Written by Will Johnson, firstname.lastname@example.org
Consanguinity refers to a shared bloodline. You are consanguineous with your ancestors and your descendants but not with your spouses nor your in-laws because you share no blood with them (at least usually). In more modern societies you are not permitted to marry a person with whom you are consanguineous in the first or second degree. Some societies do not forbid the marriage of first cousins.
Affinity refers to relationship because of a marriage. Your spouse is related to you by affinity. But similarly all of your spouses relatives, are related to you by this marriage. You have affinity with them. In some ancient and medieval societies, you could not marry persons to whom you had an affinity of this sort. For example you could not marry your sister-in-law. Those laws have been gradually removed in most or perhaps all, Western societies.
Relation proximity combines consanguinity and affinity into a single measure. You are "related" to your parents, your children, your siblings and your spouses in degree 1. Any person who is related to any of those persons, in degree 1, and is not related to you in degree 1, is related to you in degree 2. In other words, any person who is the parent, child, sibling or spouse of any of your parents, children, siblings, or spouses, is one step further removed from you, and therefore in degree 2 to you. When you calculate the number you always step further away from the subject, and not back toward them again.
Relation proximity is a way of measuring the relation-distance between you and any other person whether or not you share a common ancestor. So it can be used to declare that your mother's brother's wife's father is related to you with proximity degree 4, even though they share no direct bloodline or spousal relationship with you.
One example of the application of Relation Proximity is the Cecil Number and the Cecilweb project which attempts to show that every person who lived under King James I of England, and was armigerous (had a coat-of-arms), was related to Richard Cecil with a proximity degree no greater than ten. That is, you can step from any person, to Richard Cecil, in ten steps or less using only the relationships: "Parent of", "Child of", "Spouse of", and "Sibling of".
The following example shows that King Henry VIII is related to Richard Cecil in 7 degrees. King Henry VIII of England married as his sixth wife and her third husband to Catherine Parr. Catherine has previously been married as her second husband and his third wife, to John Neville, 3rd Lord Latimer. John Neville's son by his first marriage was John Neville, 4th Lord Latimer. This last John's daughter was Dorothy Neville, Countess Exeter. Dorothy married as his first wife to Thomas Cecil, 1st Earl of Exeter. Thomas was the son of William Cecil, 1st Baron Burghley. William was the son of Richard Cecil.
So this chain: Henry, Catherine, John, John, Dorothy, Thomas, William; has seven names, each in a primitive relation to their neighbors: either parent, child, sibling or spouse. Therefore Henry VIII is proximate to Richard Cecil in seven steps.