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I wish not to renew my subscription-instead of-I do not wish to renew my subscription.

I want not to go home-instead of-I do not want to go home.

What verbs can have the auxiliary 'do' left out, because there are verbs, such as the one below, that cannot:

I feel not angry-instead of-I do not feel angry.

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Are the constructions above without 'do' the same as the construction using the semiauxiliary 'need'? (although I don't think the above are auxiliaries because bare infinitives follow them)

I need not go home-instead of-I do not need to go home.

Thanks
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They all sound 19th century to me.
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English 1b3Are the constructions above without 'do' the same as the construction using the semiauxiliary 'need'?
They can't be the same. They use different verbs. wish and want aren't semi-auxiliaries. need is. The position of not is the same relative to the verb, however, so in that way they are the same. It's just a matter of what you mean by "same".

Your question seems to be more of a riddle than a grammar question.

The ying not is qualby. The yang not is qualby.

Are these the same? Emotion: smile

CJ
I mean more to ask how are these used?

Need is an auxliary, so I understand why 'did' is removed and the shorter, more common in Bre, version is created.

But what are these other forms examples of then? I mean it seems to work only with some verbs as well, to add to the confusion Emotion: sad
Mister MicawberThey all sound 19th century to me.

And now, that's at least 110 years ago! Emotion: rolleyes
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There may be a few differences between BrE and AmE here. In my usage:

"I wish not to..." is possible in formal English.

"I want not to..." is not common but is possible in a slightly nonstandard way ("I want not to like him, but...").

"I feel not <adjective>..." sounds archaic (or, at best, poetic or highly literary).

"I need not..." is OK but in everyday English it would normally become "I needn't..."

A whole bunch of verbs seem to allow "I <verb> not to" (e.g. "I choose/hope/agree/intend not to...").

Some "<subj> <verb> not <adj>" constructions seem to work, such as "It seemed not unlikely that...", "It proved not possible to..."