The system itself is older than both Placidus and Magini; it was known to Abraham ibn Ezra in the 12th century. Similarly, the 'modus rationalis' of Regiomontanus was known long before his time and may have originated with al-Jayy?n? in the 11th century. A good place to look for this sort of information is J.D. North's Horoscopes and History (1986).

Hello Martin,

Thats interesting. As I have noted on another forum section elsewhere on skyscript 'Horoscopes and History' has been out of print for many years and copies are extremely hard to get. I am fortunate that the National Library of Scotland retains a copy of all books published in the United Kingdom. I hope to research the edition kept there soon.

The Warburg Institute in London were meant to be producing a new edition but it has yet to appear.

In the meantime could you kindly give us the reference J.D. North uses alluding to Ibn Ezra's knowledge (use?) of the Placidus house system? Which of Ibn Ezra's books indicates this?

Thanks

Mark

MarkC wrote:As I have noted on another forum section elsewhere on skyscript 'Horoscopes and History' has been out of print for many years and copies are extremely hard to get. I am fortunate that the National Library of Scotland retains a copy of all books published in the United Kingdom.

Happily for me, the astronomy dept. at Lund University has one too. I hope Warburg does produce a new edition.

In the meantime could you kindly give us the reference J.D. North uses alluding to Ibn Ezra's knowledge (use?) of the Placidus house system? Which of Ibn Ezra's books indicates this?

Here is what North says:

On the face of it, the method seems to be that intended by Abraham ibn Ezra in his S?fer ha-moledot (Liber nativitatum) composed at B?ziers in its two versions in 1148 and 1154, as well as in the Keli ha-ne?oshet (Tractatus de astrolabio), evidently translated in England between 1158 and 1161, and also that in his book on the foundations of astronomical tables.

A footnote refers the reader to ch. xi of J. M. Mill?s-Vallicrosa, Estudios sobre historia de la ciencia espa?ola (Barcelona 1949) 'for a general study'.

Martin Gansten wrote:As the Almagest shows, he clearly had the mathematical tools to devise most or all of the quadrant systems we know today. And yet, as the Tetrabiblos shows, he didn't. 'Mikes you fink, don' it?'

Yes Browsing through Almagest, the question comes: which one - ecliptic or horizon - was base coordinate system for Ptolemy... At least one of those definitions in Tetrabiblios where he takes 90 degrees to get to Midheaven, is to take them "upward" (upper square). And he made at least one remark to the system of primary directions beeing the method commonly used, which he disagrees with, so he devises a new his own semi-arcs method (pity that he didn't described this one commonly used he disagreed with... ). Was ascendant a point on horizon for him, or was it a point on ecliptic? For a century earlier' Manilius, there was no ascendant at all. It was just orient - the place where sun rose. Looking from few centuries "after" him, when this horizontal frame was neglected and forgotten, and eclitpic only used, this seems quite convincing as equal house system as we call it today. But looking from his predecessors' point of view (especially babylonian ones) and ignoring his followers, the notion that this was asc-zenith circle comes to mind.

I used the Tetrabiblos translation of Shepherd Simpson http://www.geocities.com/astrologysources/index.htm http://www.geocities.com/astrologysourc ... /index.htm
Book III10 http://www.geocities.com/astrologysourc ... htm#side47
Perhaps Ptolemy rejected the seasonal hours when he mentioned the 'usual traditions' preferring equinoctal hours as more natural. I'm not very familiar with the Almagest but another reason for giving the tables of conversion from seasonal to equatorial hours could be for using only the equatorial rather than the seasonal hours system. Now we are so used to using equatorial hours for our mechanical clocks that we feel a bit ill at ease to convert to seasonal hours. In Ptolemy's days the whole antique world used the seasonal hours and perhaps Ptolemy wanted to use equinoctal hours which could have caused some feelinges of unaccostumedness to his contemporaries.

Another explanation could be that Ptolemy rejected the more crude system of the rising times of whole signs mentioned in Yuzuru's 's link http://www.antonblog.net/astrology/prim ... ons-vol-1/ in the the topic 'Primary Directions for mathematically challenged ?' on Anton Grigoryev's blog on Primay Directions in Tetrabiblos Book III10. His change could then have been to Placidus like methods.

