Martin Gansten wrote: In other words, the 'parallel with latitude' that I understood Petr to advocate is absolutely identical with the body of Mars. This can hardly have been Worsdale's (or anybody's) intention. So as far as I can see, we are back to the definition of a zodiacal parallel as a point on the ecliptic sharing a planet's declination. Those two points, for Mars in the nativity of Joseph Kent, are 6?15? tropical Aries and 23?45? tropical Virgo; and it is the former that concerns us here.

It should be 6.15 Aries if this point is taken without latitude because the declination for lat.0= 2.28 as Mars in the radix chart; if there is some latitude, 6.15 is wrong, Moon declination is not 2.28 anymore.

As you see traditional software consider this point on the ecliptic.



margherita

Good evening,

If Ms Margherita and Prof. Gansten are confused, then i am bollixed.

Hopefully not adding to the predicament, here is another snippet from Morinus. The direction methinks Mr John Worsdate, who apparently did not distinguish 'contra-parallels', referred to, the 22nd in his Table on page 85, Moon to the Parallel of Mars in the Zodiac, is the 2nd in the list here:
Here are the same directions with 'under the poles' selected:
Best regards,

lihin

margherita wrote:It should be 6.15 Aries if this point is taken without latitude because the declination for lat.0= 2.28 as Mars in the radix chart; if there is some latitude, 6.15 is wrong, Moon declination is not 2.28 anymore.

Yes, that is what I said, only backwards. If you try to assign latitude to the parallel, you end up with a conjunction. A parallel of declination is a circle passing through the planet and intersecting the ecliptic in two places. The only point in Aries that will have both Mars' declination and his latitude is, in fact, the body of Mars itself.

The principle of the calculation is simple. We seek a the position of the Moon, where Moon has the same declination as Mars.
The position is looking for the closest date to the date of birth. This position gives us values, longitude and latitude of the //Mars.
This can make an approximation of the tables. I used for the simplification results of Janus 4 (ephemeris calculation).
We count therefore parallels under the pole significator with modified latitude of significator.

Location of Moon is for declination 2N29 8.6.1817

L = 14?35?42??
B = - 3?33?2??
D = 2?29?

RA//Mars = arccos(( cosL x cosB / cosD )) = 14?48?34??
OA//Mars = 14?49? ? 2?28? = 12?21?

ARC = | 0?32? ? 12?21?| = 11?49?

(The exact declination of Mars = 2?28?14?? => RA//Mars = 14?47?1? and
ARC = 11?47?)

For conra//Mars :
Location of Moon is for declination 2S29 9.6.1817

L = 3?31?3??
B = - 4?13?55??
D = - 2?29?

RAcontra//Mars = 4?54?36??
OAcontra//Mars = 4?55? + 2?28? = 7?23?

ARC = | 0?32? ? 7?23?| = 6?51?
( - 2?28?14?? = 6?52?)

Thank you, Petr. This looks both mathematically simple and convincing, if we are prepared to accept that Worsdale included contraparallels under the designation 'parallel' (I am). But it strikes me as a very strange hybrid of primary and secondary motion, and raises two questions in my mind:

1. Is this how Placidus actually calculated parallels for the Moon? (The Moon would have been the only significator with latitude that he directed in the zodiac, except when one of the non-luminary planets was hyleg.)

2. If it is, did all later Placidean authors follow him (before the great confusion that arose in the mid- to late 19th century)? Or, conversely: if it isn't, when and where did the method evolve?

Good day,

In the Table of 81 primary directions from age 0 to 20 on pages 85 - 87, Mr John Worsdale lists as no. 44 Moon to the Parallel of Mars in the Zodiac with 11? 37' arc, perhaps corresponding to the third item in the above lists from Morinus.

Mr Worsdale did not include the first direction in the above lists with 2.54? arc nor the last with 18.5? arc.

However, he included for example Moon to her own Semiquartile in the Zodiac as no. 79 with 20? 34' arc, another illustration of his selected techniques.

Best regards,

lihin

Petr wrote:The principle of the calculation is simple. We seek a the position of the Moon, where Moon has the same declination as Mars.
The position is looking for the closest date to the date of birth. This position gives us values, longitude and latitude of the //Mars.


