direction to the medium cœli; substract that star's primary distance from the imum cœli from the sextile's secondary, and you will have the direction's arc to the trine of the medium cœli.

最后，若你要求向四分的推运弧，就照上面所说，把该星推向地平；但若你已有星在天空上升的一半中离中天的初距，就从该星离中天的初距中减去六分的次距，便得中天向六分的推运弧；从六分的次距中减去该星离天底的初距，便得中天向三分的推运弧。

But if the star is in the descending part of heaven, substract its primary distance from the medium cœli from that of the sextiles secondary, and you will have the direction's arc to the sextile. Substract the secondary of the sextiles to the imum cœli, from the stars primary distance, and you will have the directions are of the trine. But if the star passes from the ascendant, to the descendant part of heaven, or on the contrary, add both distances together, and you will have the arc of direction.

但若该星在天空下降的一半中，就从六分的次距中减去它离中天的初距，便得向六分的推运弧。从该星的初距中减去六分到天底的次距，便得三分的推运弧。但若该星从天空上升的一半转到下降的一半，或者相反，就把两个距离相加，便得推运弧。

Note. The △ ray to the medium cœli is the imum cœli, and the ⚹ to the medium cœli is the △ to the imum cœli. Lastly, the rays to the angles are easily calculated by the oblique ascension, of every house; for after taking the stars oblique ascension, under the pole of that house, from which it emits the ray to the medium cœli, and taking the oblique ascension of the house, from that of the star, there will remain the arc of direction required. But if the star goes to project the ray to the descending part of heaven, use the oblique ascension of the opposite place, and this method is of use also in the following Canon, being of all, the most expeditious.

注意。中天的三分光线就是天底，中天的六分就是天底的三分。最后，向四角的光线也很容易借每一宫的斜升来算；因为在该宫的极高之下取星的斜升，即星从那一宫向中天发出光线的那一宫，再从星的斜升中减去该宫的斜升，所剩就是所求的推运弧。但若星要向天空下降的一半投射光线，就用对面之点的斜升；这个方法在下一则中也有用，是所有方法中最快捷的。