III10 is a bit confusing on the midheaven. The examples he gives are the simplest possibilities. 0?Aries on the eastern and western horizon always gives 0?Capricorn and 0?Cancer in the midheaven respectively. These will be the same in both equal house system and the quadrant systems. The times of 0? to reach the horizon or meridian is easy to calculate and will be the same in every house system. However he seems to give a complicated example for 0?Aries that has passed 3 hours after the meridian.

According to the Placidus method the result will be 64 which is the same as according to Ptolemy. However I have found another method which gives a similar result. I used the following data to make the calculations with a calculator. For ease I used decimals.
Alexandria 30,4 http://www.sacred-texts.com/astro/ptb/ptb59.htm 30?22' footnote 96:2
Obliquity Ecliptic 23,8 The value used by Ptolemy seems to have been used from older sources rather than his own observations as he said http://articles.adsabs.harvard.edu//ful ... 1.000.html
With 0? having past 3 hours after the meridian the sidereal time is 3h or 45? RA 'times', resulting in a MC of 17.54 Taurus
0?Aries = 0? along the ecliptic and 0? along the equator, declination is 0?
0?Gemini = 60? along the ecliptic and 57.75? along the equator, declination is +20.46?
The equatorial distance of 0?Gemini to the meridian is 57.75? - 45? = 12,75?.
Expressed in Placidus mundane positions 0?Aries is 1/4th from the semicircle counted from west to east. Calculation is simple since declination is 0?.
The diurnal arc of 0?Gemini is 205.29. In Alexandria (or rather the alleged position) 0?Gemini rises 12.64 RA times before the equator point on the horizon and sets the same time after. 2 x 12.64 + 180 = 205.29. Divide this by 12 and you get 17.11 the 'horary magnitude' of III10.
The rising point of the diurnal arc of the 'path' of 0?Gemini is measured along the equator from 0?, 135 + 12.64 = 147.64. The position of 0?GEmini measured along the equator was 57.75. The (equinoctal) time that 0?Gemini passed its rising point is 147,64 - 57.75 = 89.98. The time it will take to set is 205.29 - 89.89 = 115.4. 115.4 : 205.29 = 0.562112853. Converted to a semicircle of 180 mundane 'degrees' gives 0.562112853 x 180? = 101.18. 0?Gemini is located in what we would call 11.18 Xth house Placidus mundane. The distance of 0?Aries to 0?Gemini measured along the ecliptic was 60?, measured along the equator was 57.75 and measured in Placidus mundane 'degrees' gives 101.18 - 45 = 56.18?. If we want to convert it to RA degrees to find the time then we calculate 56.18 : 180 = 0.3121111 this was based upon the path of 205.29 so it has to be multiplied by this which gives 64.07 degrees (which then are the years), the same result as Ptolemy's.

However, inspired by Ptolemy's first examples of calculating the time that would pass till 0?Gemini reached the same position occupied by 0?Aries I reasoned that in the last example the time it would take for (17.54?Taurus + 60? =) 17.54?Cancer to reach the meridian would resemble the most to the previous calculations. 17.54?Cancer is 107.54? along the ecliptic and 109.06? along the equator. The distance between this last position and the equatorial position of the meridian is 109.06? - 45? = 64.06? which again are the years. This is in fact resembles a variant of the solar arcs used in secondary progressions. Instead this seems to be a 'MC-arc' direction. The MC moves through the ecliptic and 'pulls' the other planets on its trail in a constantly similar distance to the MC. Even though I don't feel attracted to this (unnatural) involving the planets in the motion of the MC (like I don't feel attracted to solar-arcs either) the advantage is that the natal positions still are concentrated on the ecliptic frame unlike the Placidus type and the Meridian types which introduce 'new' natal chart positions. Could this also be done with the horizon as if the situation would be that the position of 0?Aries would be considered as 3 hours after rising? A sort of 'Ascendant-arcs' directions. I don't think so and I feel inspired by a passage in III10:

