Martin Gansten wrote: Yes, Morin was a Regiomontanus man all the way. His own house system was only intended for regions above (or below) the polar circle.

Yesterday I spent many hours to calculate primary directions based upon Campanus. The time it takes for exact calculation of directed aspects is much more with Campanus than with Placidus. The closely related Regiomontanus would even take a bit more time. Those who have tried to find a planet's latitude while knowing only the longitude and declination know how time consuming calculating these directions (that require a similar approach in Campanus/Regiomontanus) can be.

After doing these calculation I wouldn't be too surprised if Kepler indeed would have used semi-arc / Placidus like directions since these are easily calculated. On the other hand calculating Placidus house cusps though is much more time consuming than Campanus/Regiomontanus house cusps. A bit inconsistent but (because of lack of time or simply laziness) Kepler perhaps used Regiomontanus for the houses and semi-arcs for directions.

I wonder if Morin calculated the primary directions directly (from planet directed to planet) or if he would calculate house and mundane positions for every 4 minutes and then interpolate planet positions. I think this method would be less time consuming.

Eddy wrote:After doing these calculation I wouldn't be too surprised if Kepler indeed would have used semi-arc / Placidus like directions since these are easily calculated.

He didn't, though (or at least not as far as I have been able to find out). He directed the Sun by secondary motion (a day for a year), the Moon by solar arc in longitude, the MC to preserve its angle to the Sun, and the Asc to follow the MC.

I wonder if Morin calculated the primary directions directly (from planet directed to planet) or if he would calculate house and mundane positions for every 4 minutes and then interpolate planet positions. I think this method would be less time consuming.

No doubt he used ready-printed tables, such as those published by Regiomontanus himself.

Martin Gansten wrote: He didn't, though (or at least not as far as I have been able to find out). He directed the Sun by secondary motion (a day for a year), the Moon by solar arc in longitude, the MC to preserve its angle to the Sun, and the Asc to follow the MC.

Thanks for removing my last doubts Martin. Then it must be pretty sure that the assumption of Kepler's use of placidus directions is just Voltmer's (or the Strauss's). Kepler's method akin to solar arcs doesn't appeal to me either, but at least now it is clear to me what he used.

I?ve only just started reading this thread and I have to admit that I?ve only been able to read through the first few pages, so please excuse me if this has already been covered.

There have been a few references to Ptolemy?s Almagest, with the conclusion that he never touched upon methods of house division in that work. It is true that there is no explicitly ?astrological? reference in the whole of the Almagest, but I would like it if some of our more mathematically-minded members could check book II chapter 9 ?On the Particular Consequences of the Ascensions?, because his recommended method for finding the culminating degree, which requires use of the seasonal hours, seems to describe the approach that I have read Mike Wackford describe, and this obviously has to be the ?inspiration from Ptolemy? that Placidus describes.

If there is an argument that this is not describing the rationale of the Placidus house system, then I?d like to know what it is, because this looks like it to me, (though I am no expert in mathematics).

Also, it is probably worth making a link from this discussion to a recent thread where Ptolemy?s most probable method of house division was discussed (from the bottom post of the first page onwards from this link - http://skyscript.co.uk/forums/viewtopic.php?t=3549 ). This is of particular interest for those who believe that Ptolemy used the whole sign approach.

Deb wrote:It is true that there is no explicitly ?astrological? reference in the whole of the Almagest, but I would like it if some of our more mathematically-minded members could check book II chapter 9 ?On the Particular Consequences of the Ascensions?, because his recommended method for finding the culminating degree, which requires use of the seasonal hours, seems to describe the approach that I have read Mike Wackford describe, and this obviously has to be the ?inspiration from Ptolemy? that Placidus describes.

If there is an argument that this is not describing the rationale of the Placidus house system, then I?d like to know what it is, because this looks like it to me, (though I am no expert in mathematics).

I think there are two issues here that we must take care not to confuse. First, whether the (so-called) Placidus system was 'inspired' by or took its rationale from Ptolemy's writings. Second, whether Ptolemy had any such intention. Weighing the evidence, it seems pretty clear to me that the answers are Yes and No in that order. Placidus houses are obviously based on 'seasonal hours'; but just as obviously, Ptolemy makes no mention whatsoever of domification in this context, although he had every opportunity to. His explanation in II.9 is all about the relationship between the true midheaven and the ascendant, something that seems to have confused many classical authors (but is common to all quadrant house systems).

