>and no less than eight patron saints of tertiaries

It looks like the third definition, given by GuruNet may help. Perhaps there is some truth in the "third way"!

n., pl. ter·ti·ar·ies.
1. A tertiary feather.
2. Tertiary. Geology. The Tertiary Period or its system of deposits.
3. Roman Catholic Church. A member of a religious Third Order.