Often we write AB : BC : CD : DE ... = A'B' : B'C' : C'D' : D'E' ... .

The inverse is also true. If lines e

A proof based on a preliminary discussion of the properties of areas of triangles and parallelogramms goes as follows:

The quotient of areas of triangles: area(AB'B)/area(BB'C) = AB/BC. Analogously area(A'BB')/area(B'BC') = A'B'/B'C'. But area(AB'B) = area(A'BB') and area(BB'C) = area(B'BC') etc..

The argument can be reversed to prove the inverse theorem.

An important consequence relating points A*, B*, ... and O are discussed in Thales2.html .

ThalesRemarks.html

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