46 by Eddy Martin Gansten wrote:Eddy wrote:I believe the directions between planets most used would have been the proportional semi arc. Calculating directions according to the position circles is much more time consuming. Oh, definitely, at least until there were published tables (such as those of Regiomontanus). But can these be used to direct planets to planets? For example with a planet somewhere in the middle of house XI (Regiomontanus) and one somewhere at the beginning in house X first their positions according to that house system should be calculated and then the time it would take for the first planet to occupy the second planet's place. I don't know how this should be done with house tables alone. Perhaps the use of tables was only for the simple type of directions which calculate when a cusp will reach a certain planet. Martin Gansten wrote:Gjiada wrote:Are you telling that formula could be the same and I just can decide to use latitude or not, and in that case we have zodiacal directions? Is it like that? Yes, that's it: set the latitude to 0, and you have a zodiacal direction. Did the medieval astrologers consider them both correct or was there some disagreement? If they are both correct, is there a different meaning? It they did consider both correct it would be even more difficult to study PD's or to 'test' them. Ed F wrote:But that's just the kind of redefinition of accepted usage of a term that leads to confusion. There's already plenty of confusion in primary directions. I'll be more carefull in my assumptions. I didn't know before that there was a classical terminology (in mundo/in zodiaco) distiguishing the two. Martin Gansten wrote:Ed F wrote:This statement confuses me. Various circles of position (various definitions, depending on domification model) and proportional semiarc positions give different results for directions. The phrase depending on domification model rather begs the question. There are any number of house systems, but only two historically practised methods of (full-blown) primary direction; and before the 15th century there was only one in common use, namely, Ptolemy's semi-arc method (later to become the basis of the Placidus house system). Ptolemy's method was used by generations of astrologers who simultaneously employed whole-sign houses, equal houses, Porphyry houses and/or Alcabitius houses as their 'domification model'. The idea that house system and method of directions should be somehow related was apparently alien to them. Modern authors (such as Makransky) have invented various methods of so-called primary directions based on different house systems, but these are wholly theoretical constructs and were never practised historically.That confuses me too, I don't consider it very consistent. I guess the medieval astrologers did so because it may have been considered too difficult to them to calculate proportion semi-arc houses. On the other side they could have found the direct calculating of mutual planet directions too difficult in an other method than the proportions of semi arc. Perhaps the work of the "Modern authors (such as Makransky)" is more consistent and may be worth more investigation. Furthermore I would believe that an astrologer who uses PD's mundane should also look at the basis chart for moment zero i.e. the Radix that then could look quite different than the ecliptical Radix. By the way, I hope the discussion hasn't drifted too far from Mark's original subject of what to do with fixed stars that are far from the ecliptic. Quote Thu Mar 05, 2009 12:52 pm
47 by Martin Gansten Eddy wrote:But can these be used to direct planets to planets? Yes. These are not mere house tables, but Tabulae directionum profectionumque, devised with primary directions in mind. They can be viewed here: http://digital.slub-dresden.de/sammlung ... 9002181/0/ In a circle-of-position method, an artificial horizon is devised, running through the 'static' planet, and other planets are then directed to that 'horizon' by oblique ascension. Did the medieval astrologers consider them both correct or was there some disagreement? If they are both correct, is there a different meaning? It they did consider both correct it would be even more difficult to study PD's or to 'test' them. Before the 15th century, directions in zodiaco were the rule. After that time opinion has been divided on the subject. Some authors consider both kinds of direction to be valid. Ptolemy's method was used by generations of astrologers who simultaneously employed whole-sign houses, equal houses, Porphyry houses and/or Alcabitius houses as their 'domification model'. The idea that house system and method of directions should be somehow related was apparently alien to them. [...] That confuses me too, I don't consider it very consistent. It is inconsistent if and only if we presuppose that directions and house systems should be related. Ancient and medieval astrologers didn't, and I don't really see why they should have. I guess the medieval astrologers did so because it may have been considered too difficult to them to calculate proportion semi-arc houses. On the other side they could have found the direct calculating of mutual planet directions too difficult in an other method than the proportions of semi arc. Both these guesses are incorrect. Ibn Ezra described 'Placidus' houses; al-Biruni described 'Regiomontanus' directions; but neither method caught on. Don't underestimate the mathematical proficiency of the medieval authors! If they didn't do things our way, this is not necessarily because they didn't know how to. Perhaps the work of the "Modern authors (such as Makransky)" is more consistent and may be worth more investigation. Perhaps. Or perhaps they just need to read fewer maths books and more history books. Quote Thu Mar 05, 2009 4:09 pm
