第一部·星位数字的读法　第十一至十三则　位置圈的极高与相位的距离

CANON XI.

第十一则。

Of changing the equal Hours and their Minutes into Parts and Minutes of the Equator, and vice versa the Parts of the Equator into Hours, &c.

把等时及其分化为赤道的度和分，反过来把赤道的度化为时，等等。

This will constitute a part of the future volume of this work.

这将构成本书以后一卷的一部分。

CANON XII.

第十二则。

On the Circle of Position, or the Pole's Elevation of any Planet.

论位置圈，或任一行星的极高。

Under the circle of position, later authors are to be understood of the nature of that passing through the common sections of the horizon and meridians; and upon such circles they direct their moderators, and constitute the intervals of the houses.

后来的作者所说的位置圈，应理解为穿过地平与子午圈公共交点的那种圈；他们在这样的圈上推运主管者，并定出诸宫的间隔。

But how frivolous and remote from natural truth this opinion is, may be seen in my Philosophy of the Heavens, which I have largely and plainly demonstrated; but it is also against the Prince of Mathematics, PTOLEMY, who has transmitted to posterity this universal science, founded only on the sublime principles of Philosophy, which, I think, innumerable examples fully prove. Those who refuse to follow him, doubtless proceed through confused ways, which have no claim to the least commendation whatever. I desire no other guides but Ptolomy and Reason.

但这种意见多么轻浮、多么远离自然的真理，可见于我的《天的哲学》，我在那里已详尽而明白地论证过；它也违背数学之王托勒密，他把这门普遍的学问传给后世，只建立在哲学崇高的原理之上，我认为无数的例子都充分证明了这一点。拒绝追随他的人，无疑走在混乱的道路上，丝毫不值得称许。除了托勒密与理性，我不要别的向导。

I have no idea of circles of position, which are directed through the common sections of the horizon, and meridian, of those that are described by the proportional distances of the stars towards the angles; we may, by means of a very easy method, know the Pole's elevation upon the Ptolomaic circle of any star whatever. In the first place, let the quantity of the house be taken; that is, the semi-diurnal arc, which the stars, whose polar elevation is sought for, measure by lustration. This quantity of the house may be had several ways: (1.)

我不承认那些经过地平与子午圈公共交点的位置圈；而对于那些按星辰到四角的比例距离所描出的〔位置圈〕，我们可以用一个很简便的方法，求得任一星在托勒密式圆上的极高。首先，取宫的大小，即所求极高的那颗星巡行所量的半昼弧〔的一份〕。宫的大小可用几种方法求得：（一）

The horary conditionary times of that star, when doubled, produce the quantity of the starry house. (2.) The third part of the semi-diurnal arc of the stars, is the measure of the house above the earth; of the semi-nocturnal, under the earth. 3. The distance of a star from the preceding house, joined with the distance of the same star from the succedent, taking the distance as mentioned in Canon IX: I say, these distances, added together, produce the space or quantity of the house.

那颗星按其昼夜条件的时量，加倍就得星所在之宫的大小。（二）星的半昼弧的三分之一，是地上之宫的大小；半夜弧的三分之一，是地下之宫的大小。（三）星离前一宫的距离，加上同一颗星离后一宫的距离，距离照第九则所说的取法：我说，这两个距离相加，就得宫的范围或大小。

I then let the difference of the Pole's elevation be taken, which is between the succedent and preceding house, as before; in the midst of these is found the star, by the table of the polar houses; then let the distance of the star be taken, either from the succedent or preceding houses, as before mentioned. (4.) By the Golden rule. Quere, If the whole quantity of the starry house give the polar difference between the succedent and preceding houses, what part of the difference will the distance of the star from either house give?

然后取后一宫与前一宫之间的极高之差，如前所说，星就在这两宫之间，可由诸宫极高表查得；再取星离后一宫或前一宫的距离，如前所述。（四）按黄金法则。问：若星所在之宫的整个大小，给出后一宫与前一宫的极高之差，那么星离任一宫的距离，给出这差的多少？

Let the fourth number, which is the product of the Pole's elevation be augmented by the house from which the distance of the stars is taken, be added to the house's elevation; if diminishing, substracted, and the remainder or sum will be the polar elevation of that star, of which more examples follow in the nativity of Francis, the King of France, &c.

所得的第四个数，就是极高的乘积，若从所取距离的那一宫起极高是增加的，就加到那宫的极高上；若是减少的，就减去，所得的余数或和数就是那颗星的极高；关于这一点，后面法兰西国王弗朗索瓦的本命中还有更多例子，等等。

Here we must be cautious, because the polar elevations of the houses are not increased or diminished uniformly; that is, for example, to the latitude of the country 45; the polar elevation of the eleventh house is increased 18'. In 50, the twelfth house is augmented 15' nearly, and as far the horoscope is increased, 11, so that you see they have no equal increase:

这里我们必须小心，因为诸宫的极高并不是均匀地增减的；例如，在本地纬度四十五度时，第十一宫的极高增加十八分。在五十，第十二宫约增加十五分，而到上升点增加十一，所以你看它们的增加并不相等：

When a star is about the mean distance from the centers of the preceding and succeeding houses, if any one desire to have a true polar elevation of that star, he ought to avoid this inequality; as, suppose the star be in the middle distance from the medium cœli to the eleventh, where, by the golden rule, the pole increases 9° 25', which is half the eighteenth part, 50' to which the eleventh house is elevated.

