zoidsoft wrote: Therefore they are not the same arc of direction.

Yes, I agree.
They don't have the same arc, because arc is given by

arc of direction= distance* temporal hour of the moving planet

distance is fixed, but not the temporal hour, every point has its own, so the result of multiplication will be different.

margherita

zoidsoft wrote:OK. I have just skimmed the latter part of Makransky's text, but I had the impression that he was equating a primary direction method with a house system.

He does, but he is wrong to do so. He understands the mathematics of primary directions, but doesn't seem to have studied the historical development of the technique.

I read your book back in summer 2009 then got derailed by a number of issues not the least of which was the design of the Terran Atlas, but I'm back on it. Your page 56 looks like an explanation of Regiomontanus PD's.

Not exclusively. The section in question has the heading An important note on house systems. I gave the gist of it earlier.

What I want to do here is cover each method as it developed in history and I believe that the method that came after Dorotheus was Ptolemy/Alchabitius used up until Bonatti. Correct me if I'm wrong.

I can't claim complete knowledge of all the source texts, but to the best of my knowledge there were only two major methods of direction in use (apart from oblique ascensions or rising times alone) up to the 17th century:

1. The proportional semi-arc method, used by Ptolemy, al-Qabisi/Alcabitius, Bonatti (although he isn't very clear), Placidus, and many others.

2. The circle-of-position method, used by al-Biruni, Regiomontanus, Morin, William Lilly, and others.

Placidus muddied the waters somewhat by introducing a hybrid method meant as a shortcut (often called 'Placidus under the pole' today), but these are the two main schools. They differ only with regard to directions between points that are not on the angles.

All the other variables that go into a system of directions, such as whether or not to use latitude, how to calculate latitude for aspects (if at all), which significators and promissors to use, etc, vary from author to author, and I couldn't at present give a certain chronology for them. (Moreover, I wouldn't trust anyone who did, unless I were sure they had studied all the available source texts in Greek, Latin and Arabic.)

Then, of course, Placidus came along and introduced quite a number of entirely new ideas, including but not limited to his 'mundane aspects'. All dealt with in my book (I hope).

Regarding the question of the arcs from A to B (forwards in time = with the primary motion) and from B to A (backwards in time = against the primary motion): no, they are not the same, although some authors (like Alan Leo) have failed to grasp this fact.

However, please note that the idea of directions against time and the primary motion is a recent one (19th century?), and very likely the result of misunderstanding. It is not what earlier authors had in mind when they wrote of 'converse directions'.

At some point in time I hope to finish my paper on this subject (working title: Back to the future). Meanwhile, if a further plug may be excused, please see my book, pp. 98-101.

Martin Gansten wrote:[
Placidus muddied the waters somewhat by introducing a hybrid method meant as a shortcut (often called 'Placidus under the pole' today),

Can you give me a reference for this? I hate browsing Latin books

On the other hand if I have a quote I should struggle a little with Latin, but I can eventually win.

margherita

margherita wrote:Can you give me a reference for this? I hate browsing Latin books

I sympathize, but I haven't got a reference handy, and no time to find the charts in question at the moment. If memory serves, they are among those included in the Tabulae Primi Mobilis. Sorry not to be able to be more precise at present -- I'll let you know if I stumble upon them.

Martin Gansten wrote:. Sorry not to be able to be more precise at present -- I'll let you know if I stumble upon them.

grazie, thanks

margherita

Martin Gansten wrote:At some point in time I hope to finish my paper on this subject (working title: Back to the future). Meanwhile, if a further plug may be excused, please see my book, pp. 98-101.

OK. I was attracted to the way Makransky wrote the book because it is easy to program by which didn't force me to think very hard, but he took a turn that I didn't want to follow. At about the point where it would have been logical to address planet to planet directions, he went off into field planes and I have yet to see any mention of proportional semi arcs, or circles of position. Maybe later on I will get to programming that, but I feel it more pressing to do the older methods first.

