Cadent

The cadent houses are the third, sixth, ninth and twelfth, each falling away from an angle. The Greek word is apoklimata, the declining places, and the Latin cadens, from which the English word descends, means falling. Both names describe one geometry: these are the houses a rising sign has just passed through on its way down from a pivot.

The tradition counts a planet here weakest. It is the accidental debility that matters most in traditional judgement, and it is why an otherwise dignified planet can produce very little. A benefic in its own sign but in the twelfth is a good thing in a place from which it can barely act. The doctrine runs consistently from Hellenistic practice through to Lilly and is applied without much softening.

Weakness is not the same as unimportance, and the subjects of the four make that clear. The third holds siblings, neighbours and elementary learning. The sixth holds illness, servants and daily work. The ninth holds religion, philosophy, long travel and dreams. The twelfth holds imprisonment, hidden enemies and self undoing. Those are four of the most consequential regions of a life, and the tradition assigns them to the four weakest houses without evident discomfort.

All four carry planetary joys: the Moon in the third, Mars in the sixth, the Sun in the ninth, and Saturn in the twelfth.

Sources The Daimon in Hellenistic Astrology: Origins and InfluenceDorian Gieseler Greenbaum with Christian AstrologyWilliam Lilly

That the tradition put religion, learning, illness and confinement in the four weakest houses is odd enough to want an explanation, and the joys are where one is found.

Each of the seven planets has a house it is said to rejoice in, and the seven are distributed in a pattern that is clearly not random. The benefics take two places that aspect the ascendant favourably, Venus the fifth and Jupiter the eleventh. The malefics take two that cannot see it at all, Mars the sixth and Saturn the twelfth. The lights take the ninth and the third, the Sun above the horizon and the Moon below it. Mercury takes the first. Read as a whole, the scheme puts the difficult planets in the difficult houses, which suggests the cadent group acquired its subjects partly from the planet assigned to it rather than the other way round.

That reading also explains why the ninth is a strange member of its own group. It is cadent, and therefore weak by position, and it is the Sun's joy and the place the Greek sources call God, and therefore elevated by association. Traditional authors describe it in both registers and do not resolve the tension between them.

The practical use of the group is diagnostic. A chart with the majority of its planets in cadent houses is read as one in which things are hard to bring about, whatever dignity those planets hold, and the tradition treats that as a reportable condition rather than as a verdict on a person.