Yes, Janalyn, it is an old and unused word today.
My sincere apologizes ... my spelling was wrong. It is begets (plural of begat) not begates.
1. verb (used with object), be·got or (Archaic) be·gat; be·got·ten or be·got; be·get·ting. 1. (esp. of a male parent) to procreate or generate (offspring).
2. to cause; produce as an effect: a belief that power begets power.
be·get·ter, noun (www.Dictionary.com
It's a word that is most often used when one is reciting a lineage from one father as: Joseph beget John who beget Jacob who beget Jacob Jr.
It goes along with other fun lineage wording as "by and out of". "By" refers to the father or sire and "out of" refers to the mother or dam. This would read as: John by Joseph out of Martha. This reference term is great when John had more than one wife or as sometimes happens had more than one wife and more than one son named John.
As a quick side note here it was a common practice until the nineteenth century to name a new born the same name (namesake) as a child of the same family that had died. So if child number three named John died of consumption the next male child born would have been named John.
The "by and out of" is also a good reference tool when a widow married the brother of her late husband. So you can have Fred by John out of Mary and Frank by Jake out of Mary, with Fred and Frank being half-brothers, John and Jake being brothers and Mary married to two brothers.
As a second side note this also was a common practice - a man marrying his brother's widow - up into the late 1800's. This insured two things. Your brother's offspring would be raised to continue his line and as the populations of many small western settlements (US) did not have large numbers that a woman of breeding age was married and therefore creating more children.
Another great word is "ilk". This one refers to your cousins from which you wish to distance yourself or your line. "Ilk" is a negative term to the swarming brood of low class cousins that seemed to always end up in jail. Ilk originally meant "coming from the same" area, region or sire line.
Other great words include: progeny, brood, get, issue, offspring, posterity, seed, scion ...........
While I am playing with fun genealogy wording ... did you know that the term Junior does not necessarily mean that the man is the child the elder man carrying the same name. Junior originally just meant 'younger' not 'son of'. If a settlement has two men of two different generations named John that were somehow related the younger man was called Junior to distinguish him from his elder. So you could have John the Elder and his nephew John Junior the younger.
So, my apologizes for my bad spelling.