die Extremität
limb
In anatomy, a limb of the body, meaning an arm or a leg. Usually used in the plural.
Bei dem Unfall wurden seine unteren Extremitäten schwer verletzt.
His lower limbs were badly injured in the accident.

extremity
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limb
In anatomy, a limb of the body, meaning an arm or a leg. Usually used in the plural.
Bei dem Unfall wurden seine unteren Extremitäten schwer verletzt.
His lower limbs were badly injured in the accident.

The word 'Extremität' (extremity) is closely related to the adjective 'extrem' (extreme). It originally referred to the outermost ends of something. In the anatomical sense, it means the outermost parts of the body: the arms and legs.
Die Temperaturen in der Wüste sind extrem.
Temperatures in the desert are extreme.
'Extremität' (extremity/limb) is a technical term from medicine and anatomy. In normal everyday language, people use the words 'Arme' (arms) and 'Beine' (legs).
Der Arzt untersuchte die Schwellung an der rechten unteren Extremität.
The doctor examined the swelling on the right lower limb.
The word is almost always used in the plural, 'die Extremitäten' (the extremities/limbs). A distinction is often made between the 'oberen Extremitäten' (upper limbs/arms) and the 'unteren Extremitäten' (lower limbs/legs).
Kaltes Wetter kann die Durchblutung in den Extremitäten beeinträchtigen.
Cold weather can affect circulation in the extremities.
In this figurative meaning, 'Extremität' (extremity) is very rare and belongs to an elevated, almost literary style. It describes a radical attitude or action.
Sein Verhalten war von einer gewissen Extremität geprägt.
His behavior was marked by a certain extremity.
member
'das Mitglied' and 'die Extremität' can both refer to an arm or a leg, but this connection is very uneven today. 'Mitglied' in this meaning is outdated and is hardly used in normal German anymore. 'Extremität' is a medical or anatomical word and sounds technical. In everyday language, people simply say 'Arm' or 'Bein'. When talking about body parts, 'Extremität' is more precise in a medical text, while 'Mitglied' no longer sounds natural for this today.

Nach dem Unfall prüft die Ärztin, ob die Extremitäten verletzt sind.
After the accident, the doctor checks whether the limbs are injured.
In dem alten Buch steht das Wort „Mitglied“ noch für einen Arm oder ein Bein.
In the old book, the word 'Mitglied' is still used for an arm or a leg.