Question

A straight line is a line which lies evenly with the points on itself.
(Euclid's Geometry)

Can anyone simplify the property?

Answer 1

I have a little theory about what it means, it appears to make sense but don’t take my word for it:

Let’s say we have a straight line here:

Let’s divide it into 3 lines equal in length

(Sorry, my drawing is not perfect)

We’ll notice that those 3 lines are similar, they have the same slope and they have

This time, the 3 lines are equal in length, but they have different slopes/directions/angles

What defines a straight line is that when we try to cut it into smaller lines they will all have the same slope, this is not the case for a curved line.

Euclid has said “A straight line is a line which lies evenly with the points on itself.”

IMHO, this means that a straight line is the line which the points lie evenly pointing to the same slope, they aren’t going down at first then going up again like a curve, they are evenly lying there, the points are even.

I hope this helps you