Semiarc and Alchabitius directions

The subject of semiarc vs. alcabitius method of directing has been discussed since many years (( see above all Kolev and Gansten )).It’s very easy (quite easy at least) to show as the two methods are just one, and we will repeat the experiment here taking our example from Quadripartite, III, 10 (your gentle writer has read the Italian translation cura Prof. Giuseppe Bezza).

Since the directions to angles are immediate we will consider the example of the direction of two intermediate points, which is the worst can happen in a sense 🙂

Ptolemy says:

Now let it be assumed that the beginning of Aries is not on any of the angles, but removed, for example, three ordinary hours from the meridian in the direction of the leading signs, so that the 18th degree of Taurus is at mid‑heaven, and in its first position the beginning of Gemini is 13 equinoctial times removed from the mid‑heaven above the earth in the order of the following signs. If, then, again we multiply 17 equinoctial times into the three hours, the beginning of Gemini will at its second position be distant from mid‑heaven in the direction of the leading signs 51 equinoctial times, and it will make in all 64 times. (( Ptolemy. Tetrabiblos. Translation Frank Robbins. Cambridge  Mass.  ;London: Harvard University Press ;; W. Heinemann, 1980.  ))

Ptolemys example
Ptolemy's example

Primary directions
Example n.4 from Tetrabiblos III, 10
Latitude Alexandria
MC 18 Taurus
P: 0 gemini
S: 0 aries
All the data are taken from Morinus. The OA – not listed there- is the algebric sum of RA and AD.

SEMIARC

In the semiarc method we move the point which follows in the order of the signs to a preceding one, at the pace of the point which follows. (I will not enter in the difference between among promissor and significator, which is not about the movement direction, which should be always from the following to the preceding point. )
P: 0 gemini
temporal hour 17.08.22 (17.1394)
h.d. 0.42.52
S: 0 aries
h.d. 3.02.17 (3.03805555)

0.42.52+
3.02.17
——–
3.45.09=> 3.7525

3.7525*17.1394=64.316

ALCABITIUS

In Alcabitius method we will calculate the difference between the two RA and OA, and then find the difference between this two numbers. Then we will move this result to the pace of the following point.

P: 0 gemini
RA(P)=57.49.10 (57.8194)
OA(P)=70.39.26
S: 0 aries
RA(s)=0
OA(S)=0

RA(P)-RA(s)= 57.49.10-0=57.49.10
OA(P)- OA(S)=70.39.26-0=70.39.26

DELTA=70.39.26-57.49.10= 12.50.16= 12.837
12.837/6=2.1396295

(2.1396295*3.03805555)+57.8194=6.5003131+57.8194=64.319

*******

As we see from the calculation, in effect we got the same result, because these two methods are just a different way to aggregate numbers. And in the same time 64 times are the same result as Ptolemy.

In addition we can notice that Ptolemy does not use latitude (I did not use it too). How to explain this?
Argoli says:

In fact his (Ptolemy’s) examples are refererred to ecliptic positions and Promissors and Significators too (used by Ptolemy as example) are on the ecliptic.

And concludes:

Ptolemy as a man could be wrong too (( text taken from the Italian translation of Tabulae Primi Mobilis ))

Argoli did not use Alcabitius or semiarc method, but he used Regiomontanus directions.
In effect tables were very trendy during Early Modernism and more, because they would save the poor astrologer from the calculations we saw above.

And in a way they were more elegant too. Ptolemy in fact lists three ways to direct according the position of the point: to the Ascendant with OA, to the MC with RA, and with mixed ascension in intermediate position. With tables, on the other, we can always use the same method because the first two are just sub-cases of the third point.

Enjoy the calculation!

Written by Margherita Fiorello, CIDA certified member, for heaven astrolabe blog @ year 2013. If you want to be notified the next time I write something, subscribe to my RSS feed.

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