Ptolemy, Hermes & Medieval Arabic Astrology

The Astrological Computations Attributed to Ptolemy and
Hermes in Medieval Arabic Sources
Josep caSulleraS
1. Introduction
Many medieval Arabic sources attribute some of the most popular mathemat-
ical procedures and geometrical definitions applied to the practice of astrology
either to Ptolemy (c. ad 150) or to the legendary Hermes. However, these attri-
butions have little basis either in Ptolemy’s astrological work1 or in the writ-
ings related to the Hermetic tradition.2 Focusing on this apparent disagreement
between authors and attributions, in Section 1 we review the basic concepts
of natal astrology and draw up a list of the computations that have been asso-
ciated with either Ptolemy or Hermes. In Section 2, we will try to explain
the meaning of these attributions with reference to some medieval authors who
were concerned with this same question. Finally, we present some conclusions
in Section 3.
2. Houses, rays and progressions. Methods and attributions
The main practices associated with natal astrology correspond to the three
concepts of houses, rays and progressions, all of them taken from the ancient
Greek tradition.
The astrological houses are the twelve divisions of the ecliptic around the
local horizon, as represented in Figure 1. During one apparent daily revolution
of the celestial sphere, any celestial body will pass through all twelve houses.
Unlike zodiac signs, the houses vary depending upon the time and latitude for
which they are calculated. Therefore, the operation of equalizing the astrolog-
ical houses (in Arabic taswiyat al-buyūt) relates the positions of the celestial
objects to our place and moment.3
1 The Tetrabiblos or Quadripartitum, in Arabic Kitāb al-arbaʿ.
2 On Hermes and his astrological works see Sezgin, GAS VII, pp. 50–58. See also van
Bladel, ‘Hermes’.
3 See, for instance, Bouché-Leclercq, L’astrologie grecque, pp. 256–86; Casulleras and Ho-
gendijk, ‘Progressions’, pp. 38–39, and the references given there.
Ptolemy’s Science of the Stars in the Middle Ages, ed. by David Juste, Benno van Dalen, Dag Nikolaus Hasse and
Charles Burnett, PALS 1 (Turnhout, 2020), pp. 201–221
© F H G 10.1484/M.PALS-EB.5.120180
t H i S i S a n op e n a c c e S S c H a p t e r d i S t r i B u t e d u n d e r a c c B y-n c -n d 4 . 0 i n t e r n at i o n a l l i c e n S e

202 JOSEP CASULLERAS
Figure 1. The cusps of the astrological houses
The doctrine of the planetary aspects or projection of rays (in Arabic maṭraḥ
al-shu
ʿ ā ʿ āt) considers the astrological significance of certain angular distances
(60°, 90°, 120° and 180°) defined between the objects on the celestial sphere.
Figure 2 is a schematic representation of the different rays of a planet P on the
ecliptic circle: the ‘rays’ PP1, PP2, PP3 (PP7, PP6, PP5) are called the left (right)
sextile, quartile and trine rays respectively, and PP4 is called the opposition.4
Figure 2. The planetary aspects or rays
The astrological theory of progressions (in Arabic called tasyīr) establishes a
relationship between angular distances and periods of time as a basis for astro-
logical predictions. A typical example of this practice is the attempt to find
the moment of death, by giving a value of one year of life per degree of the
angle between two significant objects selected in the celestial configuration at
the moment of the individual’s birth. One of these objects is thought of as
emitting the life-force, and the other is seen as destroying life. In Figure 3,
4 cf. Bouché-Leclercq, L’astrologie grecque, pp. 165–79; Casulleras and Hogendijk, ‘Progres-
sions’, pp. 40–41.

