The article titled The Way of Wisdom says the following, which explains a connection between greed and faith,
It is usual to classify types of personality according to whether they are dominated by greed, hatred or confusion. Those who walk in greed are said to be more susceptible to faith than the other two, because of the kinship which exists between faith and greed. To quote Buddhaghosa (Visuddhimagga III,75):
"As on the unwholesome plane greed clings and takes no offense, so faith on the wholesome plane. As greed searches for objects of sense-desire, so faith for the qualities of morality, etc. As greed does not let go that which is harmful, so faith does not let go that which is beneficial."
So then, looking at the next section of Visuddhimagga, that explains a connection between aversion and wisdom (literally intelligence and understanding),
- One of intelligent temperament is parallel to one of hating temperament
because understanding is strong when profitable [kamma] occurs in one of hating
temperament, owing to its special qualities being near to those of hate. For, in an
unprofitable way, hate is disaffected and does not hold to its object, and so, in a
profitable way, is understanding. Hate seeks out only unreal faults, while
understanding seeks out only real faults. And hate occurs in the mode of
condemning living beings, while understanding occurs in the mode of condemning
Reading further in the Visuddhimagga I don't see a similar relation delusion and equanimity. Paragraph 77 relates delusion with a "speculative" temperament:
- One of speculative temperament is parallel to one of deluded temperament
because obstructive applied thoughts arise often in one of deluded temperament
who is striving to arouse unarisen profitable states, owing to their special qualities
being near to those of delusion. For just as delusion is restless owing to perplexity,
so are applied thoughts that are due to thinking over various aspects. And just as
delusion vacillates owing to superficiality, so do applied thoughts that are due to
I'm not sure that "speculative" is good nor related to equanimity.
There is one paragraph later on, though, which clearly relates delusion with equanimity ... because, it says, delusion is an equanimity cased by unknowing,
- And by seeing and so on: when one of greedy temperament sees even a slightly
pleasing visible object, he looks long as if surprised, he seizes on trivial virtues,
discounts genuine faults, and when departing, he does so with regret as if unwilling
to leave. When one of hating temperament sees even a slightly unpleasing visible
object, he avoids looking long as if he were tired, he picks out trivial faults, discounts
genuine virtues, and when departing, he does so without regret as if anxious to
leave. When one of deluded temperament sees any sort of visible object, he copies
what others do: if he hears others criticizing, he criticizes; if he hears others praising,
he praises; but actually he feels equanimity in himself—the equanimity of
unknowing. So too with sounds, and so on.
- Greed searches for and tries to keep for objects of sense-desire – faith searches for and tries to keep qualities of morality.
- Aversion rejects things because it's of a hating temperament, and looks for unreal faults – wisdom rejects formations, and looks for real faults.
- Delusion feels equanimity because it's ignorant.
The context comes from a previous paragraph, i.e. they're meant to be descriptions of different "temperaments".
- But mundane concentration should be developed by one who has taken his
stand on virtue that is quite purified in the way already stated. He should sever
any of the ten impediments that he may have. He should then approach the good
friend, the giver of a meditation subject, and he should apprehend from among
the forty meditation subjects one that suits his own temperament. After that he
should avoid a monastery unfavourable to the development of concentration and
go to live in one that is favourable. Then he should sever the lesser impediments
and not overlook any of the directions for development. This is in brief.