In the latest post (( http://heavenastrolabe.net/semiarc-and-alchabitius-directions/ )) we saw as semiarc (or alchabitius, which is another way to collect numbers) fits very well with Ptolemy’s example given in Tetrabiblos III, 10 (( Ptolemy. Tetrabiblos. Translation Frank Robbins. Cambridge Mass. ;London: Harvard University Press ; W. Heinemann, 1980. I’ve used the Italian translation cura Prof. Giuseppe Bezza, unpublished )) . But what about Regiomontanus and “under the pole” directions? Are they different methods? Are they congruent to Ptolemy?
Regiomontanus directions were used by the most famous astrologers of Renaissance and Early Modern times as Nabod, Magini, Argoli, Morin & Lilly and they are known as the “rational method”. The reason of such a great success are essentially two:
1) the elegance of the method, which allows users to use a single method whatever we want to direct a point to the Asc, to MC or to an intermediate position in the quadrant (( we don’t use the term significator/promissor because they traditionally mean something else ))
2) the use of tables, which avoid many problems with calculation.
The method is plainly described by Morin of Villefranche in his Astrologia Gallica (( Jean Baptiste Morin. Astrologia Gallica: Book Twenty-Two, Directions. Tempe, Ariz.: American Federation of Astrologers, 1994. )).
It consists in casting a new chart at a new latitude (corresponding to the pole )) and putting the significator (( we will use Morin’s terminology but see note 3 )) at the ascendant (or the descendant, if it is in western hemisphere).
In an easier way (the usual trick with numbers 🙂 Morin puts:
Arc of direction= OA (B) under A’s pole – OA (A) under A’s pole
So having calculated the pole the only thing we need is a manual of tables.
What is central in this kind of direction is THE POLE. According Regiomontanus, directions can be calculated through an artificial horizon which passes through the body of the planet and cuts the north and south points of the horizon.
Coming back to the usual example from Ptolemy Morin (but calculation can be easily check with tables of OA) says that for Alexandria, latitude 31, being MC at 18 Taurus, the promissor at 0 Gemini and the significator at 0 Aries, the new pole (ie the pole of significator) is 23°12’ so the arc is given by the difference of the OA of 0 Gemini, which is 66°55′ and OA of O Aries under its own pole which is 0 ie:
66°55 – 0°= 66°55 (Morin gives 66°52′).
Even if Ptolemy gets 64 ( and the same we have with semiarc/alchabitius method) and 66 is different than 64, still Morin concludes that Regiomontanus method is the natural and rational method of directing . No problem with the wrong result!
PLACIDIAN UNDER THE POLE DIRECTIONS
We have talked above about Regiomontanus glamour, so we are not surprised of the fact that Placidus himself was fascinated by this method which has several advantages, especially the swiftness and easyness of calculation.
Anyway he was (quite) true to Ptolemy ( even if his other guide ” (his) Reason” evidently diverges from Ptolemy ) and modified Regiomontanus system, thinking a pole which differently from Regiomontanian one is proportional to the semiarc.
Even if Ptolemy never mentions any pole and never used one, the way this pole is built and connected to the semiarc, gives results more similar to the semiarc method. In our case we can easily re-do calculation with tables of OA and Morinus software:
the Placidian pole is 16°53′ and the OA of 0 Gemini under the pole of significator is 64°14.
So we have:
Arc= 64°14- 0= 64°14
which is very near to the semiarc/alchabitius result (but not the same, with Morinus I got 64.22 against 64.26 got with semiarc/alchabitius method.