当一颗星大约在前后两宫中心的中间距离时，若有人想得到那颗星真正的极高，就应避开这种不均匀；例如，假定星在中天到第十一宫的中间距离处，按黄金法则，极高增加九度二十五分，这是第十一宫所升到的十八〔度〕五十分的一半。

A star of this kind hath, in reality, a polar elevation greater than this half, and the reason is, because the difference of the polar elevation is always diminished from the medium cœli to the horoscope; and therefore the tenth house, the polar elevation, has a greater augmentation in the first moiety, than in the latter.

这样的星实际上的极高比这一半要大，原因是极高之差从中天到上升点总是递减的；因此第十宫的极高，在前一半中的增加比后一半大。

The Pole's distance of the houses are these: 11, 15, and 19: if we divide 11 into 5, and 6, but 15 into 7 and 8; lastly, 19 into 9 and 10, the division will appear very agreeable to reason, viz. into 5, 6, 7, 8, 9 and 10, which are the difference of the Pole's elevation in all the medium of the houses; wherefore, above the given star placed in the middle distance from the culmination to the 11th, you will have the Pole's elevation 10.

诸宫的极高之差是这些：十一、十五、十九：若把十一分为五与六，十五分为七与八，最后十九分为九与十，这样的分法会显得很合理，即分为五、六、七、八、九、十，这就是诸宫中点处的极高之差；所以，对于放在从中天到第十一宫中间距离的那颗给定的星，你会得到极高十度。

But the caution is only to be observed, when a star stops about the Moon's distance from the cusps, where, first taking the proportional parts, by the golden rule, near one degree, as mentioned above, should afterwards be added or substracted; for when it remains about the cusps of the houses, it should be entirely neglected, as it makes but little difference.

但这一注意只在星停在离宫头约中间距离时才须遵守，那时先按黄金法则取比例部分，然后如上所说加上或减去将近一度；因为当它停在诸宫宫头附近时，就应完全忽略，因为差别很小。

CANON XIII.

第十三则。

The Distances of the Aspects both in the Zodiac and World, and the Degrees in them.

黄道上与世界上相位的距离，及其度数。

But because every ray is a circle, whose center is the star projecting the ray, excepting the opposition, doubtless every ray cuts the whole latitude of the Zodiac; wherefore, whenever it happens that another star passes through that ray's section, whatever latitude the other star may have, it receives the ray, and mutually projects the same from that section to another star, and only from the point of latitude which this star has there; but this manner of receiving and projecting the rays happens in the daily motion of the stars in the directions, progression, and all the motions of the stars; and indeed from the great difference of latitude of such stars are mutually aspected, there follow some difference of the ray's longitude, but of a very few minutes, which may be omitted; however, those who wish for further investigation, may consult Regiomontanus and Maginus.

但因为每一道光线都是一个圆，其圆心就是投射光线的星，除了对冲之外，每一道光线无疑都切过黄道的整个纬度宽度；所以，每当另一颗星经过那道光线的交截处，不论那颗星有多大的纬度，它都接受这道光线，并从那交截处把同样的光线回投给另一颗星，而且只从这颗星在那里所有的纬度之点回投；这种接受与投射光线的方式，发生在星辰的周日运动中，在推运、进程以及星辰的一切运动中；确实，由于这样彼此成相位的星纬度相差很大，光线的黄经会有些差别，但只有几分，可以略去；但想进一步研究的人，可以参阅雷吉奥蒙塔努斯与马吉尼。

At the medium cœli, the stars have their ⚹ from the cusp of the eighth and twelfth houses.

在中天，诸星从第八宫与第十二宫的宫头〔与之〕成六分。

QUINTILE,

五分，

When their distance from it is four of the five parts of the semi-diurnal arc, or six parts of five of the ⚹.

当它们离中天的距离是半昼弧五份中的四份，或六分〔之距〕的五分之六时。

QUADRATE,

四分，

From the eastern and western points, that is, from the ascendant and seventh.

从东方与西方之点，即从上升点与第七宫。

TRINE,

三分，

From the centre of the second and fifth houses.

从第二宫与第五宫的中心。

SESQUIQUADRATE,

倍半四分，

From the mean distance between the east, and the imum cœli, and between this and the west.

