Proposition 2

Construction

From a given point to draw a line segment equal to a given line segment.

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Construction Steps

Let A be the given point and BC  be the given line segment.

Join AB , and construct an equilateral triangle △ABD with AB  as a side.

Construct the circle through the point C centered at B and extend DB  to intersect that circle at E.

Construct the circle through the point E centered at D and extend DA  to intersect that circle at F. The line segment AF , equal to the given line segment BC , has been placed with one end at the given point A.

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Computable version

In[1]:=

GeometricScene[{{A.,B.,C.,O.,D.,E.,F.,G.},{}},​​{GeometricStep[{CircleThrough[{A.,B.,C.},O.],Line[{A.,O.,C.}],Line[{D.,E.}],EuclideanDistance[D.,E.]≤EuclideanDistance[A.,C.]}],​​GeometricStep[{F.∈Line[{A.,C.}],EuclideanDistance[A.,F.]EuclideanDistance[D.,E.]}],​​GeometricStep[{GeometricAssertion[{CircleThrough[{F.},A.],CircleThrough[{A.,B.,C.},O.]},{"Concurrent",G.}]}],​​GeometricStep[{Line[{A.,G.}]}]},​​{EuclideanDistance[A.,G.]EuclideanDistance[D.,E.]}​​]//RandomInstance

Out[]=

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Additional instances

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Dependency graphs