L = 14?35?42??
B = - 3?33?2??
D = 2?29?

So Worsdale uses a latitude which is neither the Moon's or Mars' one. Strange method, neither the latitude of Mars or of the significator, the Moon..... I could never guess.

Never seen before.... Is it by Worsdale or does somebody else use it?

margherita



margherita

margherita wrote:So Worsdale uses a latitude which is neither the Moon's or Mars' one. Strange method, neither the latitude of Mars or of the significator, the Moon..... I could never guess.

Never seen before.... Is it by Worsdale or does somebody else use it?

Yes, I was asking the same in my last post. After some research, I believe I have found the same method in Placidus' Physiomathematica sive Coelestis Philosophia (available here), Book III, chapter XIV, canon VIII, p. 270. Cooper's English edition of Primum Mobile summarizes it on p. 70:

CANON XXIV.
To direct the Significator with Latitude, wherever it is found, to the Parallels of Declination.

First find the declination of the star, to whose parallel the significator is said to be carried; then in the body of the table of declination, look up or down according to the order of degrees and signs from the significator's place, changing also the latitude in the same manner as the significator varies in his motion, till you come to the declination of the promittor or star found as above; and when you have obtained it, take the right ascension or oblique ascension of that place according to its latitude and longitude, &c. and you will have every thing entirely in the same manner as before explained.

As I said before, I find the method slightly bizarre; but I am grateful to Petr for alerting us to it. It will have to go into the dreaded Lesson 9 (on Placidean techniques) of my course!

Martin wrote: Yes, I was asking the same in my last post. After some research, I believe I have found the same method in Placidus' Physiomathematica sive Coelestis Philosophia (available here), Book III, chapter XIV, canon VIII, p. 270. Cooper's English edition of Primum Mobile summarizes it on p. 70:

CANON XXIV.
To direct the Significator with Latitude, wherever it is found, to the Parallels of Declination.

First find the declination of the star, to whose parallel the significator is said to be carried; then in the body of the table of declination, look up or down according to the order of degrees and signs from the significator's place, changing also the latitude in the same manner as the significator varies in his motion, till you come to the declination of the promittor or star found as above; and when you have obtained it, take the right ascension or oblique ascension of that place according to its latitude and longitude, &c. and you will have every thing entirely in the same manner as before explained.

As I said before, I find the method slightly bizarre; but I am grateful to Petr for alerting us to it. It will have to go into the dreaded Lesson 9 (on Placidean techniques) of my course!

Fantastic! Never seen used method, and as I see neither other software... The promissor with a special latitude....I should think about it

margherita

Thank you Martin.
I am glad, that you are found the source from which the author old Czech textbooks drew.

Good evening,

Superb that Prof. Gansten, Mr Petr and Ms Margherita are using this little thread on Mr John Worsdale's Celestial Philosophy to re-kindle one of Placido's (hardly attributable to Ptolemy) techniques!

Presumably no software including Morinus includes this technique to date. With Mr Petr's assistance Morinus may be the FIRST!

So has Mr Worsdale's calculation of one of the three 'killing directions' based on Master Joseph Kent's geniture thus been validated, although one might still object to the missing distinction between 'parallels' and 'contra-parallels'?

How should one assess as least theoretically the astrological coherence of this method of Placido for calculation of the parallels and contra-parallels? Are Ms Margherita's misgivings perhaps well founded?

Best regards,

lihin

PS There is also a French translation of Primum Mobile available to which contributed Dott. Giuseppe Bezza.

lihin wrote: Presumably no software including Morinus includes this technique to date. With Mr Petr's assistance Morinus may be the FIRST!

lihin

I'm not so in love with this method, I like to play with numbers, but I could never guess the method explained by Petr.

But at the same time I'm not in love with it, because I wonder why ZODIACAL directions should have whatever latitude... moreover when this one is not the one of the significator or promissor, but just the nearest point to the significator in order to built some direction.

I think I want to write more for my blog, if I have time (when I don't know), it was a very interesting thread

margherita