The "octotropos" or 8-house division appears in Firmicus Maternus,
Atheseos Libri VIII. I have a hard copy of the Jean Rhys Bram translation (1975, reprinted 2005, publisher Astrology Classics.) He was a Sicilian who wrote in Latin and lived ca. 280-360 AD.
Book 2 sec. XIV is titled
The Eight Houses. Maternus wrote (paragraph 1): "A little later... we shall show in detail the way in which
the individual houses may be exactly located.
(para. 3) "In general The House of Life is in the sign in which the ascendant is located; of Expectation of Inheritance and Wealth in the second house from the ascendant;..." He gives siblings to the 3rd house, parents to the 4th, children to the 5th, health to the 6th, spouses to the 7th, and death to the 8th.
This sounds so familiar that we might assume that Maternus simply forgot about the remaining 12 houses, except that he reiterates his 8-fold division:
"Beginning from the ascendant
we have listed all the houses by name: Life, Expectations of Wealth, Brothers and Sisters, Parents, Children, Health, Spouse, Death."
Eight again.
Interestingly, Maternus does not appear to use a quadrant system.
He follows in sec. XV with what does appears to be
a whole sign system using 12 houses. The degree of the ascendant must be calculated, but first he says then the MC is simply the 10th house from the ascendant. He notes that the descendent is 180 degrees from the descendant.
Then we get a different take on the degree of the MC:
(para. 4) "The Medium Caelum is the tenth house from the ascendant, but sometimes also the MC is found exactly in the 11th sign from the ascendant. In order to understand this more clearly, compute, starting from the degree of the ascendant, through the other following signs [i.e. counter-clockwise] and in whatever sign the 271st degree is found, this is alotted to the Medium Caelum."
Frankly, it is hard to know what to make of Goold's (1977) translation of Manilius's mention of the octotropos (8-house system) in 2: 968-70. The translator took serious exception to other 20th century authors claiming to see an 8-house division mentioned in
Astronomica; so much so that although the word octotropos clearly appears in the Latin text, but has been turfed out of the main portion of the English translation! It does appear in a footnote: "The founder of astrology gave to this section the title of Octotropos; the motions of the planets, which fly through it in the opposite direction, shall follow at the proper place." [Say what?]
Have you come across mention of an 8-house system in Antiochus? It's getting late: I don't have time to track it down now.
Pity I don't read Latin. Does anyone here?
Dr. Farr, you might be correct, however. This man agrees with you:
www.snowcrest.net/sunrise/aoctobj.htm . But then what do you make of the Babylonian 16-house system shown in Houlding's book?