Your text makes it easy enough to understand, but as a programmer I'm looking for algorithms (you obviously had a different audience in mind) and while I'm sure that I can do that with your book, I'll have to assemble the sequences of program logic myself (such as the problem of determining converse and direct in code - In the Makransky text, a negative arc of direction is converse). Time to study...

Thanks for your help!

Yes I see it the same way as Margherita does. An example: In northern France the shortest daytime is 8 hours and the longest 16 hours. Half daytimes are 4 and 8 hours respectively. For the moment 18:00 Sidereal Time, 0?Capricorn is on the south meridian and 0?Libra is on the horizon in the west. Since 0?Capricorn has the shortest daytime arc it will take 4 hours for 0? Capricorn to get to the west horizon and therefor in 'Placidus' terms in conjunction with the descendant. For 0? Libra to go backwards (before birthtime) to the south meridian it will take 6 hours. Both points moved 90? degrees or three cusps according to Placidus measurement, but in different speeds (like Margherita's nice hare and the tortoise example.).

When I read in your post Curtis(top p.9)

I suspect that the detour is because in the small circles on which planets are on, that a mundane conjunction is basically a perpendicular line between significator and promissor that is at a right angle to the plane of measurement (right ascension in most cases)

, I was a bit confused whether I misunderstood it. Except on the Earth's equator, a mundane conjuntion is not a perpendicular line at right angle to the plane of right ascension. In Campanus for example the perpendicular line between conjuncting planets is in a right angle to the prime vertical. Hope this picture of Campanus makes more clear.
http://www.arimoya.ru/img/campanus.gif

In your illustration and from the text I have the impression that you also use the equator as basis for mundane conjunctions. I may be wrong but I have the impression that you confused mundane conjunction as being always equatorial conjunction. If you didn't, I read it wrong. Conjunction can also be defined as being on the lines from north to south (as in Campanus, Regiomontanus and the Meridian system when on the Earths equator ), these too are 'great circles' or 'positioning circles'. Alchabitius indeed used equatorial coordinates for the house cusps see illustration http://classicalastrologer.com/Alcabitius.gif MC and Asc are converted in right ascension position. Then the division is cut in three, like Porphyry and the resulting ascensional positions converted to ecliptical. Personally I wouldn't think that Alchabitius could be used for 'in mundo' because an ecliptic dependent definition of the ascendant is required while in, Placidus, Campanus, Regiomontanus the whole horizon is related to the ascendant and is possible without dependency on the ecliptic. But this is somewhat a side path here. The illustration came from this article, where are more house systems discussed. http://classicalastrologer.com/House_Sy ... amined.htm

Both A and B trace out different arcs which are small circles. The closer to the pole, the smaller the circle.

Perhaps I understand you wrongly but since the points on the circles are always projected on the base plane of the coordinate system (i.e. the equator) both circles are equal. When no coordinate system is meant to be used the angles of the top circle is indeed smaller but since the rotation determines the measurement, the equatorial plane is the basis for all these circles notwithstanding their distance from the equator. Just like Washington D.C is almost on the same West longitude meridian as Quito, Ecuador (ca. 78? W), the former is on 38?North and the latter on the equator 0?. So when the Sun is in the south in Quito it also is in Washington. 24hours later the Sun is again in the south in both cities. The equator turned 360?. The difference that the circle around the Earth at Quito is 40,000 kilometer and at Washinton much smaller. If this was a winter day the Sun in Washington would set much earlier than in Quito, because the horizon is more tilted towards the celestial equator.

In your illustration this means that you have to look at the horizon. Just draw a line from left to right. Point B appears to be just under the horizon. To get A there moving backwards/down, you will see that the line will be a much longer one. You could imagine lines from left to right. For Campanus these are circles but for Placidus these are curves, which are more difficult to imagine and to draw. The more north a planet is, the longer the semi-arc (for the Placidus division) just like days are longer when Sun is more north. The beginning (somewhere eastern half of the horizon) point is expressed in right ascension (thus also when not on the equator itself), same is done with the end point (mirroring on the western half of the horizon). The time above the horizon can therefore be expressed in equatrorial degrees, like the 210 time degrees for Alexandria's longest day and 150 for the shortest day or 14 hours and 10 hours respectively. Expressed in seasonal hours both are 12 hours (or what one could call 180 units of 4 seasonal minutes). These hours we see reflected in Placidus's system. My apologies if I erroneously think that you confused several mathematical things Curtis. With complicated subjects like these it's difficult to see whether the one knows what the other knows.

