elements

Euclid’s first postulate

postulate1

To draw a straight line from any point to any point.

A postulate, to quote from dictionary.com is something taken as self-evident or assumed without proof as a basis for reasoning. And according to Euclid, nothing can be more self-evident than the fact that given two points, one can draw a straight line segment joining them.

Now, it is also obviously self-evident that there is exactly one such line joining two given points, i.e. that there is a unique line joining any two points.

However Euclid does not mention the uniqueness, though he seems to assume it in the subsequent proofs .. So probably a more accurate first postulate would be

To draw a straight line (which will be unique) from any point to any point.

The Processing code

int time1 = 500;
   int time2 = 2500;
   PFont f;
   
   void setup() {
     size(600, 120);
     smooth();
     f = createFont("Arial",20,true); 
}
   void draw() {
     int currentTime = millis();
     background(204);
     if (currentTime > time2) {
       ellipse(100,60,10,10);
text("A",95,90);
  fill(0);
ellipse(500,60,10,10);
text("B",495,90);
       line(100,60,500,60);
     } else if (currentTime > time1) {
       textFont(f,20); 
         fill(0);
ellipse(100,60,10,10);
text("A",95,90);
  fill(0);
ellipse(500,60,10,10);
text("B",495,90);}
    
   }