If we have proved the additive property for vectors at right-angles, then we have it for all pairs:
|P(a+b)||=||P(aperp+kb + b) for some constant k, where aperp is orthogonal to a|
|=||P(aperp + (k+1)b)|
|=||P(aperp) + (k+1)P(b) by hypothesized linearlity|
|=||P(a) + P(b)|
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