Editing Compass (drawing tool) (section)

==Compasses and straightedge==
[[Compass-and-straightedge construction|Compasses-and-straightedge constructions]] are used to illustrate principles of [[plane geometry]]. Although a real pair of compasses is used to draft visible illustrations, the ideal compass used in proofs is an abstract creator of perfect circles. The most rigorous definition of this abstract tool is the "collapsing compass"; having drawn a circle from a given point with a given radius, it disappears; it cannot simply be moved to another point and used to draw another circle of equal radius (unlike a real pair of compasses). [[Euclid]] showed in his second proposition (Book I of the ''[[Euclid's Elements|Elements]]'') that such a collapsing compass could be used to transfer a distance, proving that a collapsing compass could do anything a real compass can do.