But what if "I have discovered a truly marvelous proof of this, which this margin is too narrow to contain"?
Then you write that and wait until Andrew Wiles (version 2.0) figures out how to prove it for himself.
Write down (page number;note counter) in the margin and then elaborate on one or more pieces of vellum, parchment, paper or bit(s) that you attach with the book, or keep secure.
why is this an argument?
I think they mean that they just write their thoughts/arguments for/against whatever topic at hand in the margins. Also known as annotating I suppose.
i argue with the text, my past arguments with the text...
a lot of the notes i take on papers boil down to “underline absurd claim, write WTF in the margin”.