The most plausible and credible answer to the debate surrounding the origins of the aspects was explained to me by a mathematician friend of mine, Nick Evans, only a few weeks ago, in the middle of September 96. Far from dividing the circle by certain numbers as is believed today, it would appear that the ancients originally measured the apparent distances between planets by using simple triangular trigonometry. In my opinion this is the most logical explanation to date. It is well known that astrology developed by way of looking at the planetary movements in the night sky. The early astrologers would have looked at the planets and through time noted the various conjunctions which were easily observable to the eye. Eventually they would have realised the significance of calculating other important "distances" between two or more planets. Quite simply, Nick is saying that the aspects may have been first discovered when astrologers in the distant past decided to measure the apparent distances between planets in the night sky. His explanation was reasoned as follows:

围绕着相位起源的讨论，最似是而非和最可靠的答案是我的一个数字家朋友（尼克.伊万斯）在几个星期之前－96年的9月向我解释的。完全不象今天的人们那样把圆用特定数字划分，古人使用简单的三角法则量度行星之间的距离。以我的看法，这是今天最合乎逻辑的解释。占星学是通过观察夜空的行星运动发展而来的，那是广为人知的事情。早期的占星家观察行星，并且把可以用肉眼很容易观察到的各个相合的时间记录下来。最后，他们领悟到：计算两个或者更多的行星之间的其它重要“距离”重要性。相当简单，尼克 说：当早期的占星家决心量度夜空里的行星之间的距离的时候，这些相位会最先被发现。他解释的理由如下：

"It so happens that if a triangle were drawn such that two of its sides are the same length, possibly the length of a man's arm, and those sides contained between them an angle of 60 degrees, the length of the third side would be the same as the originals. An equilateral triangle would be formed with its associated 60 degree angle.

“常常发现如果一个三角形的其中两边是等长的，可能是一个男人的手臂长度，同时这两边的夹角是60度，那么第三条边的长度和前两边是分别相等的。一个等边三角形是由关联的60度来组成的。”

Using the same two initial arm lengths an angle of 90 degrees between them produces a third side which is the square root of 2 times the arm length. Similarly 120 degrees will form a side the length of which is the square root of 3 times the arm length. Finally the 180 degree angle will produce a side of length 2 arms, the square root of 4. This means that the relative distance apart of two planets which are in an aspect of, say, a trine is simply root 3 times the man's outstretched arm length.

使用最初的相等的两个手臂长度和之间的夹角为90度，可以产生第三条边，而变成等于2的平方根乘以手臂的长度。简而言之，夹角是120度的三角形 形成第三边长度是3的平方根乘以手臂的长度。最后180度的夹角的三角形 形成 第三边的长度是臂长的2倍，4的平方根。这也就意味着2个行星之间是三分一对座的相位的时候，它们之间的距离就是3的平方根乘以这个人伸展手臂的长度。

Yardsticks can be created based upon the length of an arm, or any other suitable length, and these can then act as an effective means of recognising any aspect in the sky. The construction of the square roots of 2, 3, and 4 by geometrical means can be done using a piece of string of length two units. The chosen unit is immaterial because the triangles constructed will maintain their inherent ratios in all cases. To make yard sticks of the required lengths an iterative process is involved which means that the yardstick of the first construction is used as the basis for the second construction and so forth.

可以根据手臂的长度、或者其它合适的长度创建标准，并且可以把这些标准当作一个有效的识别天空中任何相位的工具。几何学里面的2、3、4的平方根可以使用2个单元的长度串来完成。选择的单元是非实质性的，因为构成的三角形会维持它们的内在的比率。为了形成所要求长度的尺码，需要一个反复的过程，意味着第一个结构的尺码被用在第二个结构的基础，等等。

The fact that the square roots of 2 and 3 are irrational means that they cannot be written as fractions. In decimal form they are awkward numbers requiring the use of an infinite number of decimal places. This means the most elegant and effective method of obtaining them is geometric construction. The accuracy of the results are solely dependent upon the accuracy of the construction itself. To construct the correct lengths some knowledge of triangular geometry is necessary. In fact the theory required is known as Pythagoras' Theorem and involves the use of squares and square roots. The construction of the square roots of all integers is simple. Begin with the string of length 2 units arranged into a right angle.

