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I've already consulted 3 physics texts and none of them shed any light on this question. In one book, it says "clearly the voltage Vac = Vab + Vbc." That's it. Just because they wrote it in the form of an equation and said its clear, I guess they think they proved it. But that doesn't really prove much.

In Jewett's Physics for Scientists, their attempt at explaining this is to simply refer to a diagram and say "as can be seen, the diagram shows that these voltages add up...." Well drawing a diagram and labeling it doesn't it make it so. And this fact is used to prove the Law of Series Capacitance.

It seems to be a widely held assumption that individual voltages add up to the circuit voltage for series capacitors, but how can we assume this? I'm not aware of any conservation of voltage. Can someone please explain it?