Three-Phase Delta Network: Not all Voltage Sources are 120V?

[yosimba2000]

Using the Delta Netowrk from this image: http://www.belden.com/images/B23_WyevsDelta.jpg

Between Y-X, there should be 120V.
Between Y-Z, there should be 120V.
Between X-Z, there should be 120V.

But wait!

If we assign values to make the above statements true...

Call X = 0V, and Y = 120V, so from Y-X is 120V.
If Y-Z should be 120V, and Y is already 120V, then Z should be 240V. This is so from Y-Z is 120V.
If X-Z should be 120V, and Z is 240V, then X should be 360V.

But that can't be, since we already said X is 0V to make Y-X = 120V. From what I know, if X is held to be 0V and Z is 240V, then from Z-X is 240V!
If X is made to be 360V, then Y-Z is no longer 120V!

What am I doing wrong?

 

[cnh1995]

120V will be the rms value of voltage and not the instantaneous value. Instantaneous values will be different at each instant.

 

[jim hardy]

What am I doing wrong?

You're treating them as if they were DC voltages.

They are really sine functions, 120√2sin(377t+Φ) where Φ is 0 or ±120 degrees

they add in a manner similar to vectors.

Look up phasor notation 3 phase voltage
http://www.electronics-tutorials.ws/accircuits/phasors.html
http://ece.k-state.edu/~starret/581/3phase.html