I just want to understand the reason for calling this amplifier common-collector. the reason for my confusion is that the collector lead is not common between the input circuit and the output circuit. and I cannot understand the following from the text
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It is called the common-collector configuration because (ignoring the power supply battery) both the signal source and the load share the collector lead as a common connection point as in Figure below.

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Still the input between the base and emitter and the output in the emitter.

 

The battery at the collector is supposed to have a very low impedance so its voltage does not change with the signal. Then the collector has the same signal as ground and the collector is common to the input ground and the output ground.

A common emitter transistor has the emitter at ground then the emitter is common to the input ground and output ground.

A common base transistor has the base at ground then the base is common to the input ground and the output ground.

 

I understand that the common is the lead that has a fixed voltage, whatever the input is or the output is.
It makes sense this way.

 

I found this diagram which is in common sense with the name