Definition 4
A straight line is a line which lies evenly with the points on itself.
This statement indicates, at least, that the term "straight line" refers to a kind of line. It is hard to tell what else it means, if anything. Various commentators have interpreted in a variety of ways. The definition of plane surface in I.Def.7 uses a similar language that is equally opaque.
There are a some postulates that come a little later in Book I and give meaning to straight lines. I.Post.1 says that a straight line can be drawn between any two points, I.Post.2 says that a straight line can be extended, and the remaining postulates use the concept of straight line in one way or another.
Book I Introduction -
Definition 3 -
Definition 5.
© 1996
D.E.Joyce
Clark University