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THE PROBLEMS OF HOUSE DIVISION
Part 4: Time Based Solutions
Regiomontanus generally fell from favour in the 19th century when Placidean tables became more accessible. The Placidus system is named after the Italian Benedictine monk, Placidus de Titis (16031668), who popularized its use during the 17th century. Again, it is accepted that Placidus did not invent the method; tables were already available for it in 1604, a year after Placidus's birth, and it earlier appeared on an astrolabe in 1305. The 12th century Hebrew astrologer Abraham Ibn Ezra acknowledged it as the system employed by Ptolemy, and Placidus appears to support this view within his work where he respectfully notes "I desire no guides but Ptolemy and reason".
([9] )
The Placidus system is purely timebased and thus offers perfect harmony with the use of planetary hours, adding credence to the claim that this could have been an original method of house division, based upon the twohourly 'watches' of ancient astrologers, who numbered the constellations in the order that the stars within them rose to the ascendant during the twelve watches of the 24hour period. There seems little doubt that the symbolism attached to the interpretative use of the houses has been greatly influenced from their use as 'timemarkers', in which the movement of the planets' passage through the heavens, following the diurnal arc, is recognized. Each of the houses represents two planetary hours, the first starting at dawn with the ascendant. The area between the ascendant and the 12th house cusp represents the first two planetary hours, that between the 12th and the 11th the 3rd and 4th hour, and so on. The MC represents the end of the 6th daytime planetary hour, while the descendant corresponds to sunset. The 6th house is made up of the first two nocturnal hours, and so on round to the Ascendant. The division between the two planetary hours in any house is found by dividing the house exactly in two (see diagram above).
Not only is the system sympathetic to the use of these astrological hours, but it is also the system that lends itself to the most 'natural' system of Primary Directions endorsed by Ptolemy, and it is for this reason that its advocates claim it as the system he would have preferred. We have to accept an element of speculation here  we have no actual evidence from Ptolemy's work to endorse this view or suggest otherwise. Placidus does, however, remain the most popular quadrant system of house division in use today. It is often said that the reason for this is the ready availability of Raphael's Tables of Houses which refer to the system, but this seems a little unfair as its underlying philosophy is also clearly to be respected.
Although Placidus is simple in concept, the mathematical trigonometry behind it is complex, with cusp positions adjusted in a complicated technique based on the use of hour cycles. ([10] ) Alcabitius and Koch
are systems that work along similar timebased projections, all of which involve associating the angles with the Ascendant and Midheaven and dividing by three the time taken for the degree of the Ascendant to move to the Midheaven, to find the intermediate cusps. The fundamental differences lie in the way these projections are related to the ecliptic, by use of hour circles, vertical circles, or projection of the Ascendant. Alcabitius, which uses vertical circles, bears the name of the 12thcentury Arabian astrologer, Alchabitus, but it is unclear whether Placidus predates the Alcabitius system or vice versa. (It is clear that those whose names have become celebrated as champions of techniques are not always reliable indicators of their first invention.)
The Koch system, however, is generally accepted as being of modern development, introduced in the 1960s by the German astrologer, Dr. Walter Koch. Tables supporting its use became available in 1971, and it is currently very popular in Europe, particularly with the Ebertin and Huber schools. Koch uses projection of the Ascendant to formulate the intermediate house cusps, and its followers argue that it is the only system to fully recognise the Ascendant as the primary connecting thread between the ecliptic and the place of birth in the calculation of every cusp.
In theory, there are valid philosophical arguments that allow every house system to be perceived as most appropriate; in practice, once we move beyond understanding whether our preference is to emphasise time or space,  most of us would find that our ability to prove one house system works is a great deal stronger than our ability to prove that another system doesn't.
Keeping it Simple!
In the article, "An Astrological House Formulary," Michael Munkasey provides stepbystep instructions on the mathematical techniques needed to formulate the various systems of division. This is an excellent guide that should allow anyone with enough interest to become capable of calculating cusps without relying on astrological software. One glance at this article will probably convince most astrologers that they don't wish to do this! For many of us, it will seem too complicated to fathom and work with on a daytoday basis. This leads to an argument in support of the simpler systems; with these, at least, working astrologers can feel in control of their own calculations and thus place confidence in the associated symbolism that arises from their chosen system.
Most of the other main house systems work upon the principle that since planetary activity centers upon the path of the Sun, the ecliptic provides the ideal focus for dividing the chart into 'spheres of activity'. The simplest approaches, the equalhouse and wholesign methods,
merely require knowledge of the ascendant or ascending sign, and an equal division throughout the rest of the zodiac eliminates the need for any complicated calculations. Until recently, such an approach was considered to have an element of naiveté attached to it ideal for beginners, the unspoken implication is that astrologers with a more sophisticated grasp of trigonometry would eventually progress to a more complex method. Yet recent research into classical astrology has created a renewed interest in these simple techniques from a more scholarly perspective. The point of strength is that, regardless of the originating theory behind house division, in practice at least, classical astrologers tended to tie the houses to the signs, apparently concurring with Pelletier, who wrote in defence of the equal house method "It seems superfluous to demand mathematical or astronomical precision of a frame of reference for houses which are purely symbolic".
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The Porphyry house system is often seen as an ideal compromise here: it maintains the connection between the angles of the chart and the Ascendant and Midheaven, but it offers a simplicity of technique that merely requires trisection of the ecliptic arc between the angles to calculate the intermediate cusps.
There is, however, a great deal of confusion regarding how the houses were used in ancient times and when quadrant systenis such as Porphyry and Placidus were introduced. Passages which were once thought to clearly demonstrate the
equalhouse method in practice are now taken to be more evident of the use of Porphyry or the wholesign system; this creates some doubt about whether the equalhouse system has any theoretical basis in classical astrology at all, except as a compromise by astrologers who were attempting to align the houses with the angles and either deliberately or ignorantly failed to observe any discrepancies. Ptolemy's stance is often considered critical in matters relating to classical astrology, so his use of the houses is worth exploring in detail, particularly for those who have been persuaded that a return to the simple mechanics of the "wholesign method" would be a return to the original and purest use of houses.
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Notes & References:
© Deborah Houlding
 
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