Like the famous ghost haunting the whole Europe, now and then in the traditional lists and forums the question about the true house system used by Ptolemy arises again and again, especially because now it’s trendy in traditional astrologers of English speaking countries to use whole sign houses following Vettius Valens or to use them together with some divisional method.
I should admit that I’m absolutely agnostic and with no interest in the age-old matter because having no conclusive word by Ptolemy, everybody could say whatever without any real evidence (anyway we should say that around 1600 many astrologers had the idea it should be something like “Placido” house system. (( See for example Un precursore del padre Placido: Girolamo Diedo ))
More we could see saying about Placido Titi.
In fact if we don’t know if Ptolemy was true to Placido, was Placido true to Ptolemy? Placido writes that neminem ego alium praeter Ptolemaeum & rationem ducem volo, I don’t want other guide than Ptolemy and reason, book I, 12 . (( Placido Titi, Tabulae primi mobilis cum thesibus ad Theorigen, & canonibus ad praxim, additis in rerum demonstrationem, & supputationum exemplum triginta clarissimorum natalium thematibus (typis Pauli Frambotti bibliop., 1657). ))
Still Robert Hand and Robert Schmidt in their preface to Hindsight translation of Ptolemy’s III book of Tetrabiblos don’t think exactly like that. (( Thanks to Clelia Romano who gave me the reference and a friend who shared the book giving me the possibility to read Hindsight point of view. ))
(Placidus) created a computational approach to primaries that is compleading misleading and false trough the use of poles. The irony is that earlier Medieval astrologers such as Montulmo and Alcabitius understood Ptolemy method quite well. The net result of Placidus misreading has been to create a system of directing that is so unwieldy that has become a mathematical and procedural nightmare so complex that even in the age of computers… ( Robert Hand, Preface to the III book of Tetrablos, Hindsight )
It’s useless to highlight how “under the pole directions” are easy to calculate, they are just a difference of two oblique ascensions, so hardly they could be the nightmare of astrologers.
If we turn to Placido’s semiarc method, to be honest, even if more articulated nothing to share with Ptolemy obscure examples or with Alcabitius algorithm.
Let us try.
Before starting, it is necessary to remember that Ptolemy did NOT use the method of ascensions. In fact he writes:
However, the number of years, determined by the distances between the prorogative place and the destructive planet, ought not to be taken simply or offhand, in accordance with the usual traditions, from the times of ascension of each degree, except only when the eastern horizon itself is the prorogator, or some one of the planets that are rising in that region.
And again we must assign years to the degrees of the intervals: in the prorogation from the horoscope a number equal to the times of ascension in the latitude concerned; in the prorogation from mid‑heaven, as many as the times of the culminations; and in the prorogations from all the others, in proportion to or in accordance with the nearness of the risings, or settings, or culminations, to the angles, as we explained in the discussion of the length of life. (Tetrabiblos, III,11)
Told this we can look to the end of the same chapter where Ptolemy gives several example of directions. In the first three the significator is on one of the angles: the Ascendant, the MC, the Descendant.
In the fourth the significator is somewhere else. And where it should be considered too, because the very 2 last examples are exactly on two of the Placidean houses, the ninth and the eighth. (( See Giovanni Zattini, Anareta versus Afeta, Linguaggio Astrale no.93 year 1993 )).
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. But it made 46 times by the same procedure when the prorogative place was rising, 58 when it was in mid‑heaven, and 70 when it was setting. Hence the number of equinoctial times at the position between mid‑heaven and the occident differs from each of the others. For it is 64, and the difference is proportional to the excess of three hours, since this was 12 equinoctial times in the case of the other quadrants at the centres, but 6 equinoctial times in the case of the distance of three hours.
How to solve this with the unwieldy 🙂 method elaborated by Placido?
We know by Ptolemy himself that Significator is at 3 hours in the second quadrant. Of the Promissor Ptolemy says us both the temporal hour which is 17 and from his words we can easily calculate the hourly distance , which is 13/17= 0.76.
We can check with Morinus software: under the menu User we can inserting the longitude of 0 Gemini and we can easily calculate hourly distance and temporal hour, which are 0.72 and 17.08 we already knew from Ptolemy).
So the arc of direction is just (0.72+3)*17.08=3.72*17.08= 63.54
Let’s go on. Next example with S at two hours from MC. As we see it exactly falls on the 9th Placidus house.
For example, since the difference between the above mentioned 70 and 58 is 12 times, and it was assumed that the precedent place was removed by an equal number of ordinary hours, three, from each of the angles, which are one half of the six hours, then taking also one-half of the 12 equinoctial times and either adding them to the 58 or subtracting them from the 70, we shall find the result to be 64 times. But if it was removed two ordinary hours from either one of the angles, which are one-third of the six hours, again we shall take one-third of the 12 times of the excess, that is, 4, and if the removal by two hours had been assumed to be from the mid‑heaven, we would have added them to the 58 times, but if it was measured from the occident we would have subtracted them from 70.
In the same way with Placidus method of directing we should just to know the new hourly distance of promissor, which is (from Morinus software) 1.60.
So (1.60+2)*17.08 =3.6*17.08=61.48 (Ptolemy says 62=58+4)
In the third and last example Ptolemy puts the significator at 4 hours from the MC. As we see this point corresponds to the 8th house in Placido house system.
the promissor is in the second quadrant, at an hourly distance of 0.17, so following Placidean method we have (4-0.17)*17.05’=3.83*17.08=65.47 (Ptolemy says 70-4=66).
Up to this point we see that of the six examples of directions in Tetrabiblos, in three of them the significator is on the axes (Asc, MC and Descendant); of the other three ones, two are on a Placidean house cusp and one is in the middle of the quadrant.
It’s true like Martin Gansten says in his very nice book that we could direct planets according Placidean method without using Placidean house system, (( see page 56 of the book in bibliography )) still it’s obvious for me that this methods fits very well with semiarc method, because the houses are built using the same unit of measure of Ptolemy directions. If Ptolemy did not use “Placidean” house system (we will never know), still Placido read very carefully Ptolemy….
BIBLIOGRAPHY, READING LIST AND NOTES
The method of directing has been taken by Marco Fumagalli, I moti del Cielo (Milano: Ed. Cieloeterra, 2000).
Claudius Ptolemy, Tetrabiblos, cura Giuseppe Bezza.
Placido Titi, Astronomy and elementary philosophy translated from the Latin of Placidus de Titus: … To which are added, introductory notes and observations … The whole carefully revised by M. Sibly. (London ;and sold by Mr. Bew ;;Mr. Richardson ;;Mr. Mathews ;;Mr. Debrett ;;Messrs. M. and J. Sibly ;;and Mr. Edmund Sibly: Printed by W. Justins ;, 1789).
Martin Gansten, Primary directions: astrology’s old master Technique (The Wessex Astrologer, 2009).