Quote Ptolemy: "However, the number of years, determined by the distances between the prorogative place and the destructive planet, ought not to be taken simply or offhand, in accordance with the usual traditions, from the times of ascension of each degree, except only when the eastern horizon itself is the prorogator, or some one of the planets that are rising in that region. For one method alone is available for him who is considering this subject in a natural manner - to 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, ....". I'm not sure if I interpreted it well, I don't read Greek and the text is still a bit vague. However those who prefer Placidus may be biased too towards interpretation. Probably reading the Tetrabiblos is similar to reading that other biblos, the Bible, subject to interpretation what the reader would like to find. Coincidentally I bumped into a very interesting article of R?diger Plantiko which discusses house systems, their history and Ptolemy. http://www.astrotexte.ch/sources/others/houses.pdf

In this article I read something interesing that could explain something:

"Later astrologers7 have tried to harmonize these statements by introducing the so-called mundane aspects. But it seems more plausible to me that Ptolemy reproduces two different techniques in parallel, taken from two different traditions. Each tradition may have had its own area of validity: The "hermetic" house division may have been the right method for determining the aphetical places, while the astronomically correct Medium Coeli had been used for the computation of directions."


However I might be biased because I don't really feel for Placidus' house division. I agree mostly with the ideas of Johannes Kepler who focused rather on the aspects than the houses and the signs. If I were to use a house system I would choose Equal MC houses for the ecliptic reference frame and the Meridian houses for the equatorial frame. I prefer thes because they use normal coordinate systems (with poles perpendicular to the base plane which at its turn is divided equally) and they are based upon a moving plane (rather than Campanus and Horizon wich also use normal coordinate systems yet are based upon 'stiff' or 'rigid' planes). I think these systems are modern or even could be called post-modern because the Ascendant is reduced to a mere sensitive point in one of the houses rather than the fundamental point of a house system.

Eddy wrote:I used the Tetrabiblos translation of Shepherd Simpson

Any relation to Homer? This is the old (1940) Robbins translation.

I'm not sure if I interpreted it well, I don't read Greek and the text is still a bit vague.

In context it's actually quite clear: Ptolemy objected to directing all points using rising times; or, put differently, to always treating the significator as though it were located on the eastern horizon. This is a procedure you will find in many Greek works, e.g., those of Valens or Paul of Alexandria ('the usual tradition').

Any relation to Homer? This is the old (1940) Robbins translation.

Bart's uncle . Thanks for the clarification. I found something about the differences between Ptolemy and his contemporaries in this article of Mark Riley.
http://www.csus.edu/indiv/r/rileymt/PDF ... etical.pdf

Eddy wrote:

However I might be biased because I don't really feel for Placidus' house division. I agree mostly with the ideas of Johannes Kepler who focused rather on the aspects than the houses and the signs.

This is a little what I understood about Ptolemy, he hardly considers houses, let alone cardinal ones, if not for hyleg or for illness, when he mentions the sixth house. He prefers always using general significators.

He makes me very unconfortable because I come from horary, so I always look at houses.

Margherita

Ptolemy only seems to mention the horizon/meridian and quadrant positions in some examples: Tetr. II 6 of the position of the eclipsed sun/moon. And IV 5 Marriage.

Jim Tester's "A History of Western Astrology" mentions how the houses developed from quadrant systems via the oktotopos systems to the twelvefold division. There are also some cura.free articles on it. http://cura.free.fr/docum/02fagan.html Cyril Fagan
http://cura.free.fr/10domi1e.html

However, Bill Johnston disputes the ancient use of the oktotopos
http://www.snowcrest.net/sunrise/aoctobj.htm

Perhaps quadrants were more used than twelve quadrant based houses in the Antique era. The Placidus semicycles are very easy for determining positions of planets but more difficult for calculating the cusps, because the equatorial and declination positions of the cusps, which are needed as a basis for further calculating, are unknown. The calculations for the cusps require iterative equation formulae (see R?diger Plantiko?s article (p.36) which I mentioned). These approach the value (as exact as you wish though), while the cusps of Regiomontanus for example can be calculated directly with the basic trigonometry formulae.

