Skip to main content
History of Science and Mathematics

You are not logged in. Your edit will be placed in a queue until it is peer reviewed.

We welcome edits that make the post easier to understand and more valuable for readers. Because community members review edits, please try to make the post substantially better than how you found it, for example, by fixing grammar or adding additional resources and hyperlinks.

Required fields*

4
  • 5
    $\begingroup$ That's exactly what I don't understand: what makes it so different? Can we verify that there is only one line between any two points, no matter how far apart? That any line extends indefinitely far? That circles really intersect? That convergent lines intersect is no less or more intuitive or testable. Spherical geometry is consistent with Euclid's postulates as written (parallel postulate is vacuously satisfied), he rules it out using synthetic arguments by I.16, which equally do not "follow" from the rest of the axioms and postulates in the modern sense. $\endgroup$ Commented Dec 18, 2014 at 20:27
  • 2
    $\begingroup$ Quine points out that straight lines correspond not just to light rays but to several different phenomena of everyday life: they are the shape of the edge of a folded paper (because a straight line is the intersection of two planes) and, most pertinently, they are the shape of a string stretched between two points. (The name “line” derives from this last; it literally means a string, as in fishing line, and is cognate with the linen from which it is made.) The line as a stretched string and as a light ray both derive from the fact that it is the shortest distance between two points. $\endgroup$ Commented Dec 20, 2014 at 20:50
  • 1
    $\begingroup$ Indeed, Democritus credits Egyptian "rope-stretchers" with teaching geometry to Greeks. Apollonius talks about straight lines as abstractions from walls and roads, and how the idea of length comes from that, see p.210 in Lucio Russo's link.springer.com/article/10.1007/s004070050016. Archimedes explicitly postulates that straight line is the shortest distance between two points in one of his books. $\endgroup$ Commented Dec 21, 2014 at 2:34
  • 1
    $\begingroup$ Walls and roads are not a good standards for straight lines. Everyone knows that walls and especially roads can be curved. How can we tell than a wall is straight (flat). Only by comparing it to the light rays. How can you tell that your ruler is straight? By comparing it with the light ray. $\endgroup$ Commented Dec 21, 2014 at 9:28