The bottom line - where I will end up - is that "angles" (significantly sensitized mundane positions) are formed from

*intersections*of sufficiently important great circles.

**The First Set**

Our working mundane (local, non-celestial) framework is based on three mutually perpendicular great circles: the

**horizon,**the

**meridian,**and the

**prime vertical.**Where the

**ecliptic**intersects these, we have the most-cited, most-referenced, most-used angles.

The two opposing points where the ecliptic intersects the horizon are Ascendant and Descendant.

The two opposing points where the ecliptic intersects the meridian are Midheaven and Lower Heaven (IC).

The two opposing points where the ecliptic intersects the prime vertical are Vertex and Antivertex.

These are their ecliptical positions. For mundane positions, we measure proximity to their base great circle. We measure proximity to horizon and meridian along the prime vertical. Recent experiments have started to look at how to measure proximity to the prime vertical, and the most promising measurement so far is azimuth. However, despite these technical complications, the underlying concept is quite simple: Mundane proximity to Ascendant and Descendant is measured in proximity to the horizon; that to MC and IC is measured in proximity to the meridian; and that to Vertex and Antivertex is measured in proximity to the prime vertical.

**The Second Set**

The "second generation" points are all identified by places where two of our three primary measuring circles intersect. Intersections of any two of our primary framework circles gives the points ecliptically square the angles of the third circle. Specifically,

The two opposing points where the horizon and prime vertical intersect are the Eastpoint and Westpoint.

The two opposing points where the meridian and prime vertical intersect are the Zenith and Nadir.

The two opposing points where the horizon and meridian intersect are the Southpoint and Northpoint.

To determine the celestial longitude of these points (as for any points), we drop a great circle through a point and the ecliptical poles (

*i.e.,*at right angles to the ecliptic). When we do this, we find:

The ecliptic longitudes of Eastpoint & Westpoint (horizon meets prime vertical) are ecliptic squares to MC/IC.

The ecliptic longitudes of Zenith & Nadir (meridian meets prime vertical) are ecliptic squares to Asc/Dsc.

The ecliptic longitudes of Northpoint & Southpoint (horizon meets meridian) are ecliptic squares to Vertex/Antivertex.

How do we calculate these mundanely? I'm not sure we do. There are some interesting mathematical properties, but I'm inclined to take all of these ecliptically or, in the alternative, so say that they are already covered by other identifications. For example, the Northpoint and Southpoint, viewed mundanely, are either on the horizon or the meridian (they are the intersection of these two circles) so mundane proximity to the horizon and meridian already take care of the question. They are already absorbed into the mix.

**Unlike the First Set, they are points, not great circles.**In practice, they appear to be intrinsically ecliptical expressions.

**Is There a Third Set?**

The First Set all involved actual intersections of a great circle with the ecliptic, and the second set all involved intersections of two of our primary great circles (horizon, meridian, prime vertical). Is there a third set? If so, I'm not sure what it would be; or, rather, I don't know of anything that meets the minimum definition that is emerging that we are dealing with points formed as an

*intersection*.

For example, let's take the possibility of squares to the angles in right ascension. Are these valid? (We'll see a special case of this immediately below, involving MC, so let's skip that for the moment.) I've isolated a few charts where planets are square Asc or Vx in RA, and these have not been persuasive. For example, I have a very close friend with Saturn square Asc in RA within minutes - the ecliptical square is 6°, which is way too wide - and the person is arguably one of the least Saturnian people I know in terms of approach to life and basic values. Other examples are similar.

I could argue that my Sun square local Vx in LA (in RA) is valid (orb 06'), in a similar way to Sun being exactly on Antivertex in New York City is meaningful; but that would be an outlier example. Most that I have seen are not defensible as contacts, so I'm more inclined to think that other things in my chart explain the same phenomena.

This is important because the point on the ecliptic that marks the square in RA to Asc or Vx

*has nothing there.*There is no intersection, no independent astronomical measurement there. It would be an aspect, not a new point; and the failure of these aspects is consistent with my overall sense that

*aspects to angles are not valid*because angles are positions, not objects.

So... no, I don't think there is a Third Set of angles.

**What About the Eastpoint**

The point in the horoscope that we

*call*the Eastpoint is a special case. While the

*longitude*of the Eastpoint (intersection of horizon and prime vertical on the eastern half of the chart) is the square to MC in longitude, this point that we place in our charts is

*not*square MC exactly. Instead, it is the point of the ecliptic that is exactly square MC in right ascension (along the equator). How it differs from RA squares to Ascendant and Vertex is that

*there is really something there.*That is, the square to MC along the equator is also exactly the same as the intersection of the horizon and prime vertical. It is really a point that squares MC in three separate circles: 90° from the meridian in azimuth along the horizon, 90° from meridian in prime vertical longitude, and 90° from meridian in right ascension (along the equator). This puts it in a class of its own! - And the way we use it is not as an ecliptical point but, rather as an inference - a hint - of where a planet would be when it squares MC in RA. We always go back and check the contact in RA.

In a simpler world, I'd like to ignore it, but it's too compelling and inescapable a point. Our work in Sidereal Mundane Astrology alone has confirmed it hundreds of times over. We can't really get along without it, so it's good to observe that it has a highly distinctive astronomical importance.

That brings the number of viable points to 9 pairs, although the last one, despite its unique characteristics, is really one of the prior pairs identified in Set 2. Notice that every "angle" mentioned here is formed by a single intersection, but Eastpoint-Westpoint are formed by three different intersections that are identical: horizon-PV, horizon-equator, and PV-equator.

**What Marks Completion?**

To see if I'm missing anything, let's list all possible intersections of five great circles, and see if we have accounted for each of them. The five great circles under consideration are:

**horizon, meridian, prime vertical, ecliptic, equator**

Horizon x Meridian: Northpoint-Southpoint

Horizon x Prime Vertical: Eastpoint-Westpoint

Horizon x Ecliptic: Ascendant-Descendant

Horizon x Equator: Eastpoint-Westpoint

Meridian x Prime Vertical: Zenith-Nadir

Meridian x Ecliptic: Midheaven-Lower Heaven

Meridian x Equator:

**Midequator**[

*see below*]

Prime Vertical x Ecliptic: Vertex-Antivertex

Prime Vertical x Equator: Eastpoint-Westpoint

Ecliptic x Equator: Vernal & Autumnal Equinoxes

Of these 10 pairs of intersections of these five great circles only one is not already included in the angle sets I've outlined above (not counting the equinoxes, which have their own distinction). It is the point where the meridian intersects the equator. It is tempting to simply subsume this into the Midheaven, but it isn't quite the same,

*e.g.,*it wouldn't have the same longitude. We should at least pause to consider what this could mean.

The point already has a name. It is the

**Midequator,**the 10th cusp of the Morinus house system. What makes it intriguing is that it is

*the exact ecliptical square to the Eastpoint,*i.e., the "Eastpoint" we put on the chart, which is the ecliptical marker of the square to MC in RA. If indeed valid, it gives an argument that "squares to the Eastpoint" would be valid, and that these should be taken ecliptically. That is, mathematically, the ME falls more in the category of the Zenith-Nadir.

OK, for a coherent system, we need to start investigating the value of very precise squares to Eastpoint,

*i.e.,*conjunctions with the Midequator and its opposite. Logic doesn't always produce the right conclusion, but it's a damn fine place to start, so we have to consider it.