Euclid never defined multiplication as repeated addition, so please stop saying he did!
FACT. The words ‘add’ and ‘added’ have never appeared in any English translation of the nine propositions and proofs in Book VII of Elements reliant on Euclid’s definition of multiplication.
I have reviewed every printed English translation of Euclid's Book VII propositions and proofs. The years of publication and translators are: 1570, Henry Billingsley; 1660, Isaac Barrow; 1661, John Leeke and George Searle; 1745, Edmund Stone; 1788, James Williamson, and 1908, Thomas Little Heath.
The result of such a review is the startling fact, the words ‘add’ and added’ have never appeared in any English translation of Euclid’s proofs requiring multiplication.
“The words ‘add’ and added’ have never appeared in any English translation of Euclid’s proofs requiring multiplication.”
in 1570, Henry Billingsley, a haberdasher by trade, incorrectly translated Euclid's definition of multiplication and inserted the phrase "added to it selfe" which is not in Euclid's original Greek. He was the first to publish Euclid's Elements in English and his nonsense 'repeated addition' definition has forever been attributed to Euclid.