When did the notion of space, geometric space appear?

When in history did the notion of space, geometric space appear? I. e. when in history geometric space was treated or thought of as a whole, as the site in which all geometric objects exist? When I think of Euclid's Elements, I have the impression that it just treats relations between segments, areas; straight lines, planes (?), but doesn't treat space as a whole, as the site in which all geometric objects exist. (I am assuming the whole content in Euclid's Elements is what I said it is, but I have never read it thoroughly.)

• IMO you are right: there is no definition of "space" (maybe neither use of the word) in the text of the Elements: we may say that for Euclid geometry is the study of geometrical figures. Having said that, what do you mean with "treat space as a whole" ? Commented Jun 21, 2021 at 9:05
• If by a "space" you mean a "set" then the answer is "early 20th century," either Tarski or Birkhoff. Commented Jun 21, 2021 at 12:35
• When I say "space as a whole", I mean an object by itsel, an entity by itself, a totality, and when considered like that, we can think of it as an object having properties, or a structure corresponding to itself not to its components. For example, natural numbers were not considered as a whole, as a totality before set theory, and when considered like that, we can think of it having a structure: it is a monoid, for exaemple. Now as to a geometric space, I have the impression that a geometric space, or the space, was considered a totality before set theory... Commented Jun 21, 2021 at 19:38
• ... because Postulate 5 was intensely studied, and this might lead us to think of it not as a propierty of lines but of space. Commented Jun 21, 2021 at 19:40