petosiris wrote:Martin pointed out to the exceedingly curious passage by Ptolemy - 3.10 where an "equal house that starts 5 degrees before the ascendant" constitutes a twelfth-part and sign. Can you elucidate how this difficult passage makes sense (like you do usually), because it uses terminology that is akin to whole sign aspects?
That's a tough passage, indeed, and I'm afraid I'm not able to solve this old riddle. All I can do is present the available facts.
The earliest manuscript that contains the passage (3.11.3) is from the thirteenth century, but in the tradition, there are a couple of texual variants that considerably affect the interpretation. The text lifted from the critical edition is the following:
τόπους μὲν π??ῶτον ἡγητέον ἀφετικοὺς ???ν οἷς εἶναι δεῖ πάντως τὸν μέλλοντα τὴν κυ??είαν τῆς ἀφέσεως λαμβάνειν τό τε πε??ὶ τὸν ὡ??οσκόπον δωδεκατημό??ιον, ἀπὸ πέντε μοι??ῶν τῶν π??οαναφε??ομένων α???τοῦ τοῦ ?????ίζοντος μέχ??ι τῶν λοιπῶν καὶ ???παναφε??ομένων μοι??ῶν εἴκοσι πέντε καὶ τὰς* τα??ταις ταῖς λʹ μοί??αις δεξιὰς ἑξαγώνους (τὰς† τοῦ ἀγαθοῦ δαίμονος) καὶ τετ??αγώνους (τοῦ ὑπὲ?? γῆν μεσου??ανήματος) καὶ τ??ιγώνους (τοῦ καλουμένου θεοῦ) καὶ διαμέτ??ους (τοῦ δ??νοντος).
A translation (a slightly modified version of Schmidt's), with additions for better understanding in round brackets:
First, one must consider as places (topos) for releasing (those places) in which it is always necessary for the star which is going to assume lordship over the releasing to be: the twelfth-part around the Hour-Watcher, from the five degrees pre-ascending the horizon itself to the remaining twenty-five degrees post-ascending it; and the hexagonals (i.e., degrees*) to these 30 degrees on the right - those† of the Good Daimon; and the tetragonals - of the midheaven above the earth; and the trigonals - of the so-called God; and the diametricals - of the descendant.
The textual issues are well summarized in Schmidt's translation (p. 30, fnn. 1-2), but, fortunately, there is a little help from the indirect textual tradition that confirms the readings: (1) William of Moerbeke's 13th-century Latin translation, based on a lost Greek manuscript; (2) Ḥunayn ibn Isḥ??q's 9th-century Arabic translation from the Greek (as I have no access to the Arabic, I rely on the Latin translations by Plato of Tivoli and Aegidius de Tebaldis); (3) Hephaestio's exposition from the fifth century, and its better preserved version re-written by Isaac Argyrus in the fourteenth century; (4) the so-called "Proclus paraphrase" of uncertain age; (5) partial quotations from elsewhere.
* This is the reading of the better manuscripts (also quoted as such by "Rhetorius" [probably Zeno's astrologer from the late fifth or early sixth century]) and "Proclus", and it probably refers to degrees, which is Ḥunayn's interpretation too. Hephaestio doesn't have an article (see this below), and Moerbeke either leaves it uninterpreted and untranslated, or it was missing in his text.
† The reading of the best manuscript, referring back to the hexagonal degrees; it's confirmed by Moerbeke, Ḥunayn, Argyrus, and "Proclus".
Now, there seem to be two elements that suggest Ptolemy is introducing a "house system": (1) the use of the word "place", and (2) the use of the traditional names (Good Daimon, God, later also Bad Daimon) of the places.
(1) The question of "place". The word
topos occurs 180 times in the
Apotelesmatics, and mostly it's used in its trivial meanings like "location" or "topic". In 1.22.1 a special meaning is introduced, which is the equivalent of our "dodecatemorion", and it's never used again. Another technical meaning attested in the book is a "place" in the zodiac, that is, a degree occupied by a star or a cardine, or an interval of degrees. It's never used in the sense of "place/house" with the possible exception of 4.6.1 (which see below).
