In Carlo Beenakker's answer to [this][1] recent MO question, it turns out that the name "monoid" was first used in mathematics by Arthur Cayley for a surface of order $𝑛$ which has a multiple point of order $𝑛−1$.

On the other hand, a (old) name for the blow-up is "[monoidal transformation][2]". I suspect that there should be a link relating these two classical terminologies, but I was not able to find one. So let me ask the following

>**Question.** Why was the blow-up classically known as "monoidal transformation"? Was this related to Cayley's "monoid"?  


  [1]: https://mathoverflow.net/questions/338281/who-invented-monoid
  [2]: https://www.encyclopediaofmath.org/index.php/Monoidal_transformation