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. (( Martin Gansten, Primary directions: astrology’s old master Technique (The Wessex Astrologer, 2009 especially page  92).  ))

If in the case of mundane parallel, calculation is very simple if we  use the usual  semi-arc based on Fumagalli/Bezza method (( Marco Fumagalli, I moti del Cielo ));  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 Mobile (( 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).  ))  and comment his example.

sshot-2020-02-13-[16-07-24]In short these are Placido calculations:

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.

sshot-2020-02-13-[16-10-18]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:



199.27.42 equivalent to 199.462


b. Moon semi-arc is  85.1692


c. the difference between RA is:


as 25 < 287 I should add 360



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” (( Alan Leo, The Progressed Horoscope (( London : L. N. Fowler : Modern Astrology Office, 1906. )). 

sshot-2020-02-13-[16-10-50]Leo uses logarithms but we don’t need, because we have calculators to do multiplications and division

sshot-2020-02-13-[16-14-14]This is the speculum for Annie Besant:

sshot-2020-02-13-[16-14-58]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:



142.47.54 equivalent to 142.7983


b. Saturn semi-arc is  76.295


c. the difference between RA is:




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.



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.

3 thoughts on “Calculating rapt parallels, Placido method

  1. Margherita-Do you know if , I moti del Cielo (Marco Fumagalli book) was ever translated to english? Harold

  2. Margherita-It really seems an interesting book.Just curious if anyone has ever translated any part of it or if you know of any English sources (whether books,website) that are similar in context.-Harold

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s