Editing Mohr–Mascheroni theorem (section)

=== Notation and remarks ===
The following notation will be used throughout this article. A circle whose center is located at point {{mvar|U}} and that passes through point {{mvar|V}} will be denoted by {{math|''U''(''V'')}}. A circle with center {{mvar|U}} and radius specified by a number, {{mvar|r}}, or a line segment {{math|{{overline|''AB''}}}} will be denoted by {{math|''U''(''r'')}} or {{math|''U''(''AB'')}}, respectively.<ref>{{harvnb|Eves|1963|loc=p. 184}}</ref>

In general constructions there are often several variations that will produce the same result. The choices made in such a variant can be made [[without loss of generality]]. However, when a construction is being used to prove that something can be done, it is not necessary to describe all these various choices and, for the sake of clarity of exposition, only one variant will be given below. However, many constructions come in different forms depending on whether or not they use [[Inversion in a circle|circle inversion]] and these alternatives will be given if possible.

It is also important to note that some of the constructions below proving the Mohr–Mascheroni theorem require the arbitrary placement of points in space, such as finding the center of a circle when not already provided (see construction below). In some construction paradigms - such as in the geometric definition of the [[constructible number]] - the arbitrary placement of points may be prohibited. In such a paradigm, however, for example, various constructions exist so that arbitrary point placement is unnecessary. It is also worth pointing out that no circle could be constructed without the compass, thus there is no reason in practice for a center point not to exist.