This may be going over only material that we've gone over before, but I've been thinking through this subject for the last few days and clarifying its relative simplicity (though, initially, seeming confusion). When I write things out, I tend to get a bit more clarity for myself; so here goes...
Précis
Angles are of two types: (1) The horizon, meridian, and prime vertical circles themselves (not their intersections with anything; but the circles themselves); and (2) the longitude or right ascension of the intersections of any two of these three great circles.
Major Angles
Our working mundane (local, non-celestial) framework is based on three mutually perpendicular great circles: the horizon, the meridian, and the prime vertical. These provide the most-cited, most-referenced, and most-used angles, which, for convenience, we call major angles.
(Please get the mutually perpendicular relationships of these three circles firmly in your mind. You will be rewarded richly, throughout your study and practice of astrology, by your ability to visualize them and their interlocking relationships.)
- The eastern and western halves of the horizon are, respectively, Ascendant (Asc) and Descendant (Dsc).
- The northern and southern halves of the meridian are Midheaven (MC) and Lower Heaven (IC).
(Which angle is the northern and which the southern half depends on geographic latitude.) - The western and eastern halves of the prime vertical are, respectively, Vertex (Vx) and Antivertex (Av).
At present, we measure proximity to the horizon and meridian along the prime vertical. Experiments suggest that proximity to the prime vertical is best measured in azimuth. Other theories are possible, e.g., measuring distance from each along a perpendicular to the plane drawn through its poles (altitude for the horizon, prime vertical amplitude for the PV, and an analog of these with respect to the meridian that I have termed meridian ebb). However, the measurement in prime vertical longitude and azimuth just stated are, in the worst case, serviceable, seeming to show relative angularity accurately. (In the best case, they are exactly right.)
Despite these technical complications, the underlying concept is simple: Proximity to Ascendant and Descendant is measured by proximity to the horizon; that to MC and IC by proximity to the meridian; and that to Vertex and Antivertex by proximity to the prime vertical.
An Aside on Aspects
In practice, it appears that there is no such thing as an aspect to any angle. However, this may be a matter of how aspects are measured and defined. The wondrous interlocking of the horizon, meridian, and prime vertical provides three mutually perpendicular great circles that are permanently locked into an invariable relationship with each other. In addition to the conjunctions with each plane, though, we have oppositions (e.g., Ascendant opposite Descendant) because these three circles exist on opposite sides of the celestial sphere. We also have squares because each of the circles, at every point, is always square the other two. All points on the horizon are 90° from all points on the meridian measured along the prime vertical and 90° from all points of the prime vertical measured along the meridian. (The same is true for all combinations of these three circles.) Therefore, innate to this framework is the existence of mundane conjunctions, oppositions, and squares to each angle. If other aspects to the angles exist, we would expect that they be measured similarly for each circle in relation to the other two; e.g. (speaking theoretically), the Campanus house cusps are trines and sextiles to the meridian and horizon measured along the prime vertical. - In any case, as the angles are mundane rather than ecliptical structures, they do not have ecliptical aspects.
Minor Angles (Longitude)
The major angles (horizon, meridian, and prime vertical circles) intersect in six locations (three pairs of opposing locations) which, for convenience, we call Minor angles.
- The intersections of the horizon and prime vertical are the Eastpoint and Westpoint of the horizon (which are poles of the meridian circle).
- The intersections of the meridian and prime vertical are the Zenith and Nadir (which are poles of the horizon circle).
- The intersections of the horizon and meridian are the Northpoint and Southpoint of the horizon (which are poles of the prime vertical circle).
(Possibly the best way to think of these is as aspects - conjunctions and squares - between the great circles themselves. However, possibly that introduces unnecessary complication and is better thought a metaphor than an actuality.)
Minor angles are geometrically distinctive from major angles. Major angles are circles; minor angles are points. Practical differences observed between the two groups (e.g., different orb tolerances) likely arise from this seemingly significant distinction.
Each of these minor angle points is already "on an angle" - in fact, on more than one angle - because it is a point shared by two of the major angle circles. For example, Zenith and Nadir are formed by the intersections of the meridian and the prime vertical, so they are conjunct ("on") both of these. Simultaneously, Zenith and Nadir always exactly square the horizon measured along both the meridian and prime vertical.
Perhaps the most important distinction from major angles, though, is that minor angles - being points - can be measured in ecliptical longitude! (Ecliptical or celestial longitude is measured by a great circle passing through a point perpendicular to the ecliptic. As the major angles are all circles, by this definition they have all possible longitudes - the entire zodiac.)
Furthermore, the ecliptical longitude of the intersections of any two major angle great circles is always 90° (square) from the longitude where the third major angle intersects the ecliptic. Specifically,
- The ecliptic longitudes of Eastpoint & Westpoint (horizon crosses prime vertical) are ecliptic squares to MC/IC.
- The ecliptic longitudes of Zenith & Nadir (meridian crosses prime vertical) are ecliptic squares to Asc/Dsc.
- The ecliptic longitudes of Northpoint & Southpoint (horizon crosses meridian) are ecliptic squares to Vertex/Antivertex.
Separately, we can measure the minor angles in right ascension (RA) along the celestial equator. Of six minor angles, only two have positions unique from what we have seen above. Zenith, Nadir, Northpoint, and Southpoint all have the same RA as the meridian - of either the MC or IC - therefore, no new angles are introduced by measuring them in RA.
However, the RA of Eastpoint and Westpoint are not shared by any other angles. Their conjunctions are measured in RA. (For convenience, we place in our charts the point of the ecliptic that is exactly square MC in RA to alert us when a planet may be conjunct. We use it not as an ecliptical point but, rather as an inference - a hint - of where a planet would be when it squares MC in RA. One must always go back and check the contact in RA.)
In a simpler world, I'd like to ignore this axis, but it's too compelling and inescapable a point. Our work in Sidereal Mundane Astrology alone has confirmed it hundreds of times over. We really can't get along without it, so it's good to observe its highly distinctive astronomical importance.
Summary
Our working mundane (local, non-celestial) framework is based on three mutually perpendicular great circles: the horizon, meridian, and prime vertical.
Angles are of two types: (1) Major angles (the circles of the horizon, meridian, and prime vertical); and (2) minor angles (the longitude or right ascension of the six intersection points of any two of these three great circles).
The three circles constitute the major angles:
- The eastern and western halves of the horizon are, respectively, Ascendant (Asc) and Descendant (Dsc).
- The northern and southern halves of the meridian are Midheaven (MC) and Lower Heaven (IC).
- The western and eastern halves of the prime vertical are, respectively, Vertex (Vx) and Antivertex (Av).
These major angles intersect in three pairs of opposing points that we conveniently call Minor angles.
- The intersections of the horizon and prime vertical are the Eastpoint and Westpoint of the horizon (the poles of the meridian circle).
- The intersections of the meridian and prime vertical are the Zenith and Nadir (the poles of the horizon circle).
- The intersections of the horizon and meridian are the Northpoint and Southpoint of the horizon (the poles of the prime vertical circle).
Minor angles (being points) can be measured in ecliptical longitude or right ascension. The ecliptical longitude of the intersections of any two major angle great circles is always 90° (square) from the longitude where the third major angle intersects the ecliptic. Specifically,
- The ecliptic longitudes of Eastpoint & Westpoint (horizon crosses prime vertical) are ecliptic squares to MC/IC.
- The ecliptic longitudes of Zenith & Nadir (meridian crosses prime vertical) are ecliptic squares to Asc/Dsc.
- The ecliptic longitudes of Northpoint & Southpoint (horizon crosses meridian) are ecliptic squares to Vertex/Antivertex.
