7. the better to —— = So as to —— better:
This comment revealed this grammatical confusion of mine.
1. On the left-hand side (abbreviated as LHS) above, 'the better' is a noun.
2. Yet on the right-hand side, 'better' is an adverb, modifying the infinitive 'to ——' ? This contradicts 1?
3. Also, 'so as to' just seems to have adventitiously appeared, since it's absent on the LHS?
So how can these two phrases be equal?