The Euclid Division Lemma, often attributed to Euclid, may not have been discovered by him, as indicated by historical interpretations. The term "Euclidean division" emerged in the 20th century, referring to the division of Euclidean rings, illustrating Stigler's law of eponymy, which states that discoveries are frequently named after those who popularize them rather than their original creators. Euclid's work, particularly in geometry, laid foundational principles that influenced mathematics for over two millennia, making it fitting to associate his name with significant mathematical concepts.
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From the same article, "it seems that he did not know the existence and uniqueness theorem". My interpretation is that he (Euclid) could perform the division, but was unaware of the details of existence and uniqueness.Suyogya said:If the euclid division lemma was not discovered by euclid himself, then why was the name "euclid lemma"? (https://en.wikipedia.org/wiki/Euclidean_division#History)
Wikipedia said:The term "Euclidean division" was introduced during the 20th century as a shorthand for "division of Euclidean rings".