As the etymologically exact use of the word "circus" and the strangely technical-sounding "subtends" may already have suggested, Ithaca will draw heavily on English words derived from Latin, and, to a lesser extent, Greek. These ancient languages are the beloved province of theology (hence appropriate to a catechism), and of mathematics, biology, astronomy, medicine, law, and other scientific or quasi-scientific disciplines that seek unambiguous exactitude when analyzing the messy materials of life.
A "duumvirate" is a rule of two men (Latin vir = man). In ancient Rome duumviri were magistrates or other municipal officers who held office jointly. There is an obvious relevance here to the union of Odysseus and Telemachus, king and prince of Ithaca, walking toward the palace where they will restore proper rule to the island. The word also clearly relates to the fact that, as they walk, Stephen and Bloom "deliberate" on various topics, expressing their concurring or differing opinions on subjects as various as "Music, literature, Ireland, Dublin, Paris, friendship, woman, prostitution, diet, the influence of gaslight or the light of arc and glowlamps on the growth of adjoining paraheliotropic trees, exposed corporation emergency dustbuckets, the Roman catholic church, ecclesiastical celibacy, the Irish nation, jesuit education, careers, the study of medicine, the past day, the maleficent influence of the presabbath, Stephen's collapse." Deliberation derives from Latin librare = to weigh, and our two intellectual adult males are weighing matters, as magistrates should.
An "itinerary" is the route or proposed route of a journey (Latin iter = journey). The OED defines "paraheliotropic" (not found in many dictionaries) thus: "Of leaves: Turning their edges in the direction of incident light" (Greek para = aside + helios = sun + tropos = turning). The more common, but still foreign, word "ecclesiastical" means having to do with the institution of the church (Greek ekklesia = an assembly of citizens). A "maleficent" influence is an evil or harmful one (Latin malus = bad + facere = to do).
And so on. The reader of Ithaca who does not possess a solid grounding in ancient Latin and Greek will do well to keep a good dictionary nearby.