实际上2、3的平方根是无理的，意味着不能用分数的形式书写。用小数的形式表达，它们是很难使用的数字，小数部分的位置需要无限多个数字。这也意味着最文雅和有效的获得它们的方法就是几何结构。结果的精确度是单独依赖于结构本身的精确度的。为了构造合适的长度，需要具备一些三角几何学的知识。实际上需要的是 毕达哥拉斯 的定理，并且使用了平方是平方根。所有整数的平方根的结构是简单的。从2个单元长度串开始，安排在一个直角里面。

The length of the diagonal side will be the square root of 2. This diagonal will be used to construct the next square root by employing a similar method.

对角线的长度是2的平方根。应用类似的方法，这个对角线会被用来构造下一个平方根。

The length of the diagonal side will be the square root of 3. This diagonal can be used in conjunction with another triangle to construct the square root of 4. If the initial choice of unit is the length of a man's arm yardsticks can be constructed to pin-point the classical astrological aspects of a sextile, square, trine and opposition. The yardstick need only be held between the finger tips with outstretched arms to check for the chosen aspect between two planets".

对角线的长度是3的平方根。这个对角线用来和另一个的三角形关联，构造4的平方根。如果最初的单元选择是一个人的手臂长度，构造出来的尺码就可以识别古典的6分、4分、3分以及相冲的古典占星术相位。维持在伸展的手臂的手指尖的之间的尺码只是用来核对两个行星之间的特定相位

It is generally believed that there were whole sign aspects. The ancient Greeks were said to use them.

通常相信存在完整的星座相位。据说古希腊人使用过。

A number of theories have been put forward at various times as to the origins of the aspects. Probably the most famous was by Ptolemy who wrote that the aspects were made up of right angles and whole signs. He was obviously referring to whole sign aspects.

对于相位的起源，在各个时期都出现很多的相关理论。最著名的就是 托勒密 写的 相位由正确的角度和完整的星座组成。他明显的谈到了完整的星座相位。

"These are the ones which are in opposition, enclosing two right angles, six signs, and 180 degrees; those which are in trine, enclosing one and one-third right angles, four signs, and 120 degrees; those which are said to be in quartile, enclosing one right angle, three signs, and 90 degrees, and finally those that occupy the sextile position, enclosing two-thirds of a right angle, two signs, and 60 degrees."

“这些就是：相冲，包括了两个直角，6个星座，是180度：相拱，包括了一又三分之一个直角，4个星座，是120度；四分，包括了一个直角，3个星座，是90度；最后是六分，包括了三分之二个直角，2个星座，是60度。”

"The explanation of opposition is immediately obvious, because it causes the signs to meet on one straight line. But if we take the two fractions and the two superparticulars most important in music, and if the fractions one-half and one-third be applied to opposition, composed of two right angles, the half makes the quartile and the third the sextile and trine." (1)

“相冲的解释是非常明显的，因为它导致了两个星座在同一条直线上。但是如果我们选取2个分数和在音乐里最重要的两个超细节，并且如果分数二分之一和三分之一应用到 相冲，包括了两个直角，它的一半就是 四分，三分之一就是 六分，三分之二就是 三分。”

Ibn-Ezra wrote that "The principal judgements are [made by] the aspects. Ya'akov Al-Kindi says that since there are 12 signs, they divide by 2 and that is the opposition, and by 3 and 4 and 6, but not by other numbers. Scholars of measurements say that the circle divides only by these aspects. Every circle can be divided by a diagonal from one end to the other, and because every circle has two diagonals it divides into 4 equal sections, each at the end of a diagonal, and these are called poles, as I shall explain, and this is a quartile aspect. (2)

