Euclid Book 6 Proposition 29
Statement
Given a parallelogram ECBD with C the midpoint of and a convex polygon GHIJ, to construct a parallelogram AZKX with the same area as GHIJ and which is the union of the parallelograms AZYB and BYKX, where BYKX is similar to ECBD.
AB
Computational Explanation
GeometricSceneA.,B.,C.,D.,E.,G.,H.,I.,J.,K.,M.,N.,P.,Q.,R.,S.,X.,Y.,Z.,{},StyleLine[A.,B.],Blue,C.MidpointLine[A.,B.],GeometricAssertionParallelogramE.,C.,B.,D.,"Counterclockwise",GeometricAssertionStylePolygonG.,H.,I.,J.,Yellow,"Convex",GeometricAssertionParallelogramP.,Q.,R.,S.,"Counterclockwise",GeometricAssertionPolygonP.,Q.,R.,S.,PolygonE.,C.,B.,D.,"Similar",AreaPolygonP.,Q.,R.,S.AreaPolygonE.,C.,B.,D.+AreaPolygonG.,H.,I.,J.,Line[E.,D.,M.],EuclideanDistance[E.,M.]EuclideanDistanceP.,S.,LineE.,C.,N.,EuclideanDistance[E.,N.]EuclideanDistanceP.,Q.,Parallelogram[E.,N.,K.,M.],LineC.,B.,X.,X.∈Line[M.,K.],Line[D.,B.,Y.],Y.∈Line[N.,K.],GeometricAssertionLine[A.,Z.],LineC.,N.,"Parallel",GeometricAssertionLine[A.,Z.],InfiniteLine[K.,N.],"Concurrent",Z.,StylePolygon[A.,Z.,K.,X.],Pink,StylePolygon[B.,Y.,K.,X.],Blue,AreaPolygon[A.,Z.,K.,X.]AreaPolygonG.,H.,I.,J.,GeometricAssertionPolygon[B.,Y.,K.,X.],PolygonE.,C.,B.,D.,"Similar"
RandomInstanceGeometricSceneA.,B.,C.,D.,E.,G.,H.,I.,J.,K.,M.,N.,P.,Q.,R.,S.,X.,Y.,Z.,{},StyleLineA.,B.,Blue,C.MidpointLineA.,B.,GeometricAssertionParallelogramE.,C.,B.,D.,Counterclockwise,GeometricAssertionStylePolygonG.,H.,I.,J.,Yellow,Convex,GeometricAssertionParallelogramP.,Q.,R.,S.,Counterclockwise,GeometricAssertionPolygonP.,Q.,R.,S.,PolygonE.,C.,B.,D.,Similar,AreaPolygonP.,Q.,R.,S.AreaPolygonE.,C.,B.,D.+AreaPolygonG.,H.,I.,J.,LineE.,D.,M.,EuclideanDistanceE.,M.EuclideanDistanceP.,S.,LineE.,C.,N.,EuclideanDistanceE.,N.EuclideanDistanceP.,Q.,ParallelogramE.,N.,K.,M.,LineC.,B.,X.,X.∈LineM.,K.,LineD.,B.,Y.,Y.∈LineN.,K.,GeometricAssertionLineA.,Z.,LineC.,N.,Parallel,GeometricAssertionLineA.,Z.,InfiniteLineK.,N.,Concurrent,Z.,StylePolygonA.,Z.,K.,X.,Pink,StylePolygonB.,Y.,K.,X.,Blue,AreaPolygonA.,Z.,K.,X.AreaPolygonG.,H.,I.,J.,GeometricAssertionPolygonB.,Y.,K.,X.,PolygonE.,C.,B.,D.,Similar
Explanations
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