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The past participle is functioning as an adjective. Thus, it modifies the following noun. The connecting segments (Verbindungsstrecken) are being taken (genommen) in a certain way namely absolutely (absolut), i.e. not considering direction or sign. The phrase can be translated into English directly by saying Then the following relationship exists ...


Dann besteht zwischen den absolut genommenen Verbindungsstrecken dieser Punkte die Beziehung ... means in english: So there is the relation ... between the lengths (literally: absolute values) of the connection-lines of this points. The connection line between two points is a vector. A vector (embedded in a plane) has two coordinates, and even ...

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