以本－以斯拉写到：相位形成首要的判断。雅.阿科夫 奥－金迪 说：因为有12个星座，用2来除就是相冲，并且用3、4、6除就是三分、四分、六分，不能其它的数字。测量的学者说：圆只能用这些相位划分。每一个圆可以用对角线划分，因为每个圆都用2条对角线划分，所以被分成4个相同的部分，每一个部分都在对角线的末端，以我的话来解释，叫作柱，同时是一个四分的相位。

The circle also divides into 3 equal sections; for if you mark the point of 3/4 of the diagonal and mark the arc of the circle from both ends [of the perpendicular line to that point] the circle is divided into 3 equal sections that form an equilateral triangle inside the circle, and this is the trine aspect. When you mark a point at 1/4 of that diagonal and repeat the process an equilateral triangle is formed there [too], and each line as half the diagonal; this is 1/6 of the circle and is called the sextile aspect."(3)

一个圆也可以分成相等的3个部分；如果你在对角线的3/4的位置做标记，在该点上做垂直线，和圆相交得到一段圆弧，并且标记这段圆弧，这样就可以把圆3个相同的部分，在圆内形成一个等边三角形，这就是相拱的相位。当你在对角线的1/4处做标记，并重复这个过程，也可以形成等边三角形，每条线的长度都是对角线的一半；这就是圆的1/6，叫 六分 相位。”

Modern astrology books seem to suggest that there were three methods used for creating the major and minor aspects. The first was simply to divide the circle by a series of numbers. The second by adding, or building one aspect on top of another and the third by dividing or multiplying one aspect into smaller or larger parts.

现代占星术的书籍似乎暗示有3种方法用于创建主要和次要的相位。第一种是简单的根据数字划分圆。第二种是增加，或者在另一个相位的顶部建筑一个相位，第三种是划分或者增加一个相位到较小或者较大的部分。

As already stated it was originally thought that the aspects were created by dividing the circle by the numbers 2, 3, 4 & 6. Later the question arose as to why only these numbers. It was Kepler in the 17th century who decided that the circle could be further divided by 5 and proceeded to create the quintile family of aspects. It has also been argued that the circle can be further divided by the numbers 7 producing the septile group of aspects, 8 a semi-square, 9 a novile, 10 a decile and 12 the semi-sextile. Theoretically this can carry on ad infinitum.

正如已经指出的，最初的想法就是通过把圆分成2、3、4、6等分来创建相位。接下来的问题就是为什么使用这些数字来划分。在17世纪的开普勒确定了圆可以分成5等分，形成了5分的相位。同时也争论过可否分成7等分，形成7分的相位，8等分，9等分，10等分和12等分。理论上是可以无限等分的。

Other astrologers believed that by adding one aspect to another the sesquiquadrate, a square plus a semi-square, and the quincunx, a square plus a sextile, could be created. Some thought that the quincunx was made up of five semi-sextiles, or that it was the inversion of the semi-sextile. If true, then the question could arise as to why not a semi-sesquiquadrate of 67.5 degrees or a semi-quincunx of 75 degrees?

其他的占星家相信在另一个半象限差加上一个相位，可以创建新的相位，一个4分加上一个8分，以及梅花形，一个4分加上一个6分。如果是正确的，那么接下来的问题就是为什么不是67.5度或者 75度呢？

A further complication is mentioned by William Lilly in his book Christian Astrology. He referred to Jupiter in Cancer square the ascendant degree in Libra being equal to a trine because they were in signs of long ascension. (4) If he had measured the distance between Jupiter and the eastern horizon by using triangular geometry he would have found that Jupiter was still within the moiety of orbs of a square to the ascendant and not in trine to it.

