In English, purpose clauses are called adverb clauses. In Latin, they are Adverbial Clauses of Purpose. In each language, however, the clause serves the same purpose: to answer the question why. English likes to use the infinitive for such a clause, but other phrases can be used:
We are fighting
to defend the city
so as to defend the city
that we might defend the city
in order that we might defend the city
Why are we fighting? To defend the city, of course!
The negative is formed by adding not, ie: "We are fighting so that we might not die"
Latin however requires the use of the subjunctive mood and an introductory word, ut (for the positive), and ne (for the negative). The tense of the subordinate verb if the main verb be present, future, or future perfect, is present. All other main verb tenses (imperfect, perfect, pluperfect) are used by the Imperfect subjunctive.
Pugnamus ne superemur: We are fighting so as not to be defeated
Non pugnabamus ut superaremur; We were not fighting so as to be defeated
The negative purpose clause in English can also be introduced by lest which vaguely denotes "so as not to."
So as not to be defeated, we ran away
Lest we be defeated, we ran away
Make note of the changes of the wording in the clauses.