\(V_{id} = V_{1} - V_{2}\) (1)

Then they describe V1 and V2 in terms of their differential and common-mode terms:

\(V_{1} = \frac{V_{id}}{2} + V_{ic}\) (2)

\(V_{2} = -\frac{V_{id}}{2} + V_{ic}\) (3)

I just don't understand how they determine that half of the differential signal will be sent to the bases of both transistors, with opposite polarities. I do understand how they got equation (1), but the half Vid is confusing me.

Thanks!