Martin Gansten wrote:Morin, who was fiercely Catholic, was an out-and-out Regiomontanus man. Partridge, who was ferociously anti-Catholic, followed Placidus (generally without mentioning his name). And Placidus's Physiomathematica made the Catholic Index of forbidden books in 1687, which must have hampered the spread of his system in the Catholic world.

Hi Martin,
do you - ore anyone else - know more authorities of that time, who followed Placidus or rejected his house-system? And why?

Here is the quotat?on I mentioned above, but it is not the English version. Ralph William Holden, The Elements of House Division, 1977. Under 'The Placidus System' he wonders that the Placisdus system is nowadays so popular and certainly the most spread method, whereas it was condemned by so many authorities at the beginning.

Jonny

PS: Thanks for your J.D.North-tip! I wait for the reprint now.

johannes susato wrote:do you - ore anyone else - know more authorities of that time, who followed Placidus or rejected his house-system? And why?

Here is the quotat?on I mentioned above, but it is not the English version. Ralph William Holden, The Elements of House Division, 1977. Under 'The Placidus System' he wonders that the Placisdus system is nowadays so popular and certainly the most spread method, whereas it was condemned by so many authorities at the beginning.

I am no expert on this period, but there were several English followers of the Placidus system towards the end of the 17th century. In 1687, Richard Kirby and John Bishop published The Marrow of Astrology, an unacknowledged and somewhat abbreviated translation of Placidus?s own work with very little original content added. The book was reissued only a year later, this time under the sole name of John Bishop and with a preface by William Lilly's pupil and adopted son Henry Coley, who mentions ?Dr. Wright, Thomas Moor Esq. Mr. Worral and [?] Mr. John Partridge? as other contemporary English adherents of Placidus, and feels that their endeavours ?ought to be encouraged, and assisted, as Aiming at Truth it self, and not rejected and rediculed, (as some are too forward to do)?.

It is perhaps not surprising that many of Placidus's contemporaries rejected his teachings, which were not confined to a (rather cumbersome) method of house division, but included a number of more or less radical innovations, several of which he attempted to foist off on Ptolemy.

...who followed Placidus or rejected his house-system? And why?

I don't know who followed the system but I can imagine some reasons why it would have been rejected in the early days. Somewhere here I read that the Roman Catholic church forbade Placidus' books in 1687. In R?diger Plantiko?s article (p.30) http://www.astrotexte.ch/sources/others/houses.pdf this is mentioned too and that it came up in Great Britain some 100 years later. It is often said that the popularity of Placidus is because of the availability of tables, I believe from Raphael since the early 1800's.

When you look at the figures 12 and 13 in that article (p.27/28 ) and compare it with the figures of the other house systems it becomes clear that Placidus doesn't use position circles. The lines are 'curves' instead of circles. One of the reasons that Plantiko gives why it took so long till Placidus was used was due to this fact (p.34 point 3). The perfect ideal in rationalist thought was the circle.

I don't agree with Plantiko relating Kepler's thoughts with the Placidus system (based upon the fact that Kepler had found out that the planetary orbits are ellipses). In a French translation of Mysterium Cosmographicum it is said that Kepler viewed the human soul either as circular or as a point, thus maintaining the ideal of the circle in this field. Notwithstanding the simplicity yet intelligence of the system, for me too the "rational ideal" is one of my main objections against Placidus.

Then if you must have great circles, use Svarogich's alternate formulation of the underlying Placidus model (http://www.levante.org) (which differs only slightly until you get towards extreme latitudes, and handles points that do not rise or set somewhat differently than Mike Wackford proposes for Placidus). The main difference from other great circle based systems is that it better reflects actual ascensional motion because the great circles defining mundane positions vary as to where they intersect the horizon, rather than all originating in a single pair of points as does, for example, Regiomontanus with its position circles at the north and south points of the horizon.

I still suspect that Placidus is the real thing, though.

- Ed