Calculating rapt parallels, Placido method

August 20th, 201011:07 am @ margherita fiorello

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Calculating rapt parallels, Placido method

A rapt parallel is the aspect between two points -  both rapt by the motion of the Primum Mobile, when they have the same distance from the meridian,  which is proportional to their semi-arcs. Differently from the mundane parallel, where one point is fixed on the natal position, and the other moves, here both are directed.1

If in the case of mundane parallel, calculation is very simple if we  use the usual  semi-arc based on Fumagalli/Bezza method2;  as usually we should just  calculate the distance between the two points, but what about rapt parallels, where we should move both?

Let see at Placido Tables of Primum Mobile3  and comment his example.

Henry IV, King of France- Pau, 13th December 1553 h:2:19 am

Henry IV, King of France- Pau, 14th December 1553 h:2:15 am

In short these are Placido calculations:

original text from Placido

original text from Placido from Tabulae Primi Mobilis

Let’s repeat them: we just need the speculum from Morinus software (free download here ). Just please notice that we will use semi-arc in degrees while Placido converts it in time dividing by 15.

speculum for Moon and Mars

speculum for Moon and Mars

The arc needed is just the difference between the primary distance (the meridian distance) and the secondary distance.

We already have the primary distance from Morinus software, so we should just calculate the secondary distance, with the famous golden rule, which is just a simple proportion.

semi-arcs sum:  planet semi-arc= difference between Right Ascensions: x

a. The semi-arcs sum is:

085.10.09+

114.17.33=

199.27.42 equivalent to 199.462

**********

b. Moon semi-arc is  85.1692

**********

c. the difference between RA is:

25.50.12-287.20.29

as 25 < 287 I should add 360

385.50.12-

287.20.29=

98. 29.43 equivalent to  98.34527

so the golden rule becomes:

199.462: 85.1692= 98.34527: x

x= 41.99 which is the secondary distance.

so the arc is the difference between primary distance (MD) and secondary distance:

80.10.17-41.59=38.11 (Placido has 38.46- which could be ok considering we started from a modern software.)

**********************

In the previous example both planets where in the same hemisphere. What when the two planets are one above and the other below the horizon?

We will see examing Alan Leo example from “The Progressed horoscope”4

Annie Besant, London, 1 October 1847 h:5:30 pm

Annie Besant, London, 1 October 1847 h:5:30 pm

Leo uses logarithms but we don’t need, because we have calculators to do multiplications and division

Leo original calculations

Leo original calculations

This is the speculum for Annie Besant:

Speculum from Morinus software

As above the arc is the difference between primary distance (Meridian Distance) and the secondary distance which we can get from the golden rule.

The only difference is because Moon and Saturn are in different hemispheres we should add to the Moon  Right Ascension 180 degrees, like that:

a. The semi-arcs sum is:

066.32.10+

076.17.44=

142.47.54 equivalent to 142.7983

**********

b. Saturn semi-arc is  76.295

**********

c. the difference between RA is:

339.56.17-(103.25.50+180)

339.56.17-

283.25.50=

56. 30.27 equivalent to  56.5075

so the golden rule becomes:

142.7983: 76.295= 56.5075: x

x= 30.19  (30°11′) which is the secondary distance.

so the arc is the difference between primary distance (MD) and secondary distance:

67.53-30.11=37.42, same result as Leo.

Written by Margherita Fiorello, CIDA certified member, for heaven astrolabe blog @ year 2010. If you want to be notified the next time I write something, subscribe to my RSS feed.

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BIBLIOGRAPHY AND NOTES

For primary directions I should obviously recommend - beyond the well known because he deserves Rumen Kolev - Cieloeterra method, which is part of CieloeTerra advanced course of Giuseppe Bezza and  Marco Fumagalli unfortunately predated with various “Hour distance calculator” without any reference to the real authors.

Between Bezza students I should mention Giancarlo Ufficiale and Lucia Bellizia, who shed light about the subject in several occasions.

And last but not the least, Martin Gansten book, quoted in bibliography  below.

  1. Martin Gansten, Primary directions: astrology’s old master Technique (The Wessex Astrologer, 2009 especially page  92).  []
  2. Marco Fumagalli, I moti del Cielo []
  3. Placido Titi, Tabulae primi mobilis cum thesibus ad Theorigen, & canonibus ad praxim, additis in rerum demonstrationem, & supputationum exemplum triginta clarissimorum natalium thematibus (typis Pauli Frambotti , 1657).  []
  4. Alan Leo, The Progressed Horoscope (( London : L. N. Fowler : Modern Astrology Office, 1906. []