Old English begietan "to get by effort, find, acquire, attain, seize" (class V strong verb, past tense begeat, past participle begeaton), from be- + get (v.). Sense of "to procreate" is from c. 1200, generally used of the father only. Similar formation in Old Saxon bigitan, Old High German pigezzan, Gothic bigitan "to get, obtain." Related: Begot; begotten.
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Harper, D. (n.d.). Etymology of begat. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/begat