Medieval vault construction arose from a medieval theology and cosmology. Despite the pointed arch "occuring in ancient Assyria and passing onto medieval Europe via contact with Arabic culture", (The Gothic Cathedral p.57, Wim Swaan) the unique cosmology and theology of medieval Europe predisposed the acceptance of the medieval arch. How the medieval mind understood the cosmos played a role in the cosntruction of rib vaults.
To understand the medieval temperament, we must understand the reigning cosmology. How medieval man understood the cosmos was not remarkably different from how ancient Greek man understood the cosmos. The classical works of wisdom from Aristotle, Socrates, Euclid, and Ptolemy established the foundation from which medieval man speculated cosmologically. A distinction of the Greek mind lay in the divnity of nature, (Passage to Modernity, Lewis Dupre.) The cosmos was divine and self-sufficient. The difficulty for medieval man came from a self-sufficient God who negated the possibility of a self-sufficient cosmos. The cosmos relied upon God for its being. It was not until St. Thomas Aquinas and his Summa Theologica that we have the culmination of the medieval synthesis between Theology and Philosophy. Essentially, the cosmos was held to be dependant on God and Christ for its salvation and being. The personality of Jesus Christ being the defining characteristic of medieval culture, (Gothic Architecture, Paul Frankl).
This disposition of medieval cosmology served two purposes in establishing the dominance of rib vaults in sacred architecture. The first involves the nature of rib vaults, and the second involves the construction of rib vaults.
The nature of arches and subsequent vaults lies in the relationship between the stone and the arch form. The stone in a vault in unity whilst maintaining its personality. Each stone has its own shape, but cannot be understood in its own unique shape or unique spatial equilibrium outside of the vault. The stone is unified with the form of the vault, (Phenomenon of Man, Teillard). The unique character of Christ as simultaneously God and man predisposed the medieval mind to accept and understand vaults as a sacred manner of building.
The second influence of medieval cosmology in the acceptance of rib vaults lay in the construction of vaults and the teleology contained within the cosmology. The construction of a medieval vault was marked by the completion of tranverse and diagonal rib arches. The role of the rib in the construction of the gothic rib vault was favorable in that it established the form of the vault from an early stage. It was completed prior to any subsequent construction and reduced the amount of centering needed, (Construction of Gothic Cathedrals, John Fitchen). This form as it existed within the individual stones used, pulls the construction process forward.
Medieval cosmology predisposed the thinkers and masons of the sacred cathedrals to look upon the cosmos with a certain eye. We can see the evidence of how they looked in what they built and how they built it. Architectural innovations came from theology and cosmology as much as they did from medieval building methods.