48 by Eddy Martin Gansten wrote:Tabulae directionum profectionumque, devised with primary directions in mind. They can be viewed here: http://digital.slub-dresden.de/sammlung ... 9002181/0/ In a circle-of-position method, an artificial horizon is devised, running through the 'static' planet, and other planets are then directed to that 'horizon' by oblique ascension. Thanks for the link Martin. Unfortunately I don't read Latin but very interesting to see the ancient manuscript. I had a try with Campanus and this method came into my mind. However with this 'new' artificial horizon also a 'new' latitude of the location on Earth would been introduced. The 'horizon ' coinciding with the meridian would obviously use as latitude the Earth's equator but I didn't find a method to find the latitudes for the horizons inbetween. Instead I first calculated the distance measured along the prime vertical (pv) of the moving and the static planet, both to the point on the horizon in the east where pv and equator meet. With as known the distance along the pv and the equatorial declination I had to find the unknown new equatorial position and for this purpose first also the 'declination'(I don't know how else to call it) measured from the pv. This resembles the finding of the right ascension (and the latitude) of a planet when only the longitude and the declination are given (as some ephemerides do). Anyhow with many trigonometrical formulae I finally found out but perhaps the traditional method would require the same amount of trigonometry. Quote: ........ That confuses me too, I don't consider it very consistent. It is inconsistent if and only if we presuppose that directions and house systems should be related. Ancient and medieval astrologers didn't, and I don't really see why they should have. Two weeks ago I had been thinking on another issue that also seemed an 'inconsistency' to me, namely the use of the division of time. (I even thought of opening a thread on this but I don't have enough time yet to 'host' a thread) If Ptolemy used the proportions of semi arcs for the primary directions and derived it from the seasonal hours which apparantly were common usage in Mediterranean (civil) life in his days then these (I reasoned) rather than the equinoctial hours should have been used in the directions. The formula should then have been 4 (seasonal time) minutes (based upon the position (declination) of the Sun in the first hours after birth, equals one year. This finally would then have been totally in line with the basis of the method of division, a Placidus type house system, proportions of semi arcs and finally the seasonal hours. As far as I know this isn't done by anyone. So not alone say Alcabitius houses is used with Placidus proportions of semi arcs but also the time based upon equinoctial hours as the basis for the 4 minutes=1 year formula. This last element in fact reflects the Meridian house division. So it actually was a kind of 'three in one'. I'll have to think about all this, I don't feel I have to 'follow' the medieval astrologers on this. I believe I too have a problem with authority . Don't underestimate the mathematical proficiency of the medieval authors! If they didn't do things our way, this is not necessarily because they didn't know how to.I did tend to do so indeed. Perhaps it's because of the way how most books summarize the history of house systems. In Jim Tester's "A History of Western Astrology" it is also mentioned that the medieval astrologers/astronomers knew quite a lot about house divisions. Quote Thu Mar 05, 2009 5:35 pm
49 by Ed F Martin Gansten wrote:Ed F wrote:...Ptolemy's method was used by generations of astrologers who simultaneously employed whole-sign houses, equal houses, Porphyry houses and/or Alcabitius houses as their 'domification model'. The idea that house system and method of directions should be somehow related was apparently alien to them... OK, I understand our different uses of the terms here. - Ed Quote Thu Mar 05, 2009 6:31 pm
50 by Martin Gansten Eddy wrote:If Ptolemy used the proportions of semi arcs for the primary directions and derived it from the seasonal hours which apparantly were common usage in Mediterranean (civil) life in his days then these (I reasoned) rather than the equinoctial hours should have been used in the directions. The formula should then have been 4 (seasonal time) minutes (based upon the position (declination) of the Sun in the first hours after birth, equals one year. But the basic idea isn't 'four minutes of time equal a year', but rather 'one degree in the turning of the celestial sphere equals a year'. And the celestial sphere turns (or, in the modern understanding, the earth turns on its axis) at a constant speed, completing 360? in 23h 56m of clock time. Quote Thu Mar 05, 2009 6:45 pm
51 by Olivia I think the ancients and medieval authors had a good grasp, too. The maths are mind-bending, and in that text Schoener just breezes through them as he gets to different techniques for all sorts of calculations and then gives you the fomulas so you can do them too (after you've read it about 20 times, tried pencil and paper, tried the calculator, and finally had a sort of 'a-ha' moment). Even then it's dicey, and I'm not bad at maths. If you read Ibn Ezra, you'll find that in certain places he gives you a formula, and then says if that's too difficult for you to work out, you can do it this other way, gives you a different formula, and that'll get you to the same results. And it does. Not stupid people. At all. Quote Fri Mar 06, 2009 3:50 am
52 by Eddy Martin Gansten wrote:But the basic idea isn't 'four minutes of time equal a year', but rather 'one degree in the turning of the celestial sphere equals a year'. And the celestial sphere turns (or, in the modern understanding, the earth turns on its axis) at a constant speed, completing 360? in 23h 56m of clock time.This is an interesting detail even though I personally would prefer as basis the true solar day. Note that the sidereal day isn't constant either but because of the effect of nutation it is slightly different. However this effect is so small that the difference in time couldn't be measured with the clocks until the 19th century. Bradley had discovered the nutation in declination in the 18th century. This difference between 'mean sidereal time' and 'apparent sidereal time' is of barely any significance in practice, about less than a second. Quote Fri Mar 06, 2009 11:23 am
