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Consanguinity, literally meaning common blood, describes how close a person is related to another in the sense of a family. It is illustrated with a consanguinity chart (or table), as seen below.
Consanguinity is expressed as degree of consanguinity, which can be defined in several ways. In general, the lower the degree of consanguinity between two persons is, the closer they are related, and thus the higher the level of consanguinity (be careful to distinguish degree and level). The most common definition is the modern civil law one, which increases by 1 with each step up or down along the shortest path from one person to another in a family tree. For example, parent-child relationships are one degree apart and brothers or sisters two degrees -- one step up to the common parent, another back down to the other sibling. This is also the definition used in Roman law.
Various other definitions of degrees of consanguinity have been used at different times in canon law.
In general, the lower the number of degrees of consanguinity, the higher the risk of inbreeding. There is a degree of consaguinity below which most cultures regard sexual relationships between two persons as incest and forbid their marriage.
In the Catholic Church, a marriage with a direct line relative or collateral relative to the fourth degree is grounds for an annulment. In other words, marrying a 1st cousin (4th degree) or a grand nephew/niece (4th degree) is not allowed, but marrying a 1st cousin once removed (5th degree) is.
Given that most of them were and still are in-bred to one degree or another, European nobilities often invoke consanguinuity as a convenient means of divorce, especially in ages when religious doctrine forbade the voluntary dissolution of a failed marriage.
The succession law known as consanguinity, requires the next monarch to be of the same blood of the previous one; allowing, for example, illegitimate children to inherit.
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