Levente Laszlo wrote:Knappich couldn't have read Pingree's Hephaestio edition from 1973 since he published his astrological history in 1967 and died in 1970. It's possible, though, that he used the old Engelbrecht edition of Hephaestio, and from the fragmentary allusions he reconstructed a classification of signs related to the issue of parties (haireseis) - provided he read Ancient Greek -, which he considered the right definition of hairesis. However, I think a more plausible explanation is that he read something about the parties somewhere (e.g., in Bouché-Leclercq's handbook) but what he remembered better was Ptolemy's introduction of the solar and lunar halves, possibly in Pfaff's German translation.

Just for the record: Ptolemy is the source of this division of the zodiac (even if he's not the originator of the theory); he doesn't use the expression hairesis here; Hephaestio doesn't lift this precept even though he copies or summarizes much of Ptolemy's Apotelesmatics; and the sporadic assignments in Hephaestio, collected by Chris above, would hardly make it possible to reconstruct the rationale without the aid of Ptolemy's text.

Bouché-Leclercq in his book ''L’Astrologie grecque'' available online here - https://archive.org/details/lastrologiegrecq00boucuoft lists four schemes of separating signs according to sect on page 156. - https://i.imgur.com/Sn0QbhH.jpg

He shows first the condition that comes up in Manilius of odd and even alternating gender. This seems to be the most popular rejoicing condition that went on to become one of the 3 sect conditions in the Medieval tradition. Although one could ascribe that to the influence of Ptolemy, the fact that Dorotheus also uses it, surely adds up (unless there is an interpolation? it comes in one of the natal books as well as in Book V). Reference to that condition also appears in the summary of Antiochus, Valens, Paulus and Rhetorius.

Note that Valens and Dorotheus ascribe the triplicity rulers scheme to this specific sect condition. For example - ''When the zodiacal circle is subdivided according to similarities and differences, we find two sects, solar and lunar, day and night. The sun, being fiery, is most related to Aries, Leo, and Sagittarius, and this triangle of the sun is called “of the day-sect??? because it too is fiery by nature.'' - Valens, V. Anthologia. Translated by Mark Riley.

Or Dorotheus:

''Chapter 28. Knowledge of masculine and feminine signs, eastern and western, and diurnal and nocturnal.
Aries, Leo, and Sagittarius are masculine, eastern, [and] diurnal...'' - the eastern wind became fiery in Valens

''Look at the diurnal and nocturnal signs; I will make clear to you the diurnal among them and the nocturnal. The diurnal among them: Aries and its triplicity, Leo and Sagittarius, are diurnal, and Gemini and its triplicity, Libra and Aquarius, are diurnal. The nocturnal: Taurus and its triplicity, Virgo and Capricorn, are nocturnal, and Cancer and its triplicity, Scorpio and Pisces, are nocturnal.'' in Chapter 4 of Book 5 - Sidonius, D., & Pingree, D. (1976). Carmen astrologicum. Pingree (Hrsg.), Dorothei Sidonii Carmen Astrologicum, Leipzig.

Bouché-Leclercq then lists the condition peculiar to Manilius where the triplicities of Aries and Cancer are diurnal. He then lists the hemisphere scheme mentioned by Manilius that Aries - Virgo are diurnal while the other hemisphere nocturnal.

He finally lists the condition given by Ptolemy, which as Levente said it comes up first in his text, although he ascribes the doctrine to other people.

The condition I mentioned before that comes up in Antiochus (diurnal stars rejoicing with diurnal rulers) does not seem to be related to the signs, but more to do with the rulers? So depending on whether your think that represents a sign rejoicing/sect condition, you have 4 or 5 sect conditions related to sign in the surviving Hellenistic sources.