R. Howard Bloch, Yale's Sterling Professor of French, explains how Gothic masons built cathedrals using proportion and geometry rather than measurement. He walks through composite piers, ribbed vaults, and pointed arches, noting that pointed arches carry 25 to 30 percent more strength than round ones, then shows how the flying buttress channels thrust to the ground, illustrated with Viollet-le-Duc's drawings. The lecture connects modular bay construction to scholastic philosophy, describing the cathedral plan as 'scholasticism in stone,' and traces how Arabic mathematics from Euclid and al-Khwarizmi reached France through Spain. It closes on the medieval belief that a cathedral's ratios mirrored divine proportions given to Noah, Moses, and Solomon. Part of Bloch's Age of Cathedrals course on medieval France, this installment is dense with technical detail on structural engineering and its theological justification.