History of the mathematical notion of a single point?

[Kyriakos]

I am interested in this. I know that by Eukleid's Elements time (around 300 BC) the single point was axiomatically set as having no extention at all (ie 0 in a line, the simplest 1-dimensional form), and therefore axiomatically you can not get a line (nomatter how small) by adding up even an infinite number of single points.

This was not a random axiom, cause the lack of extention of a single point was an issue at least already 2 centuries prior to Eukleid, in the work of Democritos. For example Democritos posed the question as to what happens if one would divide the area of a cone, anywhere parallel to its base, by a single plane. Would that create two immediately equal or unequal (infinitesimally varrying) planes in the position of the cut?

If they are equal, then the cone would tend to become a cylinder, but if they are unequal this seems to mean that the cone has a step-progression in its infinitesimal differences in height.

Worth to also note that Democritos was mostly developing his own theory (of the last, smallest, particle-sized, 'atom' being the non-divided primary element of anything with mass, and the atoms existing in a huge (next to them) 'void'), as a reaction to the Eleatic philosophy, where the main argument was that there is no end to divisions to anything, which likely at least supports the notion of a 'single point' as non-extentable nomatter how many of them are added to one another.

Besides, one of the famous Paradoxa by Zeno of Elea, was that if you drop a mass of wheat to the floor, you will hear a sound, but you won't hear anything if you just drop a single bit of that wheat (ie the sound you hear cannot be sensed readily as the added sum of an infinite number of sub-parts, as in the case of the line and the single points).