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===Time-based house systems=== ====Alchabitius==== The predecessor system to the Placidus, which largely replaced the Porphyry. The difference with Placidus is that the time that it takes the ascendant to reach the meridian is divided equally into three parts. The [[Alchabitius]] house system was very popular in Europe before the introduction of the Regiomontanus system. ====Placidus==== This is the most commonly used house system in modern [[Western astrology]]. The paths drawn for each degree of the ecliptic to move from the Imum coeli to the horizon, and from the horizon to the midheaven, are trisected to determine the cusps of houses 2, 3, 11, and 12.{{sfnp|Rusborn|2023}} The cusps of houses 8, 9, 5 and 6 are opposite these. The Placidus system is sometimes not defined beyond polar circles ([[latitude]]s greater than 66°N or 66°S), because certain degrees are ''circumpolar'' (never touch the horizon), and planets falling in them cannot be assigned to houses without extending the system. This result is a weakness of the Placidean system according to its critics, who often cite the exceptional house proportions in the higher latitudes.<ref>[http://www.astrodatabank.com/AstrologyFAQ.htm#EqualHouse Astrodatabank FAQ n.5]</ref> Named for 17th-century astrologer [[Placidus de Titis]], it is thought the Placidus system was first mentioned about 13th century in Arab literature, but the first confirmed publication was in 1602 by [[Giovanni Antonio Magini]] (1555–1617) in his book "Tabulae Primi Mobilis, quas Directionem Vulgo Dicunt". The first documented usage is from Czech, 1627.{{sfnp|Singer|2007}} ====Koch==== A rather more complicated version of the Placidus system, built on equal increments of Right Ascension for each quadrant. The Koch system was developed by the German astrologer [[Walter Koch (astrologer)|Walter Koch]] (1895–1970) and is defined only for latitudes between 66°N and 66°S. This system is popular among research astrologers in the U.S. and among German speakers, but in Central Europe lost some popularity to the Krusiński house system.{{sfnp|Houlding|2006}} ====Topocentric==== This is a recent system, invented in Argentina, that its creators claim has been determined empirically, i.e. by observing events in people's lives and assessing the geometry of a house system that would fit. The house cusps are always within a degree of those given in the Placidus system. The topocentric system can also be described as an approximation algorithm for the Placidus system. Topocentric houses are also called Polich-Page, after the names of the house system creators, Wendel Polich and A. Page Nelson.{{sfnp|Houlding|2006}}
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