zoidsoft wrote:Result := EcLatitude * RadToDeg(Sin(DegToRad(90 - Aspect)))

Yep, that's it. For the classical planets the exact method isn't required unless an acurateness of finer than 0?01' in latitude is needed.

zoidsoft wrote:There is often more than one way toward achieving mathematical proofs.

In searching for calculating reference systems I usually took the roundabout route. However if this leads to a more profound understanding, it's the best way for the time being. Many roads lead to Rome.

Eddy wrote:

zoidsoft wrote:Result := EcLatitude * RadToDeg(Sin(DegToRad(90 - Aspect)))

Yep, that's it. For the classical planets the exact method isn't required unless an acurateness of finer than 0?01' in latitude is needed.

To be more precise, the formula generates increasing inaccuracy the farther you are away from the ecliptic until it is 90 degrees from the ecliptic and then you have broken the formula because at +/- 90 deg ecliptic latitude there are an infinite number of great circles that fit Bianchini.

zoidsoft wrote:To be more precise, the formula generates increasing inaccuracy the farther you are away from the ecliptic until it is 90 degrees from the ecliptic and then you have broken the formula because at +/- 90 deg ecliptic latitude there are an infinite number of great circles that fit Bianchini.

Well for a purist, the Bianchini approach is incorrect anyhow. With a 90? latitude, a planet 60? away from the max latitude (i.e. +90? or the pole of the ecliptic coordinate system) would have a latitude of 90/2 = +45?, 45? away from max lat gives 31.82?, 30? gives 51.96? and 0? away from the max lat of 90? gives 90?. Quite a curve it makes. I'll have to double check this, because it looks weird.

The conversion formula gives sin 90 * sin 30 = 1*0.5
Inv. sin 0.5 is 30?. In other words if max latitude is 90 the latitude of the planet is equal to the longitude.

Library is closing, can't continue for the moment

If I had the patience to read Martin's book all the way through first, I would imagine that Bianchini formula is in there (I've been jumping around from text to text). Seems to me that I saw it in Gansten's text so I should double check it. I find it laboriously difficult to abstain from writing code until the last pages of anything. Part of what makes writing software enjoyable for me is solving problems that I do not have the answers to off hand. If I waited until I finished the text, I also might not know where to begin.

Eddy wrote:The conversion formula gives sin 90 * sin 30 = 1*0.5Inv. sin 0.5 is 30?. In other words if max latitude is 90 the latitude of the planet is equal to the longitude.

If latitude is 90, then the point is on a longitude circle (an infinite number of them) perpendicular to the ecliptic. It would be like an hour circle for the equator.

Which means that at latitude of the tilted plane of 90?: longitude=latitude (or 90?-aspect=latitude)

My Bianchini calculations in last post weren't all correct.
For latitude: 90?
square: 0?
sextile: 45?
semisquare: 64?
semisextile: 78?
conjunction: 90?
Thus totally wrong for the aspects except square and conjunction. In fact for the conjunction at latitude 90?, this is in conjunction with every point on the ecliptic.

While the correct are:
square: 0?
sextile: 30?
semisquare: 45?
semisextile: 60?
conjunction: 90?


In a computerprogram it should therefore be made impossible to use higher latitudes than 9?. This might be problematic if you want to use directions to aspects of fixed stars and comets.

Ed F wrote:Mundane aspects mainly. Though there's no reason you couldn't use the declination circle of the zodiacal intercept of the significator. While I understand that it's the historical way of doing it, I still see little sense in using zodiacal positions in a mundane context. They strike me as incidental.

By 'mundane context', do you mean simply 'in primary directions'?

I suppose the traditional point of view would be that the zodiacal aspect points of the planets are points already existing in the radix. If we wanted to, we could mark them in the chart (49 points in all). In directing, we just track their movements as we would that of any other point.

zoidsoft wrote:If I had the patience to read Martin's book all the way through first, I would imagine that Bianchini formula is in there (I've been jumping around from text to text). Seems to me that I saw it in Gansten's text so I should double check it.

I didn't actually put it into a formula, because the method is so simple (although it is an approximation, the error margin, as mentioned by Eddy earlier, is negligible). The topic itself is discussed on pp. 68-70. In that place I also mention Morin's alternative method of assigning latitude to aspects; if you really want to get into it, including Morin's account and refutation of others' opinions on the matter, the place to look is pp. 23-57 of Holden's translation of Astrologia Gallica, Book Sixteen: The Rays and Aspects of the Planets.

I think I can understand Ed's view of the zodiacal positions in a mundane context as incidental. It's a mix of reference frames. Probably a modern view but the use of only the planets in a semi-arc frame without zodiac involved makes it much easier to imagine. When I think about the Bianchini method in combination with the concept of (traditional) converse or non-converse, my first impression is that the old guys sure knew how to complicate simple concepts.