Thanks for the feedback Martin ? that helps me to put the importance of that passage into perspective because I can completely relate to what you say. (Or, I should say ?almost completely? - the one comment I would edit out is where you say "although he had every opportunity to". Since house division was an astrological issue rather than a purely astronomical one, I can't see that he had any reason to in the Almagest.)

Thanks again
Deb

Deb wrote: but I would like it if some of our more mathematically-minded members could check book II chapter 9 ?On the Particular Consequences of the Ascensions?, because his recommended method for finding the culminating degree, which requires use of the seasonal hours, seems to describe the approach that I have read Mike Wackford describe, and this obviously has to be the ?inspiration from Ptolemy? that Placidus describes.

If there is an argument that this is not describing the rationale of the Placidus house system, then I?d like to know what it is, because this looks like it to me, (though I am no expert in mathematics).
.

Dear Deb,
in fact Almagest, II 9 is exactly the reference given by Girolamo Diedo, an Italian astronomer, in his description of his method of houses division published in 1593.

Giuseppe Bezza who loves Placidus dedicated two articles of his site to th subiect, the first is the one dedicated to Girolamo Diedo (published in his journal in 1986)

http://www.cieloeterra.it/articoli.diedo/diedo.html

The second is about IbnEzra and his house division based on 2 hour houses, like Placidus one. (published in 1986 too)

http://www.cieloeterra.it/articoli.cablais/cablais.html

In the article about IbnEzra there are calculation too, so the most versed in trigonometry could check.

The articles are in Italian but numbers are numbers. In the case if someone is interested I can translate, just ask me.

Margherita

so conclusion would be Placidus rocks

I also use Placidus the most, but I ll tell you my experience.

From my 13 year old i was strongly attached to astrology. At some point that came even to the point of obsesion. I was not interested in anythin else in that period. I had great interest for that. From your post i learned that is important connection between Mercury and 9 house and chronorators.

In Placidus system i have 9 house in Libra 0 south node, Venus is Also in 9 - 180 Jupiter in Aries. I also have Sun in Libra. Mars is 3 degrees from the cusp of 9. From that point of view symbolism of 9 house does not mark very clear that i love astrology so much, and that i earn from interpretation of horoscope.

If I put Koch system 9 house fall in sign of Virgo, Mercury as a ruler goes exact on AC without aspect. So these makes more sense.

In Equal systems of houses, the story is similar.

i have a lot of similar egzamples.

My Placidus system simply doesent work.

If your 9th is in Virgo, that means you have a Capricorn ascendant, right? And if your Sun is in Libra, Mercury can be either in Libra, Virgo or Scorpio. So there's no way he can land on your ascending degree. I think you've made a mistake and instead of MC, you wrote AC as a place where you natal (and natural ruler of astrology ) is.
Mercury on MC would explain very clearly that you love astrology because he dominates the chart from that position.
And besides, whichever house system you use, the degree of MC is always the same(I'm referring to Koch/Placidus).

Yes you are right. Mercury is in Scorpio 0 MC. In Equal or Koch Mercury rules 9, in Placidus with 8.

You mean in the Tetrabiblos? Well, he did make some reference, just not very much. And he didn?t define the calculation, but then he doesn?t really define the calculation of other techniques either. Unfortunately I think we have to concentrate on the little he did say, even if this is inconclusive, than the infinite possibility of what he didn?t say Maybe he was like Kepler, willing to use the houses, but not feeling any sense of conviction towards their objective reality. Is this is what you are suggesting?

I think the question about Ptolemy was whether he in fact advocated 'Placidus' houses, as some followers of that system like to claim. House systems are of course astrological in usage, but based on astronomical principles, so Ptolemy could conceivably have discussed the 'Placidus' or dual hour system either in the Tetrabiblos or in the Almagest; but the fact is that he did neither.

Deb wrote:And he didn?t define the calculation, but then he doesn?t really define the calculation of other techniques either.

Here I would have to differ. Ptolemy does go into the calculation of, for instance, (primary) directions; and as the Placidus house system is based on the exact same principles as directions, this is another opportunity Ptolemy missed for describing that system.