THE ASTROLOGICAL COMPUTATIONS ATTRIBUTED 203
the point F represents the destructive point that will reach the initial position
of the emitting point P after rotation over n degrees around the celestial axis.
According to this theory, the angle n corresponds to the arc of tasyīr and the
individual will live n solar years.5
Figure 3. The system of progressions
A variety of geometrical approaches are used to calculate the houses, rays and
progressions. For each one, the sources describe various methods of computation,
which all produce different results. Fortunately, this feature of astrological tech-
nique has played an important role in the development of applied mathematics,
and one major consequence of the research into the history of these methods
is that we have well-established designations for all of them. John North
first classified the medieval systems for the houses in 1986,6 and Edward S.
Kennedy extended North’s classification in 1996.7 Casulleras and Hogendijk
published a classification of the methods for the rays and the progressions in
2012.8 For the purpose of our discussion, we will focus only on the methods
that have been attributed to either Ptolemy or Hermes in the Arabic sources.
2.1. Houses
2.1.1. Ptolemy: the Standard Method and the Hour Lines Method
The most popular method for the division of houses in the Middle Ages is the
one that North called the Standard Method.9 In this method, the houses are
defined on the ecliptic by meridians crossing equal divisions of the equatorial
5 cf. Bouché-Leclercq, L’astrologie grecque, pp. 411–22; Casulleras and Hogendijk, ‘Progres-
sions’, pp. 41–43.
6 North, Horoscopes and History.
7 Kennedy, ‘The Astrological Houses’.
8 Casulleras and Hogendijk, ‘Progressions’.
9 cf. North, Horoscopes and History, p. 4.

204 JOSEP CASULLERAS
arcs lying between the local meridian and the meridians that pass through the
ascendent and the descendent points of the ecliptic. Figure 4 shows the cusps
(i.e. beginning points) of the houses of the eastern hemisphere using this pro-
cedure.
Figure 4. The Standard Method for the division of the houses
This system is pre-Islamic in origin, and it was called ‘the well-known method’
by the eleventh-century Iranian astronomer al-Bīrūnī.10 In many Andalusī
sources it is attributed to Ptolemy,11 and it is usually implemented with an
astrolabe, moving either the rule or the spider with the help of the inscribed
hour lines, in order to find the beginnings of the houses according to the defi-
nition of the method.12
The other method for the houses which is sometimes attributed to Ptolemy
is the Hour Lines Method.13 In this method, the cusps of the houses are the
intersections of the ecliptic with the lines of the even seasonal hours.
Modern astrologers attribute this system to Placidus, a seventeenth-century
Perugian monk, but the Andalusī astronomer Ibn al-Samḥ (d. 1035)14 said in
his Treatise on the Use of the Astrolabe that, according to Ḥabash [al-Ḥāsib]
(ninth century), this is Ptolemy’s method.15 This attribution was repeated by
some other Andalusī authors. The procedure can be performed with any stan-
dard astrolabe plate which has lines for the seasonal hours.
10 cf. North, Horoscopes and History, p. 6; al-Bīrūnī, Al-Qānūn, vol. III, pp. 1357–1359. On
this author see, for example, Yano, ‘Bīrūnī’.
11 cf. Calvo, ‘La résolution graphique’, pp. 35–36; Casulleras, ‘Mathematical Astrology’,
pp. 265–67.
12 The two options are described in North, Horoscopes and History, p. 59.
13 cf. North, Horoscopes and History, pp. 20–27; Kennedy, ‘The Astrological Houses’,
p. 538; Casulleras, ‘Mathematical Astrology’, p. 265; Calvo, ‘La résolution graphique’, p. 36;
Casulleras and Hogendijk, ‘Progressions’, pp. 83–85.
14 On this author see Rius, ‘Ibn al-Samḥ’.
15 Viladrich, El Kitāb al-
ʿ Amal, pp. 66, 124.

THE ASTROLOGICAL COMPUTATIONS ATTRIBUTED 205
Figure 5. The Hour Lines Method for the houses
2.1.2. Hermes: the Prime Vertical Method and the Equatorial Method
The two methods for the houses that have been associated with Hermes
are called the Prime Vertical Method16 and the Equatorial Method17 in the
North-Kennedy classification. They define the houses as the intersections of
the ecliptic with certain great circles on the celestial sphere passing through the
North and South points of the local horizon, which are called position circles.
Figure 6. The Prime Vertical Method for the houses
For the first method (Figure 6), these position circles cross equal divisions of
the prime vertical, which is the great circle passing through the local zenith
and the East and West points on the local horizon. For the Equatorial Method,
they cross the celestial equator (Figure 7).
16 North, Horoscopes and History, pp. 32–33, 47; Kennedy, ‘The Astrological Houses’,
pp. 541–43; Casulleras and Hogendijk, ‘Progressions’, pp. 82–83.
17 North, Horoscopes and History, pp. 27–30, 47; Kennedy, ‘The Astrological Houses’,
pp. 543; Casulleras and Hogendijk, ‘Progressions’, pp. 80–82.