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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 ...


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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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