Das Negative zu tun, ist uns noch auferlegt; das Positive ist uns schon gegeben.
Doing the negative thing is imposed on us, an addition; the positive thing is given to us from the start. [Kaiser/Wilkins]
We are instructed to do the negative; the positive is already within us. [Hofmann]
Hofmann takes greater liberties here than Kaiser/Wilkins, and loses the sense of "noch," which is that the negative is added to us. The implication, then, is that the positive, being opposed to the negative, must be the opposite of what is added, that is, what is innate, and hence already within us, but doesn't this entail an assumption? I don't think we should conflate what is given to us from the start with what we are.
The negative thing is not given to us from the start but imposed later; does this mean there are no imposed positives, and therefore any positive thing is given at the beginning only?
I think the emphasis here is on the idea of the negative as alien deviation from any previously-determined direction. If this is taken as an axiom, it does not necessarily follow that any change in direction is negative. It may negate the direction taken up to now, but if this happens because you are opting for a new direction, then this would be a new positive, and hence, by this definition, a new beginning. The positive, then, would necessarily be the beginning of something. Therefore the negative is a deviation that does not begin anything new.
The negative might be sloppiness, but then that doesn't explain the idea of imposition. Who imposes? Perhaps it doesn't matter who. But no one thinks of sloppiness in terms of an imposition, do they? Imposed sloppiness. What would that be? Confusion, induced by circumstances? This negative is far more general, and should be treated as any interference; perhaps especially as self-interference.