53 by Martin Gansten Eddy wrote:This is an interesting detail even though I personally would prefer as basis the true solar day. Hardly a detail, surely? Note that the sidereal day isn't constant either My psychic powers must be up: I knew you'd say that! But (as you also say) this minute difference is not relevant for our purposes. Quote Fri Mar 06, 2009 1:52 pm
54 by Eddy Martin Gansten wrote:Eddy wrote:This is an interesting detail even though I personally would prefer as basis the true solar day. Hardly a detail, surely? Hmm... rather a cornerstone . Can you tell me if Ptolemy had the sidereal time in mind or rather the degree? If it is the time I wonder why the secondary progressions then never would have been used in his days. After all when the basis is considered 4 sidereal minutes (which in fact is the same as 1 equatorial degree) = 1 year, then I can imagine that they also would have thought about 4 sidereal minutes (or 1 equatorial degree) = 1 day. I always had these time proportions in mind and therefore it always has baffled me that the secondary progressions only were used from the 16th/17th century. On the other hand if it originally was intended a pure space basis 1 degree = 1 year then I can understand the criticism of Pico, Gassendi etc (according to Jim Tester's book) who considered this as rather arbitrary. "Why not 2? per year?": one could say. If this is the case then I have a sort of theory that in the centuries before Ptolemy the astrologers worked with forerunners of Chronocrators and Ferdariae assigning years to the signs. For example many years to Capricorn Aquarius (because of Saturn) and few to Cancer (Moon), perhaps referring to the planet ages (Moon=4years, Mercury=10y....etc.). Then came a first 'scientification' based upon rising times per sign which finally were refined by Ptolemy. I could be totally wrong but perhaps the primary directions were derived from this and therefore the secondary directions came later. Quote: Note that the sidereal day isn't constant either My psychic powers must be up: I knew you'd say that! But (as you also say) this minute difference is not relevant for our purposes. I often can keep my mind busy for hours by thinking over these differences, building theories upon it etc. Quote Fri Mar 06, 2009 4:38 pm
55 by Martin Gansten Eddy wrote:Can you tell me if Ptolemy had the sidereal time in mind or rather the degree? Here is Robbins's translation (p. 289): [...] calculate after how many equinoctial periods* the place of the following body or aspect comes to the place of the one preceding at the actual time of birth, because the equinoctial periods pass evenly through both the horizon and the mid-heaven, to both of which are referred the proportions of spatial distances, and, as is reasonable, each one of the periods has the value of one solar year. The word translated as 'period' is ?????? chronos. Robbins adds in a footnote: 'An "equinoctial period" or "time" is the length of time which is takes one degree on the equator to pass a fixed point, i.e. 1/360 of 24 hours.' I can understand the criticism of Pico, Gassendi etc (according to Jim Tester's book) who considered this as rather arbitrary. Well, what part of astrology would be immune to that sort of criticism, if viewed with an unsympathetic mindset? If this is the case then I have a sort of theory [...] I could be totally wrong but perhaps the primary directions were derived from this and therefore the secondary directions came later. Simple directions by rising times (noting the motion of degrees and terms over the ascendant) seem to be one of the oldest techniques there are. And as I have mentioned before, I believe there is reason to suppose that Balbillus (and perhaps Thrasyllus before him) directed by a method quite similar to Ptolemy's (I plan to write something on this). So I don't think your theory is borne out by the evidence. And I can't see what is so compelling about secondary directions, or how they would follow naturally from Real Directions (if you will pardon the Frawleyism). Quote Fri Mar 06, 2009 9:33 pm
56 by Graham F Hello Martin You write: Robbins adds in a footnote: 'An "equinoctial period" or "time" is the length of time which is takes one degree on the equator to pass a fixed point, i.e. 1/360 of 24 hours.' This is the classic "1? = 1 year" key. Do you think Robbins had a solid justification for his assertion that this is what an "equinoctial period" was for Ptolemy, or for the tradition which Ptolemy drew on? It's hard of course to decide which key works best in practice, but in theory the 1/360th of a circle = 1yr seems rather arbitrary, whereas the Naibod or "Kepler/Brahe" keys (the distance represented by the mean or true apparent solar movement in a day = 1 year) seem more satisfying (especially, I'd have thought, the true rate, as it embodies an observable or measurable instance of the 1 day = 1 year axiom). What's your view about this? (I'm talking more in theory than in practice - I think you told me that empirically you tend to favour 1? = 1yr, or sometimes Naibod, but not the true solar rate). Graham Quote Sat Mar 07, 2009 12:44 am
57 by Eddy Martin Gansten wrote:The word translated as 'period' is ?????? chronos. Robbins adds in a footnote: 'An "equinoctial period" or "time" is the length of time which is takes one degree on the equator to pass a fixed point, i.e. 1/360 of 24 hours.'So it was 1?=1 year. Like Graham I would feel more comfortable with 1/365.25th of a day (either sidereal or (true) solar (which I would prefer)) as one year. And I can't see what is so compelling about secondary directions, or how they would follow naturally from Real Directions (if you will pardon the Frawleyism). I think I simply like to systematize. This wouldn't make me different from the Greeks, would it ? Quote Sat Mar 07, 2009 9:56 am