Eddy wrote:My apologies if I erroneously think that you confused several mathematical things Curtis. With complicated subjects like these it's difficult to see whether the one knows what the other knows.

No problem. I haven't spent much time on primary directions, but I do have a background in astronomy and mathematics and used Jean Meeus's Astronomical Algorithms text to program much of my software in the early days before I had access to the Swiss Ephemeris. I'm not used to the lack of standards where one astrologer calls something by one name and another calls it by something else. It makes for difficulty in identification to say this technique is a "such and such", but wait, its called this by so and so and this by someone else (significators and promissors, promittors, mediator, take your pick and feel free to reverse the meanings of significator and promittor depending upon the era if you wish).

At this point I have 3 sources and each does primaries a different way and I made the mistake at first of assuming that the mathematics would all be in agreement. I think instead that I'm just going to settle on Gansten's approach and think it through and it will eventually become clear. Thanks for your help.

Jean Meeus? work is magnificent. I have the book(s) too. For people who are interested, there appear to be several downloads of his ?Astronomical formulae for calculators? (the forerunner of his Astronomical Algorithms), like here http://www.general-search.com/fileinfo/2916384#
I once calculated my own chart from the orbital elements with a calculator. These calculations are shorter than the method used in Astronomical Algorithms. Very instructive, I can advise it to anyone. The hard labor will be rewarded with an insight in astronomy and mathematics, and shows how much work is going on in a computer.

I'm wondering if anyone here knows what constitutes latitude of an aspect (such as the dexter trine of Venus)? I'm setting up the classes for the significator/promissor object in the Alchabitius method right now... Zodiacal directions are obvious, but is there an in mundo latitude to an aspect in Ptolemy? I might assume that for an opposition for instance that if north latitude of +2 degrees, then the opposition would be -2 degrees below the ecliptic and of course proportional according sextile / Trine, and the square would be 0 here by my assumption - this is in keeping with my idea that aspect rays should be cast on the great circle from the planet casting the ray (this probably has a name by some author in history because I can't believe that I would have been the first to think of this issue). If I used latitude of promissor the same through each, then it is a small circle and can't be a great circle unless it has 0 latitude. Perhaps this line of thinking is not Alchabitius altogether?

Of course aspects might not just be cast from a frame of reference such as the plane of the ecliptic; one could use right ascension to cast aspects as well with very different results, but I do not know what these variations go by name wise by historical convention.

zoidsoft wrote:I'm wondering if anyone here knows what constitutes latitude of an aspect (such as the dexter trine of Venus)? I'm setting up the classes for the significator/promissor object in the Alchabitius method right now... Zodiacal directions are obvious, but is there an in mundo latitude to an aspect in Ptolemy?

Ptolemy doesn't mention latitude (nor, to my knowledge, do other Greek-language authors), but the Arabic authors do. You will find information on this on pp. 68-70 of my book (see also pp. 88-91). Briefly, aspects may be taken in a great circle passing through the body of the aspecting planet and inclined to the ecliptic by the extent of that planet's latitude. This is the most common method, though others have been proposed (Morin, for instance, had his own method).

Please note that what has commonly been called 'mundane aspects' or 'aspects in mundo' since the time of Placidus is something entirely different than zodiacal aspects with latitude.

I might assume that for an opposition for instance that if north latitude of +2 degrees, then the opposition would be -2 degrees below the ecliptic and of course proportional according sextile / Trine, and the square would be 0 here by my assumption - this is in keeping with my idea that aspect rays should be cast on the great circle from the planet casting the ray (this probably has a name by some author in history because I can't believe that I would have been the first to think of this issue).

No, you're not! This is the most common method, as mentioned above. It is usually named after Bianchini (Blanchinus).