Which preposition to use with complementary

to Occurrences 6%

Even where, for example, in the question of the origin and meaning of sacrifice, they seem to necessitate a modification of the somewhat elaborate à priori definition, popular in some modern schools (though not in them all), yet that modification is altogether favourable to the sounder conception of the Eucharistic Sacrifice as a food-offering complementary to the Sacrifice of the Cross.

of Occurrences 3%

Here, then, we find the initial Polarity of Universal Spirit and Universal Substance, each being the complementary of the other, and out of this relation all subsequent evolution proceeds.

Which preposition to use with  complementary