在威廉.莉莉的基督教占星学的书里面谈到了更为复杂的现象。他提到了在巨蟹座的木星和在天秤座的上升点相刑等于相拱，因为它们都位于长期上升的星座内。（4）如果他用三角几何量度木星和东边地平线之间的距离，他会发现木星仍然位于和上升点相刑的二分之一的轨道而不是和它相拱。

In his analysis of one horoscope he says that "The Moon in the next place translating the influence of Mars who hath dignities in the seventh, to Saturn, having vertue in the ascendant though by a square aspect (yet out of signs of long ascension) did much facilitate the matter." He was implying that the square was somehow equal to a trine. (5)

在他的星盘分析里面，他讲到：“在下一个位置的月亮转换了位于第七星座的高贵的火星的影响，转为对位于上升点的古典的土星的影响，通过一个相刑的相位（然而在长期上升的范围之外），从而促进了该事情的发展。”他暗示有时候相刑的作用等于相拱。

At this point I would like to suggest a theory as to the origins of the aspect symbols. I believe that those symbols that are used for the aspects were intended to depict the distances between planets in the sky and not the division of the circle by numbers which would create angles as seen here on earth. In my opinion the aspect symbols are telling us to measure distances and not to divide the circle by numbers.

在这点上，我愿意提出一个有关相位符号起源的理论。我相信那些用于相位的符号是有意描述天空中行星之间的距离，而不是在地球上看到的把圆用数字分割创建角度。我的看法就是相位符号告诉我们量度距离而不是用数字划分圆。

The symbol for the conjunction is a small circle with a short line rising above it. This line is the radius of the circle which points to a position in the sky represented by the small circle. The conjunction is not a measurement but a location or place in the heavens. This was one reason why it was never considered to be an aspect. Another reason was because of the origins of the word aspect meaning "looking or fronting in a given direction" which comes from the Latin aspectus. (6)

相合的符号是一个有一条上升短线在上面的小圆。这根线是圆的半径，指出了天空的一个位置，而小圆就是指天空。相合不是一个测量法，而是在天空的一个位置或者地点。这也是从不把它看成一个相位的其中一个理由。另外一个理由就是 单词 相位的起源意味着 “在特定的方向往前看”，来源于拉丁的说法。

The opposition is portrayed by a line connecting two small circles. The line depicts the diameter of the circle and the two small circles represent two planets at their greatest distance from each other.

相冲被描述为连接两个小圆的一根线。这根线描述了圆的直径，以及两个小圆代表了两个行星之间的最大距离。

The equilateral triangle which we use as shorthand for the trine aspect shows the measurement between three planets at equal distances from each other in the sky. The small circles which are a vital component in the conjunction and opposition were no longer necessary to illustrate planets and, I would suggest, were discarded in this aspect as well as in the sextile and square.

我们使用等边三角形作为相拱相位的简称，表示了3个行星之间的距离相等。小的圆形在相合和相冲里面是很重要的部分，没有必要阐明行星，以及，我建议，在这个相位以及6分和4分里面忽略。

The symbol for the square shows four lines measuring the distance of four planets placed at the point where each pair of lines meet.

4分的符号表示了四根测量4个行星的距离的线，这4个行星是位于每对线都合适的点上。

If we continue this line of reasoning then the symbol for the sextile should rightly be a hexagon, in other words six lines measuring the distance between six planets at the points where each pair of lines meet. I would propose that because this symbol was awkward to draw it became distorted and evolved into the symbol that we use today, three lines intersecting in the middle looking almost like a star.

如果我们继续这个推理的思路，那么6分的符号应该是一个六边形，换句话说 6个行星之间的6根线相同，而6个行星位于每对线合适的点上。我建议因为这个符号是很难画出来的，被扭曲了并且发展成我们今天使用的符号，3根中间交叉的线，看上去好像一个恒星。

To my mind, Nick 's persuasive theory that the origins of the aspects are to be found in triangular geometry and Pythagoras' Theorem is certainly the most convincing to date and is worthy of very serious study by the astrological community.

根据我的意见，尼克的有关相位起源的解释理论可以在三角几何里面被发现，并且毕达哥拉斯的定理在今天当然是最令人信服的，值得占星团体认真学习。