I am currently reading Oliver Bryne's edition of Euclid's Elements, and in The Elements many arithmetic propositions are proved geometrically, and it feels to me that numbers are always treated as something that is tied to a geometrical object (be it the length of a segment, the area of a shape, or the angle between two lines) and never as entities independent of a geometrical realisation. For example, Euclid never seems to bring up the product of more than three quantities, which would indicate that his idea of the product was rooted in its geometric interpretation (as well as that he was probably limiting himself to only three dimensions).
Euclid also categorises quantities as being of one of four "kinds" : linear, superficial, solid, and angular, and he never adds two quantities of different kinds together, indicating that he really thought of them as distinct in nature. To me, this is very reminiscent of dimensional analysis, but it leads me to wonder if Euclid thought that quantities consisted of a number and a kind (or a number and a unit, in modern terms), or if the number itself was of a certain kind. In other words, if presented with a segment of length $2$ and a square of area $2$, would both $2$s have been considered the same or different?
Furthermore, I know that Pythagorean scholars represented integers as dots arranged in triangles, rectangles, and other shapes, which allowed to think about them in simple geometrical ways.
This leads me to ask myself if Greek mathematicians of the Antiquity ever considered numbers as independent mathematical objects, which were not necessarily geometrical quantities. The use of dots by Pythagoreans makes me think that it could be the case, but still they did arrange them in geometrical shapes, so I am still unclear.
(I am not just asking if Euclid or Pythagoreans ever did consider numbers as such, but if there was a point in the vast period that is Greek Antiquity where numbers were considered to be separable from geometry.)