The two phrases quō..eō (hōc), tantō…quantō (hōc) can be broadly translated as ‘the more…the more.’ They are ablatives of degree of difference used to correlate to comparatives.
- quō minus cpiditātis, eō plus auctōritātis, the less greed, the more authority
- quantō erat gravior oppūgnātiō, tantō crēbriōrēs litterae mittēbantur, the severe the siege was, the more frequently letters were sent
The third variation is simply emphatic.
- quantō plus crustulōs murī dabis, tantō hōc plus crustulīs eget: the mouse’s desire for cookies will increase in exact proportion to the number of cookies that you give him.
A&G note that this correlative construction later mutated to describe Cause instead of Degree of Difference.
- eō mē minus paenitet, for that reason I regress less.
(Severe addicts should check out A&G’s note on this section 414an1, which details how the English ‘the…the’ is actually a direct descendent of these expressions, emerging from the instrumental case of a pronoun in Angle-Saxon, thȳ.)
The Essential AG: 414a, 414an