However I understand how difficult it is to abandon the zodiac. (It actually doesn't need to be abandoned but can be used in co-existence with other frames of reference without mixing.) In that case I wouldn't mix it with non zodiacal frames but only Ascendant and MC and their directions to the 49 aspect points. Seen from the perspective of planetary zodiacal positions as points projected on the ecliptic even the MC and Asc are odd ones out. Being coinciding points of Meridian and horizon respectively with the ecliptic, they are neither projections nore nodes. Calculating MC and Asc are based on projected points though, with the result on the ecliptic placed 90? forwards or backwards. This would make the I and X (and opposed) cusps of the Morin house system, theoretically very fitting to the concept of projected points on the ecliptic.

Placidus in Mundo doesn't really project on a plane of a reference frame but each semi-arc is a plane in which the proportionat position is calculated. Until very recently I considered this a totally unacceptable method because of the 'unequalness' in respect to the viewpoint of a coordinate system with an equally divided base plane and poles perpendicular to it. Once I saw that this traditional coordinate system is only one of the ways of imaging, my inhibition appeared as pointless. All systems have the mathematical equalness in perspective of their own reference system. The projection in another frame/mindset makes them appear unequal. I haven't become a convert though , my set of subjective preferences is still inclined towards spheres and base circles (ecliptical, rectascensional and horizontal coordinate systems). However now I can live with it and calculating all these different systems (included Placidus) litterally gives one different perspectives on the same chart. Possibly also metaphorically. Calculating different frames late at night gives some feeling of altered state of mind. Perhaps this sounds a bit vague, but no fluffiness intended here, only maths and its relation to the brain here I think.

A few days ago I made an illustration of the Placidus system on a piece of paper in equatorial position. Unfortunately I don?t manage to copy the scanned picture in my post.

I was wondering if in the pyMorinus software, with 3 options for aspects (aspects of promissor to significator, aspects of significator to promissor, or both), does both mean both of the former or does it mean that an aspect of a significator can also be directed to an aspect of a promissor? Or is it the case that one of the 2 (sig or pro) has to be a bodily conjunction?

I would think the most usual case would be aspects of promissor to significator, where the significator signifies an area of life or subject matter. An aspect of a significator would seem to be an indirect effect on the subject matter.

Eddy wrote:I think I can understand Ed's view of the zodiacal positions in a mundane context as incidental. It's a mix of reference frames. Probably a modern view but the use of only the planets in a semi-arc frame without zodiac involved makes it much easier to imagine. When I think about the Bianchini method in combination with the concept of (traditional) converse or non-converse, my first impression is that the old guys sure knew how to complicate simple concepts.

Exactly what I mean.

However I understand how difficult it is to abandon the zodiac. (It actually doesn't need to be abandoned but can be used in co-existence with other frames of reference without mixing.)

I also agree with this. We're so used to thinking about these viewpoints (mundane and zodiacal) in terms of the given synthesis we've inherited. But they can be looked at independently, and be synthesized in other ways.

Placidus in Mundo doesn't really project on a plane of a reference frame but each semi-arc is a plane in which the proportionat position is calculated. Until very recently I considered this a totally unacceptable method because of the 'unequalness' in respect to the viewpoint of a coordinate system with an equally divided base plane and poles perpendicular to it. Once I saw that this traditional coordinate system is only one of the ways of imaging, my inhibition appeared as pointless. All systems have the mathematical equalness in perspective of their own reference system. The projection in another frame/mindset makes them appear unequal. I haven't become a convert though , my set of subjective preferences is still inclined towards spheres and base circles (ecliptical, rectascensional and horizontal coordinate systems). However now I can live with it and calculating all these different systems (included Placidus) litterally gives one different perspectives on the same chart. Possibly also metaphorically. Calculating different frames late at night gives some feeling of altered state of mind. Perhaps this sounds a bit vague, but no fluffiness intended here, only maths and its relation to the brain here I think.

The semiarc positions are easily normalized to points on the equator via proportion (or more complexly using the Svarogich method). But you have to give up the assumption of right projection being a requirement of a coordinate system. Once you accept Mike Wackford's "It's the oblique sphere, stupid" comment, it falls into place nicely.

- Ed

zoidsoft wrote: I would think the most usual case would be aspects of promissor to significator, where the significator signifies an area of life or subject matter. An aspect of a significator would seem to be an indirect effect on the subject matter.

That's what I thought too, and is what I originally programmed into AstroFrames. But then Anthony Louis corrected me, saying that the traditional method is hits to the aspects of the significators. So I reprogrammed it. I'm sure Martin can clarify.

- Ed

Ed F wrote:

zoidsoft wrote: I would think the most usual case would be aspects of promissor to significator, where the significator signifies an area of life or subject matter. An aspect of a significator would seem to be an indirect effect on the subject matter.

That's what I thought too, and is what I originally programmed into AstroFrames. But then Anthony Louis corrected me, saying that the traditional method is hits to the aspects of the significators. So I reprogrammed it. I'm sure Martin can clarify.

- Ed

So for example, Jupiter is promissor and Sun is significator. If I want to find the traditional way of finding the opposition ray of Jupiter conjunct the Sun, I'm supposed to find the opposition to the Sun and direct Jupiter (bodily) to it?

I had it the other way around (though I'd planned doing both). I found the opposition to Jupiter and directed it to the Sun.