# Straightedge and compass

According to most discussions of Euclid's Elements, this work - and indeed, much of Ancient Greek geometry - should be seen as engaged in the game of figuring out what can be done with straightedge and (collapsible) compass.

Although Euclid's Elements can certainly be (mathematically) interpreted in this way, Euclid never says anything to explicitly support this. Nor does one find an explicit discussion of the idea that this is how we should view the ancient practice of geometry (with respect to Euclid or the Greek geometrical tradition in general) in Plato, Aristotle, Proclus and so on - as far as I can tell.

Is there any ancient source who specifically talks about straightedges and compasses and the idea that much of geometry revolves around questions of what can and can't be done with such tools? I am aware that much discussion of Greek mathematics simply assumes this, so I'm not looking for references to modern people who repeat this piece of folklore - there are examples of that everywhere. I'm rather looking for actual extant ancient texts that support this piece of folklore.

• The three construction postulates of Euclid's Elements are:"To draw a straight line from any point to any point", "To produce a finite straight line continuously in a straight line", and "To describe a circle with any center and radius". "Straightedge and compass" is simply a convenient shorthand. If you are asking about physical straightedges and compasses the Platonist tradition opposed acknowledgement of such lowly sensible tools when describing the pure intelligibles of geometry. Apr 4 '18 at 2:13
• "Straightedge and compass is simply a convenient shorthand" is still a claim that needs to be justified. Apr 4 '18 at 2:21
• You'll have to be more specific as to what you mean by "justified". Straightedges draw straight lines and compasses draw circles according to their dictionary definitions. Apr 4 '18 at 2:26
• I'm talking about the ordinary sense of justification. Just because someone is talking about circles, doesn't mean they are talking about compasses. Apr 4 '18 at 3:39
• I do not follow. Euclid does not use the straightedge and compass terminology, we do, to describe what he is doing. And we do it because it is short, because teachers did use literal straightedges and compasses in the recent centuries, etc. Egyptian land measurers, from whom Pythagoreans imported geometry, used stretched ropes for both purposes instead, hence the nickname rope stretchers. Apr 4 '18 at 4:25