My reaction when reading Bob's letter was very much the same as Ken's
Newton "abstracted" from "equal ratios" to "a single ratio"
sand I just want to add, that "playing with words" he is going from "a unit" to "a unity".
I also find it interesting that as all applied mathematicians know the arguments of a mathematical function have to be "numbers", not lengths or weights or anything else - if "physical dimensions" are included then it is no longer mathematics, but physics.
So, going back in history we do find that physicists and mathematicians did have an intuitive feeling for the importance of numbers - long before they had measured the continuum with numbers.
What I have in mind is that Euclid as a mathematician only allowed proportions where both magnitudes were of the same kind - had he been a physicist he could have divided weight by volume to define density ...