Another way to check the straightness of an edge is to draw or scribe a line against it on paper/parchment, etc, then turn it around and draw the same line holding the candidate straight edge against it in the other direction - not a perfect test, as anything with 180 degree rotational symmetry will pass, but it’s agood way of testing whether an edge has overall curvature.
Fairly flat surfaces occur in nature - the cleavage planes of slate, for example (not guaranteed or perfect, but good enough for many primitive purposes)
One way to resolve what Euclid (or any of the earlier creators of geometry) meant in talking about a line in his writings on geometry would be to find the etymology of the word in Ancient Greek. It appears to me that the word “line” in most European languages derives from the Latin word for flax or linen, which was also used for strings, threads, and cords made from linen. I think the word in Ancient Greek for “line” was cognate with the Latin word. So Euclid in defining the word “line” in his geometry was using the word for “string.” It appears then that at the time of the creation of geometry among the Greeks (or among earlier creators of it) in talking about a line they were implicitly talking about a stretched cord. This would seem to say that the first straight edge was a stretched cord.
Take you alleged straight edge; draw a line. Then flip it over and draw the same line with the edge on the other side of the line. Plane where needed and repeat. This gives a straight line accurate to the quality of your pencil/knife line. if you are before paper or whatever, do it in the dust.
This is similar to the board edge test, which is similar to Malacandra’s blacking and high points test.
Try this: Choose two points A and B. Set your compass to any random width, and draw two circles at that radius around A and around B. The two circles intersect at two points; mark them for later, and forget about the rest of the two circles. Now, set the compass for another random width and do it again. Now you have four points. Keep on going until you have lots and lots of points, and they will all be in one straight line.
That line, coincidentally, will bisect the line segment AB, and be perpendicular to it, but that’s a free bonus. You wanted a line, you got one.
The only difference that I can see between Vorpal Blade’s question and my answer, is in the practical vs. theoretical: Swinging a compass to create a circle works even in the real world, and the circle is complete without taking the pencil off the paper. But my answer works only theoretically: The line will not be complete until one repeats my procedure an infinite number of times.
You sure about that? Because even a stretched cord of sufficient length will bow due to gravity the cord having mass. But a cord hanging straight down - a plumb bob - won’t.
You first establish a flat horizontal surface - say, for instance, by scraping the ground flat. You punch something into the ground and let that be a point. You punch something into the ground somewhere else and let that be another point. You stretch a cord tight between these two points and tie each end to the things you have punched into the ground, letting the cord be flat right on the ground. That’s a line between those two points, or it’s as close as someone at the time of Euclid could get to it.
I’m not sure what you’re saying about gravity distorting the cord. Did you think that I was talking about a vertical surface? That’s a downright bizarre misunderstanding of what I wrote. Of course I was talking about a stretched cord on a horizontal surface.
No, I meant a horizontally stretched cord. Given sufficient length, they sag in the middle due to their own weight and therefore do not give a true flat edge.
Any physical representation of the geometric abstraction of a line will be imperfect. An actual line has only two dimensions. Cord, pencil mark, whatever, will always have three dimensions.
Three surfaces ground against each other automatically gives you a flat surface. It doesnt take any special skills or materials. Its so easy a caveman could do it. And once you have a flat surface, its a very good reference for the edge you are trying to make, MUCH better than taught lines or plum bobs or drawn lines or folded materials. BTW I’ve tried all those methods and they are a pita compared to physically flat or staight surface.
With the flat surface method, its easy peasy to get something flat to within a thousandth of an inch over a span of many inches. If the surfaces are made of a clear material like glass, its easy to get em flat over that same span on the order of WAVELENGTHS of light. And, if you are willing to work at it a bit, to within fractions of a wavelength of light.
The only downside to the 3 ground/flat surfaces method is how big can you make em before handling becomes an issue.
There are references in early texts to using water to check horizontal surfaces for flatness, and using stretched cords to get straight lines. Not a direct attestation of prehistoric practices, of course, but probably descended from prehistoric practices.
Another helpful trick that might not be as old as Neolithic but definitely goes back to early historical times is the use of Pythagorean triples to make straight-sided right angles. If you have a loop of cord with length 12 units, for instance, and you measure 3 units from your right-angle bend in one direction and 4 units from the bend in a perpendicular direction, stretching the cord taut at those points will produce a 3-4-5 triangle with a square right angle. (Of course, you have to be able to keep the cord straight enough to measure accurately in the first place, but for early civil engineering the tolerances are good enough.)
