Editing Mohr–Mascheroni theorem (section)

=== Outline ===
To prove the theorem, each of the [[Compass-and-straightedge construction#The basic constructions|basic constructions of compass and straightedge]] need to be proven to be possible by using a compass alone, as these are the foundations of, or elementary steps for, all other constructions. These are:
#Creating the line through two existing points
#Creating the circle through one point with centre another point
#Creating the point which is the intersection of two existing, non-parallel lines
#Creating the one or two points in the intersection of a line and a circle (if they intersect)
#Creating the one or two points in the intersection of two circles (if they intersect).

'''#1 - A line through two points'''

It is understood that a straight line cannot be drawn without a straightedge. A line is considered to be given by any two points, as any such pair define a unique line. In keeping with the intent of the theorem which we aim to prove, the actual line need not be drawn but for aesthetic reasons.

'''#2 - A circle through one point with defined center'''

This can be done with a compass alone. A straightedge is not required for this.

'''#5 - Intersection of two circles'''

This construction can also be done directly with a compass.

'''#3, #4 - The other constructions'''

Thus, to prove the theorem, only compass-only constructions for #3 and #4 need to be given.