The fourth house is the fourth of the twelve houses of the horoscope, and one of the four angular houses, the strongest kind. It begins at the lowest point of the chart, the imum coeli or nadir, and it governs the home, the family, the roots and ancestry, and one of the parents, the private foundation of a life, its origins and its innermost base. As an angular house it is held to give planets placed in it considerable force. These are the interpretive conventions of the astrological tradition for this division of the chart, in which the fourth house describes the ground a person stands on, the family and dwelling from which they come, and the end of matters; it stands opposite the tenth house of career and public standing across the vertical axis of the wheel.
The Greek name for the fourth house, Hypogeion, the place beneath the earth, describes the geometry directly: it is the point diametrically below the horizon at the moment of birth, the mirror image of the tenth house at the top of the chart, and the Hellenistic astrologers who fixed this scheme, already traditional in Vettius Valens around 175 CE and systematised by Paulus Alexandrinus in 378, read it as the place of the unseen foundation, ancestry, and the grave, the end of a matter as much as its root. No planet was assigned a joy here, unlike the houses on either side of it, and the later medieval tradition, working from Arabic sources, is chiefly responsible for the parent and homeland associations now attached to the fourth, a layer added on top of the older Hellenistic reading of hidden origins and final outcomes.
Sources A History of Western AstrologyNicholas Campion with Introduction to Astrology (Eisagogika)Paulus Alexandrinus