从东方与天底之间的中点，以及天底与西方之间的中点。

BIQUINTILE,

倍五分，

When their distance from the imum cœli is two of the five parts of the semi-nocturnal arc, or three of the five parts from east to west below the earth.

当它们离天底的距离是半夜弧五份中的二份，或在地下从东到西〔的半弧〕五份中的三份时。

OPPOSITION,

对冲，

From the imum cœli.

从天底。

At the horoscope, the stars have the sextile from the cusp of the eleventh and third houses.

在上升点，诸星从第十一宫与第三宫的宫头〔与之〕成六分。

QUINTILE,

五分，

When the distance from the east is four of the five parts of the semi-diurnal arc, or nocturnal; or in other words, when they are distant one part out of five of the above arc from the medium cœli, or imum cœli, towards the east.

当离东方的距离是半昼弧或半夜弧五份中的四份时；换句话说，当它们离中天或天底，朝东方，相距上述弧的五分之一时。

QUADRATE.

四分。

The Medium and Imum Cœli.

中天与天底。

TRINE,

三分，

From the cusp of the ninth and fifth.

从第九宫与第五宫的宫头。

SESQUIQUADRATE.

倍半四分。

From the middle distance between the medium cœli and west, and between the west and imum cœli.

从中天与西方之间的中点，以及西方与天底之间的中点。

BIQUINTILE,

倍五分，

When the distance is two out of five parts from the west above and below the earth.

当离西方的距离是五份中的二份，在地上与地下时。

To the Sun and Moon existing in the cusp of any house, the rest of the planets have their rays in the world in like manner towards the angles, that if they abide in the cusp of the ninth house they have Opposite to them.

对于位于任一宫宫头的太阳与月亮，其余诸行星同样照着四角在世界上取它们的光线，所以若两光停在第九宫宫头，〔第三宫宫头的星〕就与它们对冲。

The SEXTILE,

六分，

From the cusp of the eleventh and west.

从第十一宫宫头与西方。

QUINTILE,

五分，

When the distance from the luminary is beyond the Sextile of the fifth part, from a double gemination of the horary times, and diurnal of a star, remains above the earth; nocturnal, if below; for the Quintile has twelve parts more than the ⚹, which are the fifth part of it.

当离那颗光体的距离超过六分，多出〔六分的〕五分之一时；六分由时量两倍再两倍而成，星若在地上取昼时量，在地下取夜时量；因为五分比六分多十二〔度〕，正是它的五分之一。

QUADRATE,

四分，

From the cusp of the twelfth and sixth houses.

从第十二宫与第六宫的宫头。

TRINE,

三分，

From the east and cusp of the fifth.

从东方与第五宫宫头。

SESQUIQUADRATE,

倍半四分，

When their distance beyond the Trine is one change in the horary times, in like manner conditionary, i. e. nocturnal; I may say, when their distance beyond the Quadrate is in the medium of the semi-nocturnal arc, because both the Sesquiquadrate to the cusp of the ninth house, fall below the earth.

当它们超出三分的距离是一个时量的变化，同样按条件取，即夜的；我可以说，当它们超出四分的距离是在半夜弧的中点时，因为两种倍半四分对第九宫宫头都落在地下。

BIQUINTILE,

倍五分，

When they are distant beyond the Trine twice the fifth part of the nocturnal Sextile, i. e when taken below the earth, or when their distance from the opposition of the luminary is two of the five parts of the semi-nocturnal arc; and in like manner, whatever other place they are found, whether luminaries, or any other star, the rays in the world are taken by a proportional division of the same nocturnal and diurnal arc.

当它们超出三分的距离，是夜间六分五分之一的两倍时，即在地下取时；或当它们离那光体的对冲点的距离，是半夜弧五份中的二份时；同样，无论它们在别的什么地方，不论是两光还是任何别的星，世界上的光线都按同一半昼弧与半夜弧的比例划分来取。

PARALLELS in the ZODIAC,

黄道上的平行，

Which are commonly called antiscions, are circles equi-distant from the equator, and are taken from the equal declination of the stars of what latitude soever, which, if it be of the same name, are called equal in dignity; if one circle be northern, the other southern, the former is said to be of authority, but the latter in subjection.

通常称为映点，是与赤道等距的圆，由不论什么纬度的星的相等赤纬来取；若它们同名，就称为同等尊贵；若一个圆在北，另一个在南，前者称为居命令之位，后者称为居服从之位。

PARALLELS in the WORLD,

世界上的平行，

Are distances equally proportional; both parts from one of the cardinal houses; though, indeed, they appear to have distances equally proportionate to all the cardinal; as the eleventh with the ninth and third; and they are taken by a proportion of the semi-diurnal and nocturnal arcs of the stars.

是两边离某一个角按比例相等的距离；虽然它们看来对所有的角都有按比例相等的距离；如第十一宫与第九宫、第三宫；它们按星的半昼弧与半夜弧的比例来取。