Given a line L and a point P on that line another line passing through
P perpendicular to L can be constructed [Proof]
Given a unit length (one) the integers
can be constructed.
Given a point P and a line L another line can be constucted going through
P and perpendicular to L.
Given a point P and a line L another line can be constucted going through
P and parallel to L.
The rational numbers can be
constructed.
Given any two numbers (lengths) A and B their product, (A x B), can be
constructed.
Given any two numbers (lengths) A and B their sum, (A + B), can be constructed.
For any given line segment the point bisecting that line segment can be
constructed.
Given a number, T, the square root of T can be constructed.
Given an arbitrary rectangle a square of the same area can be constructed.
Given an arbitrary triangle a rectangle of the same area can be constructed.
Given two squares a third square of area equal to the sum of the first
two can be constructed.
Given any finite polygon a square of equal area can be constructed.
Given two arbitrary angles an angle equal to their sum can be constructed.
Given a right triangle a lune of equal area can be constructed. |