Lazarus wrote:The thing that worries me is that in the lesson on primary directions given by Zoller he only gives three methods of calculating these directions. They are I. Directing by Right Ascension II. Directing by Oblique Ascension III. Directions involving degrees not angular.

Those are the 3 formulas that I told you about in regards to proportional semi-arc directions. You can only use the difference in right ascensions in the case where one of the points is directed to the MC. The 2nd is to be used when directing a point to the horizon and the 3rd is the longest formula for use in any situation.

All direction types are about defining what constitutes a direction. As Martin Gansten says, there can be no argument about when a planet crosses the horizon or meridian. However what constitutes a conjunction between points not on these planes is a matter of interpretation. Ptolemy said that when a planet sweeps the same proportional arc that another planet has in regards to it's proportion of distance between the asc and mc, then they are considered conjunct.

So what is done is to find where the significator is (lets say that it has 1/2 the arc between the ascendant and mc). If the diurnal semi-arc is 108 degrees, then 1/2 of that is 54 degrees. Then the arc of the other planet must be considered and if the promissor's arc would total 122 degrees between the asc and mc, then 1/2 of that arc is 61 degrees... The 1/2 technical term is called the PP (Proportional Point).

Now much determines what points to use, such as whether to use the bodies of the planets (with latitude) or their ecliptic projections, whether to do the same with aspects of these points (are they cast along the ecliptic? the equator? or symmetrical to the ecliptic (Bianchini)?) What constitutes a conjunction to these (proportions, theoretical horizons (regio and use of derived poles that one can cast a meridian or horizon line through)? All of these questions are answered differently depending upon the method being used (Polich Page, Under the Pole, Ptolemy, etc).

What is sought is called the AOD (Arc of Direction) and then a key is applied to this arc to convert it into time. Ptolemy is 1 degree = 1 year, Naibod mimics the solar motion, Placidus does similar but according to each particular day of motion (as a variable), etc...

Joao Ventura those are helpful articles you've written. I'll probably have to reread them. One thing that would make them clearer is if you actually worked out the examples mathematically instead of just giving the formula.

Curtis based on everything I still am not understanding how the longer arc for the Sun/MC is more correct from an ancient of ptolemic standpoint as it seems that all the sources I am reading point to getting the difference between RAMC and RAPlanet for the directional arc for planets above the horizon and the MC... perhaps I'm not clearly understanding this still

Okay I finally, by using the third kind of calculation for directing points not angular, arrived at the correct arc of direction for MC to the Sun in this chart... however at first I calculated the Oblique Ascension of the MC by SUBTRACTING the Ascensional Difference of the MC to the RA of the MC because (and this is according to Zoller's instructions) the declination of the MC is north of the equator (+21d8m) and this means subracting. Yet in the long run this gave me the wrong arc of direction (again assuming it is wrong because it does not produce the results of the softwares). So I went back and just for the hell of it tried instead adding the AD to the RAMC and proceeded with the rest of my calculations. I arrived, this way, at the same arc of direction (or very close) that the softwares are giving. So what am I missing now?????? My answer is correct but the method is technically wrong????

Lazarus wrote:Okay I finally, by using the third kind of calculation for directing points not angular, arrived at the correct arc of direction for MC to the Sun in this chart... however at first I calculated the Oblique Ascension of the MC by SUBTRACTING the Ascensional Difference of the MC to the RA of the MC because (and this is according to Zoller's instructions) the declination of the MC is north of the equator (+21d8m) and this means subracting. Yet in the long run this gave me the wrong arc of direction (again assuming it is wrong because it does not produce the results of the softwares). So I went back and just for the hell of it tried instead adding the AD to the RAMC and proceeded with the rest of my calculations. I arrived, this way, at the same arc of direction (or very close) that the softwares are giving. So what am I missing now?????? My answer is correct but the method is technically wrong????

If I remember off hand correctly you might be subtracting a negative which in math is technically an addition.

Lazarus wrote:Curtis based on everything I still am not understanding how the longer arc for the Sun/MC is more correct from an ancient of ptolemic standpoint as it seems that all the sources I am reading point to getting the difference between RAMC and RAPlanet for the directional arc for planets above the horizon and the MC... perhaps I'm not clearly understanding this still

I wouldn't say that it is more correct, just more traditional. Traditionally it should be a measurement of the arc in the direction of the diurnal rotation from east to west. If the direction of the rotation is reversed to one going backward in time, this is a neo-converse direction and a modern interpretation. It would not be the same arc as directing the MC (as sig) to the Sun (promissor) which is a traditional converse direction or the Sun (as promissor) to the MC (as significator) which would be a traditional direct direction. Traditional directions go from east to west, so if you have to move the signpost (significator) to the promissor, this is converse traditionally, but moving a promissor west toward a significator is traditional direct.

If we look at two planets in the sky, each one traces it's own arc (think of time lapse astrocartography that shows stars on film tracing arcs. They are all parallel to each other like this pic:
https://www.google.com/search?q=celesti ... B475%3B316

Each is a different arc so when doing proportions of the DSA (Diurnal Semi Arc) or NSA (Nocturnal Semi-Arc) it matters which arc you take the proportion from to get the proportional point.

Lazarus wrote:Joao Ventura those are helpful articles you've written. I'll probably have to reread them. One thing that would make them clearer is if you actually worked out the examples mathematically instead of just giving the formula.

Well, in truth I derived the formula from the picture which is immediately above [I'm talking about this formula: Arc = (PropDist Promissor ? PropDist Significator) * SA Promissor].

But I guess a concrete example is quite illustrative. If you post here the chart data, and which directions you would like to calculate (only direct semi-arc directions), I may find the available time to show how you can use the formula above to manually calculate the directions.


Regards,
Jo?o Ventura

The Ascensional Difference of the MC was calculated like this

SinAD=(tan21d08m)(tan40dN43m)
=(0.386536)(0.860464)
=0.33269
AD=Sin-1 (0.332669)
=19.43085 = 19d26m

Then OAMC = RAMC + AD
63d05m - 19d26m = 43d39m (THIS GAVE THE WRONG ARC IN THE END)
By addition it is 63d05 +19d26m = 79d02m (THIS GAVE THE CORRECT ARC IN THE END)

Neither the RA or AD is a negative value so subtraction does not end up giving addition in this case...

The chart data is:

March 24, 1990 4pm Manhattan NY