(2) The traditional names. While Ptolemy seems to apply the traditional place names to the new 30-degree sections (provided we accept the readings as above), he actually refers to "the so-called God" and later (3.11.4) to twelfth-part, "which is called Bad Daimon". (The reading is confirmed by Moerbeke, Ḥunayn, Argyrus, and "Proclus".) This suggests he's referring an "equal" convention known by others.
Let's assume he's introduced a new, equal "house system". Curiously enough, he resumes it only once (4.6.1):
[For the topic of children,] it will be necessary to examine (the stars) present or configured with the place at the peak (i.e., the zenith) or (the place) following it, that is, (the place) of the Good Daimon.
Although Hephaestio explicitly tells that Ptolemy selected the whole chapter from the works of Petosiris, which may allow the speculation Ptolemy's simply using whole signs, he might also be bringing in his new "house system" again. Anyway, the earliest horoscope interpretation I know that uses Ptolemy's method, that of Constantine VII Porphyrogenitus (Hor. gr. nat. 905.IX.3), interprets (12.1) the midheaven and the Good Daimon as signs.
Let's now see what the interpretations and commentaries say, roughly in chronological order until the late antiquity.
(A) According to Hephaestio (2.11.6-7, skipped by Argyrus), most people would interpret Ptolemy as introducing 30-degree zodiacal sections. The same seems to apply to the Greek "anonymous commentary". However, no instructions are given in either of the sources whether it was used by them outside the length of life calculations, and the issue isn't rehearsed for the topic of children.
(B) The omission of the article enables Hephaestio to hint (2.11.4-5, also Argyrus 25.13) that Ptolemy might be referring to "sides" instead of 30-ecliptical-degree sections and that by this he must be alluding to the expansion or shrinking of the 30 degrees as necessitated by the size of the quadrants. A commentator, Pancharius is reported to have done exactly this (as described in Hephaestio 2.11.8-15 and also, better, in Argyrus 25.14-26), introducing a curious division in which the "cardinal houses" consist of 30 degrees uniformly, and the remaining "houses" are of equal size within a quadrant (one-third of the length of the quadrant, each). Hephaestio doesn't represent Pancharius's system as a new "house system" or as anything for general usage, though.
(C) The fragment of a commentary (preserved in "Porphyry" 43, which is most probably not by Porphyry) attempts to third the quadrants and shrink or expand the 5 degrees pre-ascending proportionately and concludes it's impossible to constitute 30-degree zodiacal sections in this manner. It's likely, therefore, that this author wasn't aware of Pancharius's solution. There's, however, no hint that the author conceived Ptolemy's description as introducing a new "house system".
(D) "Rhetorius" (5.46, copied into the manuscripts of "Porphyry" as 52) third the quadrants with an offset of 5 degrees. This is actually the introduction of the "Porphyry" houses, and the first attestable time Ptolemy's instructions are taken as referring to a "house system". In the same recension of "Rhetorius" appears Pamprepius's horoscope (Hor. gr. nat. 440.IX.29), where whole-signs and a quadrant-based computation are used together.
(E) "Rhetorius" (actually, probably Zeno's astrologer; Ep. IV 12) gives a detailed computation of something that would be called the "Alchabitius" system for a horoscope (Hor. gr. nat. 428.IX.8; possibly Zeno's) with a 5-degree offset, explicitly referring to Ptolemy. The other version of the same horoscope, preserved by M??sh??ʾall??h and Abū ʿAlī al-Khayy??ṭ, apparently uses whole signs, which implies the two computations may have been used together.
(F) Eutocius's horoscope (Hor. gr. nat. 497.X.28 ), as reported by "Rhetorius" (6.52), depicts "Porphyry" houses without the 5-degree offset.
To sum up, until ca. 500, the interpretations of Ptolemy's instructions ranged from an "equal system"-like to a quadrant-based proportional, but there's no evidence that the instructions were considered to be introducing a "house system". It's "Rhetorius" who describes modified versions of the "Porphyry" and "Alchabitius houses" as "house systems" proper, but apparently together with a whole-sign system. It seems the medieval commentators (the earliest available to me being ʿAlī ibn Ri???w??n from the early 11th century) would continue interpreting Ptolemy's words as instructions for a house system while the use of whole-signs parallelly or independently ceases.
That's all.