Polygon antialiasing.

I do some antialiasing for poligons with GL_POLYGON_SMOOTH the code:
glEnable (GL_BLEND);

With this params for BlendFunc qudas is properly antialiased but when I change GL_ONE to GL_ONE_MINUS_SRC_ALPHA the black diagonal line appears across them why? like this:
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Because the incomming fragment contribution is reduced by the destination edge fragment’s alpha. The totals should be one but in doing the modulation of destination by 1-source the total or the contribution from both polygons on the edge is no longer 1.0 where they share a pixel.